Model Validation of a Single Degree-of-Freedom Oscillator: A Case Study

In this paper, we investigate a validation process in order to assess the predictive capabilities of a single degree-of-freedom oscillator. Model validation is understood here as the process of determining the accuracy with which a model can predict observed physical events or important features of the physical system. Therefore, assessment of the model needs to be performed with respect to the conditions under which the model is used in actual simulations of the system and to specific quantities of interest used for decision-making. Model validation also supposes that the model be trained and tested against experimental data. In this work, virtual data are produced from a non-linear single degree-of-freedom oscillator, the so-called oracle model, which is supposed to provide an accurate representation of reality. The mathematical model to be validated is derived from the oracle model by simply neglecting the non-linear term. The model parameters are identified via Bayesian updating. This calibration process also includes a modeling error due to model misspecification and modeled as a normal probability density function with zero mean and standard deviation to be calibrated.

Automated summary

This paper investigates the validation process of a single degree-of-freedom oscillator to assess its predictive capabilities. Model validation is the process of determining the accuracy of a model in predicting observed physical events or system features. Virtual data is generated from a non-linear oscillator, and a mathematical model is derived by neglecting the non-linear term. Bayesian updating is used to identify model parameters, including calibration of the normal probability density function representing model error.