Robust Leak Tests for Transmission Systems Using Nonlinear Mixed-E↵ect Models

Problem: Leakage of the transmission fluid or oil in powertrain systems (i.e., transmissions, cylinder heads, engine blocks, etc.) can cause engine overheating and/or permanent damage. Therefore, it is crucial to run a leak test to inspect for any possible porosity in the casting parts. However, the inspection results for the amount of leakage at given testing times are sensitive to the tested part’s temperature, which varies from part to part but was not previously incorporated in the leak testing systems. The objective of this paper is to develop a robust leak testing system that is insensitive to the part temperature variations in real production processes. Approach: In the production line, a part is tested at a temperature that is generally not equal to the calibration temperature at which the inspection threshold for leakage was set. To achieve a robust leak test that is insensitive to temperature variation in the tested part, we propose a temperature compensation algorithm to adjust the measured leak flow, taking into account the tested part temperature and the calibration temperature. For this purpose, a nonlinear mixed-e↵ect model is first developed for modeling the leak flow profile as a function of both the leak testing time and the part temperature. Then, the fitted mixed-e↵ect model is used to adjust the leak flow based on the calibration temperature. If the amount of the adjusted leakage at the given inspection time exceeds the inspection threshold, the part is rejected; otherwise, the part is accepted. Results: The proposed compensation algorithm is developed and validated using a set of training samples and another set of test samples, respectively. We use the percentage of error reduction in the leak flow measurements at di↵erent temperatures as the criterion to validate the developed compensation algorithm. The results show that the average percentage of error reduction for the test samples is about 92%. This indicates a significant improvement in the leak testing results.