A robust and convex metric for unconstrained optimization in statistical model calibration—probability residual (PR)

Abstract

Statistical model calibration is a practical tool for computational model development processes. However, in optimization-based model calibration, the quality of the calibrated model is often unsatisfactory due to inefficiency and/or inaccuracy of calibration metrics. This paper proposes a new calibration metric, namely, probability residual (PR). PR quantifies the degree of agreement or disagreement between the computational response and experimental results. The PR metric is defined as the sum of the product of a scale factor and the squared residual. First, the scale factor defines the shape of the squared residual to maintain consistent sensitivity during the optimization process. Thus, the number of function evaluations can be reduced. Second, the mathematical form of the squared residuals is used to make convex optimization feasible. Therefore, the existence of a global minimum is guaranteed. To evaluate the performance of the proposed metric, numerical examples are shown in a case study. Various system functions—including linear, non-linear, and elliptical—are incorporated into the statistical model calibration. A case study that examines journal bearing rotor systems is presented to demonstrate the application of the proposed calibration metric to a real-world engineered system.