**2. Method**

## *2.1. Data Collection*

The data used in this study were collected from ride comfort evaluations by an automotive manufacturer. In the test, a vehicle was driven at 30 km/h on a road with a speed bump, as shown in Figure 2. The test vehicle was a small sedan with several sensors. Accelerometers were installed at several positions of the vehicle to measure three-dimensional accelerations at those positions. Gyroscopes were also installed at several positions to measure three-dimensional angular rates. The front and rear dampers had three adjustable settings: hard, medium, and soft. A professional test driver evaluated the vehicle with nine combinations of dampers.

The subjective rating was reported in the form of absolute ratings defined in SAE J1441 [31], which are presented in Table 1. The ratings given by the test driver are shown in Table 2. The test driver evaluated the ride comfort in two categories: primary ride and impact comfort. Fractional expressions

were used to obtain a finer resolution, which were transformed to numbers; for example, "6+" was changed to 6.33, "6+ to 7" was changed to 6.5, and "6 to 6+" was changed to 6.16.

**Figure 2.** Ride comfort evaluation on a road with a speed bump.


**Table 1.** Subjective rating scale.

Most ride issues were disturbance events, while most handling issues were control events.


**Table 2.** Subjective evaluation results of ride comfort.

H, M, and S stand for hard, medium, and soft, respectively.

The objective data were collected using several sensors and included the velocities, accelerations, and forces at several positions on the test vehicles. A total of 120 types of sensor signals were collected. The driver kept the speed at 30 km/h as much as possible to avoid disturbances from speed differences. The test driver drove the vehicle multiple times for each damper setting, and four sets of objective data were collected for each setting. Therefore, the total number of datasets was 36.

#### *2.2. Ride Comfort Evaluation Model*

The basic concept of the model is as follows. First, an image was created by combining the spectrograms of measured signals, and then gram matrices were extracted from the image as numerical representations of ride comfort. An artificial neural network was then trained to find a relationship between the numerical representations and the subjective ratings. Based on this concept, we designed a model structure to predict the difference of the subjective ratings between two vehicles rather than predicting the absolute rating of ride comfort, as shown in Figure 3. A comparative model was designed to increase the number of training datasets.

**Figure 3.** Structure of ride comfort evaluation model. VGG: Visual Geometry Group.

Two artificial neural networks were used in the model: one for extracting a numerical representation of the ride comfort and another for the correlation model between the extracted numerical representation and the subjective ratings. Extracting ride comfort did not require any datasets for training because the extraction was performed by a pre-trained convolutional neural network (CNN). However, building the correlation model required datasets for training. The 36 datasets collected were not sufficient. We designed a comparative model to increase the number of training sets. The input was the difference between the numerical representations of ride comfort that were extracted from the measurements of two vehicles, and the output was the difference between the vehicles' subjective ratings.

#### 2.2.1. Extraction of Ride Comfort from Measurements

Instead, the style was implicitly defined in the pre-trained network. The numerical representation of the style of an image is a set of gram matrices, [*G*1, *G*2, ···, *G*16], of the filter responses in the layers of VGG-19, as shown in Figure 4. Each layer produces an abstract concept of the image. In the CNN, each layer further abstracts the pixel representations of the image.

**Figure 4.** Extracting a numerical representation of ride comfort based on the ideas of the artistic style transfer algorithm. The network input is an image transformed from the measured temporal data.

The algorithm uses the filter responses at all layers as a representation of the contents of the original image. The gram matrices of the filter responses of all layers are used as a representation of the artistic style of the original image. The content and style are separate, and the data dimensions of the content and style are larger than the dimensions of the original image because they are expressed with several levels of abstraction. Using the same method, the gram matrices of the filter responses of all layers were extracted as a numerical representation of the style or feel of ride comfort. Extraction of the ride comfort did not require any modification of the networks. The only di fference between the extraction of ride comfort and the extraction of the artistic style of an image was the nature of the input data. The input to the former was the measured temporal data, and the input to the latter was spatial data or an image. The temporal data were transformed into an image to use the pre-trained CNN without re-training the network.

#### 2.2.2. Preprocessing Input Data

A spectrogram of the temporal data was used to transform it into an image. Sometimes called a color map, a spectrogram is a visual representation of the spectrum of frequencies of a temporal signal as it varies with time. It e ffectively shows signal patterns in both the frequency domain and the time domain simultaneously. Most objective metrics for ride comfort are defined using characteristics in the frequency domain or in the time domain, which makes a spectrogram a good visual representation of the possible metrics of ride comfort.

Another issue in the transformation of the temporal data is that multiple spectrograms are generated from the temporal data because the data are a set of signals. A single image was input to the VGG-19 network, and thus multiple spectrogram images must be combined to feed them to the network. As shown in Figure 5, the spectrogram images were stacked line by line to strengthen the spectral and temporal correlations of the input data. Before the transformation, all signals were normalized so that the ranges of the values were between −1 and 1. Furthermore, the spectrograms were clipped along the frequency axis to remove the signal noise and bias.

**Figure 5.** Preprocessing input data. Raw measured signals were transformed into an image for input.

#### 2.2.3. Vector of Ride Comfort Difference

Once the numerical representation of ride comfort was extracted, a neural network could be built to map from the numerical representation, [*G*1, *G*2, ···, *G*16], to the subjective rating. The output of the comparative model was the difference between the subjective ratings of two vehicles, and the input was the difference between the two numerical representations of the two vehicles. The set of norms of the gram matrix difference was defined as a vector of the ride comfort difference, as shown in Figure 6. This approach expanded the number of training sets from 36 to 36C2 = 630, as shown in Figure 7.

**Figure 6.** Comparative model of ride comfort. The output was a vector of the ride comfort difference. If the vector was a zero vector, the two vehicles had an identical ride comfort.

**Figure 7.** Expansion of datasets for model training.

#### 2.2.4. Comparative Model of Ride Comfort

We designed a neural network for the correlation between the vector of ride comfort difference and the subjective rating difference. The network had eight fully connected hidden layers, as shown in Figure 8. The last hidden layer was designed for the visualization of the results with two nodes, *x*1 and *x*2.

**Figure 8.** Correlation networks from the vector of ride comfort difference to the subjective rating difference. The neural network was composed of eight fully connected layers.

#### **3. Results and Discussion**

For both the primary ride comfort and impact comfort, 500 out of 630 datasets were used for training, and 130 sets were used for testing. Seven measured signals were used as the input data. The signals were the front-wheel damping force, rear-wheel damping force, vertical acceleration of the center of gravity, vertical acceleration of the left seat rail, vertical acceleration of the right seat rail, pitch, and pitch rate.

For the primary ride comfort, the root mean square error (RMSE) for training was 0.0049, and that of the test was 0.0465. For impact comfort, the RMSE for training was 0.0040, and that of the test was 0.071. The RMSEs of previously reported correlation models for the objectification of subjective evaluation were in the range of 0.1 to 0.7 [13,17,20,27]. One possible reason for the higher accuracy of the proposed method was the use of a CNN that enabled rich feature extraction without the predefinition of features. Another reason was the use of a neural network for the correlation between the vector of ride comfort difference and the subjective rating difference.

In Figure 9, the trained models for primary ride comfort and impact comfort were plotted as functions of *x*1 and *x*2, which were the node values of the last hidden layer. *x*1 predominantly affected the primary ride comfort, whereas *x*2 predominantly affected the ride comfort during impact. These models predicted how much the ride comfort differed between two given vehicles but did not give any information about which vehicle had the better ride comfort. One possible way to overcome this limitation was by comparing the ride comfort of a vehicle to that of another vehicle that had the lowest subjective rating.

In our data, the vehicle with the lowest rating was the one with the H/S damper setting. Figure 10a shows the result of the comparison to this vehicle. A result farther from the origin indicated a better ride comfort. A similar model could also be extracted using the vehicle with the highest subjective rating, as shown in Figure 10b. The vehicle with the highest ride comfort was the one with the M/H damper setting. In this case, a closer result to the origin meant a better ride comfort.

**Figure 9.** Three-dimensional view of the comparative models. The data points on the model were from test dataset. (**a**) Primary ride comfort (**b**) Impact ride comfort.

**Figure 10.** Comparative model (**a**) with respect to a vehicle with the lowest rating of ride comfort and (**b**) with respect to a vehicle with the highest rating of ride comfort.

#### **4. Case Study for Use of the Correlation Model**

#### *Sensitivity Evaluation of Signal Changes to Ride Comfort*

One useful application for this method is evaluating the sensitivity of the ride comfort rating to changes in the measured signals. The proposed model represented mapping functions from measured signals or vehicle dynamic states to subjective ratings. This model could tell what kinds of dynamic responses are beneficial for good ride comfort.

As examples of sensitivity analyses, we synthesized signals of the pitch angle and vertical acceleration, which were the most representative signals for primary ride comfort. Pitch angle variations that remained for a long time after passing over a speed bump negatively affected ride comfort. We synthesized the pitch angle signal such that it would decay faster after a speed bump. This signal change seemed to help improve primary ride comfort, as shown in Figure 11. The comparative model based on the worst-rated vehicle predicted a low correlation between this change and the ride comfort, but the comparative model based on the best-rated vehicle predicted a positive relationship.

**Figure 11.** Ride comfort rating with respect to pitch decay rate change.

We performed a similar analysis with the vertical acceleration at the seat rail position. The vertical acceleration was synthesized to have a small magnitude reduction after passing over the bump, as shown in Figure 12. Both comparative models predicted no significant change in the primary ride comfort.

**Figure 12.** Ride comfort rating with respect to vertical acceleration change.

In the last case study, an analysis was performed on the reduction of the phase difference between the pitch rate and vertical acceleration at the center of gravity. When the phase difference was reduced, both comparative models predicted a significant improvement in the ride comfort, as shown in Figure 13. Other examples are shown in Table 3, which demonstrate that the proposed model could be used to identify the designed signal patterns without doing additional expensive experiments. Once the desired signal patterns were identified, tuning could be performed to improve the ride comfort in the early design stages if a simulation of a vehicle model with a high fidelity was available, as shown in Figure 14.


**Table 3.** Subjective evaluation of the ride comfort in a speed bump test.

**Figure 13.** Ride comfort rating with respect to the change of phase difference between the pitch rate and vertical acceleration.

**Figure 14.** Possible use of evaluation model in vehicle design.
