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Peer-reviewedCC BY 4.0Mathematics

A Novel Solving Method for Multi-Constrained Optimization of Ceramic Composite Armor with Failure Considerations Based on an Improved Response Surface Methodology–Adaptive Moment Estimation (RSM-Adam) Framework

  • Shibao Wu1,2
  • Yongjie Gui3
  • Guanjie Wang1
  • Xiaojun Wei1
  • Guan Wang4
  • Zhonghai Xu1,2
4 affiliations
  1. 1National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150080, China
  2. 2Suzhou Research Institute of HIT, Harbin Institute of Technology, Suzhou 215104, China
  3. 3School of Computer Science and Technology, Tongji University, Shanghai 201804, China
  4. 4Institute of Petrochemistry, Heilongjiang Academy of Sciences, Harbin 150040, China
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Abstract

Optimizing the design of Ceramic Composite Armor Systems (CCASs) is crucial for liberating redundant design space and enhancing ballistic performance. However, existing solution frameworks still exhibit deficiencies in handling multi-constrained optimization, particularly regarding surrogate model generalization and the nonlinearity and non-convexity of solution algorithms, leading to suboptimal accuracy and efficiency. This study proposes a novel Response Surface Methodology–Adaptive Moment Estimation (RSM-Adam) framework to address these challenges. The developed RSM surrogate model integrates key CCAS failure characteristics, such as structural deformation, fiber/matrix failure and interfacial debonding/delamination into the optimization analysis using few finite element analysis (FEA). This approach overcomes the limitation of conventional theoretical models that focus solely on ballistic performance, establishing a foundation for a generalized multi-constrained optimization model. Meanwhile, an improved Adam method incorporating a cosine step-size adjustment strategy demonstrates superior capability in handling nonlinearity and non-convexity during iteration compared to conventional algorithms like the Simulated Annealing Algorithm (SAA), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA). It achieves over 60% reduction in computational error compared with conventional intelligent algorithms, while maintaining a computational cost comparable to or lower than most of them, proving highly effective and efficient for complex multi-constrained models. The rationality and accuracy of the RSM-Adam framework are validated through ballistic testing and FEA of an Al2O3/Carbon Fiber (CF)/Aramid Fiber (AF) composite armor sample, with systematic analysis of the influence of key framework parameters on optimization outcomes. It is also confirmed that the proposed RSM-Adam framework provides a practical, widely applicable, and engineering-valuable solution for the multi-constrained optimal design of the CCAS.

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Cite

BibTeXRIS
BibTeX
@article{wu2026novel,
  title = {{A Novel Solving Method for Multi-Constrained Optimization of Ceramic Composite Armor with Failure Considerations Based on an Improved Response Surface Methodology–Adaptive Moment Estimation (RSM-Adam) Framework}},
  author = {Shibao Wu and Yongjie Gui and Guanjie Wang and Xiaojun Wei and Guan Wang and Zhonghai Xu},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213945},
  url = {https://www.mdpi.com/2227-7390/14/21/3945},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A Novel Solving Method for Multi-Constrained Optimization of Ceramic Composite Armor with Failure Considerations Based on an Improved Response Surface Methodology–Adaptive Moment Estimation (RSM-Adam) Framework
AU  - Shibao Wu
AU  - Yongjie Gui
AU  - Guanjie Wang
AU  - Xiaojun Wei
AU  - Guan Wang
AU  - Zhonghai Xu
PY  - 2026
DA  - 2026/10/29
JO  - Mathematics
DO  - 10.3390/math14213945
UR  - https://www.mdpi.com/2227-7390/14/21/3945
AB  - Optimizing the design of Ceramic Composite Armor Systems (CCASs) is crucial for liberating redundant design space and enhancing ballistic performance. However, existing solution frameworks still exhibit deficiencies in handling multi-constrained optimization, particularly regarding surrogate model generalization and the nonlinearity and non-convexity of solution algorithms, leading to suboptimal accuracy and efficiency. This study proposes a novel Response Surface Methodology–Adaptive Moment Estimation (RSM-Adam) framework to address these challenges. The developed RSM surrogate model integrates key CCAS failure characteristics, such as structural deformation, fiber/matrix failure and interfacial debonding/delamination into the optimization analysis using few finite element analysis (FEA). This approach overcomes the limitation of conventional theoretical models that focus solely on ballistic performance, establishing a foundation for a generalized multi-constrained optimization model. Meanwhile, an improved Adam method incorporating a cosine step-size adjustment strategy demonstrates superior capability in handling nonlinearity and non-convexity during iteration compared to conventional algorithms like the Simulated Annealing Algorithm (SAA), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA). It achieves over 60% reduction in computational error compared with conventional intelligent algorithms, while maintaining a computational cost comparable to or lower than most of them, proving highly effective and efficient for complex multi-constrained models. The rationality and accuracy of the RSM-Adam framework are validated through ballistic testing and FEA of an Al2O3/Carbon Fiber (CF)/Aramid Fiber (AF) composite armor sample, with systematic analysis of the influence of key framework parameters on optimization outcomes. It is also confirmed that the proposed RSM-Adam framework provides a practical, widely applicable, and engineering-valuable solution for the multi-constrained optimal design of the CCAS.
SN  - 2227-7390
ER  -