A Framework for Determining the Optimal Vibratory Frequency of Graded Gravel Fillers Using Hammering Modal Approach and ANN
Abstract
:1. Introduction
2. The Method of Determining fov
2.1. Material
2.2. Experimental Design
2.3. The Tests of Determining f0
2.4. Relationship between fo and fov
3. ANN-Based Predictive Model for fov
3.1. Key Feature of fov
3.2. Dataset of ANN Model
3.3. Establishment and Evaluation of ANN-PM
3.4. Sensitivity Analysis of ANN-PM
4. Results and Analysis
4.1. Establishment of ANN-PM Based on the Training Set
4.2. Evaluating the Impact of Key Features on the ANN-PM Performance
4.3. Evaluation of ANN-PM Based on the Testing Set
4.4. Sensitivity Analysis of ANN-PM
5. Discussion
6. Conclusions
- In the vibratory compaction experiments, maximum dry density ρdmax, stiffness Krd, and bearing capacity coefficient K20 of different gradation HRGG fillers all obtained optimal states when the vibratory frequency was set as f0, which indicated that f0 was the fov.
- Based on the gray relational analysis algorithm, the key features influencing the fov were determined to be the maximum particle diameter dmax, gradation parameters b and m, flat and elongated particles in coarse aggregate Qe, and the Los Angeles abrasion of coarse aggregate LAA.
- The key feature influencing the fov was used to establish the ANN-PM. Then, based on the ablation study, it was indicated that the impact hierarchy of the five key features on the ANN-PM predictive performance was dmax > b > m > Qe > LAA.
- On the training and testing sets, the goodness-of-fit R2 of ANN-PM all exceeded 0.95, and the prediction errors were small, which indicated the strong prediction capability of ANN-PM for fov.
- Based on the sensitivity analysis, the distribution of R2 for the ANN-PM closely approached 1, with its mean value exceeding 0.9. In addition, the MSE distribution for the ANN-PM approached zero. It was clear that the ANN-PM exhibited excellent robust performance.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Gradation | f (Hz) | ω (%) | mp (kg) | re (mm) | me (kg) | Dc (mm) | h0 (mm) |
---|---|---|---|---|---|---|---|
G1 | 40 | 3.6 | 600 | 18.0 | 4.7 | 200 | 155 |
G2 | 34 | 4.0 | 600 | 25.1 | 4.7 | 200 | 155 |
G3 | 26 | 5.4 | 600 | 44.4 | 4.7 | 200 | 155 |
Performance feature | Cu | Cc | dmax | d ≤ 0.5 | d = 0.5~1.7 | d ≥ 1.7 | LAA | Qe | Wac | Waf | LL | PL |
Correlation coefficient R | 0.58 | 0.5 | 0.75 | 0.73 | 0.68 | 0.71 | 0.64 | 0.66 | 0.56 | 0.55 | 0.1 | 0.22 |
Hyperparameters | α | Neurons1 | Neurons2 | Epoch | Batch Size |
---|---|---|---|---|---|
ANN | 0.001 | 100 | 100 | 200 | 16 |
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**ao, X.; Li, T.; Lin, F.; Li, X.; Hao, Z.; Li, J. A Framework for Determining the Optimal Vibratory Frequency of Graded Gravel Fillers Using Hammering Modal Approach and ANN. Sensors 2024, 24, 689. https://doi.org/10.3390/s24020689
**ao X, Li T, Lin F, Li X, Hao Z, Li J. A Framework for Determining the Optimal Vibratory Frequency of Graded Gravel Fillers Using Hammering Modal Approach and ANN. Sensors. 2024; 24(2):689. https://doi.org/10.3390/s24020689
Chicago/Turabian Style**ao, **anpu, Taifeng Li, Feng Lin, **nzhi Li, Zherui Hao, and Jiashen Li. 2024. "A Framework for Determining the Optimal Vibratory Frequency of Graded Gravel Fillers Using Hammering Modal Approach and ANN" Sensors 24, no. 2: 689. https://doi.org/10.3390/s24020689