Objective Rating Metric for Dynamic Systems

Computer Aided Engineering (CAE) has become a vital tool for product development in the automotive industry. Various computer programs and models are developed to simulate vehicle crashworthiness, dynamic, and fuel efficiency. To maximize the effectiveness and the use of these models, the validity and predictive capabilities of these models need to be assessed quantitatively. For a successful implementation of CAE models as an integrated part of the current vehicle development process, it is necessary to develop an objective metric that has the desirable metric properties to quantify the discrepancy between physical tests and simulation results. However, one of the key difficulties for model validation of dynamic systems is that most of the responses are functional responses, such as time history curves. This calls for the development of an objective metric that can evaluate the differences of the time history as well as the key features, such as phase shift, magnitude, and slope between test and CAE curves. In this paper, four state-of-the-art objective rating metrics are investigated. Multiple dynamic system examples for both tests and CAE models are used to show their advantages and limitations. Further enhancements are proposed to improve the robustness of these metrics. A new combined objective rating metric is developed to standardize the calculation of the correlation between two time history signals of dynamic systems. Multiple vehicle safety case studies are used to demonstrate the effectiveness and usefulness of the proposed metric for future ISO Technical Specification and Standard for the TC22/SC10/SC12/WG4 “Virtual Testing” Working Group. INTRODUCTION Prototype tests to evaluate safety performance of a new vehicle in order to meet current and future safety requirements are on the rise. Computer modeling and simulations are playing an increasingly important role in reducing vehicle prototype tests and shortening product development time. To achieve these goals, the validity and predictive capabilities of the computer models for various vehicle dynamic systems must be assessed objectively, quantitatively, and systematically. Model validation is the process of comparing model outputs with experimental observations in order to assess the validity or predictive capabilities of computer models. The fundamental concepts and terminology of model validation have been established mainly by various standard committees and professional societies ([1], [2], [3], [4], [5]). One of the critical tasks to achieve quantitative assessments of models is to develop a validation metric that has the desirable metric properties to quantify the discrepancy between functional or time history responses from both physical tests and simulation results ([6], [7], [8]). However, the primary consideration in the selection of an effective metric should be based on the application requirements. In general, the validation metric shall be a quantitative measurement to judge whether a computational model is adequate for its intended usage. In this paper, four validation metrics for dynamic responses are investigated and they are: CORrelation and Analysis (CORA) metric [9], Enhanced Error Assessment of Response Time