**5. Discussion**

The best performing network architectures using frequency analysis input data (FFT and STFT) require a small size of the pooling layer as well as a small size of the receptive field. The extreme case of *e* = 1 and *p* = 1 even results in a simple scaling of the frequency analysis of each sensor signal and averaging across the data points of all sensor signals. The actual classification is performed in the fully connected layer using those averaged frequency analysis data points. This raises the question of whether a CNN is necessary or if a Multi-Layer Perceptron (MLP) neural network is sufficient for solving the classification task. Therefore, a MLP neural network consisting of only a fully connected layer with 128 neurons was trained using the FFT input data. The resulting classification accuracy on the test dataset was 87.27 %, 72.97 % on the mass dataset and 68.37 % on the tire dataset. This demonstrates that the convolutional operation adds robustness to the performance of the neural network.

While promising results for diagnosing defective dampers using Convolutional Neural Networks are presented in this paper, limitations for a real-world implementation still exist, which will be discussed in the following paragraphs.

There are only data of one specific vehicle used in this paper's investigations. All networks were trained and tested using data of this vehicle. Recording training data for every unique vehicle configuration with different damper defects during the development phase seems challenging for an actual implementation. Therefore, portability of a trained classification system with high generalization capabilities for the diagnosis of different vehicles is desirable.

Robustness is a critical aspect for a real-world application. Even though the network architectures showed a robust behavior for tire and mass variations, further robustness analysis is necessary because there is a grea<sup>t</sup> variety of different circumstances during the usage of a vehicle.

Real damper defects might not occur in a switching manner, but the loss of damping forces might increase gradually over a long period of time. A classification process for the damper's health state might therefore not detect a minor defect. This can be encountered in two ways: Adding additional

classes or predicting a continuous score for the health state of each damper. However, both approaches raise the need of additional training data.

## **6. Conclusions**

This paper analyzed the suitability of using Convolutional Neural Networks for the diagnosis of automotive damper defects using driving data of the longitudinal and lateral acceleration as well as yaw rate and wheel speeds. The classification performance using different pre-processing methods was analyzed. Using detrended time-signals as well as frequency analyses such as FFT or STFT showed the best results.

The analysis of the network architecture showed that the size of the receptive field and the size of the pooling layer needs to be chosen according to relevant oscillation frequencies of the input signal when using time-related detrended input data. The analysis of the trained kernel weights demonstrated that a frequency analysis is performed by the CNN for detrended time-signal input data.

Using FFT input data results in the overall best classification performance. A small size of the pooling layer performs best and the size of the receptive field can be chosen arbitrarily. The trained kernels perform a comparison of the amplitudes for several frequency differences.

Using STFT input data results in a similar classification performance as using FFT input data. The investigation of the trained kernels showed that the time information is not used by the CNN. Therefore, the STFT pre-processing does not result in any benefit. The reduced frequency resolution compared to a FFT pre-processing even decreased the robustness regarding unknown characteristics in the testing data such as additional mass or changed tires.

Table 3 shows the performance of the best network configurations of the three investigated pre-processing methods. The number of Floating Point Operations (FLOPs) for the execution of the model as well as the number of tuneable parameters are an indicator of the possibility of an implementation on the Electronic Control Unit (ECU) of a vehicle. However, since a specific value for the computing power of an automotive ECU cannot be found, the authors are not able to judge about the real-time implementation. The selected network configurations were chosen with regard to the performance of the three different datasets. The best classification accuracy results from using FFT input data with less network parameters than when using STFT input data.

The software and data of this paper are available online [53] (see the Supplementary Materials).


**Table 3.** Comparison of best performing network configurations

**Supplementary Materials:** The software and data is available online at [53]. https://github.com/TUMFTM/ Damper-Defect-Detection-Using-CNN/.

**Author Contributions:** T.Z. (corresponding author) initiated this paper. His contribution to the overall methodology of the proposed approach was essential and he performed the analyses presented in this paper. T.Z. supervised the master thesis of T.H.-P. who made essential contributions to the implementation of the proposed approaches. Both implemented this paper. M.L. made an essential contribution to the conception of the research project. He revised the paper critically for important intellectual content. M.L. gave final approval of the version to be published and agrees to all aspects of the work. As a guarantor, he accepts responsibility for the overall integrity of the paper. Conceptualization, T.Z.; methodology, T.Z. and T.H-P.; software, T.Z. and T.H-P.; validation, T.Z. and T.H-P.; formal analysis,T.Z. and T.H-P.; investigation, T.Z. and T.H-P.; resources, T.Z.; data curation, T.Z.; writing–original draft preparation, T.Z. and T.H-P.; writing–review and editing, T.Z.; visualization, T.Z. and T.H-P.; supervision, T.Z. and M.L.; project administration, T.Z.; funding acquisition, M.L. All authors have read and agreed to the published version of the manuscript.

*J. Sens. Actuator Netw.* **2020**, *9*, 8

**Funding:** The work described in this paper was supported by the basic research fund of the Institute of Automotive Technology from the Technical University of Munich. This work was supported by the German Research Foundation (DFG) and the Technical University of Munich (TUM) in the framework of the Open Access Publishing Program.

**Acknowledgments:** We would like to thank the vehicle manufacturer for supplying us with a research vehicle.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **Appendix A. Implementation Details**

The CNN were implemented in TensorFlow 1.9 using Python 3.5. During training, we use Adam optimizer [54] with a mini-batch size of 128. The optimizer minimizes the sum of a Sparse Softmax Cross Entropy plus the sum of weight decay (L2 regularization). Training is stopped after 650 epochs or if the accuracy with validation data has not significantly improved for 50 epochs (Early Stopping). Kernels and weights are initially set following He Initialization scheme [55] and the bias terms are initially set to a small constant (0.01). We use Rectified Linear Unit (ReLU) activation functions for every layer except for the output units, which are linear neurons.
