Evaluating Reliability of Multiple-model System Identification

This paper builds upon previous work by providing a statistical basis for multiplemodel system identification. Multiple model system identification is useful because many models representing different sets of modeling assumptions may fit the measurements. The presence of errors in modeling and measurement increases the number of possible models. Modeling error depends on inaccuracies in (i) the numerical model, (ii) parameter values (constants) and (iii) boundary conditions. Onsite measurement errors are dependent on the sensor type and installation conditions. Understanding errors is essential for generating the set of candidate models that predict measurement data. Previous work assumed an upper bound for absolute values of composite errors. In this paper, both modeling and measurement errors are characterized as random variables that follow probability distributions. Given error distributions, a new method to evaluate the reliability of identification is proposed. The new method defines thresholds at each measurement location. The threshold value pairs at measurement locations are dependent on the required reliability, characteristics of sensors used and modeling errors. A model is classified as a candidate model if the difference between prediction and measurement at each location is between the designated threshold values. A timber beam simulation is used as example to illustrate the new methodology. Generation of candidate models using the new objective function is demonstrated. Results show that the proposed methodology allows engineers to statistically evaluate the performance of system identification.