Nonlinear Regression Analysis by Global Optimization: A Case Study in Space Engineering
The search for a better understanding of complex systems calls for quantitative model development. Within this development process, model fitting to observational data (calibration) often plays an important role. Traditionally, local optimization techniqu
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Abstract The search for a better understanding of complex systems calls for quantitative model development. Within this development process, model fitting to observational data (calibration) often plays an important role. Traditionally, local optimization techniques have been applied to solve nonlinear (as well as linear) model calibration problems numerically: the limitations of such approaches in the nonlinear context—due to their local search scope—are well known. In order to properly address this issue, global optimization strategies can be used to find (in practice, to approximate) the best possible model parameterization. This work discusses an application of nonlinear regression model development and calibration in the context of space engineering. We study a scientific instrument, installed onboard of the International Space Station and aimed at studying the Sun’s effect on the Earth’s atmosphere. A complex sensor temperature monitoring objective has motivated the adoption of an ad hoc calibration methodology. Due to the apparent non-convexity of the underlying regression model, a global optimization approach has been implemented: the LGO software package is used to carry out the numerical optimization required periodically for each stage of the analysis. We report computational performance results and offer related insight. Our case study shows the robust and efficient performance of the global scope model calibration approach.
J.D. Pintér () Lehigh University, Bethlehem, PA, USA PCS Inc., Halifax, NS, Canada e-mail: [email protected]; [email protected] A. Castellazzo • M. Vola Altran Italia S.p.A., Consultant c/o Thales Alenia Space Italia S.p.A., Turin, Italy e-mail: [email protected]; [email protected] G. Fasano Exploration and Science, Thales Alenia Space, Turin, Italy © Springer International Publishing Switzerland 2016 G. Fasano, J.D. Pintér (eds.), Space Engineering, Springer Optimization and Its Applications 114, DOI 10.1007/978-3-319-41508-6_11
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Keywords Regression analysis • Nonlinear model fitting to data • Global optimization • Space engineering applications • Composite periodic functions • Trend analysis • Failure detection
MSC Classification (2000): 62J02, 90C26, 90C30, 90C90, 90-02, 90-08
1 Introduction Regression analysis [1–7] is an important subject across a broad range of studies in econometrics, engineering, and the sciences. Nonlinear regression is a general framework for regression analysis in which the observational data are modeled by a postulated nonlinear function: this function is then parameterized according to a stated optimality criterion. A quick Internet search for the key words “Nonlinear Regression” returns close to 2,700,000 results (as of March 2016, using Google’s search engine), clearly indicating a substantial interest towards the subject. The most frequently used classical optimization method to find the parameters of a nonlinear regression model (based on the minimization of the corresponding least sq
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