Fourier series-based approximation of time-varying parameters in ordinary differential equations
Fourier series-based approximation of time-varying parameters in ordinary differential equations
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DOI：
10.1088/1361-6420/ad1fe5
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发表时间：
2024-03-01
期刊：
影响因子：
2.1
通讯作者：
Arnold，Andrea
中科院分区：
文献类型：
--
作者：
Fitzpatrick，Anna;Folino，Molly;Arnold，Andrea
许多使用微分方程建模的真实世界系统涉及未知或不确定的参数。在这种情况下，解决参数估计逆问题的标准方法通常集中在估计常数上，但一些不可观测的系统参数可能会随时间而变化，而无需已知的演化模型。在这项工作中，我们提出了一种新的近似方法的启发傅立叶级数估计时变参数（TVP）的确定性动力系统建模与常微分方程。使用集合卡尔曼滤波结合傅立叶级数为基础的近似模型，我们详细介绍了两种可能的实施方案，顺序更新的时变参数估计给出嘈杂的观测系统状态。我们证明了所提出的方法在估计周期参数，无论是当周期是已知的和未知的，以及非周期TVP的不同形式与几个计算的例子，使用强迫谐振子的能力。结果强调的频率和数量的近似模型项的时变参数估计和相应的动力系统预测的重要性。
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some unobservable system parameters may vary with time without known evolution models. In this work, we propose a novel approximation method inspired by the Fourier series to estimate time-varying parameters (TVPs) in deterministic dynamical systems modeled with ordinary differential equations. Using ensemble Kalman filtering in conjunction with Fourier series-based approximation models, we detail two possible implementation schemes for sequentially updating the time-varying parameter estimates given noisy observations of the system states. We demonstrate the capabilities of the proposed approach in estimating periodic parameters, both when the period is known and unknown, as well as non-periodic TVPs of different forms with several computed examples using a forced harmonic oscillator. Results emphasize the importance of the frequencies and number of approximation model terms on the time-varying parameter estimates and corresponding dynamical system predictions.