The shock absorber of a vehicle is not only needed for a comfortable driving experience, but it is also essential for vehicle safety. Especially in autonomous driving, vehicles must monitor themselves and schedule maintenance before a component fails. In this work, we develop a methodology to predict the degradation of a shock absorber using machine learning methods and perform predictive maintenance recommendations. In the first step, we learn the damping coeficient from acceleration data using a neural network. Afterward, we extrapolate this value to predict future behavior. For this, we use the concept of operational design domains to formalize the point up until vehicle functionality is unrestricted and there is no risk to vehicle safety.
work appropriately. Our research addresses the suspension systems and especially the shock absorbers of a car. The health monitoring task provides the current state within the ODD of the shock absorber, while the predictive maintenance task estimates degradation by predicting violations of the ODD specification. This leads to a timely call for maintenance.
Various shock absorber models have been studied in the past. In [
In [
Absorbers
Most predictive maintenance methods work according to the same scheme [15]. In the first step,
sensor data from the vehicle is acquired and pre-processed. Then, the health indicator (HI) of
the vehicle is determined. The HI represents the current condition of the shock absorber. Based
on this, we make a rest of useful life (RUL) prediction. If the HI describes the temporal position
of the shock absorber within the ODD, the RUL is a metric between the current HI and the
boundary of the ODD, i.e., RUL() := (HI(), ODD). We then utilize the estimated RUL
to make a predictive maintenance recommendation. In our simulation, we use the quarter car
model [16]. The basic assumption is that the weight of the car is distributed equally among
the four wheels. We can then describe the vertical dynamics by a system of partial diferential
equations. For the street model, we use road data captured by a LIDAR scanner from [17] and
extract several street profiles (Figure 1).
in the number of full cycles of the shock absorber, i.e., maximal deflections for some constants
, , ∈ R. Let denote the damping coeficient value, for which we assume that the component
can no longer safely perform its actual functionality. The corresponding ODD is then given
as ODD = {︀ ⃒⃒ () ≥ }︀ and its boundary ODD = {︀ ⃒⃒ () = }︀ . Then, using the
OpenODD notation [
}︃ − , 0 .
(1) (2) Hence, for a RUL prediction, it is suficient to estimate , , . For our example of a predictive maintenance recommendation, we use the following procedure (Figure 2). At first, we collect vertical acceleration data for the shock absorber model, which can be assumed to be measured by vehicle sensors.
() { ()| ≤ } , , Vehicle
Neural Network
Feature Store
RUL prediction
Predictive Maintenance recommendation In our simulation environment, we generate this data by solving the quarter-car model for a randomly selected road using a given data set with decreasing damping values over time. Our implementation uses an Euler method [19] to solve the model for a defined input signal . The resulting signal values are transmitted to the cloud. Afterward, the signal is transmitted to a neural network , with parameters , that estimates the current damping coeficient () ≈ (). The network is trained on simulated data of possible roads with diferent damping coeficients and has learned to interpolate the space of possible damping coeficient values on the known roads. The past determined values for the damping coeficient represent the degradation of the shock absorber. Each time a new damping value is estimated, a new model is fitted to this data that describes the decrease in the damping coeficient by solving the minimization problem
min ∑︁ (︁ ,, =0
︁) 2 + ︁) − () , (3) that we get from comparing the estimated damping coeficients to the general form given in (1). After estimating the parameters, we use them to determine the future behavior. Then, we can check whether this determined value still lies in the ODD and whether to give a predictive maintenance recommendation.
We use a ResNet18 network [20] for determining the damping coeficient, which achieves an average error of 5.67 on test data with values between 1400 and 1000. For now, we use the mean squared error as training loss. In the future, we also want to test loss functionals that penalize too-high determined damping constants more than too-low ones. In this way, we want to ensure that predictive maintenance recommendations are issued too early rather than too late since we consider a safety-critical domain. For solving the optimization problem in (3) we use the BFGS algorithm (Figure 3). In some of our experiments, a problem occurs when the algorithm gets stuck in a local minimum such as a horizontal best-fit line. In future work, we want to solve this problem by additional regularization terms. In this paper, we assumed that the degradation depends only on the time steps but not the street profile. In future work, we also want to include the absorbed energy by the shock absorber in our degradation model. In our example, we have considered a fixed number of road profiles and used a neural network to interpolate the space of possible damping coeficients on this limited set. Later we want to examine an extended pipeline able to estimate the degradation for roads that are not part of the training data within a realistic vehicle simulator [21]. All in all, we have demonstrated a way to denote the RUL of a shock absorber as a metric to the ODD boundary and estimate it through machine learning. In conclusion, Figure 3: Predicting Damping Coefian eficient estimation of the damping coeficient opens cients many possible use cases. Risk, Maintenance, and Safety Engineering (QR2MSE), IEEE, 2013, pp. 1762–1764. doi:10. 1109/QR2MSE.2013.6625917. [15] G. Xu, M. Liu, J. Wang, Y. Ma, J. Wang, F. Li, W. Shen, Data-Driven Fault Diagnostics and Prognostics for Predictive Maintenance: A Brief Overview, in: 2019 IEEE 15th International Conference on Automation Science and Engineering (CASE), IEEE, 2019, pp. 103–108. doi:10.1109/COASE.2019.8843068. [16] M. Mitschke, H. Wallentowitz, Dynamik der Kraftfahrzeuge, VDI, 4., neubearb. aufl. ed., Springer, Berlin and Heidelberg, 2004. URL: http://digitale-objekte.hbz-nrw.de/webclient/ DeliveryManager?pid=1493716&custom_att_2=simple_viewer. [17] M. Kane, A 3d texture dataset of 27 km road, Data in Brief 35 (2021) 106855. URL: https://www.sciencedirect.com/science/article/pii/S2352340921001396. doi:10.1016/j. dib.2021.106855. [18] X. Yao, M. Pecht, Performance Degradation of Hydraulic Vehicle Dampers, 2018 Prognostics and System Health Management Conference (PHM-Chongqing) (2018). [19] P. Balzer, Dynamik eines Viertelfahrzeugs, 2011. URL: https://www.cbcity.de/ dynamik-eines-viertelfahrzeugs. [20] K. He, X. Zhang, S. Ren, J. Sun, Deep residual learning for image recognition, 2015. URL: https://arxiv.org/pdf/1512.03385. [21] A. Dosovitskiy, G. Ros, F. Codevilla, A. Lopez, V. Koltun, CARLA: An Open Urban Driving Simulator, 2017. URL: https://arxiv.org/pdf/1711.03938.