Generally, various measurements and data mining methods are susceptible to uncertainties that threaten the accuracy of data validation models if not properly managed. This is why taking into account the uncertainties in the model updating and validation has been highly encouraged. Presently, stochastic model updating methods are widely used together with uncertainty quantification metrics to provide accurate uncertainty measurements. The system parameters in uncertainty quantification are generally grouped into three: those without uncertainties, those with only epistemic uncertainties and those with both epistemic and aleatoric uncertainties.
Several methodologies for stochastic model updating have been developed. Regardless of the method used, the uncertainty quantification metric definition is of great importance in defining the uncertainty discrepancy in a data sample. However, uncertainty quantification metric with the ability to capture higher level data has remained a great challenge. Alternatively, researchers have recently identified Bhattacharyya distance, a measurement method between two sample data taking into account the probability distribution, as a promising solution for capturing high-level statistical information. Even though it has high potential for improving the uncertainty treatment, its application in stochastic model updating has not been fully explored due to its complexity and time-consuming nature.
To this note, Leibniz University Hannover scientists: Dr. Sifeng Bi, Dr. Matteo Broggi and Professor Michael Beer looked at the feasibility of using Bhattacharyya distance as an uncertainty quantification matrix in the stochastic model updating approach. Fundamentally, they aimed at solving the NASA uncertainty quantification challenge problems including the uncertainty characterization based on the approximate Bayesian computational approach. Additionally, they investigated the advantages of using the Bhattacharyya distance metric in solving real-world practical problems. Their work is currently published in the journal, Mechanical Systems and Signal Processing.
In brief, the research team scrutinized the available stochastic measurements methods including the Euclidian, Mahalanobis, and Bhattacharyya distances model updating metrics. Secondly, they developed a fully embedded Bhattacharyya distance-based updating framework using the transitional Markov chain Monte Carlo algorithm. On the other hand, a binning algorithm was used to evaluate the Bhattacharyya distance between various sets of data samples. Additionally, Euclidian and Bhattacharyya distances were combined in the initial steps to developed a two-step Bayesian updating framework to enhance the results accuracy. Eventually, they performed a stochastic sensitivity analysis by ranking the input parameters based on the uncertainty properties of their corresponding outputs.
The Bhattacharyya distance was observed to demonstrate powerful uncertainty quantification metric abilities for the model updating framework. This was attributed to the effective connection between the updating framework and the Bhattacharyya distance. In addition, it was worth noting that the Bhattacharyya distance metric was an ideal alternative for replacing the Euclidian distance in stochastic model updating frameworks.
In summary, Professor Michael Beer and his research team demonstrated the role of Bhattacharyya distance in stochastic model updating thus enabling efficient stochastic sensitivity analysis. To actualize their study, they accessed the performance of the developed framework in two different applications: simulated mass-spring problem and benchmark-based uncertainty treatment problem. Interestingly, in all the two cases, a quality gain for stochastic updating was obtained. Therefore, the study will advance future uncertainty characterization and stochastic model updating.
Bi, S., Broggi, M., & Beer, M. (2019). The role of the Bhattacharyya distance in stochastic model updating. Mechanical Systems and Signal Processing, 117, 437-452.Go To Mechanical Systems and Signal Processing