# Parameter-Matching Multi-Objective Optimization for Diesel Engine Torsional Dampers
## 5 Conclusions  
To address the limitations of dual-pendulum-based damper configuration methods, this study proposes an integrated framework combining three critical advancements. First, a multi-degree-of-freedom dynamic model accurately characterizes crankshaft system dynamics, enabling high-precision free vibration analysis via the modified Jacobi sweep method--demonstrating superior numerical stability and computational accuracy compared to conventional Jacobi iterations. Harmonic responses are subsequently derived through decoupling transformations and modal superposition. Second, a Bayesian-hyperparameter-optimized neural network establishes nonlinear mapping relationships between damper parameters and system responses, achieving 96.8% prediction accuracy on validation datasets. SHAP interpretability analysis further quantifies inherent trade-offs: torsional stiffness suppresses the twist angle but amplifies stress concentration, while damping coefficients exhibit unidirectional benefits for vibration control, aligning with their upper-bound optimization. Finally, NSGA-II multi-objective optimization generates Pareto-optimal solutions that simultaneously minimize torsional amplitudes and component stresses. Key findings include:  
1. Multi-cylinder diesel crankshaft models frequently exhibit poor numerical conditioning. The modified Jacobi sweep method resolves this through threshold-controlled iterations, reducing eigenfrequency errors to <1% relative to ANSYS benchmarks.
2. Traditional inertia ratio recommendations (0.1-0.3) fail to concurrently optimize vibration suppression and stress mitigation. SHAP analysis confirms bidirectional effects of inertia ratios: high inertia ratios (>0.25) effectively reduce torsional amplitudes but marginally impact stress concentrations, while low ratios (<0.15) decrease peak alternating stresses despite slightly increased vibrations.
3. Tuning ratio optimization reveals distinct regimes: high-inertia dampers (0.25-0.3) achieve near-theoretical tuning ratios for balanced performance, whereas low-inertia configurations require 15-20% upward tuning ratio adjustments to maximize stress reduction. SHAP-based sensitivity maps validate this compensation mechanism, linking stiffness-tuning trade-offs to nonlinear inertia-stress coupling.
4. Damping coefficients consistently converge to the upper bounds of dual-pendulum recommendations, enhancing both vibration attenuation and fatigue resistance. SHAP values reinforce this practice, showing damping's unidirectional positive contributions.  
Conceptualization, Z.T. and Z.G.; methodology, Z.T.; software, Z.T.; validation, Z.T. and Z.G.; formal analysis, Z.G.; investigation, Z.T.; resources, Z.T.; data curation, Z.G.; writing--original draft preparation, Z.G.; writing--review and editing, Z.T.; visualization, Z.G.; supervision, Z.T.; project administration, Z.T.; funding acquisition, Z.T. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Key R&D Program of China (14 th Five-Year Plan), grant number 2023 YFD2400800.  
**Institutional Review Board Statement**: Not applicable.  
**Informed Consent Statement**: Not applicable.  
**Data Availability Statement**: The raw data supporting the conclusions of this article will be made available by the authors on request.  
**Conflicts of Interest**: The authors declare no conflicts of interest.