预测具有隐式随机性的自主非线性双稳态系统中的状态跃迁
Predicting State Transitions in Autonomous Nonlinear Bistable Systems with Hidden Stochasticity
AI总结：
针对双稳态自主系统状态跃迁现有估计方法不准、蒙特卡洛模拟成本高的问题，提出考虑非线性漂移和状态相关白噪声的扩展Eyring-Kramers公式，适配隐式噪声场景，在工业电子案例中精度优于现有非蒙特卡洛方法。
摘要：
双稳态自主系统存在于诸多科学领域中。当内在噪声强度较大时，这类系统会呈现出从一个亚稳态稳态向另一个亚稳态稳态的随机跃迁。在电子双稳态存储器中，这类跃迁属于故障，通常以蒙特卡洛方式进行模拟，CPU时间成本高昂。现有的闭式公式依赖非线性系统动力学的近稳态近似来估计平均跃迁时间，已被证明准确性不足。我们的贡献分为两方面。基于过阻尼自主系统的一维随机模型，我们提出了一种扩展的Eyring-Kramers解析公式，该公式同时考虑了非线性漂移和与状态相关的白噪声方差，由Itô随机演算严格推导得出。我们还将其适配于实际的系统工程场景：内在噪声源是隐式的，仅能通过稳态下测得的可观测量的波动来推断。在工业电子案例研究中的初步数值试验表明，我们的近似预测公式达到了显著的准确性，性能优于以往的非蒙特卡洛方法。
英文摘要：
Bistable autonomous systems can be found inmany areas of science. When the intrinsic noise intensity is large, these systems exhibits stochastic transitions from onemetastable steady state to another. In electronic bistable memories, these transitions are failures, usually simulated in a Monte-Carlo fashion at a high CPU-time price. Existing closed-form formulas, relying on near-stable-steady-state approximations of the nonlinear system dynamics to estimate the mean transition time, have turned out inaccurate. Our contribution is twofold. From a unidimensional stochastic model of overdamped autonomous systems, we propose an extended Eyring-Kramers analytical formula accounting for both nonlinear drift and state-dependent white noise variance, rigorously derived from Itô stochastic calculus. We also adapt it to practical system engineering situations where the intrinsic noise sources are hidden and can only be inferred from the fluctuations of observables measured in steady states. First numerical trials on an industrial electronic case study suggest that our approximate prediction formula achieve remarkable accuracy, outperforming previous non-Monte-Carlo approaches.
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