A Digital Twin Framework for Monitoring and Fault Diagnostics of Marine Internal Combustion Engines

1. Introduction

Internal combustion engines (ICE) are key components of a ship power plant, and their reliable operation directly affects the economic efficiency of vessel operation, navigation safety, and the level of environmental impact. Therefore, continuous efforts are being devoted to improving engine design, optimizing engine working processes and operational methods [1], as well as adapting engines to new fuels and regulatory requirements [2].

One of the major directions contributing to the improvement of marine ICE operation efficiency is the implementation of modern digital technologies for continuous technical condition monitoring, automation of engine control, and development of onboard self-diagnostic systems capable of assessing the current engine condition during operation. The development of this field has led to the emergence and practical implementation of digital twin (DT) technologies [3,4].

Manufacturers of modern marine engines already offer commercial services based on DT technologies. Everllence provides the PrimeServ Assist platform for real-time monitoring and AI-based diagnostics [5]. Wärtsilä offers the Operational Performance Improvement & Monitoring (Operim) system, which integrates a virtual twin for comparison between actual and expected engine performance [6]. WinGD developed the WinGD Integrated Digital Expert (WiDE) platform , which utilizes a customized DT model based on factory test data to provide actionable engine health assessment [7,8]. Nevertheless, further improvement of this technology remains an important research task.

A digital twin can be defined as a virtual representation of an internal combustion engine that reproduces selected aspects of its operation and behavior. Depending on its intended purpose, a DT should provide the most reliable possible prediction of variations in engine and subsystem parameters under different operating conditions. Digital twins of ICE may serve different purposes and can be classified as follows.

By purpose:

• engine control;
• engine diagnostics and condition monitoring;
• engine repair and maintenance;
• engine design and optimization;
• personnel training and teaching;

By primary focus:

• engine operating process;
• wear, lubrication, and cooling processes;
• thermal and mechanical stresses;
• engine component design and assembly.

By deployment architecture:

• embedded into the engine ECU;
• remotely accessible cloud-based systems;
• standalone PC-based installations.

Digital twins have a potential of application during the whole engine lifecycle, starting from its design and production [9]. The most challenging task in terms of achieving both high computational speed and high prediction accuracy is the development of DT intended for real-time engine control [10]. Such DTs may operate as “shadow models” running in parallel with real ECUs to validate control actions or predict engine behavior before actual actuation. DT could be an effective and cost-saving instrument for educational and training purposes [11].

However, the most widespread application of digital twins for marine ICE is technical condition diagnostics and condition monitoring. Intensive research efforts in this area are aimed both at improving mathematical models specifically adapted for DT applications [12,13] and at enhancing interaction between the digital twin and the real engine through sensor systems [14], including integration into comprehensive ship power plant diagnostic systems [15,16]. Particular attention should also be paid to the growing application of machine learning techniques in systems employing digital twins [17,18,19,20,21].

Despite the significant progress achieved in this field, the effective application of DT for diagnostics and condition monitoring of marine ICE still requires overcoming several important challenges. First, it is necessary to ensure an appropriate balance between the level of detail of the DT mathematical model and computational speed, especially for online monitoring applications or when diagnostic conclusions must be obtained during real-time engine operation [22]. Second, reliable identification of the current engine operating mode by the digital twin must be ensured, which requires determination of the necessary sensor set and appropriate methods for sensor data processing [23]. Finally, robust methods for fault identification and technical condition assessment using digital twins should be developed to ensure acceptable diagnostic reliability, support automation, and provide unambiguous diagnostic conclusions.

2. Definitions

Although the application of mathematical modeling to the diagnosis of the technical condition of ICE is a widespread practice, the theoretical foundations and methodological approaches to the application of DT for technical condition diagnostics remain insufficiently systematized. In particular, the application of DT for representing engine working processes requires the development of algorithms for automated simulation and extraction of diagnostic features capable of indicating deviations in engine technical condition.

Consider several definitions. An engine operating mode is defined as the set of operational engine parameters that characterize the current load and control state of the engine without considering its technical degradation. An engine possesses a set of operating modes $\mathcal{O}$, while each individual operating mode $\overline{O}$ belongs to this set:

$$\overline{O}\in \mathcal{O};\overline{O}=(n_{crank},P_b,p_i,b_b,...,t_t),$$

(1)

A technical condition of the engine is defined as the set of parameters describing the technical properties and degradation state of the engine and its subsystems. For the set of technical conditions $\mathcal{H}$, each particular technical condition $\overline{H}$ is considered as:

$$\overline{H}\in \mathcal{H};\overline{H}=(p_{compr},b_b,b_{oil},P_{b.max},...,p_{max}),$$

(2)

The reference technical condition ${\overline{H}}_{etalon}\in \mathcal{H}$ is defined as the factory condition of the engine or as its optimal technical condition.

Monitoring of the engine working process is defined as the observation, analysis, and statistical processing of a set of measurable engine parameters under given operating conditions. For the space of observable parameters $\mathcal{Y}$, a particular available vector of the monitored parameter may be denoted as $\overline{Y}$:

$$\overline{Y}\in \mathcal{Y};\overline{Y}=(p_{oil},t_{w1},n_{crank},...,p_s).$$

(3)

Figure 1 shows schematically the interaction of vectors $\overline{O}$, $\overline{H}$ and $\overline{Y}$ as constituents of their sets for a given engine under given conditions of operation. While some of the parameters are common for all three vectors, another are specific for each.

The mathematical model of an engine working processes may be represented in the following general form:

$$\overline{R}=f\left(\overline{I},\overline{C},\overline{O},\overline{H}\right);\overline{R}=\left(\begin{array}{c}{P}_b\\ b_b\\ \begin{array}{c}...\\ t_t\end{array}\end{array}\right);\overline{I}=\left(\begin{array}{c}{D}_{cyl}\\ S_{pist}\\ \begin{array}{c}...\\ {\mathsf{\phi }}_{inj}\end{array}\end{array}\right);\overline{C}=\left(\begin{array}{c}{p\text{'}}_{max}\\ {p\text{'}}_i\\ \begin{array}{c}...\\ {p\text{'}}_s\end{array}\end{array}\right),$$

(4)

where, the resulting vector $\overline{R}$ is a function of the input parameter vector $\overline{I}$, the calculation control vector $\overline{C}$, the engine operating mode vector $\overline{O}$, and the technical condition vector $\overline{H}$.

The vector $\overline{R}$contains the simulation results, including engine working process parameters and corresponding process diagrams. The vector $\overline{I}$ represents the input data used for calculations. This vector may be divided into two components: the vector of constant parameters ${\overline{I}}_{const}$, which remains unchanged between calculations for a given digital twin application scenario, and the vector of variable parameters ${\overline{I}}_{var}$, whose values change depending on the engine operating mode:

$$\overline{I}=({\overline{I}}_{const},{\overline{I}}_{var}),$$

(5)

the constant parameters may include, for example, the geometric dimensions of the cylinder–piston group, the number of cylinders, and fuel injector characteristics. It should be noted that the set of constant parameters is specific to each engine and depends on the particular digital twin application scenario. The most commonly used variable parameters include crankshaft rotational speed, fuel injection timing, injection duration, boost pressure, and similar operating variables.

The vector ${\overline{I}}_{var}$ may also be divided into two components: parameters available from sensor measurements and parameters that remain unknown due to the absence of corresponding sensors or the impossibility of direct measurement. Determination of the latter component represents a significant challenge and may influence the selection and configuration of the vector $\overline{C}$.

The vector $\overline{C}$ may be interpreted as a set of parameters defining the calculation strategy or computational mode. For example, calculations may be performed with balancing of turbine and compressor power within the turbocharging system and determination of boost pressure, or alternatively with prescribed boost pressure values. Similarly, calculations may involve determination of the fuel injection timing required to achieve a specified maximum cylinder pressure, or may be carried out with fixed injection timing values.

3. Digital Twin Framework

According to the conceptual diagram presented in Figure 2, the application of a DT for diagnostics issues involves several functional stages:

• Calibration of the mathematical model of the DT for a particular engine using available experimental and documentation data.
• Determination of the sensor set through which the DT receives information about the current engine operating mode and its parameters.
• Determination of objective and constraint parameters, as well as parameters carrying diagnostic information regarding the engine technical condition.
• Definition of fault types and the corresponding healthy technical condition of the engine.

Therefore, calibration of the mathematical model for a digital twin involves not only performing simulations, but also comparing the obtained results with documentation and experimental data. Such comparison is performed for a subset of analyzed operating modes:

$${\mathcal{O}}_{cal}\subset \mathcal{O};{\overline{O}}_k\in {\mathcal{O}}_{cal},k=1,2,...,N.$$

(6)

For each operating mode ${\overline{O}}_k$, a discrepancy vector ${\overline{\mathsf{\delta }R}}_k$ is determined:

$${\overline{\mathsf{\delta }R}}_k=g\left({\overline{R}}_{etalon}\left({\overline{O}}_k\right)-{\overline{R}}_{model}\left({\overline{O}}_k\right)\right),$$

(7)

$$\overline{\mathsf{\delta }R}=\left(\begin{array}{c}{\mathsf{\delta }}_{p_{max}}\\ {\mathsf{\delta }}_{p_i}\\ \begin{array}{c}...\\ {\mathsf{\delta }}_{p_s}\end{array}\end{array}\right);{\overline{R}}_{etalon}=\left(\begin{array}{c}{p\text{'}}_{max}\\ {p\text{'}}_i\\ \begin{array}{c}...\\ {p\text{'}}_s\end{array}\end{array}\right);{\overline{R}}_{model}=\left(\begin{array}{c}{p}_{max}\\ p_i\\ \begin{array}{c}...\\ p_s\end{array}\end{array}\right),$$

(8)

in this formulation, the vector${\overline{\mathsf{\delta }R}}_k$ may be interpreted as a vector of relative deviations between the simulation results and the available literature or experimental data.

The calibration process of the mathematical model may therefore be represented as an optimization problem aimed at minimizing the following functional:

$$\mathrm{m}\mathrm{i}\mathrm{n}{\sum }_{{\overline{O}}_k\in {\mathcal{O}}_{cal}}{‖{\overline{R}}_{etalon}\left({\overline{O}}_k\right)-f\left(\overline{I},\overline{C},{\overline{O}}_k,{\overline{\delta R}}_k\right)‖}^2.$$

(9)

An important stage in the application of a DT is identification of the current engine operating mode using the available (often highly limited) data obtained from sensors installed on the engine. These data may be represented by the observation vector ${\overline{Y}}_{sensor}\in {\overline{R}}_{actual}$. For this reason, preliminary calibration and tuning of the mathematical model are essential. The process of engine operating mode identification may also be represented as the following optimization problem:

$$\underset{\overline{\mathsf{\delta }R}}{\min }‖{\overline{Y}}_{sensor}-f\left(\overline{I},\overline{C},\overline{\mathsf{\delta }R}\right)‖.$$

(10)

The application of a DT for diagnostic purposes must solve the principal problem not merely of performing parallel simulation of engine working processes during diagnostic analysis, but also of developing algorithms capable of producing additional diagnostic criteria or indicators characterizing the technical condition of the engine. This may be formulated as determination of the engine technical condition deviation vector $\overline{\mathsf{\delta }H}$, which contains deviations between a selected set of characteristic engine parameters and their corresponding reference (desired) values:

$$\overline{\mathsf{\delta }H}=h\left({\overline{H}}_{actual}-{\overline{H}}_{etalon}\right);$$

(11)

$$\overline{\mathsf{\delta }H}=\left(\begin{array}{c}{\mathsf{\delta }}_{P_b}\\ {\mathsf{\delta }}_{b_b}\\ \begin{array}{c}...\\ {\mathsf{\delta }}_{g_{NOx}}\end{array}\end{array}\right);{\overline{H}}_{actual}=\left(\begin{array}{c}{P\text{'}}_b\\ {b\text{'}}_b\\ \begin{array}{c}...\\ {g\text{'}}_{NOx}\end{array}\end{array}\right);{\overline{H}}_{etalon}=\left(\begin{array}{c}{P}_b\\ b_b\\ \begin{array}{c}...\\ g_{NOx}\end{array}\end{array}\right),$$

(12)

importantly, the values of the vectors ${\overline{H}}_{actual}$ and ${\overline{H}}_{etalon}$ may be obtained either experimentally, through simulation, or by a combination of both approaches, which introduces additional variability into digital twin applications.

From this perspective, minimization of the vector $\overline{\mathsf{\delta }H}$ may be considered a formal representation of the diagnostic fault identification process, particularly when a set of parameters used for such minimization can be specified:

$$\underset{\overline{\mathsf{\delta }H}}{\min }‖{\overline{H}}_{actual}-f\left(\overline{I},\overline{C},\overline{\mathsf{\delta }H}\right)‖.$$

(13)

It may therefore be stated that the vector $\overline{C}$activates specific DT algorithms aimed at reliable identification of a particular fault.

Thus, the operation of a marine engine DT may be formally represented as an optimization problem whose solution consists in identifying the factors (parameters governing engine operation) responsible for the actual deviation of engine operating parameters from their reference or expected values. Analysis of these parameters and their values constitutes the diagnostic feature indicating a particular fault condition.

The development of effective methods and algorithms for solving this optimization problem therefore remains an important research problem.

4. Discussion

The presented results on engine condition diagnostics based on digital twin simulation demonstrate both the significant potential of the proposed approach and a number of challenges that must be addressed before its practical implementation in marine engine operation.

Indeed, provided that a properly calibrated digital twin is available, Design of Experiments (DoE) methods can be employed to investigate the influence of various faults and malfunctions within engine systems on the parameters of the working process. Furthermore, the proposed methodology enables estimation of the quantitative values of fault-related parameters, which can subsequently be verified during engine inspection and maintenance procedures.

An important advantage of the proposed approach is its potential for automation. In principle, the digital twin may continuously compare actual engine performance against the reference performance of a healthy engine and automatically identify probable causes of detected deviations. Such functionality could significantly enhance the capabilities of modern condition monitoring systems.

However, the conducted investigations have also revealed several challenges that require further research:

• Improvement of numerical experiment design and response surface analysis methods to ensure reliable identification of response function extrema and elimination of physically unrealistic solutions.
• The digital twin must incorporate physical parameters of engine systems and components that can be directly measured during condition assessment. This requirement necessitates an adequate level of model detail and adaptation of the mathematical model to the specific engine under consideration.
• The factors selected to represent potential faults should, as far as possible, influence the engine process independently and exhibit minimal correlation with one another.

Therefore, further development of the proposed methodology requires an appropriate level of physical detail within the engine model to represent the most probable fault mechanisms of a specific engine. This will facilitate the selection of diagnostic factors that satisfy the fundamental requirements of Design of Experiments theory, namely controllability, measurability, independence, compatibility, uniqueness, significance, and reproducibility.

In addition, practical implementation of the proposed approach under real operating conditions must account for cycle-to-cycle variability of the engine working process and uncertainties associated with measurement systems and sensors.

Following the successful validation of the methodology using a virtual test case, the next logical step is experimental verification on a research engine. Under real operating conditions, diagnostic procedures become substantially more challenging due to cycle-to-cycle combustion variability and measurement uncertainties affecting both conventional engine parameters and indicator diagrams.

To enable such investigations, controlled modifications of the engine working process must be introduced experimentally. For example, a throttle valve was installed upstream of the compressor inlet to simulate variations in intake system resistance, as illustrated in Figure 12. And Figure 13 presents an example of the resulting influence on engine performance. Additional factors that may be varied experimentally include fuel delivery parameters, exhaust system resistance, and fuel properties.

5. Conclusions

The application of digital twin technology to monitoring and diagnostic systems for marine internal combustion engines represents an important step toward more automated and efficient operation of marine power plants. Early detection of engine faults contributes not only to improved navigational safety and reduced risk of failures, but also to lower fuel and lubricant consumption and reduced environmental impact.

An engine digital twin should provide an adequate level of detail in the simulation of engine working processes and include, among its input variables, physical parameters describing the principal engine systems and components that may be associated with fault development. Particular importance is attached to the calibration of the mathematical model and to the integration of the digital twin with the actual engine through sensor-based data acquisition.

The digital twin enables both the establishment of reference engine performance based on manufacturer specifications and sea-trial data, and the continuous assessment of deviations between actual and reference operating parameters during service.

From a practical perspective, one of the most important advantages of the proposed approach is the ability to identify probable faults responsible for observed deviations from reference performance. To achieve this objective, the use of Design of Experiments methodology and numerical multifactor experiments has been proposed. By minimizing response functions associated with the selected objective functions, it becomes possible to estimate the values of fault-related parameters that characterize the engine condition.

The conducted investigations have demonstrated that successful fault identification strongly depends on the proper selection of factors and on accurate representation of their physical influence within the engine mathematical model. Particular attention should be paid to ensuring factor independence and compliance with the fundamental assumptions of experimental design theory.

Further development and practical implementation of the proposed methodology require consideration of cycle-to-cycle variability of engine working processes as well as measurement uncertainties associated with the sensors supplying input data to the digital twin.