A numerically efficient inverse method for parametric model uncertainty identification using maximum likelihood estimation is presented. The goal is to identify a probability model for a fixed number of model parameters based on a set of experiments. To perform maximum likelihood estimation, the output probability density function is required. Forward propagation of input uncertainty is established combining Polynomial Chaos and moment matching. High-order moments of the output distribution are estimated using the generalized Polynomial Chaos framework. Next, a maximum entropy parametric distribution is matched with the estimated moments. This method is numerically very attractive due to reduced forward sampling and deterministic nature of the propagation strategy. The methodology is applied on a wet clutch system for which certain model variables are considered as stochastic. The number of required model simulations to achieve the same accuracy as the brute force methodologies is decreased by one order of magnitude. The probability model identified with the high order estimates resulted into a true log-likelihood increase of about 4% since the accuracy of the estimated output probability density function could be improved up to 47%.

中文翻译：

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基于湿式摩擦离合器的多项式混沌和高阶矩匹配的反参数不确定性识别

提出了一种使用最大似然估计的参数模型不确定性识别的数值有效逆方法。目标是基于一组实验为固定数量的模型参数确定概率模型。为了执行最大似然估计，需要输出概率密度函数。结合多项式混沌和矩匹配建立输入不确定性的前向传播。使用广义多项式混沌框架估计输​​出分布的高阶矩。接下来，最大熵参数分布与估计矩匹配。由于传播策略的前向采样减少和确定性，该方法在数值上非常有吸引力。该方法应用于湿式离合器系统，其中某些模型变量被认为是随机的。实现与蛮力方法相同的精度所需的模型模拟数量减少了一个数量级。使用高阶估计确定的概率模型导致真实对数似然增加约 4%，因为估计输出概率密度函数的准确性可以提高到 47%。