Establishment of artificial neural network for suspension spring fatigue life prediction using strain and acceleration data

Abstract

This study presents establishment of multiple input prediction model for automotive coil spring fatigue life estimation to shorten automotive suspension design process. Automotive suspension design is a lengthy work where any changes of the design lead to repetition of the entire process. It was hypothesised that the established model could be used to predict the spring design fatigue life without using any strain measurements. To initiate this model establishment, five sets of strain and acceleration measurement across different road conditions were collected and used for validations. To include spring stiffness as a parameter, a quarter car model was generated to obtain the force time histories from spring and vertical vibration of vehicle mass. In addition, artificial road profiles of road classes “A” to “D” were also generated for the quarter car simulation. Through adjusting the spring stiffness in the quarter car model, the spring and vehicle responses were varied. The simulated force time histories were used to predict springs’ fatigue life while acceleration time histories were used to calculate ISO 2631 ride-related vertical vibration. Subsequently, multiple linear regression approach was applied to determine the relationship between vehicle body frequency, ISO 2631 ride-related vertical vibration and spring fatigue life. The obtained regression had shown significance to the spring fatigue life with coefficient of determination of 0.8320. Reciprocally, multiple linear regression models were also used to predict the ISO 2631 ride-related vertical vibration with a coefficient of determination at 0.8810 and mean squared error values below 0.3430. To optimise the prediction results, artificial neural network was trained for the fatigue and vibration prediction purposes. The architectures of the artificial neural network were designed in terms of number of neurons and hidden layers to achieve a higher coefficient of determination of 0.9926 and lower mean squared error of 0.0824. For vibration prediction, the vehicle body frequency and spring fatigue life has shown a significant coefficient of determination to the ISO 2631 weighted vertical vibration, reaching 0.9579 with mean squared error of 0.0004. Based on the experimental strain and acceleration results, the predicted fatigue lives of multiple linear regression models were correlated well with the experimental results with coefficient of determination value of 0.9275. Meanwhile, the maximum difference of vibration prediction to experimental value using multiple linear regression models was only 18%. For artificial neural network predictions, the fatigue lives were mostly distributed within 1:2 or 2:1 life correlation and vibration prediction results were within 12%. For a good prediction, the target correlation value was above 0.80 to demonstrate a good fitted curve and the difference below 20%. The trained artificial neural network has shown outstanding capability in fatigue life or ride-related vertical vibration predictions. In this research, the main novelty was the trained artificial neural network for spring fatigue life or ride-related vertical vibration predictions which serve to reduce some procedures of automotive suspension design. The outcome of this study can be used to provide a new knowledge towards the field of fatigue research as well as vehicle ride dynamics. This research contributes to automotive industries especially in suspension spring design where the analysis of fatigue and ride-related vibration are provided.