Data-driven parametric optimization for pre-calibration of internal combustion engine controls

This paper presents an efficient pre-calibration method for combustion engine controls. In particular, it focuses on the initial shaping of multiple Lookup Tables (LUTs) within LUT-based Multiple-Input Single-Output (MISO) engine control systems. The approach addresses the increasing complexity of engine software, the rising number of calibration variables, and the time pressures prevalent in automotive development. Employing a white-box Model-in-the-Loop (MiL) optimization reduces the demands on hardware reliance and optimization time compared to conventional engine calibration techniques. The white-box model enables the pre-calibration of LUTs using known system inputs, expected system outputs, and the control system model structure. To optimize the white-box control system model, LUTs are parametrized through Rational Bézier Regression (RBR), facilitating Sequential Quadratic Programming (SQP) for optimization. RBR, which includes both Rational Bézier Curve Regression (RBCR) and Rational Bézier Surface Regression (RBSR), allows for flexible and smooth shaping of 1D and 2D LUTs with a unified and few number of parameters. The pre-calibration process is further improved using historical calibration data from various vehicle variants stored in a relational database. This ensures that the final outputs of the LUT-based MISO control system closely approximate the expected target outputs with high shape similarity. The proposed method is exemplified using an oil temperature control model from a state-of-the-art hybrid powertrain with an internal combustion engine. The results demonstrate Pearson Correlation Coefficients (PCCs) exceeding 0.8 between target and pre-calibrated LUTs, indicative of high shape similarity. Additionally, the system outputs of pre-calibrated control system models closely match expected system outputs with an $R^2$ value of $0.9385$. This underscores the practical applicability of the proposed pre-calibration method for internal combustion engine controls.