A New Calibration Metric – Probability Residual (PR) and Its Validation Practice for Rotor Dynamics Model of a Journal Bearing Rotor System

Abstract

In constructing the computational model of engineered systems such as a journal bearing rotor systems, statistical model calibration method is often used since the statistical model emulates the actual behavior of the engineered systems with uncertainties. A calibration metric, which quantifies the degree of agreement or disagreement between computational and experimental results, is one of the key components in the statistical model calibration. However, some existing calibration metrics such as log-likelihood and Kullback-Leibler divergence (KLD) have limitations in constructing an accurate computational model. To overcome this problems, this study proposes a new calibration metric, probability residual (PR). The PR metric is defined as the sum of the product of scale factor and square of residuals. The scale factor scales the PDF in specific range, which enables to improve the calibration efficiency. The square of residuals makes the PR a convex form, which guarantees existence of global optimum. So as to evaluate the performance of the PR metric, this study uses mathematical models and employs statistical models of the journal bearing rotor system appropriate to normal and rubbing state. As a result, the PR metric performed better than other metrics including log-likelihood and KLD in terms of the calibration accuracy and efficiency, and the calibrated journal bearing rotor model with PR was proved in valid by the hypothesis testing. In summary, the proposed PR metric is promising to be applied in building an accurate computational model.