# Parameter-Matching Multi-Objective Optimization for Diesel Engine Torsional Dampers
## 1 Introduction  
The crankshaft system, a core component of diesel engines, operates under complex conditions and directly impacts engine power output, making the study of its vibrations--particularly torsional oscillation suppression--a long-standing research priority. Conventional mitigation methods involve installing torsional vibration dampers at the crankshaft free end, where optimal damper parameter selection critically determines vibration control efficacy [1, 2, 3, 4]. Although traditional damper selection relies on dual-pendulum models, the inherent simplicity of this low-degree-of-freedom framework inevitably introduces inaccuracies and uncertainties when characterizing torsional dynamics in multi-cylinder engine systems. Furthermore, evolving demands for diesel engine reliability necessitate more comprehensive and precise damper-engine matching strategies. This study addresses these challenges through advanced dynamic modeling and systematic parameter optimization, establishing methodologies to enhance vibration suppression accuracy while balancing operational stresses--an approach particularly relevant for modern high-performance multi-cylinder configurations. The early torsional vibration analysis of crankshaft systems primarily employed the Holzer method combined with dual-pendulum models for damper parameter matching. Subsequent studies have expanded optimization approaches. [PERSON] et al. [5] enhanced energy harvesting in regenerative arm-teeth shock absorbers via Taguchi-based tuning for ISO road profiles, and [PERSON] et al. [6] achieved a 72.6% weight reduction in TI-6 AL-4V brackets through topology optimization. [PERSON] et al. [7] developed mathematical models linking piston displacement to viscosity-temperature interactions in silicone oil dampers, whereas [PERSON] et al. [8] achieved a 50.17% vibration reduction in DMRV-TVD systems through genetic algorithm-driven viscous material optimization. While these efforts have significantly advanced parameter-specific tuning, limitations persist in holistically addressing multi-cylinder system complexities and balancing conflicting objectives like stress mitigation versus vibration suppression. Recent progress has shifted toward multi-objective optimization frameworks. [PERSON] et al. [9] pioneered adaptive MR-TVAs with axial/circumferential coil configurations that simultaneously achieve load-specific damping and lightweight design. However, [PERSON] et al. [10] critically noted that conventional damper designs relying solely on theoretical optimal parameters risk over-idealization, warning that neglecting crankshaft stress variations under changing conditions may lead to fatigue fractures. This critical understanding has propelled the integration of sophisticated monitoring technologies into optimization processes [11; 12; 13]. [PERSON] et al. [14] devised shell dampers incorporating quasi-static hysteresis modeling for the control of industrial vibrations. [PERSON] et al. [15] formulated a hybrid framework combining variational mode decomposition and least mean squares (VMD-LMS) and a long short-term memory (LSTM) network optimized by the northern goshawk algorithm, thereby achieving remarkable accuracy in spindle vibration prediction. [PERSON] et al. [16] deployed low-power smart sensors integrated with near real-time deep neural networks, which enabled micron-level precision in spindle condition monitoring. Despite significant progress in the optimization of dampers for vibration control, there are still aspects that require further improvement. The existing methods have the following issues: Firstly, the traditional dual-pendulum model is overly simplistic and fails to accurately represent the complex dynamics of multi-cylinder diesel engines. This limitation hinders the selection of dampers with optimal performance. Secondly, the current proprietary software has deficiencies in achieving the maximum efficiency and precision in the selection of dampers.