The operational reliability of a high performance marine vessel depends critically on the health of its marine propulsion systems, which are increasingly subjected to diverse operational loads and environmental stressors. This paper proposes a robust mathematical framework for non-linear state-space forecasting of marine engine parameters using adaptive-window multi-particle stochastic differential equations. Traditional time-series models such as Vector Autoregressive Integrated Moving Average, often fail to capture the inherent stochasticity and transient dynamics of complex systems due to their reliance on fixed-window linear assumptions. To address this, we develop a dual-layered estimation approach: first, an adaptive lookback mechanism dynamically adjusts the learning window size based on the instantaneous drift magnitude, ensuring responsiveness during non-stationary regimes. Second, a Multi-Particle ensemble is evolved via Euler-Maruyama discretization, where each particle trajectory represents a stochastic realization of the system state. To refine the ensemble mean and mitigate the "noise-chasing" behavior of raw estimators, a Girsanov transform induced change of probability measure is implemented, assigning higher probabilistic weights to particles that align with the physical drift. Theoretical evaluation and empirical benchmarking demonstrate that the proposed adaptive SDE framework significantly outperforms classical statistical baselines in multi-step prediction stability and computational efficiency. The model provides a scalable, "grey-box" solution for real-time risk quantification in systems characterized by high-frequency volatility and non-linear transitions.

翻译：高性能船舶的运行可靠性关键取决于其推进系统的健康状态，而推进系统日益承受着多样化的运行负载和环境应力。本文提出一种基于自适应窗口多粒子随机微分方程的非线性状态空间预测鲁棒数学框架，用于预测船舶发动机参数。传统的时序模型（如向量自回归移动平均模型）因依赖固定窗口线性假设，往往难以捕捉复杂系统固有的随机性和瞬态动力学特征。为解决此问题，我们开发了双层估计方法：首先，自适应回溯机制根据瞬时漂移幅度动态调整学习窗口尺寸，确保在非平稳状态下的响应灵敏度；其次，通过Euler-Maruyama离散化方法演化多粒子集成，其中每个粒子轨迹代表系统状态的一种随机实现。为优化集成均值并抑制原始估计器的"噪声追逐"行为，采用Girsanov变换诱导的概率测度变化，对符合物理漂移的粒子赋予更高概率权重。理论评估与实证基准测试表明，所提出的自适应SDE框架在多步预测稳定性和计算效率方面显著优于经典统计基线模型。该模型为具有高频波动性和非线性转变特性的系统提供了可扩展的"灰箱"解决方案，适用于实时风险量化。