Performance Based Track Geometry Phase 2 (2015)

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C H A P T E R 3 Findings and Application 3.1 Model Validation A NUCARS model was built to represent the PATH PA5 car, using design data updated by the measured characteristics. The model included a full nonlinear representation of the air suspension, including the effects of damping due to air flow in the orifices between the reservoirs and airbags. The measured track geometry was used as input to the model. A simulation of the same conditions as the ride quality test was done to determine if the model accurately predicted the vehicle performance. Figures 33 and 34 compare the acceleration test data and modeling results for the section of track between Harrison and Journal Square stations. The plots show data collected on the floor in the driver’s cab. In the NUCARS model, representative wheel and rail profiles were used. The NUCARS model predicted the same general trends as the actual measurement data. Figure 33 shows vertical accelerations. The trends and amplitudes are similar between test data and modeling results. The difference in amplitudes may be due to the damping in the system. In the model, vertical dampers were assumed to be in new condition, and the damping properties were those provided by the damper manufacturer. The actual dampers on the car were not tested. This may contribute to the under prediction of vertical accelerations. Figure 34 shows lateral accelerations. The model predicts the same trend as the test data; however, the magnitude is under predicted. The small differences in the magnitude may be due to the difference in the actual rail profiles and what was used in the simulation. A representative rail profile was used in the simulations. Wheel/rail interaction affects the lateral response of the car. Figures 35 and 36 show the frequency content of the model and test data. Both the model and the test had a response similar frequency content for both lateral and vertical accelerations. 30

Figure 33. Measured Vertical Accelerations Compared with Predicted Vertical Accelerations -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 22,000 Dr iv er 's Ca b Ve rt ic al A cc el er at io ns (g 's) Distance (ft) Test-Vertical Model-Vertical 31

Figure 34. Measured Lateral Accelerations Compared to Predicted Lateral Accelerations -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 22,000 Dr iv er 's Ca b La te ra l A cc el er at io ns (g 's) Distance (ft) Test-Lateral Model-Lateral 32

Figure 35. Measured Vertical Acceleration Frequency Content Compared with Predicted Frequency Content Figure 36. Measured Lateral Acceleration Frequency Content Compared with Predicted Frequency Content 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0 1 2 3 4 5 6 7 8 9 10 M ag ni tu de Frequency (Hz) Test-Cab-Vertical Model-Cab-Vertical 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0 1 2 3 4 5 6 7 8 9 10 M ag ni tu de Frequency (Hz) Test-Cab-Lateral Model-Cab-Lateral 33

3.2 Neural Net Development A complex dynamic relationship exists between vehicle response and track geometry. PBTG inspection emphasizes that car dynamic response directly results from a combination of many track geometry variables acting together with vehicle operating conditions. Unwanted vehicle responses do not always result from individual track geometry defects, but from the dynamic interaction of the vehicle with all the track geometry parameters in the track segment where the unwanted response occurs. Use of NNs in the PBTG system allows all track geometry parameters and vehicle operating conditions to be related to vehicle performance. NNs, such as the ones built under this task, are networks of artificial neurons or nodes consisting of many input paths and one output path. Figure 37 shows a simplified architecture of a NN. Figure 37. NN Schematic The nodes in NNs can be connected in many ways. In this study, the architecture used to connect the nodes is multilayer perceptron (MLP). It consists of an input layer, two hidden layers, and an output layer. The input signal propagates through the network in a forward direction. To train an MLP, a back-propagation algorithm is used and is based on the error-correction learning rule. The rule applies forward passes and backward passes through all the network layers. In the forward pass, an input vector is applied to the nodes of the network, and the effect from applying that input vector propagates through the NN layers. Thus, an output is produced as an actual 34

response of the network. If the network response is not adequately close to the desired response, a backward pass is used and the NN weights are iteratively adjusted based on an error-correction rule to fine-tune the response in order to move it closer to the desired response. In addition, the number of nodes in the NN hidden layers is determined by the cascade learning method. In this method, one or more hidden nodes are added at a time until performance on an independent test set within the NN shows no additional improvement The NNs are trained to learn and recognize patterns and relationships in vehicle/track interaction data. Once a NN is trained for a specific vehicle, it acquires the aptitude to predict the dynamic response of that particular vehicle. As a result, track segments that induce unwanted vehicle response can be identified. Two approaches were used to building the NNs: • Point-by-point approach aligns the track geometry data with the measured vehicle response based on 1-foot increments. • Segment-based approach uses the variable statistics, such as maximum, minimum, standard deviations and averages, from a 150-foot-long segment of track geometry. This information is related to the vehicle response over that segment of track. 3.2.1 DART NN Development The NN was first developed under Phase 1 of this project, using a DART vehicle model and track geometry collected on the DART system in August 2010 to train the NNs.6 Alignment, surface, gage, curvature, and superelevation were used. Operational speeds from the ride quality tests were also used in the NN training. Carbody and axle accelerations measured during the ride quality test in August 2010 were used to train and determine the effectiveness of the NNs to predict ride quality. The first task was to align the track geometry and vehicle response data. The vehicle response data was shifted to align with the track geometry data. The location of the accelerometer, speed of vehicle, and a visual tool were used to align the data. Figure 38 shows the data before and after alignment. 6 Ketchum, C. and N. Wilson. TCRP Web-only Document 52: Performance Based Track Geometry Phase 1. Transportation Research Board of the National Academies, 2012. http://onlinepubs.trb.org/onlinepubs/tcrp/tcrp_w52.pdf 35

Figure 38. DART – Alignment of Ride Quality Data and Track Geometry Data The NNs were trained using a portion of the measured ride quality data. The trained NNs were then deployed to predict ride quality on a section of track not seen by them. This information is called validation data. It is an indicator of the accuracy of the trained NNs to predict ride quality for the DART SLRV on the DART red line. Figure 39 shows a NN trained using the point-by-point approach on data collected between Walnut Hill and Forest Lane Stations. The blue line represents the lateral accelerations measured under the operator’s seat at the A-end of the car. The red line represents the predicted accelerations from the training data. Before Completing Alignment After Completing Alignment Before Co pleting Alignment After Completing Alignment 36

Figure 39. DART – Neural Net Training Data for Point-by-Point Approach Figure 40 shows the trained NN deployed on LBJ station to Spring Valley Stations track geometry for validation. The NN predicted the lateral accelerations with 0.1 percent confidence. The NN model performed very poorly on the validation data, although it performed satisfactorily on the training data. Figure 40. DART – Point-by-Point Approach deployed on LBJ to Spring Valley Station Data Training Data ACTUAL PREDICTED ACTUAL PREDICTED 37

Figure 41 shows NN training and validation data using a segment-based approach. The NN predicted the carbody vertical accelerations with 0.25 percent confidence. This NN model, too, presented a poor predictive performance on the validation data. Figure 41. DART – Segment-based Approach deployed on LBJ to Spring Valley Station Data Both models displayed a case of what is known as “overfitting,” meaning, the NN models learned just to memorize the training data, but were unable to generalize from trending patterns present in the validation data. Lacking high dynamic events in the training data (and validation data as well), the data used to build the models may have been seen as patternless noise during the NN training process, which NN models tend not to recognize. From past experience, NN model performance would have been better if training data had contained a wide range of significant track geometry deviations and corresponding high dynamic events in terms of accelerations. 3.2.2 PATH NN Development Data was selected and processed to build a synchronized database of ride quality and track geometry. The data was comprised of dynamic response of the PATH PA5 car to wide-ranging track and operating conditions. The database was used to build NN algorithms that relate the track geometry conditions to the likely ride quality accelerations of the PA5 car. The segment-based approach was used in this effort. Variable statistics, such as maximum, minimum, standard deviations and averages, from a 150-foot-long segment of track geometry were utilized the build the NN models. The following variables were used as input for developing the NNs: • Track alignment • Track surface • Gage • Curve and Superelevation • Operating speed • Centrifugal force (synthetic channel) created from curvature and speed ACTUAL PREDICTED 38

Carbody accelerations were the output variables the NN models were trained to predict. Figure 42 shows an example of a predicted front carbody vertical acceleration (in red) versus actual data (in blue). The validation data, as shown in the graph, is deployment data that was not used during the NN training. The correlation coefficient of 81 percent measured the strength of association between the NN predictions and actual response. Figures 43 and 44 show predicted carbody center and driver cab accelerations versus actual data. The correlation coefficients were 78 and 71 percent, respectively. Figure 42. PATH Training and Validation Data at Front Carbody Acceleration Ve rt ic al C ar bo dy A cc el er at io n (g ’s ) 1.2 1.1 0.8 0.6 0.4 0.2 0 ACTUAL PREDICTED 39

Figure 43. PATH Training and Validation Data at Center Carbody Acceleration Figure 44. PATH Training and Validation Data at Driver Cab Carbody Acceleration The predictions of these preliminary NN models were adequate and represent a significant improvement in comparison with the NN models built using the DART data, because of the following conditions: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 5 105 205 305 405 505 605 Dr iv er C ab V er tic al A cc el er at io n (g 's) Driver Cab Vert Predicted Training Validation Training Ve rt ic al C ar bo dy C en te r A cc el er at io n (g ’s ) ACTUAL PREDICTED ACTUAL PREDICTED 40

• More track geometry deviations trends and corresponding high dynamic responses were present in the data collected on PATH tracks • Geometry deviations and high dynamic responses are patterns that NN models are capable of recognizing reasonably well if available in the training data. By contrast, good track conditions and low dynamic response are seen as patternless noise that the NNs tend not to recognize the trends or the patterns. 41