Uncertainty quantification metrics have a critical position in inverse problems for dynamic systems as they quantify the discrepancy between numerically predicted samples and collected observations. Such metric plays its role by rewarding the samples for which the norm of this discrepancy is small and penalizing the samples otherwise. In this paper, we propose a novel entropy-based metric by utilizing the Jensen–Shannon divergence. Compared with other existing distance-based metrics, some unique properties make this entropy-based metric an effective and efficient tool in solving inverse problems in presence of mixed uncertainty (i.e. combinations of aleatory and epistemic uncertainty) such as encountered in the context of imprecise probabilities. Implementation-wise, an approximate Bayesian computation method is developed where the proposed metric is fully embedded. To reduce the computation cost, a discretized binning algorithm is employed as a substitution of the conventional multivariate kernel density estimates. For validation purpose, a static case study is first demonstrated where comparisons towards three other well-established methods are made available. To highlight its potential in complex dynamic systems, we apply our approach to the NASA LaRC Uncertainty Quantification challenge 2014 problem and compare the obtained results with those from 6 other research groups as found in literature. These examples illustrate the effectiveness of our approach in both static and dynamic systems and show its promising perspective in real engineering cases such as structural health monitoring in conjunction with dynamic analysis.

不确定性量化指标在动态系统逆问题中具有至关重要的地位，因为它们量化了数值预测的样本与收集到的观测值之间的差异。这种度量标准通过奖励差异较小的样本并以其他方式对样本进行惩罚来发挥其作用。在本文中，我们通过利用詹森-香农散度提出了一种新的基于熵的度量。与其他现有的基于距离的度量标准相比，某些独特的属性使该基于熵的度量标准成为解决混合不确定性（例如，不确定性和认知不确定性的组合）存在下的逆问题的有效工具，例如在不精确概率的情况下遇到的问题。 。实施方面，在提出的度量完全嵌入的情况下，开发了一种近似的贝叶斯计算方法。为了降低计算成本，采用离散化分箱算法替代了传统的多变量内核密度估计。为了进行验证，首先演示了一个静态案例研究，其中可以与其他三种行之有效的方法进行比较。为了突出其在复杂动态系统中的潜力，我们将我们的方法应用于NASA LaRC不确定性量化挑战20​​14问题，并将获得的结果与文献中发现的其他6个研究组的结果进行比较。