A New Validation Metric for Models With Correlated Responses Using Limited Experimental and Simulation Data

Model validation is the process of determining the degree to which a model is an accurate representation of the real object. Most of the existing model verification metrics rely on massive data, which are expensive to obtain in complex engineering problems. This paper first proposes a new enhanced Mahalanobis distance (EMD) metric by multiplying the original Mahalanobis distance with a direction angle to incorporate the correlation information using limited experimental and simulation data. Combining with EMD, an angle metric is developed as an alternative of the area metric to reduce the misjudgment rate of model validation. In order to quantify the uncertainty due to insufficient experimental and simulation data, the angle metric is further extended to a new interval angle metric, namely the interval EMD-pooling angle metric as the ultimate metric, for validating models at multiple sites. The proposed interval EMD-pooling angle metric is compared with other existing metrics through three numerical case studies to demonstrate its advantages when both experimental and simulation data are insufficient. An engineering example regarding ultrasonic welding is also provided to demonstrate the effectiveness of the proposed metric for practical model validation problems.