# Penetration Overload Prediction Method Based on a Deep Neural Network with Multiple Inputs

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Method

#### 3.1. Penetration Simulation and Data Set Introduction

#### 3.1.1. Selection of the Penetration Overload Data Extraction Position

#### 3.1.2. Selection of the Penetration Overload Data Set Label Type

#### 3.2. Model Introduction

#### 3.2.1. The Principle of the Transformer

_{i}, R is the normalized matrix, K

^{T}is the transposed matrix of K, A′ is the matrix obtained after we normalize matrix A, O is the matrix of outputs B

_{i}, and W

^{q}W

^{k}W

^{v}are the parameters matrix that can be learned by the model.

#### 3.2.2. The Improved PF-Informer Model

#### Informer Model Architecture

_{i}for all keys. The second half is the arithmetic average of q

_{i}for all keys. According to the above evaluation method, the ProbSparse self-attention formula is obtained, where $\overline{Q}$ is the sparse version of the original Q matrix. The Informer model uses ProbSparse self-attention to select appropriate q-k pairs.

#### Modification of the Time Input of the PF-Informer Model

#### Modification of the Non-Variable Physical Quantity Inputs of the PF-Informer Model

## 4. Experiments

- (1)
- The PF Informer model is used, in which time series prediction only takes time as input for model training.
- (2)
- The PF Informer model is used, in which the time and various projectile parameters are used as the input of time series prediction for model training.

#### 4.1. Training Environment

#### 4.2. Model Training

#### 4.2.1. Local Prediction Effect of the Multilayer Target Model

#### 4.2.2. Local Prediction Effect of the Thick Target Model

#### 4.3. Results of Model Prediction

#### 4.4. Forecasting Model Test

#### 4.5. Comparison with Other Models

## 5. Discussion

#### 5.1. Model Training of Small Batch Data

#### 5.2. Model Accuracy and Operation Speed

#### 5.3. Motivation and Contribution of the Study

#### 5.4. Limitations and Future Direction

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Ziming, G.; Qin, F.; Yadong, Z.; Haichun, Y.; Rui, H. Numerical simulation of oblique penetration of steel long rod projectile into medium thick target. J. PLA Univ. Sci. Technol.
**2001**, 66–70. [Google Scholar] - Rong, L.; Lihong, D.; Minzhong, W.; Zhihao, S.; Chuhui, L. Mechanism of super-high speed penetration fuze multi-layer target overload interlayer adhesion. J. Detect. Control
**2020**, 42, 1–4+9. [Google Scholar] - Anonymous. Call for Abstracts for 65th Annual Fuze Conference. In Proceedings of the 65th Annual Fuze Conference, Renton, WA, USA, 10–12 May 2022; Volume 106. [Google Scholar]
- Backman, M.E.; Goldsmith, W. The mechanics of penetration of projectiles into targets. Int. J. Eng. Sci.
**1978**, 16, 1–99. [Google Scholar] [CrossRef] - Wang, J.F. A review of the research status of penetration. China Science and Technology Information
**2005**, 2, 129–130. [Google Scholar] - Hochreiter, S.; Schmidhuber, J. Long Short-Term Memory. Neural Comput.
**1997**, 9, 1735–1780. [Google Scholar] [CrossRef] - Jing, L.; Gulcehre, C.; Peurifoy, J.; Shen, Y.; Tegmark, M.; Soljacic, M.; Bengio, Y. Gated Orthogonal Recurrent Units: On Learning to Forget. Neural Comput.
**2019**, 31, 765–783. [Google Scholar] [CrossRef] - Williams, W.; Prasad, N.; Mrva, D. Recurrent Neural Network Regularization. arXiv
**2014**, arXiv:1409.2329. [Google Scholar] - Vaswani, A.; Shazeer, N.; Parmar, N.; Uszkoreit, J.; Jones, L.; Gomez, A.; Kaiser, L.; Polosukhin, I. Attention Is All You Need. arXiv
**2017**, arXiv:1706.03762. [Google Scholar] - Liu, W.; Li, R.; Shi, L.N.K. Research status and prospect of hard target penetration and detonation control technology. J. Mil. Eng.
**2022**, 1–19. [Google Scholar] [CrossRef] - Liu, Z.; Gao, S.; Liu, H.; Zhang, D.; He, L. Nonlinear adaptive noise-induced algorithm and its application in penetration signal. Measurement
**2014**, 58, 556–565. [Google Scholar] [CrossRef] - Zhao, H.; Zhang, Y.; Li, S. Underdetermined blind source separation and feature extraction of penetration overload signal. J. Instrum.
**2019**, 40, 208–218. [Google Scholar] - Zhang, C.; Zhang, Y.; Li, S. Blind separation of penetration overload signal based on variational mode decomposition. Vib. Shock.
**2022**, 41, 280–286. [Google Scholar] - Fang, A.; Li, R. Neural network method for accurate layer identification of penetration fuze based on data enhancement. J. Detect. Control
**2022**, 44, 1–6. [Google Scholar] - Huang, J.; Liu, R.; He, X.; Sun, G.; Xu, P. Data Processing Method of Penetration Overload Test Signal. Explos. Shock.
**2009**, 29, 555–560. [Google Scholar] - Hao, H.; Li, X.; Sun, Y.; Liu, M. Analysis Method of Structural Response Frequency Characteristics of Projectile during Penetration. Vibration. Test
**2013**, 33, 307–310+343. [Google Scholar] [CrossRef] - Xiaolong, Z.; Tiehua, M.; Peng, X.; Jinbiao, F. Measurement and analysis of acceleration signal of projectile penetrating concrete. Explos. Impact
**2014**, 34, 347–353. [Google Scholar] - Hua, Z.; Shi, Y.; Mi, Z.; Wang, Y.; Shi, Y. Zero drift processing method based on empirical mode and low-pass filtering. J. Detect. Control
**2022**, 44, 66–72. [Google Scholar] - Huang, N.E.; Shen, Z.; Long, S.R.; Wu, M.C.; Shih, H.H.; Zheng, Q.; Yen, N.-C.; Tung, C.C.; Liu, H.H. The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis. R. Soc. Proc. Math Phys. Eng. Sci.
**1971**, 454, 903–995. [Google Scholar] [CrossRef] - Dragomiretskiy, K.; Zosso, D. Variational Mode Decomposition. IEEE Trans. Signal Process.
**2014**, 62, 531–544. [Google Scholar] [CrossRef] - Qianhua, S.; Kai, S.; Hanyu, Z. Preprocessing method of penetration fuze layer counting signal based on box differential filtering. J. Detect. Control
**2020**, 42, 27–30. [Google Scholar] - Dai, Z.; Gao, S.; Li, Z.; Zhang, Y. Dynamic threshold layer counting algorithm based on envelope prediction. J. Weapon Equip. Eng.
**2020**, 41, 53–56. [Google Scholar] - Han, X.; Wang, Y.; Jiao, C. Research on layer number recognition of multilayer penetration fuze. Electron. Compon.
**2019**, 42, 761–766. [Google Scholar] - Zhang, J.; Li, C.; Yang, X.; Xu, L. Research on the filtering method of earth penetrating projectile penetrating soil vibration signal. Prot. Eng.
**2016**, 26–29. [Google Scholar] - Wang, Y.L. Study on Overload Characteristics of Flat nosed Projectile Penetrating Aluminum Target at Low Speed and Ultra Low Speed. Master’s Thesis, Southwest University of Science and Technology, Mianyang, China, 2019. [Google Scholar]
- Liu, S.H. Analysis and Modeling of Fuze Dynamic Response Characteristics in High Speed Penetration Environment. Master’s Thesis, Beijing University of Technology, Beijing, China, 2018. [Google Scholar]
- Xu, Y.Y. Experimental Study on Overload Characteristics of Low Speed Penetration of Projectile. Master’s Thesis, Southwest University of Science and Technology, Mianyang, China, 2018. [Google Scholar]
- Zhou, H.; Zhang, S.; Peng, J.; Zhang, S.; Li, J.; Xiong, H.; Zhang, W. Informer: Beyond Efficient Transformer for Long Sequence Time- Series Forecasting. arXiv
**2020**. [Google Scholar] [CrossRef] - Joyce, J.M. Kullback-Leibler Divergence; Springer: Berlin/Heidelberg, Germany, 2011. [Google Scholar]
- Clevert, D.-A.; Unterthiner, T.; Hochreiter, S. Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUS). arXiv
**2016**, arXiv:1511.07289. [Google Scholar] - Zhang, J.; Li, Y.; Xiao, W.; Zhang, Z. Non-iterative and Fast Deep Learning: Multilayer Extreme Learning Machines. J. Frankl. Inst.
**2020**, 357, 8925–8955. [Google Scholar] [CrossRef] - Zhang, J.; Zhao, Y.; Shone, F.; Li, Z.; Frangi, A.F.; Xie, S.Q.; Zhang, Z.-Q. Physics-Informed Deep Learning for Musculoskeletal Modeling: Predicting Muscle Forces and Joint Kinematics From Surface EMG. IEEE Trans. Neural Syst. Rehabil. Eng.
**2023**, 31, 484–493. [Google Scholar] [CrossRef]

**Figure 8.**Local time series prediction for multilayer target. (

**a**) First single timing prediction; (

**b**) second single time series prediction; (

**c**) first multivariate element prediction; (

**d**) second multivariate element prediction.

**Figure 9.**Local time series prediction effect obtained for thick targets. (

**a**) First single timing prediction; (

**b**) second single time series prediction; (

**c**) first multivariate element prediction; (

**d**) second multivariate element prediction.

**Figure 12.**Prediction and actual overload curves for a multilayer target. (

**a**) Global map of the multilayer target prediction results; (

**b**) partial enlarged view of the multilayer target prediction results; (

**c**) global map of the multilayer target prediction results; (

**d**) partial enlarged view of the multilayer target prediction results.

**Figure 13.**Prediction and actual overload curve for a thick target. (

**a**) Global map of thick the target prediction results; (

**b**) partial enlarged view of the thick target prediction results; (

**c**) global map of thick the target prediction results; (

**d**) partial enlarged view of the thick target prediction results.

Encoder | Decoder | Model Dimension | Multiple Attention Heads | Number of Convolutional Network Layers | Training Epochs | Patience Training Rounds | Algorithm Optimizer | Learning Rate | Batch Size |
---|---|---|---|---|---|---|---|---|---|

5 | 5 | 512 | 8 | 1024 | 100 | 20 | Adam | 0.0001 | 128 |

Single Multilayer Target (First Test) | Single Multilayer Target (Second Test) | Multi Element Multilayer Target (First Test) | Multi Element Multilayer Target (Second Test) | Single Thickness Target (First Test) | Single Thickness Target (First Test) | Multi Element Thick Target (First Test) | Multi Element Thick Target (Second Test) | |
---|---|---|---|---|---|---|---|---|

MSE | 0.411 | 0.421 | 0.226 | 0.221 | 5.395 | 5.560 | 0.462 | 0.452 |

MAE | 0.491 | 0.502 | 0.260 | 0.252 | 1.825 | 1.856 | 0.718 | 0.705 |

PF-Informer | GRU-ODE-BAYES | GRU | LSTM | ARIMA | CNN | N-BEATS | |
---|---|---|---|---|---|---|---|

MSE | 0.221 | 0.366 | 0.464 | 0.452 | 0.932 | 0.822 | 0.343 |

MAE | 0.252 | 0.387 | 0.520 | 0.502 | 1.012 | 0.942 | 0.369 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ma, H.; Sun, H.; Li, C.
Penetration Overload Prediction Method Based on a Deep Neural Network with Multiple Inputs. *Appl. Sci.* **2023**, *13*, 2351.
https://doi.org/10.3390/app13042351

**AMA Style**

Ma H, Sun H, Li C.
Penetration Overload Prediction Method Based on a Deep Neural Network with Multiple Inputs. *Applied Sciences*. 2023; 13(4):2351.
https://doi.org/10.3390/app13042351

**Chicago/Turabian Style**

Ma, Haoran, Hang Sun, and Changsheng Li.
2023. "Penetration Overload Prediction Method Based on a Deep Neural Network with Multiple Inputs" *Applied Sciences* 13, no. 4: 2351.
https://doi.org/10.3390/app13042351