Retrieving Interpretability to Support Vector Machine Regression Models in Dynamic System Identification

Johan Pena-Campos^1,2*Diego Patino²Carlos Ocampo-Martinez³Julio C. Ramos-Fernández⁴Margot Salas-Brown⁵Alexander Caicedo^2,6

• ¹Automatic Control Department (ESAII), Universitat Politecnica de Catalunya, Barcelona, Spain
• ²Faculty of Engineering, Pontifical Javeriana University, Bogotá, Colombia
• ³Universitat Politecnica de Catalunya, Barcelona, Spain
• ⁴Universidad Distrital Francisco Jose de Caldas, Bogotá, Colombia
• ⁵Universidad Sergio Arboleda, Bogotá, Colombia
• ⁶Ressolve S.A.S., Bogotá, Colombia

Black-box models are commonly used to identify dynamic systems. However, due to their nature, it is difficult to understand how each input variable contributes to the model output. Therefore, interpretability of black-box models has recently gained attention in the community. This paper proposes an algorithm to decompose the output of an already identified nonlinear system. The algorithm uses a support vector machine (SVM) regression, and it decomposes the model output into a sum of nonlinear contributions of the inputs regressors using nonlinear oblique subspace projections (NObSP). Each component of the decomposition represents the partial (non)linear contribution of each input variable on the output. This paper presents an extension of NObSP for dynamic systems and an out-of-sample extension in which the computational complexity is reduced from the original NObSP. The arithmetic complexity for the original NObSP is changed from O N3 , being N the number of observations, to O Nd2 , where d is the number of support vectors. Several simulations were performed considering Wiener and Hammerstein structures of the system to identify. The numerical simulations indicate that NObSP is able to retrieve the partial nonlinear contribution of each input variable on the output, and the computational complexity of the method can be reduced.