Submitted:
30 July 2025
Posted:
06 August 2025
You are already at the latest version
Abstract
Keywords:
1. Introduction
1.1. Design Method Based on Spatial Scale Study
1.2. Design Method Based on Modularization Idea
1.3. Design Method Based on Performance Constraint Theory
1.4. Sketch of the Algorithm
2. Correlation Degree Between Functional Facilities
3. Positive Characterization of the Correlation Matrix
4. Functional Facilities Grouping Model
4.1. Factor Analysis
- (1).
- X = (x1, x2, …, xn)T is an observable random vector with covariance matrix Σ.
- (2).
- The common factor vector F = (F1, F2, …, Fm) (m<n) is an unobservable random vector with mean vector E(F) = 0 and covariance matrix D(F) = I, i.e., the components in the common factor vector F are independent of each other.
- (3).
- The error vector ε = (ε1, ε2, …, εn) Tis independent of the common factor vector F with mean vector E(ε) = 0, and its covariance matrix Σε is diagonal, i.e.:
4.2. Error Analysis
4.3. Grouping Model Based on Factor Analysis
- (1)
- Record the usage time ti (i = 1, 2, …, n) spent by users on functional facility xi.
- (2)
- Calculate the correlation degrees between different functional facilities based on equation (3), and then construct the correlation degree matrix Σ.
- (3)
- Calculate the eigenvalues of Σ and arrange all the eigenvalues in descending order as λ1>λ2>…>λn.
- (4)
- Calculate the eigenvector ei corresponding to the eigenvalue λi (i = 1, 2, …, n).
- (5)
- For the given error β, calculate the number of eigenvectors m for constructing the factor loading matrix according to Equation (16), and then construct the factor loading matrix A from the first m eigenvectors according to Equation (13).
- (6)
- Grouping of all the functional facilities according to Equation (10).
5. Case Analysis
6. Conclusions and Discussion
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Florin, B. ; Nicolae, V, B.; Lucian, F, T.; et al. Improving electric vehicle arrange and thermal comfort through an innovative seat heating system. Sustainability, 2023: 15, 5534. [Google Scholar]
- Berg, J.; Henriksson, M. ; Ihlstrom.; et al. Comfort first! Vehicle-sharing systems in urban residential areas: The importance for everyday mobility and reduction of car use among pilot users. Sustainability. 2019, 11: 2521. [Google Scholar]
- Nagl.; Kurt. Auto suppliers cut costs as vehicle output slows: Companies reduce manufacturing capacity, headcount amid uncertainty. Crain’s Detroit Business 2024, 45: 1.
- Tawan, C.; Peerawat, S.; Nuwong, C.; et al. Total cost of ownership (TCO) analysis of electric vehicle in ASEAN. Energy. Sustain. Dev. 2025, 85: 101650. [Google Scholar]
- Nade, L.; Ashima, K. ; Brandon, J, P.; et al. Understanding older adults’ needs for and perceptions of shared autonomous vehicle interior features: A focus group and user enactment study. Appl. Ergon. 2025, 123: 104408. [Google Scholar]
- Ksander, N, W.; Tugru, l I.; Riender, H. et al. Standards for passenger comfort in automated vehicles: Acceleration and jerk. Appl. Ergon. 2023, 106: 103881.
- Brischetto, A.; Lotti, G.; Tosi, F. Ergonomics in design: The human-centred design approach for developing innovative motor recreational vehicle systems. Advances in Intelligent Systems and Computing, 2019: 824, 1066. [Google Scholar]
- Liu, Z, M.; Chen, X, H.; Liang, X, A. Growable design of passenger vehicle interior space based on FAHP and FQFD. 2024, PloS one. 19: e0303233.
- Salami, B, S.; Siti, A, B.; Azizan, A.; et al. An ergonomics study and rapid upper limb assessments (RULA) for a car interior to support limb disabled drivers. Journal of Management Science & Engineering Research 2022, 2:17-30.
- Yang, Q, X.; Ai, M, C.; Tong, X, Y.; et al. Demands exploration of future interior layout in shared mobility using design fiction. Lecture Notes in Networks and Systems. 2021, 276:259-267.
- Koo, S. An observation on alterations of usability in automobile interior design with autonomous driving technology escalation. Transactions of the Korean Society of Automotive Engineers, 2019, 27: 693-700.
- Stefan, J, B.; Stella, C. A theoretical framework of haptic processing in automotive user interfaces and its implications on design and engineering. Front Psychol, 2019: 10, 1470.
- Sun, X. Research on architectural interior space design based on design psychology. Psychol. Rep. 2024, 127: 253-254.
- Zhang, X, N.; Wang, X, Y.; Xu, W, A. Research on user demands and functional design of an AR-based interior design and display platform for recreational vehicles. Appl. Sci, 2024: 14, 1056.
- Zhang, Z, N.; Zhuge, X.; Li, X.; et al. An object-oriented approach to the modular design of mechatronic systems. IEEE. Trans. Eng. Manag. 2024, 71: 2623-2639.
- Li, Z, C.; Bao, C, J.; Li, R, H.; et al. Design research of scenic camp construction vehicle based on function analysis method. Journal of Machine Design, 2022, 39:129-137.
- Fu, M. ; Hao, Y, L.; Gao, Z, F., Ed.; et al. User-driven: A product innovation design method for a digital twin combined with flow function analysis. Processes. 2022, 10: 2353. [Google Scholar]
- Liu, F. ; Jing, Y, C.; Shao, P.; et al. Research on design method of product functional hybridization for integrated innovation. Appl. Sci, 1: 12, 1030. [Google Scholar]
- Yu, F. ; Jia, X, C.; Zhao, X, W.; et al. A method for inspiring radical innovative design based on cross-domain knowledge mining. 2024, Systems. 2022, 12: 102.
- Mollajan, A. ; Thomson, V, J; Iranmanesh, S, H. Engineering management and modular design: A path to robust manufacturing processes. 2025, Processes. 13: 160.
- Darwish, A. ; Elgenedy, M, A.; Williams, B, W. A review of modular electrical sub-systems of electric vehicles. 2024, Energies. 17: 3474-3503.
- Xu, W, B.; Ma, X, J.; Jin, Y. A modular mathematical modeling method for smart deign and manufacturing of automobile driving axles. J. Circuit. Syst. Comp, . 2024, 33: 1-17.
- Davood, O. ; Seyed, M, S.; Ali, B, A., Ed.; et al. A sustainability approach to vehicle modular platform design: A mathematical model. Proc. Inst. Mech. Eng. E. J. Process. Mech. Eng. 2022, 236: 2296-2310. [Google Scholar]
- Santiago, M, Z.; Nathalie, K.; Cristovao, S.; et al. Multi-agent system for perturbations in the kitting process of an automotive assembly line. Eng. Appl. Artif. Intell, 2024: 135, 1086.
- Ganesh, S. ; Phi, R, T.; Aybike, O. Development of a parametric packaging and sizing tool for autonomous electric bus system. Proc. Inst. Mech. Eng. D. J. Automob. Eng, 2021: 235, 1713. [Google Scholar]
- Lv, T, T.; Wang, D, F.; Du, X, J. Dual-scale parametric modeling and optimal design method of CFRP automotive roof beam. Compos Struct, 2023: 308, 1166.
- Yuki, S. Efficiency optimization design that considers control of interior permanent magnet synchronous motors based on machine learning for automotive application. IEEE. Access. 2023, 11: 41-49.
- Song, W, F.; Xie, X, Z.; Huang, W, Y.; et al. The design of automotive interior for Chinese young consumers based on Kansei engineering and eye-tracking technology. Appl. Sci-Basel. 2023, 13, 1067.
- Zhou, X, Y.; Lin, M, W.; Wang, W, W. Statistical correlation coefficients for single-valued neutrosophic sets and their applications in medical diagnosis. AIMS. Math. 2023, 8: 16340-16359.
- Zhang, J.; Yu, X. ; Deng, S, M.; et al. Estimation of correlation coefficient with monotone transformation and multiplicative distortions. Commun. Stat – Theor. M. 2025, 54: 1-33.
- Sardarabadi, A, M. Complex factor analysis and extensions. IEEE. T. Signal. Proces. 2018, 66: 954-967.
- Forni, M.; Hallin, M.; Lippi, M.; et al. Dynamic factor models with infinite-dimensional factor space: Asymptotic analysis. J. Econom. 2017, 199: 74-92.
- Elías, D, N.; Dylan, S, C, A.; Giuliano, R, F, Q.; et al. Statistical package for computing precision covariance matrices via modified Cholesky decomposition. SoftwareX. 2025, 30: 10, 2125.
- Deliang, D.; Chengcheng, H.; Shaobo, J.; ea, al. Regularized estimation of Kronecker structured covariance matrix using modified Cholesky decomposition. J. Stat. Comput. Simul. 2025, 95: 905-930.
- Yang, J, S.; Wan, Z, Q.; Hector, J. An efficient strategy for information reuse in probability density evolution method considering large shift of distributions with multiple random variables. Probabilist. Eng. Mech, 2025: 79, 103728.
- Yannick, R.; Carolin, S. Identifying informative predictor variables with random forests. J. Educ. Behav. Stat. 2024, 49: 595-629.


| x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| x1 | 0 | 225 | 280 | 2 | 5 | 210 | 15 | 205 | 208 | 10 | 25 | 215 | 8 | 282 |
| x2 | 225 | 0 | 55 | 223 | 220 | 15 | 210 | 20 | 17 | 215 | 200 | 10 | 217 | 57 |
| x3 | 280 | 55 | 0 | 278 | 275 | 70 | 265 | 75 | 72 | 270 | 255 | 65 | 272 | 2 |
| x4 | 2 | 223 | 278 | 0 | 3 | 208 | 13 | 203 | 206 | 8 | 23 | 213 | 6 | 280 |
| x5 | 5 | 220 | 275 | 3 | 0 | 205 | 10 | 200 | 203 | 5 | 20 | 210 | 3 | 277 |
| x6 | 210 | 15 | 70 | 208 | 205 | 0 | 195 | 5 | 2 | 200 | 185 | 5 | 202 | 72 |
| x7 | 15 | 210 | 265 | 13 | 10 | 195 | 0 | 190 | 193 | 5 | 10 | 200 | 7 | 267 |
| x8 | 205 | 20 | 75 | 203 | 200 | 5 | 190 | 0 | 3 | 195 | 180 | 10 | 197 | 77 |
| x9 | 208 | 17 | 72 | 206 | 203 | 2 | 193 | 3 | 0 | 198 | 183 | 7 | 200 | 74 |
| x10 | 10 | 215 | 270 | 8 | 5 | 200 | 5 | 195 | 198 | 0 | 15 | 205 | 2 | 272 |
| x11 | 25 | 200 | 255 | 23 | 20 | 185 | 10 | 180 | 183 | 15 | 0 | 190 | 17 | 257 |
| x12 | 215 | 10 | 65 | 213 | 210 | 5 | 200 | 10 | 7 | 205 | 190 | 0 | 207 | 67 |
| x13 | 8 | 217 | 272 | 6 | 3 | 202 | 7 | 197 | 200 | 2 | 17 | 207 | 0 | 274 |
| x14 | 282 | 57 | 2 | 280 | 277 | 72 | 267 | 77 | 74 | 272 | 257 | 67 | 274 | 0 |
| No. | Eigenvalue | Eigenvector | Cumulative variance contribution |
| 1 | 8.42 | (0.28,0.25,0.19,0.28,0.29,0.27,0.29,0.27,0.27,0.29,0.29,0.26,0.28,0.18)T | 60.11% |
| 2 | 4.73 | (-0.25,0.28,0.33,-0.25,-0.25,0.27,-0.23,0.26,0.27,-0.24,-0.21,0.27,-0.25,0.32)T | 93.93% |
| 3 | 0.54 | (0.04,-0.11,0.59,0.04,0.05,-0.27,0.04,-0.28,-0.28,0.05,0.03,-0.22,0.05,0.60)T | 97.99% |
| 4 | 0.12 | (-0.41,-0.05,-0.01,-0.36,-0.23,-0.01,0.34,0.01,-0.01,0.06,0.72,-0.03,-0.06,-0.01)T | 98.59% |
| Grouping results | Functional area | Functional facilities |
|---|---|---|
| Group 1 | Living and washing area | beds, ventilation windows, hanging cabinets, showers, toilet, dressing mirror, standing cabinet |
| Group 2 | Recreation area | sofas, parlor table |
| Group 3 | Dining and kitchen area | stoves, sinks, refrigerator, cupboards, storage cabinet |
| Grouping results | Functional area | Functional facilities |
|---|---|---|
| Group 1 | Living area | beds, hanging cabinets, dressing mirror, standing cabinets |
| Group 2 | Washing area | ventilator windows, showers, toilet |
| Group 3 | Recreation area | sofas, parlor table |
| Group 4 | Dining and kitchen area | stoves, sinks, refrigerator, cupboards, storage cabinet |
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