Prediction of Military Vehicle’s Drawbar Pull Based on an Improved Relevance Vector Machine and Real Vehicle Tests
"> Figure 1
<p>(<b>a</b>) Integrated data acquisition system; (<b>b</b>) Instrumented test vehicle.</p> "> Figure 2
<p>Effect of velocity on drawbar pull at various levels of vertical load, inflation pressure and slip ratio. (<b>a</b>) Slip ratio s = 0.2, inflation pressure Ip = 240 kPa; (<b>b</b>) Slip ratio s = 0.4, inflation pressure Ip = 340 kPa.</p> "> Figure 3
<p>Effect of vertical load on drawbar pull at various levels of inflation pressure and slip ratio. (<b>a</b>) Slip ratio s = 0.1; (<b>b</b>) Slip ratio s = 0.2; (<b>c</b>) Slip ratio s = 0.3; (<b>d</b>) Slip ratio s = 0.4; (<b>e</b>) Slip ratio s = 0.5; (<b>f</b>) Slip ratio s = 0.6.</p> "> Figure 4
<p>Drawbar pull with respect to vertical load.</p> "> Figure 5
<p>Effect of inflation pressure on drawbar pull at various levels of vertical load and slip ratio. (<b>a</b>) Slip ratio s = 0.1; (<b>b</b>) Slip ratio s = 0.2; (<b>c</b>) Slip ratio s = 0.3; (<b>d</b>) Slip ratio s = 0.4; (<b>e</b>) Slip ratio s = 0.5; (<b>f</b>) Slip ratio s = 0.6.</p> "> Figure 6
<p>Drawbar pull with respect to inflation pressure.</p> "> Figure 7
<p>Effect of slip ratio on the drawbar pull at various levels of vertical load and inflation pressure. (<b>a</b>) Inflation pressure Ip = 140 kPa; (<b>b</b>) Inflation pressure Ip = 240 kPa; (<b>c</b>) Inflation pressure Ip = 340 kPa.</p> "> Figure 7 Cont.
<p>Effect of slip ratio on the drawbar pull at various levels of vertical load and inflation pressure. (<b>a</b>) Inflation pressure Ip = 140 kPa; (<b>b</b>) Inflation pressure Ip = 240 kPa; (<b>c</b>) Inflation pressure Ip = 340 kPa.</p> "> Figure 8
<p>Drawbar pull with respect to slip ratio.</p> "> Figure 9
<p>Process of optimizing the RVM parameters with NDIWPSO.</p> "> Figure 10
<p>Schematic overview of the proposed RVM model.</p> "> Figure 11
<p>Prediction results of the three RVM model with three kernel functions on the training set and the testing set. (<b>a</b>) MkRVM on the training set; (<b>b</b>) MkRVM on the testing set; (<b>c</b>) GaussRVM on the training set; (<b>d</b>) GaussRVM on the testing set; (<b>e</b>) PolyRVM on the training set; (<b>f</b>) PolyRVM on the testing set.</p> "> Figure 12
<p>The comparison of the absolute percentage predictionerrors among the MkRVM, GaussRVM and PolyRVM.</p> "> Figure 13
<p>The comparison of correlation coefficient between measured Dp and predicted Dp from the MkRVM, GaussRVM and PolyRVM.</p> "> Figure 14
<p>Prediction results of the SVM model and GRNN model on the training set and the testing set. (<b>a</b>) SVM on the training set; (<b>b</b>) SVM on the testing set; (<b>c</b>) GRNN on the training set; (<b>d</b>) GRNN on the testing set.</p> "> Figure 15
<p>The comparison of the absolute percentage prediction errors among the MkRVM, SVM and GRNN.</p> "> Figure 16
<p>The comparison of correlation coefficient between measured Dp and predicted Dp from the MkRVM, SVM and GRNN.</p> "> Figure 17
<p>The comparison of the absolute percentage prediction errors between the MkRVM and Wong’s model.</p> "> Figure 18
<p>The comparison of correlation coefficient between measured Dp and predicted Dp from the MkRVM and Wong’s model.</p> ">
Abstract
:1. Introduction
2. Experimental Data Acquisition and Analysis
2.1. Dynamic Testing System
2.2. Test Procedures
2.3. Preliminary Experimental Data Analysis
2.3.1. Effect of Velocity on Drawbar Pull
2.3.2. Effect of Vertical Load on Drawbar Pull
2.3.3. Effect of Inflation Pressure on Drawbar Pull
2.3.4. Effect of Slip Ratio on Drawbar Pull
3. Methodology
3.1. Relevance Vector Machine
3.2. Multiple-Kernel RVM
3.3. Parameter Optimization of RVM Based on PSO
3.4. Satisfactory Criteria
4. Results and Discussion
5. Conclutions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Velocity V (m/s) | Vertical Load W (kN) | Inflation Pressure Ip (kPa) | Slip Ratio s |
---|---|---|---|
1.8 | 8 + 1 | 140 | 0.1 |
3.6 | 8 + 2 | 240 | 0.2 |
5.4 | 8 + 3 | 340 | 0.3 |
7.2 | 8 + 4 | - | 0.4 |
- | 8 + 5 | - | 0.5 |
- | - | - | 0.6 |
RVM Kernels | Training Set | Testing Set | ||||
---|---|---|---|---|---|---|
MAPE | RMSE(N) | R2 | MAPE | RMSE(N) | R2 | |
Mk | 14.70% | 22.94 | 0.9948 | 9.023% | 37.29 | 0.9961 |
Gauss | 19.96% | 25.01 | 0.9940 | 12.44% | 46.64 | 0.9956 |
Poly | 24.99% | 29.34 | 0.9916 | 13.97% | 52.03 | 0.9951 |
Models | Training Set | Testing Set | ||||
---|---|---|---|---|---|---|
MAPE | RMSE(N) | R2 | MAPE | RMSE(N) | R2 | |
MkRVM | 14.70% | 22.94 | 0.9948 | 9.023% | 37.29 | 0.9961 |
SVM | 17.43% | 24.08 | 0.9944 | 11.71% | 44.21 | 0.9962 |
GRNN | 48.91% | 49.50 | 0.9785 | 37.22% | 73.52 | 0.9804 |
Models | MkRVM | GaussRVM | PolyRVM | SVM | GRNN |
---|---|---|---|---|---|
Parameteroptimization | 342.7 s | 169.33 s | 181.14 s | 25.65 s | 2.945 s |
Training | 0.0607 s | 0.0667 s | 0.0522 s | 0.0092 s | 0.0295 s |
Testing | 0.000088 s | 0.000059 s | 0.000081 s | 0.00045 s | 0.0038 s |
Terrain Parameters | Vehicular Parameters | ||||||
---|---|---|---|---|---|---|---|
c(kPa) | Φ(°) | K(m) | n | kc(kN/mn+1) | kΦ(kN/mn+2) | D(m) | b(m) |
7.58 | 14 | 0.025 | 0.85 | 43.68 | 499.3 | 0.98 | 0.32 |
Models | Testing Set | ||
---|---|---|---|
MAPE | RMSE(N) | R2 | |
RVM | 9.023% | 37.29 | 0.9961 |
Wong | 23.91% | 61.54 | 0.9838 |
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Yang, F.; Sun, W.; Lin, G.; Zhang, W. Prediction of Military Vehicle’s Drawbar Pull Based on an Improved Relevance Vector Machine and Real Vehicle Tests. Sensors 2016, 16, 351. https://doi.org/10.3390/s16030351
Yang F, Sun W, Lin G, Zhang W. Prediction of Military Vehicle’s Drawbar Pull Based on an Improved Relevance Vector Machine and Real Vehicle Tests. Sensors. 2016; 16(3):351. https://doi.org/10.3390/s16030351
Chicago/Turabian StyleYang, Fan, Wei Sun, Guoyu Lin, and Weigong Zhang. 2016. "Prediction of Military Vehicle’s Drawbar Pull Based on an Improved Relevance Vector Machine and Real Vehicle Tests" Sensors 16, no. 3: 351. https://doi.org/10.3390/s16030351