自适应奇异进化插值卡尔曼滤波及其在二维水污染模型数据同化中的应用

T. T. Hà, Hoang Hong Son, N. H. Phong
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引用次数: 0

摘要

本研究提出了一种新的水污染传播估计算法,其主要目标是为决策者提供更可靠和高质量的估计。目前,广泛使用的变分方法计算量大,限制了其在实际中的应用。此外,该方法以初始状态为控制变量,对于确定初始误差非常敏感,特别是对于不稳定的动力系统。本文提出的自适应滤波器(AF)旨在克服变分方法中的这两个缺点:就其性质而言,AF是连续的(不使用大的批量同化窗口),即使对于不稳定的动态也是稳定的,增益参数作为控制变量。本文提出的AF是奇异进化插值卡尔曼滤波器(SEIKF)的自适应版本。这个AF的一个新版本是它使用了SEIKF增益的时变结构。为了处理系统参数和噪声协方差的不确定性,本文提出的自适应SEIKF (ASEIKF)利用同化过程中迭代的降阶协方差和自适应调整的相关增益参数,使系统输出的预测误差最小。由于采用了一种称为同步扰动随机逼近算法的优化工具,该优化工具只需要对数值模型进行两次积分,因此大大减少了实现ASEIKF的计算负担。不像标准梯度下降优化算法那样,在每个同化瞬间都需要迭代循环。利用seeikf和ASEIKF对河内市青汉湖进行了数据同化实验,并与ASEIKF和seeikf进行了性能比较,结果表明所提出的ASEIKF具有较高的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Adaptive Singular Evolutive Interpolated Kalman filter and its application to data assimilation in 2D Water pollution model
This study promotes a new algorithm for estimating the water pollution propagation with the primary goal of providing more reliable and high quality estimates to decision makers. To date, the widely used variational method suffers from the large computational burden which limits its application in practice. Moreover, this method, considering the initial state as a control variable, is very sensitive in specifying initial error, especially for unstable dynamical systems. The adaptive filter (AF), proposed in this paper, is aimed at overcoming these two drawbacks in the variational method: by its nature, the AF is sequential (no large batch assimilation window used) and stable even for unstable dynamics, with the gain parameters as control variables. The AF, developed in this paper, is an adaptive version of the Singular Evolutive Interpolated Kalman Filter (SEIKF). One of the new versions of this AF is that it uses a time-varying structure of the gain of SEIKF. To deal with the uncertainty of the system parameters and of the noise covariance, the proposed adaptive SEIKF (ASEIKF) makes use of the covariance of reduced rank iterated during assimilation process and of some pertinent gain parameters tuned adaptively to yield the minimum prediction error for the system output. The computational burden in implementation of the ASEIKF is reduced drastically due to applying the optimization tool known as a simultaneous perturbation stochastic approximation algorithm, which requires only two integrations of the numerical model. No iterative loop is required at each assimilation instant as usually happens with the standard gradient descent optimization algorithms. Data assimilation experiment, carried out by the SEIKF and ASEIKF, is implemented for the Thanh Nhan Lake in Hanoi and the performance comparison between the ASEIKF and SEIKF is given to show the high effectiveness of the proposed ASEIKF.
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