Online State Estimation of Fine Powder Processes by the Adaptive Extended Kalman Filter

通过自适应扩展卡尔曼滤波器对细粉过程进行在线状态估计

• 批准号: 03650516
• 负责人: OKANO Yasuhiko
• 金额: $ 1.15万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1991
• 资助国家: 日本
• 起止时间: 1991 至 1992
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03650516/
• 关键词: extended Kalman Filter; state estimation; Riccati equation; optimal sampling; Lorenz system; chaos; LQG control; H-infinity control; 誤差共分散行列; strange attractor; 共役勾配法; discrete vortex simulation; カルマンフィルタ; 非線形

The switching mode enhanced extended Kalman(SEEK) filter algorithm has been developed to estimate strongly nonlinear and noisy dynamical systems. The SEEK algorithm is based on optimally selecting the observation matrix so as to ensure the convergence of the estimation error covariance matrix is maximized. The basic concept has been outlined using a second order linear system and successfully verified by numerical demonstrations. Then the SEEK filter algorithm has been applied to estimate the Lorenz system with superimposed Gaussian white noise. The SEEK filter has returned good estimates of this chaotic system though the conventional extended Kalman filter absolutely failed to obtain accurate state estimates. The optimization algorithm for selecting the optimal sampling mode has been developed and applied to estimate the Lorenz system with a switched parameter. We regard this demonstration as convincing evidence of the power of the SEEK filter as an accurate estimator of the state variables even for strongly nonlinear systems such as this particular relization of the Lorenz system. The SEEK algorithm has also been applied to identify evolving large structure in flows accompanied with micro-structure diffusion in a discrete vortex simulation. The SEEK filter achieved accurate estimation even in a high level noisy environment. Then only diagonal elements of the Jacobian matrix have been found to be dominant in applying the SEEK algorithm to the discrete vortex simulation. This evidence should be quite useful to reduce the calculation time in a large code estimation. Then, from the viewpoint of applicability of Kalman filtering technology to control practices, therefore, control performances have been compared among the cases of conventional PID, LQG and H-infinity controls, supposing a typical transfer function of the control object,which is certainly common to powder processes.

开关模式增强了扩展的Kalman（SEEK）滤清器算法，以估计强烈的非线性和嘈杂的动力学系统。 Seek算法基于最佳选择观察矩阵，以确保最大化估计误差协方差矩阵的收敛性。基本概念已使用二阶线性系统概述，并通过数值演示成功验证。然后，已应用Seek Filter算法来估计用叠加的高斯白噪声估算Lorenz系统。 Seek过滤器返回了该混乱系统的良好估计值，尽管常规扩展的Kalman过滤器绝对无法获得准确的状态估计。已经开发了用于选择最佳采样模式的优化算法，并应用于使用开关参数估算Lorenz系统。我们认为，即使对于强烈的非线性系统（例如，洛伦兹系统的特殊依赖），该证明是对寻求过滤器的力量的令人信服的证据。 Seek算法还应用于鉴定在离散涡流模拟中伴随微结构扩散的流中发展的大结构。即使在高水平的嘈杂环境中，SEEK过滤器也达到了准确的估计。然后，仅发现雅各布基质的对角线元素在将Seew算法应用于离散的涡流模拟中占主导地位。这些证据对于减少大量代码估计的计算时间应该非常有用。然后，从卡尔曼过滤技术对控制实践的适用性的角度来看，在常规的PID，LQG和H-含量控制的情况下，已经比较了控制性能，假设控制对象的典型传递功能，这无疑是粉末过程的共同点。