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Polynomial chaos-based parameter estimation methods applied to a vehicle system

机译：基于多项式混沌的参数估计方法在车辆系统中的应用

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摘要

Parameter estimation for large systems is a difficult problem, and the solution approaches are computationally expensive. The polynomial chaos approach has been shown to be more efficient than Monte Carlo for quantifying the effects of uncertainties on the system response. This article compares two new computational approaches for parameter estimation based on the polynomial chaos theory for parameter estimation: a Bayesian approach, and an approach using an extended Kalman filter (EKF) to obtain the polynomial chaos representation of the uncertain states and the uncertain parameters. The two methods are applied to a non-linear four-degree-of- freedom roll plane model of a vehicle, in which an uncertain mass with an uncertain position is added on the roll bar. When using appropriate excitations, the results obtained with both approaches are close to the actual values of the parameters, and both approaches can work with noisy measurements. The EKF approach has an advantage over the Bayesian approach: the estimation comes in the form of a posteriori probability densities of the estimated parameters. However, it can yield poor estimations when dealing with non-identifiable systems, and it is recommended to repeat the estimation with different sampling rates in order to verify the coherence of the results with the EKF approach. The Bayesian approach is more robust, can recognize non-identifiability, and use regularization techniques if necessary.
机译：大型系统的参数估计是一个难题，解决方案的计算量很大。多项式混沌方法已被证明比蒙特卡洛方法更有效地量化不确定性对系统响应的影响。本文比较了基于多项式混沌理论进行参数估计的两种新的参数估计计算方法：贝叶斯方法和使用扩展卡尔曼滤波器（EKF）获得不确定状态和不确定参数的多项式混沌表示的方法。将这两种方法应用于车辆的非线性四自由度侧倾平面模型，其中在侧倾杆上添加了具有不确定位置的不确定质量。当使用适当的激励时，两种方法所获得的结果都接近参数的实际值，并且两种方法都可以在噪声测量下工作。 EKF方法优于贝叶斯方法：估计以估计参数的后验概率密度的形式出现。但是，在处理无法识别的系统时，可能会得出较差的估计值，建议使用不同的采样率重复进行估计，以验证EKF方法的结果是否一致。贝叶斯方法更健壮，可以识别不可识别性，并在必要时使用正则化技术。

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