Statistical Adjustment and Calibration of Complex Systems considering Multiple Outputs: Case Study of Laser-Assisted Micromachining Process

Document Type : Article


1 PhD Candidate, Industrial engineering, K. N. Toosi Technical university, Tehran, Iran

2 Dept. of Industrial Engineering, K.N. Toosi University of Technology

3 Department of Industrial Engineering, Assistant Professor of K. N. Toosi University,


By rapid advancements in technologies, studying and simulating a complex system with uncertain parameters is too demanding. Based on the literature, there are three approaches to identify and simulate different systems: engineering, statistical, and engineering-statistical approaches. The purpose of this study is to apply the engineering-statistical approach to calibration and adjustment of a Laser Assisted Micro-Machining (LAMM) process with two correlated outputs which are basically known as cutting and thrust forces. This paper contributes to the existing literature by extending the most relevant approach of the calibration of single-output complicated processes to multi-output settings where discrepancy function is modeled by a multivariate Gaussian process and multivariate analysis of variance is used to identify variables whose adjustment benefits the most. For the best case reported in previous studies, Mean Squared Prediction Error (MSPE), as the comparison index, was reported around 1.48 for thrust force whereas the proposed approach resulted in a better value of 1.9425×10-4. Moreover, for cutting force output, the index was obtained as 0.21 by the Kennedy and O’Hagan, 1.41 by Roshan and Yan, and 1.6×10-8 by the presented model. These values demonstrate reasonable and comparable results for the MSPE, in comparison with the models considering the outputs individually.