A Mobility Impedance Index for Data-Driven National Bridge Preservation Prioritization

1. Introduction

Transportation agencies routinely manage bridge and pavement assets using separate decision-support systems, despite both directly influencing highway mobility. Bridge management systems primarily emphasize structural condition, deterioration, safety, and maintenance needs [1], whereas pavement management systems evaluate roadway serviceability through performance measures such as the International Roughness Index (IRI) [2]. Traffic demand is commonly incorporated as a distinct dimension of network performance and infrastructure criticality[3]. Consequently, infrastructure preservation decisions are often based on individual asset characteristics rather than on their combined influence on traffic movement. This separation makes it difficult to identify bridges where deteriorating infrastructure coincides with high or increasing traffic demand and, therefore, where preservation investments may produce the greatest mobility benefits across a transportation network. The problem is particularly important for the National Highway System (NHS), where bridges function as network links whose disruption can impose substantial mobility consequences through traffic diversion and detour effects [4]. A bridge with moderate structural deterioration may have limited consequences when located on a lightly traveled route, whereas a similar bridge carrying high average daily traffic (ADT) along a major freight corridor may have substantially greater implications for mobility, reliability, and future preservation planning. Conversely, bridges in excellent structural condition may still contribute to reduced mobility if they are located on roadway segments with poor pavement condition carrying rapidly growing traffic volumes. These examples illustrate that infrastructure condition and traffic demand jointly influence transportation performance, yet they are rarely evaluated within a unified analytical methodology.

National datasets now provide an opportunity to integrate these complementary perspectives. The National Bridge Inventory (NBI) contains detailed information describing bridge condition, geometry, and traffic characteristics [5], while the Highway Performance Monitoring System (HPMS) provides roadway attributes, including pavement roughness and roadway classification [6]. Together, these databases provide national coverage across the contiguous United States (CONUS). However, combining them into a consistent bridge-level analytical dataset presents several practical challenges. Differences in spatial representation, roadway and bridge identifiers, county coding, and data completeness require substantial quality assurance before meaningful integrated analyses can be performed. Moreover, no standard data-driven methodology currently exists for integrating pavement condition, bridge condition, and traffic demand into a single bridge-level measure for network-scale mobility prioritization.

Several studies have developed condition-based bridge assessment and prioritization indices [7], data-driven measures for evaluating bridge health and deterioration [8], or multi-criteria optimization approaches for bridge maintenance prioritization [9]. Others have examined pavement performance using IRI and related deterioration measures [10], incorporated traffic exposure into bridge assessment and monitoring decisions [11], examined traffic-dependent bridge criticality and network consequences [12], or evaluated bridge-network resilience through integrated structural and transportation characteristics using largely independent analytical frameworks [13]. Composite indicators have also been applied to transportation infrastructure because they combine multiple technical, socioeconomic, and spatial dimensions into interpretable measures for comparison and prioritization [14]. Nevertheless, existing approaches generally focus on either structural condition or transportation performance rather than explicitly integrating both within a data-driven bridge-level prioritization method using nationally available transportation data. Furthermore, relatively few studies have examined the robustness of data-driven bridge prioritization metrics with respect to weighting assumptions, temporal consistency among source variables, and spatial clustering at the national network scale.

The goal of this paper is to develop and evaluate a data-driven mobility impedance index (MII) that quantifies the relative potential for NHS bridges to constrain roadway mobility by integrating pavement condition, bridge condition, current traffic demand, and projected traffic growth into a single composite measure for network-level prioritization. The MII is intended to represent joint risk exposure—the co-occurrence of infrastructure deficiency and traffic demand—rather than a direct, calibrated measure of realized traffic obstruction, delay, or economic loss.

The research addresses the following question: Can nationally available HPMS and NBI data be integrated into a transparent, transferrable, and scalable data-driven methodology that produces a robust MII for consistently identifying and prioritizing bridges and regions with relatively greater potential mobility constraints across the CONUS NHS? To address this question, the study first develops a workflow for extracting, cleaning, and spatially integrating HPMS roadway records with NBI bridge records. Bridge and roadway records are then subjected to systematic quality screening to construct a nationally consistent analytical dataset. Four complementary mobility components are combined into the proposed MII using percentile normalization and an equal-weight baseline formulation. Distributional analyses characterize the statistical behavior of both the component variables and the resulting index. Local Getis-Ord $G_i^{*}$ statistics are subsequently used to identify statistically significant spatial clusters of elevated and reduced mobility impedance across the national network. Finally, sensitivity analyses evaluate the robustness of bridge rankings and hotspot patterns under alternative weighting schemes and bridge-condition representations, while a temporal comparability assessment examines whether differences in component observation years materially influence the results.

This paper makes five principal contributions. It develops a reproducible data-integration workflow for combining the HPMS and NBI databases through spatial matching, quality screening, and phased verification to construct a national bridge-level analytical dataset suitable for network-scale mobility assessment (Section 3.1). It introduces the MII, a data-driven composite indicator that combines the IRI, bridge deck condition, ADT, and projected traffic growth into a single bridge-level measure for mobility-oriented network prioritization (Section 3.2, Section 3.3 and Section 3.4). It evaluates the statistical and spatial characteristics of the proposed index, including its distributional behavior and geographically significant hotspot patterns identified using local Getis-Ord $G_i^{*}$ analysis (Section 4.1 and Section 4.2). It demonstrates the robustness of the proposed methodology through structured sensitivity analyses and temporal comparability testing, showing whether bridge rankings and regional hotspot patterns remain stable under reasonable modeling assumptions (Section 4.3). It provides a scalable, data-driven decision-support methodology that complements existing bridge and pavement management practices by identifying and prioritizing bridges and regions where infrastructure preservation may provide comparatively greater mobility benefits (Section 5 and Section 6).

The remainder of this paper is organized as follows. Section 2 reviews related research on bridge management, pavement performance, composite infrastructure indices, and spatial prioritization methods. Section 3 describes the study area, data sources, bridge-road integration workflow, MII formulation, and analytical methods. Section 4 presents the statistical, spatial, robustness, and temporal-comparability results. Section 5 discusses the interpretation, practical implications, limitations, and opportunities for future research. Finally, Section 6 summarizes the principal findings and conclusions.

2. Literature Review

This section reviews five bodies of research that directly inform the present study: bridge management and condition-based prioritization, pavement performance and mobility, traffic demand and transportation-system performance, composite transportation indices, and spatial infrastructure prioritization. It then considers the data-integration challenges that arise when national bridge and roadway databases are combined and identifies the specific research gaps addressed by the proposed MII.

2.1. Bridge Management and Condition-Based Prioritization

Bridge management systems have evolved primarily to support infrastructure preservation by evaluating structural condition, deterioration, safety, and life-cycle costs. Most national bridge inventories report condition ratings for bridge decks, superstructures, and substructures, which transportation agencies commonly use to prioritize maintenance, rehabilitation, and replacement activities [15]. Numerous bridge health indices and composite condition measures have been proposed to summarize multiple inspection variables into a single indicator that supports engineering decision making [16]. These approaches have generally improved the consistency of bridge condition assessment while facilitating network-level asset management.

Previous studies also developed multi-criteria decision methodologies incorporating structural condition [17], bridge age [18], geometric characteristics [19], traffic exposure [20], economic considerations [21], and expert judgment [22]. Studies have applied techniques such as the analytic hierarchy process [23], fuzzy inference [24], Bayesian networks [25], machine learning [26], and optimization models [27] to rank candidate projects under budget constraints. These methods demonstrated that infrastructure prioritization benefits from simultaneously considering multiple engineering and operational factors rather than relying solely on individual condition ratings.

Despite these advances, the primary objective of bridge management remains the preservation of structural assets. Traffic variables are commonly incorporated as measures of exposure or consequence but are seldom integrated with pavement performance and projected traffic growth into a unified measure of bridge-related mobility. Consequently, current bridge prioritization methods generally seek to determine which bridges require preservation, rather than which bridges constrain mobility the most.

2.2. Pavement Performance and Mobility

Pavement management has developed largely independently of bridge management. The IRI has become the most widely accepted measure of pavement ride quality because it is objective, repeatable, and strongly associated with vehicle operating costs, ride comfort, travel speed, and user satisfaction [28]. Transportation agencies routinely use IRI to monitor pavement condition, evaluate maintenance effectiveness, and support pavement preservation programs.

Numerous studies have examined the relationships between pavement roughness, vehicle operating costs, fuel consumption, emissions, travel time, and freight efficiency [29]. These investigations consistently demonstrated that deteriorating pavement influences transportation performance beyond engineering condition alone [30]. As a result, IRI has become a standard performance measure within pavement management systems and national transportation reporting.

Recent research has also demonstrated that IRI can be estimated or monitored using increasingly diverse sensing and analytical approaches, including low-cost mobile platforms [31], hybrid machine-learning methods incorporating traffic and pavement characteristics [32], and artificial neural networks that account for roadway age and traffic loading [33]. These developments increase the potential availability of pavement-condition information for network-level planning. Nevertheless, pavement analyses typically treat roadway segments as independent assets. Bridge condition rarely enters pavement prioritization methodologies except where bridge rehabilitation directly affects pavement construction activities. Consequently, pavement condition and bridge condition continue to be evaluated largely within separate management systems despite jointly influencing mobility along the same transportation corridors.

2.3. Traffic Demand and Transportation System Performance

Traffic demand represents another fundamental determinant of transportation performance. ADT has long been used to estimate infrastructure utilization, exposure to deterioration, congestion, safety risk, and user impacts [34]. More recent studies have incorporated traffic growth projections to support long-term infrastructure planning [35], recognizing that preservation decisions made today influence future transportation performance over several decades. Similarly, transportation planning studies have evaluated future travel demand when forecasting infrastructure investment needs. Several bridge prioritization frameworks have incorporated current traffic volumes as weighting factors or consequence measures [36]. Traffic information also influences the allocation of monitoring and management resources because highly trafficked structures may warrant greater attention when resources are constrained. However, projected traffic growth has generally been considered independently from pavement condition and bridge condition rather than as an integrated mobility measure. Consequently, relatively little work has examined how present infrastructure condition interacts with anticipated future traffic demand to influence bridge prioritization at the national scale.

2.4. Composite Transportation Performance Indices

Composite indices have become increasingly common in transportation engineering because they synthesize multiple performance dimensions into interpretable indicators suitable for comparison, prioritization, and policy evaluation. Previous studies have developed composite indices describing roadway condition [37], pavement quality [38], bridge health [39], transportation resilience [40], freight performance [41], accessibility [42], sustainability [43], vulnerability [44], and network performance [45]. Such indices provide practical decision-support tools by reducing multidimensional datasets to a manageable number of performance measures.

Developing a practical and effective composite index requires several methodological decisions, including variable selection, normalization, weighting, and aggregation. Previous studies have employed min-max normalization, z-score standardization, percentile transformation, and fuzzy membership functions to place variables on comparable scales [46]. Weighting approaches have ranged from equal weighting to expert judgment, optimization, entropy methods, principal component analysis, and other statistically derived techniques [47]. Similarly, additive, multiplicative, and geometric aggregation methods have each been proposed depending on the intended interpretation of the index [48].

Although considerable research has examined alternative normalization and weighting techniques, there is no universally accepted procedure applicable across all transportation applications. Equal weighting continues to be widely adopted when empirical evidence does not justify preferential weighting among conceptually distinct dimensions [49]. Sensitivity analysis is therefore recognized as an important component of composite-index development because apparently modest methodological choices can materially alter composite scores and rankings [50]. Prior bridge research likewise showed that repair priorities can change under alternative methodological assumptions, reinforcing the need to report robustness explicitly [51].

Most transportation composite indices, however, have focused either on roadway performance or on bridge condition independently. Few have explicitly integrated pavement condition, bridge condition, present traffic demand, and projected traffic growth into a single bridge-level measure intended to represent mobility impedance.

2.5. Spatial Prioritization of Transportation Infrastructure

Transportation infrastructure exhibits strong spatial dependence because neighboring facilities frequently share similar traffic characteristics, environmental conditions, maintenance histories, and socioeconomic influences. Consequently, spatial statistical methods have become increasingly important for identifying geographic patterns that cannot be detected through independent asset evaluation.

Previous studies have applied global and local spatial autocorrelation techniques to transportation safety, pavement deterioration, bridge condition, freight movement, congestion, resilience, and infrastructure investment [52]. Among these approaches, the local Getis-Ord $G_i^{*}$ statistic has become a widely used method for identifying statistically significant clusters of unusually high or unusually low values while accounting for neighborhood relationships [53]. Such hotspot analyses support geographically targeted intervention strategies by distinguishing isolated observations from systematic regional concentrations.

Most transportation hotspot studies have examined single variables, including crash frequency [54], pavement condition [55], bridge condition [56], or traffic congestion [57]. Comparatively fewer investigations have evaluated hotspot patterns derived from composite infrastructure indices, particularly at national scales. Furthermore, relatively little attention has been given to assessing the robustness of identified hotspot locations under alternative index specifications.

2.6. Data Integration Challenges

The increasing availability of national transportation datasets has expanded opportunities for integrated infrastructure analyses. The NBI and HPMS together provide comprehensive information describing bridge characteristics, roadway geometry, pavement condition, traffic demand, and functional classification across the United States [58]. Previous studies have frequently analyzed these databases independently or joined them for specific regional investigations [59]. For example, national bridge records have supported machine-learning prediction of bridge-deck deterioration [60], probabilistic prediction of future condition levels, and deterioration grouping based on shared bridge characteristics [61]. However, integrating national infrastructure datasets consistently remains challenging because bridge and roadway records use different spatial representations, identifiers, reference systems, and reporting practices.

Data-quality research has shown that missing values, anomalous observations, and inconsistent records in the NBI can materially affect downstream analytical models [62]. Machine-learning anomaly detection has likewise identified data irregularities that can reduce the reliability of bridge-management decisions if they remain uncorrected [63]. These findings support explicit data-quality screening before national infrastructure databases are combined. Missing county identifiers, incomplete roadway attributes, inconsistent route information, and differences in spatial location therefore require substantial quality assurance before reliable bridge-road associations can be established. Broader infrastructure-management research has also identified fragmented databases and coordination across infrastructure systems as persistent barriers to integrated asset management [64].

Digital technologies increasingly provide mechanisms for integrating heterogeneous infrastructure information. Previous studies demonstrated that interoperable digital-twin environments can combine bridge data streams to improve maintenance decision support [65], while advanced inspection technologies can supplement conventional bridge-condition records through damage-sensitive monitoring [66], internal defect mapping [67], and combined thermal and surface-condition assessment [68]. These approaches improve bridge-specific information, but they do not resolve the problem of creating consistent national bridge-road linkages by themselves.

Although spatial matching methods have become increasingly sophisticated, relatively few published studies have documented transparent and auditable workflows for constructing quality-controlled national bridge-road analytical datasets suitable for mobility-oriented analysis. As a result, many national-scale integration procedures remain difficult to reproduce or evaluate.

2.7. Research Gap

The existing literature demonstrates substantial progress in bridge management, pavement management, traffic analysis, composite transportation indices, and spatial infrastructure prioritization. However, these research areas have largely advanced independently. Current bridge management methods primarily evaluate structural preservation needs, pavement management emphasizes roadway condition, and traffic-demand analyses focus on infrastructure utilization or future capacity. Existing composite indices similarly tend to represent individual infrastructure systems rather than the combined mobility implications of bridge condition, pavement condition, and traffic demand.

The literature also increasingly recognizes that bridge importance extends beyond physical condition. Network studies have shown that resilience depends on how structures function within the broader transportation system, while maintenance frameworks increasingly consider operational consequences alongside structural performance [69]. Nevertheless, these lines of research do not provide a transparent and practical bridge-level metric that jointly represents pavement roughness, bridge condition, present traffic intensity, and future traffic growth. In addition, relatively little research has developed auditable national workflows for integrating the NBI and HPMS into a unified bridge-level analytical dataset while explicitly addressing spatial matching, data quality, and temporal comparability. Published studies have also given limited attention to evaluating whether bridge prioritization and spatial hotspot identification remain robust under alternative weighting assumptions, bridge-condition representations, and differences in component observation years.

This study addresses these gaps by integrating nationally available bridge and roadway datasets to develop an MII that combines IRI, bridge deck condition, current ADT, and projected traffic growth into a single bridge-level measure of potential mobility constraint for open, unrestricted mainline NHS bridges in the CONUS. The study further develops a transparent bridge-road integration workflow, evaluates the statistical and spatial characteristics of the resulting index, and systematically examines its robustness through sensitivity analysis and temporal comparability assessment. Together, these contributions extend existing bridge and pavement management research by providing a transparent and transferrable methodology for mobility-oriented infrastructure prioritization using nationally available transportation data.

3. Methodology

This section describes the data sources, bridge-road integration workflow, MII formulation, and analytical methods used to evaluate bridge-level mobility constraints. The methodology proceeds from data extraction and quality assurance through index development, statistical characterization, spatial hotspot analysis, sensitivity testing, and temporal comparability assessment. The analytical workflow described was implemented in Python 3.13 using pandas 2.3.2 for tabular data processing, NumPy 2.3.2 for numerical computation, GeoPandas 1.1.1 and Shapely 2.1.1 for geospatial processing, SciPy 1.16.1 for statistical analyses, libpysal 4.13.0 and esda 2.7.1 for local Getis-Ord $G_i^{*}$ analysis, Matplotlib 3.10.6 for visualization, and QGIS 3.44 for selected GIS data preparation and quality-assurance tasks.

3.1. Data Extraction and Analytical Sample Construction

The analytical dataset was constructed by linking roadway-condition data from the HPMS [6] with bridge condition and traffic data from the NBI [5]. At the time of retrieval in 2026, both datasets contained records with observation years extending into 2025. Although the bulk HPMS geospatial release is documented through 2024, 2025 was retained as the reference year because a subset of ADT and inspection records carried 2025 observation dates.

The workflow proceeded through eight processing stages comprising sequential filtering followed by automated and manual bridge–road recovery procedures (Table 1). The final analytical dataset therefore reflects both operational eligibility screening and analytical suitability for index construction. Table 2 summarizes the actual fields retained from the HPMS and NBI databases. Each construction stage imposed a specific geographic, operational, spatial, or analytical eligibility requirement. Stages 6a–6c represent successive automated recovery rules applied only to the subset of bridges that failed the preceding county-agreement criterion rather than to the entire retained sample. Records excluded at one stage were not reintroduced, except where explicitly recovered through a phased bridge–road verification procedure. The retained sample after Stage 7b represents the reconciled bridge population after both automated and manual recovery.

The subsections that follow further describe each stage of the data extraction and cleaning workflow.

3.1.1. HPMS Roadway Extraction and Geographic Preparation

The national HPMS geospatial files were obtained using the HPMS Geospatial Data Extractor software, version 1.1. The extractor combined state-level files into one national GeoPackage of size 10.5 gigabytes containing 19,573,739 roadway records and 86 attributes. The first filter retained records for which the HPMS NHS indicator equaled one. This step retained 3,622,383 roadway records, or 18.5% of the national HPMS file. Most excluded records (15,908,499; 81.3%) had missing NHS designations and only a few (42,857; 0.2%) had valid non-NHS values. The roadway file was then restricted to the 48 contiguous states and the District of Columbia, which retained 3,563,899 (98.4%) of the extracted NHS segments. Of these, 3,467,570 (97.3%) had valid state and county FIPS values and 3,339,315 (93.7%) had valid IRI values. Records with missing road county identifiers were retained to attempt spatial county code recovery in the bridge–road matching stage, whereas records lacking valid IRI values remained eligible for matching but were subsequently removed only if required during the final complete-case analytical screening. The workflow constructed fip5_r as a five-character road county identifier by concatenating the standard two-digit Federal Information Processing (FIP) state identifier code stored in the field StateID, and the three-digit FIP county identifier stored in the field County_ID, with leading zeros retained.

3.1.2. NBI Bridge Extraction and Homogeneous Bridge Definition

The original NBI file contained 624,193 bridge records. The bridge sample was restricted to a homogeneous group of open, mainline NHS highway bridges located in the CONUS. Hence, a bridge was retained when all of the following conditions were satisfied, based on the field value indicated: open_closed_posted_041 = A, highway_system_104 = 1, service_on_042a = 1, service_level_005c = 1, record_type_005a = 1. These criteria retained bridges that were open without restrictions, carried an NHS highway, provided mainline highway service, and represented the route carried on the structure rather than a route passing beneath it. The filter excluded closed or restricted structures, non-highway structures, bypass or non-mainline facilities, and records describing an underpassing route. The bridge county identifier fip5_b was the string concatenation of state_code_001 and county_code_003. This process retained 109,713 bridges, representing 17.6% of the original NBI inventory.

3.1.3. Nearest-Road Spatial Matching

Each of the retained NBI bridge points was matched to its nearest retained CONUS NHS road segment. All spatial operations, including nearest-road matching, linear referencing, and snap-distance calculations, were performed using the NAD83 / Conus Albers equal area projection (EPSG:5070), with distances computed in meters. No maximum distance threshold was imposed at this initial stage because the purpose was to create a complete candidate bridge–road linkage for subsequent quality screening. Each bridge point was moved to the closest position along the matched road geometry using linear referencing. The road geometry remained unchanged, and no road vertices were added. The spatial match inherited the following HPMS fields after normalizing all to lowercase: fip5_r, route_id, route_number, routename, f_system, facility_type.

All 109,713 bridge points received a nearest-road candidate. The median snap distance was 3.2 meters and the 95th percentile was 38.8 meters. However, the unconstrained mean was 5,882.1 meters because a small number of implausible matches occurred over extremely large distances, including a maximum of 8,177,496.8 meters, most plausibly reflecting erroneous or incomplete coordinate values in the source NBI records; none of these extreme-distance candidates survived the subsequent screening stages. Extreme snap distances confirmed that nearest-neighbor assignment alone was insufficient and required additional route, county, and geometric plausibility checks. These summary statistics describe the initial unconstrained nearest-neighbor matches before subsequent quality screening.

Missing road county identifiers were imputed only when the original HPMS value was absent. An official 2020 county layer from the United States Census Bureau (USCB) was used because its county geography retained the legacy Connecticut county codes that were compatible with the bridge and roadway files [70]. Of 7,808 matched roads that did not have a $FIP{5}_R$ value, 7,800 were assigned through the county polygons, leaving eight unresolved values to propagate to the final manual resolution stage because state-agreement (Eq. 6) could not be evaluated without a $FIP{5}_R$ value.

3.1.4. Mainline Roadway Homogeneity Filter

The matched bridge–road records were next restricted to HPMS facility_type 1 and 2, where type 1 denotes a one-way roadway and type 2 denotes a two-way roadway. This criterion removed ramps, non-mainline facilities, and non-inventory directions. The mainline roadway filter retained 81,773 of the 109,713 matched bridges, or 74.5%. County agreement was initially defined as

$$E_i^{FIP}=\left\{\begin{array}{cc}0,& {fip5\_r}_i={fip5\_b}_i,\\ 1,& otherwise.\end{array}\right.$$

(1)

A total of 80,385 (98.3%) of the mainline records had direct bridge–road county agreement, while 1,388 records required further assessment, including the eight unresolved county records propagated from the previous stage.

3.1.5. Snap-Distance Excess Measure

The geometric plausibility of each bridge–road match was evaluated relative to the estimated half-width of the bridge. The effective bridge width, $W_i$, was assigned using the following priority:

$$W_i=\left\{\begin{array}{cc}{\mathrm{deck}\text{\_}\mathrm{width}\text{\_}\mathrm{mt}\text{\_}052}_i,& \mathrm{if}\mathrm{valid}\mathrm{and}\mathrm{positive},\\ {\mathrm{appr}\text{\_}\mathrm{width}\text{\_}\mathrm{mt}\text{\_}032}_i,& \mathrm{otherwise},\mathrm{if}\mathrm{valid}\mathrm{and}\mathrm{positive},\\ 3.66\times {\mathrm{traffic}\text{\_}\mathrm{lanes}\text{\_}\mathrm{on}\text{\_}028\mathrm{a}}_i,& \mathrm{otherwise},\mathrm{if}\mathrm{the}\mathrm{lane}\mathrm{count}\mathrm{is}\mathrm{valid},\\ \mathrm{missing},& \mathrm{otherwise}.\end{array}\right.$$

(2)

The first option uses the NBI bridge deck width. The second uses the roadway width approaching the bridge when deck width was unavailable. The final fallback used a standard highway lane width of 12 feet (3.66 meters), consistent with FHWA design practice [71], multiplied by the reported number of traffic lanes. The allowable centerline displacement was defined as one-half of the estimated bridge width:

$$b_i={\displaystyle \frac{W_i}{2}}.$$

(3)

The excess snap distance was then calculated as

$$e_i=\mathrm{m}\mathrm{a}\mathrm{x}\left(0,d_i-b_i\right).$$

(4)

where d_i was the snap distance in meters. Thus, $e_i=0$ indicates that the nearest matched road centerline falls within the estimated half-width of the bridge footprint. A positive value indicates that the bridge point moved farther than the estimated bridge half-width: $e_i>0⟹d_i>b_i.$ This measure does not treat every nonzero snap distance as an error. Instead, it distinguishes ordinary displacement from displacement extending beyond the approximate lateral extent of the bridge structure.

3.1.6. Phased Recovery of County-Mismatch Records

The 1,388 records with $FIP{5}_R\ne FIP{5}_B$ were evaluated using a hierarchical recovery procedure. Route identifiers were standardized to integers before comparison. Route agreement was defined as

$$M_i^{route}=\left\{\begin{array}{cc}1,& \mathrm{i}\mathrm{n}\mathrm{t}\left({\mathrm{route}\text{\_}\mathrm{number}}_i\right)=\mathrm{i}\mathrm{n}\mathrm{t}\left({\mathrm{route}\text{\_}\mathrm{number}\text{\_}005\mathrm{d}}_i\right),\\ 0,& \mathrm{otherwise},\end{array}\right.$$

(5)

provided both fields were present. State agreement was determined from the first two digits of $FIP{5}_R$ and $FIP{5}_B$:

$$M_i^{state}=\mathbb{1}\left[FIP{5}_{R,i}\left[1:2\right]=FIP{5}_{B,i}\left[1:2\right]\right].$$

(6)

The mismatch records were assigned sequentially to four mutually exclusive phases:

$$Phas{e}_i=\left\{\begin{array}{cc}1,& M_i^{route}=1\mathrm{and}{M}_i^{state}=1,\\ 2,& M_i^{route}=1\mathrm{and}{e}_i=0,\\ 3,& M_i^{state}=1\mathrm{and}{e}_i=0,\\ 4,& \mathrm{otherwise}.\end{array}\right.$$

(7)

Phase 1 recovered 937 records through route and state agreement. Phase 2 recovered 56 additional records through route agreement and zero excess snap distance. Phase 3 recovered 103 records through state agreement and zero excess snap distance. The remaining 292 records were manually inspected as described below.

3.1.7. Manual Verification and Final Bridge–Road Sample

The manual inspection used alternative bridge and roadway identifiers where available. A record was considered verified when text contained in at least one bridge identifier matched text contained in at least one road identifier. The bridge identifiers were route_number_005d, facility_carried_007, and LRS_inv_route_013a. The roadway identifiers were route_number, routename, route_ID, and the roadway name displayed in the GIS map view. Manual review verified 81 of the 292 remaining records. The other 211 records were excluded. The final bridge–road dataset therefore contained 81,562 records, corresponding to 99.7% of the 81,773 mainline bridge candidates.

The retained file preserved the bridge variables needed to construct the MII, including current and future traffic demand, traffic reference years, lane count, IRI, deck condition, bridge widths, snap distance, $b_i$, $e_i$, route-agreement indicators, county-agreement indicators, recovery-stage codes, and manual verification status. It also retained the inherited HPMS route and facility, traffic, and pavement-condition fields required for auditing.

3.1.8 Complete-Case and Metric-Validity Screening

The final analytical screen retained records with valid values for all fields required to calculate the four MII components. Complete-case filtering retained 80,088 (98.2%) records. Most exclusions resulted from missing values in one or more of the four MII component fields (IRI, deck condition, current ADT, or future ADT), whereas missing lane count and ADT reference-year fields contributed comparatively few additional exclusions. The remaining records were then screened for valid logarithmic and growth calculations. Specifically, iri > 0, adt_029 > 0, future_adt_114 > 0, traffic_lanes_on_028a > 0, and year_of_future_adt_115 > year_adt_030. These checks removed another 493 records. Nearly all of these records failed the positivity requirements for logarithmic transformation or contained nonpositive ADT forecast intervals, rather than producing nonfinite calculated metrics. No records produced nonfinite calculated metrics after the validity screen. The final MII analytical dataset contained 79,595 bridges, representing 99.4% of the verified bridge–road sample. Within the final analytical dataset, 68.2% of retained bridges exhibited $e_i=0$, with a median retained excess snap distance of 0.0 m, confirming that most bridge–road matches satisfied the adopted bridge-width tolerance after all screening and recovery stages.

3.2. Mobility Impedance Index Formulation

The MII was developed to quantify the relative potential for a bridge to impede traffic movement by combining measures of traffic demand and infrastructure condition into a single composite indicator. The selected components represent complementary dimensions of mobility performance. Together, they describe both current mobility conditions and anticipated future demand. Two variables describe current and future traffic demand, while two characterize the physical condition affecting traffic flow. Together, they capture both the magnitude of traffic exposed to potential disruption and the infrastructure characteristics that influence the severity of that disruption.

Traffic demand was represented by the logarithm of ADT per lane and the annual logarithmic growth rate in ADT per lane. Dividing ADT by the number of traffic lanes provides a measure of traffic intensity rather than total traffic volume, allowing facilities with different cross-sectional capacities to be compared on a common basis. The annual growth term identifies bridges where future traffic demand is expected to increase, indicating greater potential for future mobility constraints. The traffic components do not represent physical obstruction or infrastructure deterioration. Instead, they quantify the magnitude of current and anticipated traffic exposed to potential mobility disruption should infrastructure condition deteriorate. Consequently, the MII represents the joint influence of infrastructure condition and traffic exposure on potential mobility constraints rather than a direct measure of realized traffic impedance.

The International Roughness Index (IRI) was selected because pavement roughness directly influences travel speed, ride quality, operating costs, cargo damage, and vehicle delay [29]. Bridge deck condition rating was included because structural deterioration often results in maintenance activities, operational restrictions, or eventual rehabilitation that affect traffic movement. Unlike traditional bridge condition indices that emphasize structural integrity, the MII emphasizes factors that influence the movement of vehicles across the transportation network.

3.2.1. MII Component Design

The continuous variables were first transformed to reduce skewness. The logarithm of IRI and the logarithm of ADT per lane were computed as

$$IR{I}_{LN}=\mathrm{l}\mathrm{n}\left(IRI\right)$$

(8)

and

$$AD{T}_{LN}=\ln \left({\displaystyle \frac{ADT}{L}}\right)$$

(9)

where L is the number of traffic lanes. Annual traffic growth was expressed as the difference in logarithmic traffic intensity divided by the forecast interval,

$${AG}_{LN}={\displaystyle \frac{\ln \left(\frac{AD{T}_{future}}{L}\right)-\ln \left(\frac{AD{T}_{current}}{L}\right)}{Y_{future}-Y_{current}}}$$

(10)

where Y denotes the corresponding ADT reference year. This simplifies to

$${AG}_{LN}={\displaystyle \frac{\ln \left(AD{T}_{future}\right)-\ln \left(AD{T}_{current}\right)}{Y_{future}-Y_{current}}}$$

(11)

Since these variables have different units and distributional characteristics, each continuous component was converted to an empirical percentile rank,

$$X_i^{\mathrm{*}}={\displaystyle \frac{r_i-1}{n-1}}$$

(12)

where $r_i$ is the average rank of bridge i and n is the total number of bridges. This transformation maps every continuous variable onto the interval [0, 1], which preserves the observed ordering of bridges, reduces sensitivity to extreme values, and avoids requiring a particular probability distribution. The resulting normalized values are relative to the analytical dataset used to construct the index and therefore reflect each bridge’s standing within the national bridge population rather than an absolute engineering threshold.

Note that percentile ranking is invariant to any strictly monotonic transformation; consequently, the logarithmic transformations applied to IRI and ADT per lane do not alter the resulting percentile ranks or the MII itself. The annual traffic-growth term is a derived log-difference rather than a monotonic transform of a single variable, so its logarithmic construction does materially affect its ranking.

Unlike the continuous variables above, bridge deck condition is an ordinal engineering rating defined on a fixed 10-point national scale. Consequently, it was normalized using the fixed rating scale rather than empirical percentile normalization to preserve the engineering interpretation of equal rating intervals across the NBI. Although this approach yields a different empirical distribution than the percentile-normalized continuous variables, the subsequent sensitivity analysis explicitly evaluates the influence of alternative deck-condition representations, empirical percentile normalization of the deck component, and alternative treatment of N-coded bridges (deck condition coded as “N” for not applicable) on bridge rankings and hotspot identification.

For numeric ratings, deck condition was converted to a linear impedance scale

$$D_i={\displaystyle \frac{9-R_i}{9}}$$

(13)

where $R_i$ is the reported NBI deck-condition rating from 0 to 9. Thus, a rating of 9 (excellent) corresponds to $D_i=0$, whereas a rating of 0 (failed) corresponds to $D_i=1$. The NBI category “N,” indicating that a deck-condition rating is not applicable, was retained and assigned $D_i=0$. This treatment avoids imposing an artificial deterioration penalty when deck condition is not applicable, while recognizing that assigning zero necessarily lowers the deck contribution to the composite index relative to bridges with numeric ratings. This assignment represents a modeling assumption rather than an empirically validated mobility relationship, adopted because the “N” designation denotes an inapplicable attribute rather than an unknown condition. Missing, invalid, or out-of-range values other than “N” were excluded.

3.2.2. Correlation of MII Components

Prior to additive aggregation, inter-component dependence was evaluated using Spearman rank correlations among the normalized IRI, ADT per lane, ADT growth, and deck-condition impedance components, the last of which incorporates the zero-impedance assignment for bridge conditions coded “N” as described in the previous subsection. Spearman correlation was selected as the primary diagnostic because the three continuous components were percentile normalized while deck condition originated from an ordinal engineering scale. Pearson correlations were also calculated as a secondary diagnostic. The conclusions were unchanged regardless of the correlation measure used. Since N-coded bridges contribute a fixed zero value to the deck-condition component, the correlation analysis was also repeated for the 59,953 bridges with numeric deck-condition ratings only. The purpose of this assessment was to determine whether strong pairwise associations could indicate redundant information and thereby produce disproportionate representation of a common underlying dimension in the composite index. An absolute Spearman correlation of |ρ| ≥ 0.70 was adopted as a conventional descriptive threshold for a strong association that may indicate substantial overlap between composite-index components, consistent with correlation-screening conventions used in composite-indicator construction guidance [72]. Inter-component correlations provided no evidence of strong redundancy among the four MII dimensions (Figure 1).

The largest Spearman correlation was between IRI and deck-condition impedance (ρ = 0.304), followed by deck condition and ADT per lane (ρ = 0.216). The remaining associations were weak, ranging in absolute magnitude from 0.007 to 0.092. Of particular relevance to potential overlap between the two demand measures, ADT per lane and annual ADT growth were essentially uncorrelated (ρ = −0.007). No pair approached the predefined ∣ρ∣ = 0.70 diagnostic threshold. Pearson correlations produced nearly identical results, with a maximum absolute correlation of 0.315. Excluding N-coded bridges further reduced the maximum absolute Spearman correlation—the IRI–deck association—from 0.304 to 0.083. These findings indicated no strong pairwise redundancy among the four components and showed that the low correlations were not attributable to attenuation caused by the fixed zero assignment for N-coded bridges. These findings provide empirical support for their subsequent additive aggregation.

3.2.3. MII Construction

The baseline Case 1 MII was computed as the weighted sum

$$MI{I}_i=w_{1}IR{I}_i^{\mathrm{*}}+w_{2}AD{T}_i^{\mathrm{*}}+w_3{AG}_i^{\mathrm{*}}+w_4{D}_i$$

(14)

subject to

$${\displaystyle \sum _{j=1}^4}{w}_j=1.$$

(15)

for the baseline analysis $w_1=w_2=w_3=w_4=0.25$. Equal weighting was adopted for the baseline because current empirical evidence does not provide a defensible basis for assigning greater importance to one mobility dimension over another. Even so, this assumption does not imply that pavement roughness, traffic demand, traffic growth, and bridge condition have identical physical effects on mobility. Rather, it provides a transparent reference model that treats each dimension as equally informative in the absence of objective evidence supporting differential weighting. This approach minimizes subjective judgment, facilitates interpretation, and establishes a neutral benchmark against which alternative assumptions can be evaluated.

A simple additive formulation was selected instead of a multiplicative or geometric index. An additive index expects that mobility impairment arises from the cumulative influence of multiple factors, each contributing independently to the overall level of impedance. This formulation permits partial compensation among components, reflecting the practical reality that a bridge with one unfavorable characteristic may still exhibit moderate overall mobility performance if the remaining characteristics are favorable. Accordingly, bridges in excellent physical condition may receive elevated MII values when they support substantial current or future traffic demand because the index is intended to prioritize potential mobility consequences rather than existing operational delay.

The additive formulation assumes compensability among the four components, such that a higher impedance contribution from one dimension can be offset by lower contributions from others. This assumption is deliberate and reflects the interpretation of the MII as a composite prioritization measure rather than a model in which any single adverse component necessarily determines overall mobility impedance. In contrast, multiplicative indices strongly amplify interactions among variables and can produce disproportionately large penalties when a single component approaches an extreme value. Such behavior is appropriate only when strong empirical evidence demonstrates synergistic effects among components. Because no nationally validated functional relationship currently exists for these bridge mobility variables, the additive formulation provides a more transparent, interpretable, and reproducible baseline.

The baseline index is subsequently subjected to a structured sensitivity analysis that varies component weights and the transformation of bridge deck condition. These scenarios are not intended to represent competing formulations of the MII or alternative statements of truth. Instead, they evaluate the robustness of the baseline definition by determining whether bridge rankings, spatial hotspot patterns, and county-level clustering remain stable under a range of reasonable modeling assumptions. A stable response across these scenarios increases confidence that the principal findings are driven by the underlying data rather than by a particular specification of the composite index.

3.3. Distributional Characterizations

Composite indices are influenced by the statistical properties of their constituent variables. Before constructing the MII, the distributions of its four component variables were evaluated to verify that the selected transformations adequately reduced skewness and to characterize their statistical behavior. Although the MII ultimately employs empirical percentile normalization rather than distribution-specific transformations, understanding the underlying distributions provides insight into the behavior of each mobility dimension and demonstrates that the normalization procedure is appropriate across variables exhibiting different distributional forms.

The four MII components and the final Case 1 MII were each compared with five candidate continuous probability distributions: normal, skew-normal, Student’s t, Johnson SU, and generalized normal. These families span a broad range of symmetric, asymmetric, and heavy-tailed behaviors [73]. For a random variable X, each candidate distribution was estimated by maximum likelihood. Let $\theta =\left({\theta }_1,{\theta }_2,\dots ,{\theta }_k\right)$ denote the vector of estimated distribution parameters. The log-likelihood is

$$\mathcal{l}\left(\theta \right)={\displaystyle \sum _{i=1}^n}\ln \left[f\left(x_i\mid \theta \right)\right],$$

(16)

where $f\left(\cdot \right)$ denotes the corresponding probability density function. Candidate distributions were compared using Akaike’s information criterion (AIC),

$$AIC=2k-2\mathcal{l}\left(\theta \right),$$

(17)

where k is the number of estimated parameters. Lower AIC values indicate greater support for a candidate distribution while balancing goodness of fit against model complexity. Bayesian information criterion (BIC) was also reported as a secondary measure,

$$BIC=k\mathrm{l}\mathrm{n}\left(n\right)-2\mathcal{l}\left(\theta \right)$$

(18)

where n is the sample size. Relative support among competing models was summarized using Akaike weights,

$$w_i={\displaystyle \frac{\exp \left(-\frac{{\mathsf{\Delta }}_i}{2}\right)}{{\displaystyle {\sum }_{r=1}^R}\exp \left(-\frac{{\mathsf{\Delta }}_r}{2}\right)}}$$

(19)

where

$${\mathsf{\Delta }}_i=AI{C}_i-AI{C}_{min}.$$

(20)

The Akaike weight approximates the probability that a candidate model is the best approximating distribution among the set of competing models.

Two descriptive goodness-of-fit statistics were also reported. The Kolmogorov-Smirnov (KS) statistic measures the maximum absolute difference between the empirical and fitted cumulative distribution functions,

$$D=\underset{x}{\mathrm{s}\mathrm{u}\mathrm{p}}∣F_n\left(x\right)-F\left(x\right)∣,$$

(21)

where $F_n\left(x\right)$ is the empirical cumulative distribution function and $F\left(x\right)$ is the fitted theoretical cumulative distribution function. The Cramér-von Mises (CvM) statistic evaluates the integrated squared difference between the two cumulative distributions,

$$W^2=n{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}{\left[F_n\left(x\right)-F\left(x\right)\right]}^{2}dF\left(x\right).$$

(22)

Since distribution parameters were estimated from the same observations used for model evaluation, the associated hypothesis-test p-values were interpreted descriptively rather than inferentially. Instead, emphasis was placed on the relative ranking of candidate distributions through AIC, supported by the magnitudes of the KS and CvM statistics.

This distributional assessment serves two purposes. First, it confirms that the logarithmic transformations substantially reduce skewness while recognizing that different variables continue to exhibit distinct distributional characteristics. Second, it demonstrates that the empirical percentile normalization adopted for the MII does not depend on any single probability distribution, making the index applicable even when individual mobility components follow different statistical families.

3.4. Spatial Hotspot Analysis

After computing the MII for each bridge, spatial analysis was conducted to determine whether elevated or reduced mobility impedance occurred in statistically significant geographic clusters rather than being randomly distributed. Identifying such clusters provides a network-level perspective by revealing locations where neighboring bridges collectively exhibit unusually high or low mobility impedance. These spatial patterns can inform agencies of regions where coordinated infrastructure investment may produce greater system-wide mobility benefits than isolated bridge improvements.

Spatial clustering was evaluated using the local Getis-Ord $G_i^{*}$ statistic [74]. Unlike global measures of spatial autocorrelation, local $G_i^{*}$ identifies the specific locations that contribute to clustering while distinguishing statistically significant hotspots from coldspots. This local perspective is appropriate because bridge performance is expected to vary across transportation corridors, metropolitan regions, and rural networks rather than exhibiting a single national pattern. For bridge i, the local $G_i^{*}$ statistic is

$$G_i^{\mathrm{*}}={\displaystyle \frac{{\displaystyle {\sum }_{j=1}^n}{w}_{ij}{x}_j-\overline{x}{\displaystyle {\sum }_{j=1}^n}{w}_{ij}}{S\sqrt{\frac{n{\displaystyle {\sum }_{j=1}^n}{w}_{ij}^2-{\left({\displaystyle {\sum }_{j=1}^n}{w}_{ij}\right)}^2}{n-1}}}}$$

(23)

where

• $x_j$ is the MII of bridge $j.$
• $w_{ij}$ is the spatial weight relating bridges $i$and $j$.
• $\overline{x}$ is the mean MII.
• S is the sample standard deviation.

$$S=\sqrt{{\displaystyle \frac{{\displaystyle {\sum }_{j=1}^n}(x_j-\overline{x}{)}^2}{n}}}.$$

(24)

Positive standardized $G_i^{*}$ values indicate that a bridge is surrounded by neighboring bridges with similarly high mobility impedance, whereas negative values indicate neighborhoods with consistently low impedance. An adaptive k-nearest-neighbor spatial weights matrix was employed with k = 8 neighbors, consistent with established best-practice guidance for local $G_i^{*}$ hot-spot analysis [75]. Binary spatial weights were defined as

$$w_{ij}=\left\{\begin{array}{cc}1& \mathrm{if}\mathrm{bridge}j\mathrm{is}\mathrm{among}\mathrm{the}\mathrm{eight}\mathrm{nearest}\mathrm{neighbors}\mathrm{of}\mathrm{bridge}i\\ 0& \mathrm{otherwise}.\end{array}\right.$$

(25)

The $G_i^{*}$ formulation includes each bridge as a member of its own neighborhood. Adaptive nearest-neighbor weights were selected because bridge density varies substantially across the CONUS. Fixed-distance neighborhoods would produce isolated bridges without neighbors in sparsely populated regions while generating excessively large neighborhoods within dense metropolitan areas. Adaptive neighborhoods ensure that every bridge contributes to the analysis while maintaining a consistent local sample size across the national network. This property is particularly advantageous for nationwide analyses where bridge density varies substantially between metropolitan and rural regions.

Statistical significance was evaluated using 999 conditional random permutations, following standard practice for local $G_i^{*}$ inference [74]. For each bridge, the observed $G_i^{*}$ statistic was compared with the permutation distribution to obtain a pseudo p-value,

$$p={\displaystyle \frac{r+1}{R+1}}$$

(26)

where r is the number of simulated statistics at least as extreme as the observed statistic and R = 999 is the number of random permutations. Bridges with $p\le 0.05$ and positive $G_i^{*}$ $z$-scores were classified as statistically significant hotspots, whereas bridges with $p\le 0.05$ and negative $G_i^{*}$ $z$-scores were classified as statistically significant coldspots. Confidence classes corresponding to the 90%, 95%, and 99% significance levels were retained in the analysis, although subsequent interpretation focused primarily on the conventional 95% significance threshold. Since local Getis-Ord $G_i^{*}$ constitutes an exploratory local spatial-analysis procedure with strongly dependent neighboring tests, formal multiplicity corrections (e.g., Bonferroni or false discovery rate adjustment) were not applied. Instead, the hotspot analysis was interpreted as a descriptive tool for identifying geographically coherent clusters rather than as a collection of independent confirmatory hypothesis tests.

3.5. Sensitivity Analysis of the MII

The baseline MII was intentionally designed as a transparent reference model based on equal component weights and a linear bridge deck impairment function. Since no nationally accepted mobility model exists that specifies the relative contribution of pavement condition, structural condition, current traffic demand, and future traffic growth, it is important to evaluate how much the resulting bridge rankings and spatial prioritization depend on these modeling assumptions. Rather than proposing alternative definitions of the MII, the sensitivity analysis was designed as a series of structured stress tests that quantify the robustness of the baseline formulation under plausible departures from the reference assumptions (Table 3). Two sources of specification uncertainty were examined. The first concerns the relative importance assigned to each MII component. The second concerns the representation of bridge deck condition, including its functional form, normalization basis, and the treatment of N-coded bridges.

3.5.1. Component-Weight Stress Tests

To evaluate robustness, four alternative weighting scenarios were constructed by assigning one component one-half of the total index weight while distributing the remaining half equally among the other three components,

$$w_f=0.50,w_r={\displaystyle \frac{0.50}{3}}=0.1667$$

(27)

where $w_f$ denotes the emphasized (“focal”) component and $w_r$ denotes each remaining component.

The choice of a 50% focal weight represents a deliberately strong but still plausible perturbation of the baseline model. Doubling the weight assigned to one component creates a meaningful departure from equal weighting while preserving contributions from the remaining dimensions. Smaller departures (e.g., 30% or 40%) would likely produce only minor changes, whereas substantially larger weights (e.g., 70%–90%) would imply that one mobility dimension dominates all others without empirical or policy justification. The selected weighting therefore provides a structured stress test that challenges the stability of the MII while remaining within a defensible range of engineering judgment. More extreme weighting schemes (e.g., 70%–90% assigned to a single component) were therefore not evaluated because they would represent fundamentally different single-dimension prioritization strategies rather than plausible variants of a balanced mobility index. Importantly, these weighting scenarios are not intended to identify an optimal weighting scheme. Instead, they evaluate whether reasonable changes in subjective weighting materially alter bridge prioritization or the resulting spatial patterns.

3.5.2. Deck-Condition Representation Stress Tests

To examine how much the MII depends on the assumed functional relationship between deck condition and mobility impairment, a second stress test replaced the continuous deck score with a categorical step function,

$$D_i^{cat}=\left\{\begin{array}{cc}0.0& R_i=7\text{–}9\\ 0.5& R_i=5\text{–}6\\ 1.0& R_i=0\text{–}4\\ 0.0& R_i=N\end{array}\right.$$

(28)

The category boundaries follow the NBI engineering interpretation that ratings 7–9 generally represent bridges in good condition, ratings 5–6 indicate fair condition requiring increased maintenance attention, and ratings 0–4 represent poor condition requiring substantial rehabilitation or replacement consideration. The corresponding impedance values (0, 0.5, and 1.0) intentionally define broad mobility classes rather than attempting to reproduce the precise numerical spacing of the original rating scale. Two scenarios employed this categorical representation. One retained equal component weights, while the other combined the categorical deck scale with the 50% deck-emphasis weighting. Together, these scenarios evaluate how much conclusions depend primarily on the weighting assigned to deck condition, on the mathematical representation of deck condition itself, or on both simultaneously. Another stress test (C8_N_RENORM) retained the baseline formulation for numerically rated bridges but excluded the deck term for N-coded bridges and renormalized the three remaining component weights from 0.25 to 1/3 each. An additional stress test (C9_DECK_PCT) replaced the fixed engineering deck-impedance scale with an empirical percentile normalization while retaining equal component weights and the baseline treatment of N-coded bridges.

3.5.3. Bridge Rank and Hotspot Stability

Bridge-level robustness was quantified using Spearman’s rank correlation coefficient,

$$\rho =1-{\displaystyle \frac{6{\displaystyle {\sum }_{i=1}^n}{d}_i^2}{n\left(n^2-1\right)}}$$

(29)

where $d_i$ is the difference between the ranks assigned to bridge i under two sensitivity scenarios. Spearman’s coefficient was selected because bridge prioritization depends on relative ordering rather than absolute index values and because it does not assume normally distributed data.

Spatial robustness was evaluated by comparing the sets of statistically significant $G_i^{*}$ hotspot bridges identified under each sensitivity scenario with those identified under the equal-weight baseline. Similarity was quantified using the Jaccard similarity coefficient,

$$J\left(A,B\right)={\displaystyle \frac{\mid A\cap B\mid }{\mid A\cup B\mid }}$$

(30)

where A and B denote the hotspot bridge sets produced by two scenarios. The numerator represents the number of hotspot bridges common to both scenarios, while the denominator represents the total number of distinct hotspot bridges identified by either scenario. The Jaccard coefficient ranges from 0 (no common hotspots) to 1 (identical hotspot sets). Since the objective is to evaluate the stability of hotspot locations rather than the agreement of non-hotspot observations, the Jaccard coefficient provides a more informative measure than overall classification accuracy.

3.5.4. County Level Stability

Transportation investment decisions are commonly made at regional or county scales rather than for individual bridges. Therefore, hotspot bridges were aggregated by county, counties were ranked according to the number of significant hotspot bridges, and each sensitivity scenario was compared with the equal-weight baseline. Counties were ranked in descending order of hotspot-bridge count using average ranks for ties. Thus, counties with identical hotspot counts received the mean of the rank positions they jointly occupied rather than being ordered using an arbitrary secondary criterion. The same tie-handling rule was applied to the baseline and every sensitivity scenario. For county c, the rank change was computed as

$$\mathsf{\Delta }{R}_c=R_c^{\left(k\right)}-R_c^{\left(0\right)}$$

(31)

where $R_c^{\left(k\right)}$ is the county rank under sensitivity scenario k and $R_c^{\left(0\right)}$is the corresponding rank under the baseline scenario. Since tied counties receive fractional average ranks, $\mathsf{\Delta }{R}_c$ measures changes in relative county position while remaining invariant to arbitrary ordering within tied hotspot counts. Negative values indicate movement toward a higher-priority county, whereas positive values indicate movement toward a lower-priority county. Absolute rank changes were also summarized to characterize the overall stability of county prioritization across all sensitivity scenarios.

Together, the bridge-level rank correlations, hotspot-set similarities, and county rank changes provide complementary measures of robustness. Agreement across these three levels of analysis demonstrates whether the principal conclusions of the proposed MII remain stable under reasonable alternative assumptions regarding component weighting, deck-condition representation, normalization basis, and treatment of N-coded bridges.

3.6. Temporal Comparability

The MII combines roadway roughness, bridge deck condition, and traffic-demand measures that are not necessarily observed in the same calendar year. Therefore, a temporal comparability assessment was conducted to determine whether differences in component timing could materially affect bridge rankings or spatial hotspot results. The assessment focused on the observation years associated with IRI, deck inspection, and current ADT. The future ADT term was not treated as a contemporaneous observation because it represents a forecast used to derive the annual growth component.

The component years were parsed from their source fields as follows:

$$Y_{IRI,i}=\mathrm{year}\left({\mathrm{iri}\text{\_}\mathrm{d}}_i\right)$$

(32)

where iri_d, originally encoded as a Unix timestamp [76], was converted to a calendar year in Coordinated Universal Time;

$$Y_{Deck,i}=\mathrm{year}\left({\mathrm{date}\text{\_}\mathrm{of}\text{\_}\mathrm{inspect}\text{\_}090}_i\right)$$

(33)

where the NBI inspection date was parsed primarily as an MMYY value, including records where the leading zero in the month was omitted; and

$$Y_{ADT,i}={\mathrm{year}\text{\_}\mathrm{adt}\text{\_}030}_i.$$

(34)

A two-digit year pivot of 70 was used for the inspection-date field [77]. Values from 00 through 70 were assigned to 2000–2070, while values from 71 through 99 were assigned to 1971–1999. Parsed years were required to fall within the valid range used by the study. No component year exceeded the 2025 reference year, which was adopted because both downloaded databases contained observations through 2025 at the time of extraction, even though the HPMS geospatial release retained its published 2011–2024 series designation. The age of each component relative to the 2025 reference year was calculated as

$$A_{k,i}=2025-Y_{k,i},$$

(35)

where k is one of the three MII components. Lower values indicate more recent observations. The median IRI and deck-inspection ages were each one year, while the median ADT age was three years. Thus, the condition measures were generally more current than the traffic-demand observations.

Pairwise temporal gaps were defined as

$$\begin{gathered} G_{IRI,Deck,i}=∣Y_{IRI,i}-Y_{Deck,i}∣,G_{IRI,ADT,i}=∣Y_{IRI,i}-Y_{ADT,i}∣, \\ {G}_{Deck,ADT,i}=∣Y_{Deck,i}-Y_{ADT,i}∣ \end{gathered}$$

(36)

The overall within-record temporal span was calculated as

$$S_i=\max \left(Y_{IRI,i},Y_{Deck,i},Y_{ADT,i}\right)-\min \left(Y_{IRI,i},Y_{Deck,i},Y_{ADT,i}\right).$$

(37)

This statistic captures the largest observation-year difference among the three contemporaneous inputs for each bridge. Records were classified as temporally aligned for the robustness test when $S_i\le 3.$ The three-year threshold was selected as a deliberately conservative comparability criterion. It requires all three component observations—not merely one pair—to fall within a compact period while retaining a sufficiently large national sample for recomputing the MII and local Gi* statistics. The threshold was used as a diagnostic stress test rather than as a new eligibility rule.

Figure 2 evaluates the temporal consistency of the three MII components. Of the 79,595 retained NHS bridges, 79,582 (99.98%) contained valid observation years for all three components, and no records contained future-year observations relative to the 2025 reference year. Applying the predefined temporal-alignment criterion of a maximum 3-year within-record span identified 49,702 bridges (62.5%) as temporally aligned, while the remaining observations exhibited progressively larger differences among component years.

Panel A demonstrates that the three component datasets are concentrated within recent observation years, although their temporal distributions differ. IRI measurements are highly concentrated in 2024, reflecting the recent HPMS pavement condition cycle. Deck-condition observations are similarly recent, with most inspections occurring during 2023–2024, whereas ADT observations span a broader range of years, extending back more than a decade for a subset of bridges.

Panel B further illustrates this pattern by expressing observation years relative to the 2025 reference year. IRI measurements were the most current (median age 1 year), followed closely by deck inspections (median 1 year), while ADT estimates were older (median 3 years) and exhibited substantially greater variability (interquartile range 2–6 years).

Despite the broader age distribution of ADT observations, within-record temporal consistency remained favorable for most bridges. Panel C shows that the median maximum difference among the three component years was two years, with 34.4% of bridges having component years within one year, 52.0% within two years, and 62.5% within the predefined three-year alignment threshold. Approximately 78.0% of bridges exhibited a maximum temporal spread of five years or less, while only a relatively small proportion displayed substantially larger temporal differences.

Pairwise comparisons (Panel D) indicate that the strongest temporal agreement occurred between IRI and deck inspections. Specifically, 94.0% of bridges had IRI and deck observations within one year, increasing to 98.7% within two years and essentially complete agreement (99.9%) within three years. In contrast, agreement involving ADT was lower because traffic estimates are updated less frequently. Nevertheless, 63.3% of IRI–ADT pairs and 68.5% of deck–ADT pairs were within three years, increasing to 78.5% and 80.8%, respectively, within five years.

To evaluate whether temporal differences materially influenced the MII, the baseline MII was recomputed using only the 49,702 temporally aligned bridges. The resulting bridge rankings were virtually identical to those obtained from the complete dataset, with a Spearman rank correlation of 0.999, a mean absolute MII difference of 0.0067, and a median absolute difference of 0.0064. Spatial hotspot patterns also remained highly consistent, yielding a Jaccard similarity of 0.836 between the hotspot sets and a county hotspot-rank Spearman correlation of 0.910.

Collectively, these findings indicate that although the three data sources were not collected simultaneously for every bridge, the observed temporal differences have a negligible influence on bridge prioritization or the resulting national hotspot patterns, supporting the use of the complete analytical dataset for subsequent analyses.

4. Results

4.1. MII Component Distribution

The three continuous MII inputs were logarithmically transformed before model development to reduce skewness and place variables on comparable scales. Candidate probability distributions were evaluated using Akaike’s information criterion (AIC), with Bayesian information criterion (BIC), Kolmogorov-Smirnov (KS), and Cramér-von Mises (CvM) statistics reported as supporting diagnostics. Figure 3 shows the empirical distributions, corresponding best-fitting probability density functions, and statistics such as the mean and the standard deviation (SD).

The log-transformed IRI was best represented by a skew-normal distribution, indicating a modest positive asymmetry after transformation.

The logarithm of ADT per lane was best described by a Johnson SU distribution, reflecting residual asymmetry and heavier tails than a normal distribution. In contrast, annual logarithmic growth in ADT per lane was best represented by a Student’s t distribution, indicating a sharply centered distribution with occasional larger deviations. Akaike weights of 1.0 for all three variables indicated decisive support for the selected distributions over the competing candidates.

The transformed IRI distribution exhibited an approximately bell-shaped form centered at 4.7 (SD = 0.5), confirming that logarithmic transformation substantially reduced the right skew. The logarithm of ADT per lane was centered at 8.5 (SD = 1.0) and remained moderately asymmetric despite transformation, supporting the selection of the Johnson SU distribution. Annual logarithmic growth in ADT per lane was tightly concentrated around zero (mean = 0.017, SD = 0.031), indicating that, for most bridges, projected traffic volumes differ only modestly from current conditions on an annualized logarithmic basis.

Figure 3D presents the distribution of bridge deck-condition values after preprocessing. The final analytical dataset contains 59,953 bridges with numeric NBI deck ratings and an additional 19,642 bridges coded “N,” representing facilities for which a deck-condition rating is not applicable. Summary statistics (mean = 6.6, SD = 0.88, median = 7, range = 2–9) are reported only for the numeric ratings because “N” is a categorical designation rather than an ordinal condition score.

4.2. MII Distribution

The Case 1 MII was computed for the 79,595 retained NHS bridges using equal weights (0.25 each) assigned to normalized IRI, logarithm of ADT per lane, annual logarithmic ADT growth, and bridge deck-condition impedance. Continuous variables were transformed to empirical percentile ranks before aggregation, while deck condition was converted to a linear deficiency scale ranging from 0 (excellent condition) to 1 (failed condition). This rank-based normalization placed all continuous variables on a common scale while reducing sensitivity to differences in measurement units and extreme observations. The resulting composite index (Figure 4) ranged from 0.008 to 0.842, with a mean of 0.426 and standard deviation of 0.141. These values reflect the observed range within the analytical dataset rather than theoretical limits.

Five candidate probability distributions were evaluated to characterize the statistical behavior of the Case 1 MII. Based on minimum AIC, the generalized normal distribution provided the best representation of the observed data and received complete model support with Akaike weight = 1. Although formal goodness-of-fit tests were statistically significant because of the large sample size, the small Kolmogorov-Smirnov statistic (0.018) and close agreement between the fitted curve and empirical histogram indicate that the generalized normal distribution adequately characterizes the overall shape of the index. The MII exhibited a unimodal and nearly symmetric distribution, indicating that the equal-weight formulation produced a balanced composite measure without excessive skewness or dominance by any individual component. Most bridges clustered within intermediate mobility-impedance values, whereas relatively few bridges occupied the extreme lower or upper tails of the distribution. This behavior is desirable because it preserves discrimination across the bridge population while avoiding saturation at either end of the index.

Local Getis-Ord $G_i^{*}$ analysis further demonstrated that bridge mobility impedance exhibits strong spatial organization rather than random geographic variation (Figure 5). Significant hotspots ($G_i^{*}$, p ≤ 0.05) were identified for 20,621 bridges (25.9%), while 18,050 bridges (22.7%) formed significant coldspots. Hotspots occurred primarily along densely populated metropolitan regions and major interstate freight corridors, including the Northeast Corridor, coastal California, western Washington, south Florida, and portions of the Southeast.

In contrast, extensive coldspot clusters were observed across much of the northern Great Plains and central Midwest, reflecting regions with comparatively lower combined mobility impedance. These spatial patterns demonstrate that bridge mobility constraints occur in geographically coherent clusters, supporting the use of local spatial statistics to identify regions where infrastructure investments may yield the greatest network-wide mobility benefits.

4.3. Sensitivity Analysis

Figure 6 summarizes the sensitivity of bridge rankings and hotspot patterns to alternative weighting schemes and deck-condition formulations.

Across the eight alternative sensitivity cases, bridge-level rankings remained strongly correlated with the equal-weight linear baseline (Spearman ρ = 0.807–0.965), indicating that the proposed mobility impedance index is generally robust to reasonable variations in model specification. Hotspot patterns exhibited a similar level of stability. Relative to the equal-weight baseline, hotspot-set overlap (Jaccard similarity) ranged from 0.446 to 0.801.

The percentile-normalized deck-condition scenario (C9_DECK_PCT) produced the greatest agreement (0.801), followed by equal weighting with categorical deck scoring (C6_EQ_CAT; 0.780) and strong linear deck emphasis (C5_DECK_LIN; 0.762). In contrast, the categorical deck-emphasis scenario (0.446) and the traffic-growth emphasis scenario (0.525) generated the largest changes in hotspot membership. Emphasizing annual traffic growth produced the next largest change (C4_GRW_LIN; ρ = 0.829), demonstrating that projected demand influences prioritization more strongly than comparable changes to the other individual components.

Excluding the deck term for N-coded bridges and renormalizing the remaining three components (C8_N_RENORM) retained strong agreement with the baseline at both the bridge and regional levels (bridge-rank ρ = 0.935; hotspot Jaccard = 0.774; county-rank ρ = 0.910), with a median absolute county-rank change of 17 positions. A descriptive comparison indicated that N-coded bridges exhibited a lower mean MII than bridges with numeric deck-condition ratings (0.304 versus 0.465) and were less frequently identified as statistically significant hotspots (14.7% versus 29.6%). These differences are consistent with assigning zero deck impedance when deck condition is not applicable. These findings indicate that the national prioritization results are not materially dependent on the baseline treatment of N-coded bridges.

The percentile-normalized deck-condition scenario (C9_DECK_PCT) produced the closest agreement with the baseline among all alternative sensitivity cases (Spearman ρ = 0.965; hotspot Jaccard = 0.801), while county-level prioritization also remained highly consistent, with a median absolute county-rank change of only 25.5 positions. These findings indicate that the use of a fixed engineering deck-condition scale rather than empirical percentile normalization has little influence on the resulting bridge rankings or spatial prioritization patterns.

County-level prioritization remained comparatively stable for most alternative formulations. Median absolute county rank changes ranged from 13.0 positions for the ADT-emphasis case to 100.0 positions for the traffic-growth emphasis case. Linear deck emphasis (23.5) and equal-weight categorical deck scoring (16.5) produced only modest deviations from the baseline, whereas strong categorical deck emphasis yielded a substantially larger median shift (72.5). Although several counties experienced pronounced rank changes under the most extreme scenarios, these were isolated cases rather than widespread reordering, as illustrated by the concentration of values near zero in the hotspot-rank heatmap.

Collectively, these results indicate that the proposed MII is robust to plausible changes in weighting and deck-condition representation. Moderate modifications produce highly consistent bridge rankings and hotspot locations, while larger departures occur primarily when future traffic growth or categorical deck penalties receive substantially greater emphasis. These findings support the use of the equal-weight linear formulation as a stable national baseline while demonstrating that the sensitivity framework provides decision makers with a transparent means of exploring alternative policy priorities.

4.4. County Burden of MII Hotspot Bridges

Figure 7 summarizes the county-level burden of nationally significant MII hotspot bridges using both the absolute number of hotspot bridges (Panel A) and the percentage of retained NHS bridges classified as hotspots (Panel B).

The hotspot bridges were distributed across 864 of the 2,795 counties containing retained NHS bridges, indicating that elevated mobility impedance is geographically concentrated rather than uniformly distributed. Panel A highlights counties with the largest absolute numbers of hotspot bridges, reflecting locations where preservation needs are concentrated within extensive NHS bridge inventories.

Los Angeles County, California, contained the greatest number of hotspot bridges (837), followed by Dallas County, Texas (656); Harris County, Texas (639); San Diego County, California (432); and Tarrant County, Texas (326). Additional counties with large hotspot inventories included Riverside County, California (270); Bexar County, Texas (250); Miami-Dade County, Florida (239); Orange County, Florida (231); and San Bernardino County, California (220). These counties largely correspond to major metropolitan areas with extensive bridge inventories and high transportation demand.

Panel B normalizes hotspot counts by each county’s retained NHS bridge inventory, providing a measure of relative maintenance burden independent of system size. Several counties exhibited 100% hotspot prevalence, indicating that every retained NHS bridge within the county was identified as a statistically significant hotspot. These counties generally contained relatively small NHS bridge inventories. They include Mecklenburg County, North Carolina; Pierce County, Washington; Plymouth County, Massachusetts; Essex County, Massachusetts; Delaware County, Pennsylvania; Queens County, New York; Monroe County, Florida; Norfolk County, Massachusetts; and Iredell County, North Carolina. Although many of these counties contain relatively small NHS bridge inventories, the results indicate complete concentration of mobility impedance within those systems.

The comparison between Panels A and B demonstrates that absolute hotspot counts and hotspot percentages capture complementary aspects of infrastructure burden. Large metropolitan counties dominate the national inventory of hotspot bridges because of their extensive transportation networks, whereas percentage-based results identify counties where mobility impairment affects a greater proportion of the local NHS bridge system. Considering both measures provides a more balanced perspective for national bridge preservation planning by distinguishing counties requiring substantial investment because of network size from those where mobility deficiencies are pervasive despite comparatively smaller bridge inventories.

5. Discussion

The MII developed in this study integrates pavement roughness, bridge deck condition, current traffic demand, and projected traffic growth into a single bridge-level measure of potential mobility constraint. Rather than replacing existing bridge management or pavement management metrics, the MII provides a complementary mobility-oriented perspective by identifying locations where infrastructure condition and traffic demand jointly indicate elevated potential for mobility impairment. The principal findings demonstrate that the proposed methodology produces stable bridge rankings, geographically coherent hotspot patterns, and interpretable county-level prioritization while remaining robust to alternative weighting schemes and modest temporal differences among the underlying datasets.

The distributional analysis indicates that the logarithmic transformations successfully reduced the pronounced skewness of the pavement roughness and traffic variables, allowing all four components to contribute on comparable scales before normalization. The resulting MII followed a generalized normal distribution with substantial dispersion across the NBI, indicating that the index effectively differentiates bridges over a broad range of mobility conditions rather than concentrating observations within a narrow portion of the scoring range. Such discrimination is desirable for national prioritization because it provides greater separation among bridges competing for preservation resources while reducing the likelihood of large groups of assets receiving nearly identical priority scores. The resulting generalized normal distribution also supports the use of the MII as a continuous prioritization measure rather than requiring discrete priority classes.

The analytical workflow retained 79,595 bridges, including 19,642 N-coded bridges. The subsequent permutation-based $G_i^{*}$ analysis identified 20,621 as statistically significant local hotspots (25.9% of the analytical dataset), demonstrating that mobility constraints are concentrated within geographically connected portions of the NHS rather than being randomly dispersed. Hotspot concentrations were most evident throughout major metropolitan regions, high-demand freight corridors, and coastal transportation networks where elevated traffic demand coincides with comparatively poorer infrastructure condition. Conversely, extensive coldspot regions were observed across areas exhibiting comparatively low composite mobility impedance. These findings suggest that mobility constraints emerge as characteristics of transportation networks rather than isolated bridge deficiencies, reinforcing the importance of evaluating bridges within their broader operational context.

County-level summaries further demonstrate that absolute hotspot counts and hotspot percentages provide complementary perspectives for infrastructure prioritization. Counties containing the largest numbers of hotspot bridges generally correspond to large metropolitan areas with extensive NHS bridge inventories and substantial travel demand. In contrast, several counties exhibited very high or complete hotspot prevalence despite having comparatively smaller bridge inventories, indicating that mobility constraints affect a large proportion of the local NHS bridge system. Together, these measures distinguish counties requiring substantial investment because of network size from those where mobility deficiencies are proportionally more pervasive, thereby supporting different planning objectives at national, state, and regional levels.

The inter-component correlation assessment further supports the construction of the composite index. Pairwise Spearman correlations were uniformly low, with a maximum of 0.304, and the two traffic-demand measures were essentially uncorrelated. Thus, the four components do not simply reproduce a common underlying characteristic such as roadway class or traffic intensity. Instead, they contribute complementary information describing pavement condition, bridge condition, present traffic exposure, and anticipated traffic growth. This result suggests that additive aggregation does not materially overrepresent any single latent dimension through correlated inputs.

An important outcome of this study is the demonstrated robustness of the proposed MII. Across eight alternative weighting, deck-condition, and normalization formulations—including omission and renormalization of the deck component for N-coded bridges—bridge-level rankings remained strongly correlated with the equal-weight baseline (Spearman ρ = 0.807–0.965). Likewise, hotspot-set similarity remained substantial across all scenarios (Jaccard similarity = 0.446–0.801), indicating that the principal spatial patterns are largely determined by the observed characteristics of the bridge inventory rather than by a particular choice of model specification. The greatest deviations from the baseline occurred when projected traffic growth received substantially greater emphasis or when a strong categorical deck-condition representation was adopted, yet these stress tests were intentionally designed to represent extreme policy scenarios rather than realistic alternatives. Consequently, the equal-weight linear formulation provides a transparent and practical national reference specification while allowing agencies to evaluate alternative priorities through the proposed sensitivity framework.

The temporal comparability assessment provides additional confidence in the analytical workflow. Although only 62.5% of bridges satisfied the predefined three-year alignment criterion, restricting the analysis to this temporally aligned subset produced virtually identical bridge rankings (Spearman ρ = 0.999) and highly consistent hotspot patterns. The very small differences observed between the complete dataset and the aligned subset indicate that modest differences among observation years do not materially influence bridge prioritization or regional hotspot identification. Preserving the complete analytical dataset therefore provides substantially greater national coverage without compromising the validity of the resulting prioritization.

Beyond the proposed index itself, this study demonstrates a practical methodology for integrating the HPMS and the NBI into a unified mobility-oriented assessment. Although these databases are widely used independently for pavement and bridge management, they are seldom integrated at the national scale. The spatial matching procedures, automated quality screening, and targeted manual verification developed in this study demonstrate that high-quality bridge-road integration is achievable while maintaining transparent processing steps. The resulting methodology provides a transferrable foundation for constructing bridge-level datasets that jointly characterize structural condition, pavement performance, and traffic demand.

From a transportation planning perspective, the results support preservation strategies that explicitly consider both infrastructure condition and mobility consequences. Traditional bridge management emphasizes structural condition, whereas pavement management focuses on roadway performance. The proposed MII complements these systems by identifying bridges where deteriorating infrastructure coincides with greater present or future traffic demand, thereby highlighting locations where preservation activities are likely to provide broader mobility benefits. Incorporating projected traffic growth also introduces a forward-looking perspective that identifies bridges whose relative importance may increase as travel demand evolves, allowing agencies to consider anticipated mobility needs alongside current infrastructure conditions.

The data integration and quality-control process also provided insight into the strengths and limitations of the underlying national datasets. Most bridge-road linkages were successfully established through direct spatial agreement or structured recovery procedures, while only a small fraction of records required manual verification before exclusion. Nevertheless, several recurring data-quality issues were identified. Numerous HPMS roadway records lacked NHS designations, some roadway segments were missing county identifiers, and incomplete pavement roughness observations reduced the number of bridges available for analysis. Although some of these limitations were addressed through spatial correction, structured quality screening, and complete-case analysis, improving the completeness and consistency of NHS designation, county identifiers, pavement condition, and traffic reporting would further strengthen future national HPMS–NBI integration efforts while reducing the need for extensive post-processing.

Several limitations define the scope of the present study while motivating future research. First, the proposed MII is intended as a relative prioritization measure rather than a predictive model of structural failure, travel delay, or economic loss. The index identifies bridges with comparatively greater potential for mobility impedance but does not estimate the magnitude of operational impacts associated with individual structures. The additive formulation also permits compensation among components; consequently, the MII should be interpreted as an integrated relative priority measure rather than as a threshold model in which an extreme value of any single component automatically determines priority. Second, the equal-weight baseline was intentionally adopted as a transparent and practical reference specification because nationally accepted empirical relationships among the four mobility dimensions are not presently available.

The MII uses percentile normalization for pavement roughness, traffic demand, and projected traffic growth, making component values relative to the analytical sample rather than absolute engineering thresholds. Consequently, MII values represent each bridge’s relative national priority at the time of analysis and may change as the national distribution of bridge conditions and traffic characteristics evolves, even if an individual bridge remains unchanged. For this reason, future updates should recompute the index using the complete national analytical dataset so that all bridges are evaluated against a common contemporaneous reference population.

The treatment of bridges coded with the valid NBI deck-condition category “N” represents a related modeling assumption. These structures were assigned zero deck impedance because the “N” designation indicates that a deck-condition rating is not applicable rather than unavailable. Accordingly, the zero-impedance treatment should be interpreted as a consequential modeling assumption: N-coded bridges exhibited systematically lower MII values and hotspot representation than numerically rated bridges, although these differences may also reflect underlying differences in the characteristics of structures for which deck condition is not applicable. A targeted sensitivity test addressed this assumption by excluding the deck component for N-coded bridges and renormalizing the remaining three weights; the resulting bridge rankings and hotspot patterns remained strongly aligned with the baseline (ρ = 0.935 and Jaccard = 0.774, respectively). Similarly, investigating alternative weighting strategies using observed traffic disruptions, freight performance measures, travel-time reliability, or other operational outcomes are opportunities for future research. In addition, the annual ADT growth term implicitly assumes a constant lane count between the current and forecast years; where roadway widening or lane reductions are anticipated, this assumption may understate or overstate future traffic intensity.

Third, the current methodology considers infrastructure condition and projected traffic demand but does not explicitly incorporate network redundancy, resilience, freight composition, detour availability, or climate-related hazards, all of which may further refine mobility-oriented prioritization as suitable national datasets become available. In addition, the local $G_i^{*}$ analysis relies on a fixed adaptive k = 8 nearest-neighbor specification; while consistent with established hotspot analysis guidance [75], alternative neighborhood sizes were not tested, and hotspot boundaries in sparsely populated regions with large inter-bridge distances could be sensitive to this choice.

The hotspot analysis likewise should be interpreted within the context of exploratory spatial analysis. Statistical significance was evaluated independently for each bridge using permutation-based local $G_i^{*}$ inference without formal multiplicity adjustment. Although neighboring bridge tests are spatially dependent and therefore do not satisfy the independence assumptions underlying many conventional multiple-comparison procedures, some false-positive hotspots may nevertheless be expected. The hotspot results are intended to identify geographically consistent areas for further engineering evaluation rather than to establish definitive statistical significance for individual bridges. Consequently, a false-discovery-rate-adjusted comparison is identified as an opportunity for future validation of the hotspot set.

Finally, the scope of inference should be interpreted carefully. The analytical sample was intentionally restricted to open, unrestricted, mainline NHS bridges within the CONUS to produce a homogeneous population suitable for national comparison. Consequently, the findings apply specifically to this bridge population and should not be generalized to the broader NBI, which also includes local-road bridges, ramps, bypass structures, restricted facilities, closed bridges, and other non-mainline structures without additional evaluation.

Overall, this study demonstrates that integrating pavement condition, bridge condition, traffic demand, and projected traffic growth into a single composite mobility measure provides a practical, transparent, and transferrable approach for identifying bridges and regions where preservation activities are likely to yield the greatest mobility benefits. By combining nationally maintained roadway and bridge databases within a unified analytical workflow and demonstrating robustness to alternative model specifications and temporal differences, the proposed MII advances mobility-oriented infrastructure assessment while providing transportation agencies with a scalable decision-support tool that complements existing bridge and pavement management practices.

6. Conclusions

This study affirmatively answers the study’s guiding question by demonstrating that nationally available HPMS and NBI data can be successfully integrated into a transparent, transferable, and scalable data-driven methodology for national bridge preservation prioritization. The resulting workflow produced a robust mobility impedance index (MII) for open, unrestricted mainline National Highway System (NHS) bridges in the contiguous United States by integrating pavement roughness, bridge deck condition, current traffic demand, and projected traffic growth into a single mobility-oriented indicator. A transparent data-integration and prioritization workflow was developed to spatially integrate the Highway Performance Monitoring System (HPMS) and National Bridge Inventory (NBI), perform systematic quality screening, and construct a national analytical dataset comprising 79,595 bridges suitable for bridge-level and network-scale analyses. The workflow also retained bridges with the valid NBI deck-condition category “N” by assigning zero deck impedance when a deck-condition rating was not applicable, thereby preserving analytical coverage while maintaining a consistent interpretation of the index.

The proposed MII produced a well-behaved distribution that effectively differentiated bridges across the national inventory. The MII identified 20,621 bridges (25.9% of the analytical dataset) as statistically significant local hotspots under the permutation-based $G_i^{*}$ analysis. These hotspots were concentrated along major metropolitan regions and high-demand transportation corridors, indicating that elevated mobility impedance occurs within geographically connected transportation networks rather than as isolated structures. County-level summaries further demonstrated that evaluating both the absolute number of hotspot bridges and the proportion of hotspot bridges provides complementary perspectives for network-level infrastructure prioritization, distinguishing counties with large hotspot inventories from those where mobility impairment affects a greater share of the local NHS bridge system.

Sensitivity analyses demonstrated that the proposed MII remained stable across reasonable alternative weighting schemes, deck-condition representations, normalization approaches, and treatment of N-coded bridges. Bridge-rank correlations with the baseline equal-weight specification ranged from 0.807 to 0.965, while hotspot-set similarities ranged from 0.446 to 0.801, indicating that the principal prioritization results are robust despite substantial changes in model assumptions. The equal-weight linear formulation therefore provides a transparent and transferrable baseline for data-driven national bridge prioritization while allowing agencies to evaluate alternative policy priorities through the proposed sensitivity framework.

The temporal comparability assessment further demonstrated that differences in component observation years have minimal influence on the resulting prioritization. Although only 62.5% of bridges satisfied the predefined three-year alignment criterion, restricting the analysis to this temporally aligned subset produced virtually identical bridge rankings (Spearman ρ = 0.999) and highly consistent hotspot patterns. These findings supported the use of the complete national analytical dataset while preserving substantially greater geographic coverage than would be achieved through more restrictive temporal filtering.

Beyond the proposed index itself, this study demonstrates a practical data-integration methodology for integrating nationally maintained roadway and bridge databases into a unified mobility-oriented assessment. The data integration and quality-control procedures identified opportunities to improve future national analyses through more complete and consistent reporting of NHS designation, pavement condition, traffic attributes, and county identifiers within the HPMS and NBI databases. Continued improvements in these datasets will further strengthen their value for transportation planning, infrastructure management, and data-driven decision support.

The MII is intended as a relative prioritization tool rather than a prediction of structural failure or traffic delay. Its purpose is to identify bridges and regions where infrastructure condition and traffic demand jointly indicate greater potential for mobility constraints. Accordingly, the findings apply specifically to open, unrestricted mainline NHS bridges and should not be generalized to the broader NBI without additional evaluation.

Overall, the proposed MII provides a practical foundation for incorporating mobility considerations into data-driven national bridge preservation prioritization. By combining bridge-level prioritization with network-scale spatial hotspot identification and demonstrating robustness to alternative model specifications and temporal differences, the MII offers transportation agencies a scalable data-driven decision-support method that complements existing bridge and pavement management systems while supporting more informed infrastructure preservation planning and investment decisions.