论文标题
通过Fokker-Planck类型残差估算参数估计：应用于线性固定随机振动
Parameter Estimation via Fokker-Planck Type Residual: Application to Linear Stationary Random Vibration
论文作者
论文摘要
在这项研究中，我们提出了一种基于从随机动力学系统测量的概率密度函数（PDF）数据，该方法可用于估计随机微分方程（SDE）模型的未知参数值。由于我们的方法不需要对PDF的明确描述，因此即使由于多重噪声术语，非线性条款等，它几乎不明确地将其PDF应用于SDE模型。因此，我们的方法有望提供一种多功能工具，以动态参数化测量的PDF数据。在我们提出的方法中，假定测得的PDF是从随机动力学系统中获得的，其结构由已知的具有未知参数值的SDE模型描述。借助ItôCilculus，Fokker-Planck方程（FPE）源自SDE模型。测得的PDF和参数值的候选者被取代为FPE，以计算FPE残差。我们的方法应用于两个随机振动系统。由于参数值倾向于精确值，因此它们的FPE残差趋于零，这表明我们提出的FPE残差可用于SDE模型的未知参数估计。
In this study, we propose a new method that is useful for estimating unknown parameter values of stochastic differential equation (SDE) models, based on probability density function (PDF) data measured from random dynamical systems. As our method does not require explicit description of PDF, it can be applied to the SDE models even when their PDFs are hardly derived in explicit forms due to multiplicative-noise terms, nonlinear terms, and so on. Therefore, our method is expected to provide a versatile tool to dynamically parameterize measured PDF data. In our proposed method, it is assumed that a measured PDF is obtained from a random dynamical system whose structure is described by a known SDE model with unknown parameter values. With the help of Itô calculus, the Fokker-Planck equation (FPE) is derived from the SDE model. The measured PDF and a candidate of parameter values are substituted into the FPE to calculate a FPE residual. Our method is applied to two random vibration systems. Their FPE residuals tend to zero as the parameter values tend to exact values, showing that our proposed FPE residual can be utilized for unknown parameter estimation of SDE models.
