# Full Waveform Prediction of Blasting Vibration Using Deep Learning

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. LSTM Network for Blast Waveform Superposition

_{1}, x

_{2}, …, x

_{n}} for the media monitoring points at n consecutive equal intervals. For the sampling data that correspond to any time t, either the speed or acceleration is included. The output data are n consecutive equally spaced speed or acceleration {y

_{1}, y

_{2}, …, y

_{n}} at the monitoring points.

#### 2.2. Structure of the Memory Unit of LSTM

#### 2.3. Acquisition of Blasting Vibration Waveform Data

#### 2.4. Training Algorithm

## 3. Waveform Prediction Experiment: Porous Rock Blasting

#### 3.1. Data Preparation

_{n}is the distance from the nth blast hole to the test point, S

_{n}(t) is a function of the velocity waveform of a single initiation of the nth blast hole, and δ

_{n}is the time taken for the vibration caused by the nth blast hole to be transmitted to the monitoring point.

_{n}= 1. The five blast holes detonate at the same time, so that the waveform excited by the blast holes are the same and are formed by superimposing two sine waves. Assuming K = 1, B = 1, and A = 1, forty randomly generated pairs of sine waves are superimposed into a vibration waveform S

_{n}(t) of the 20 blast holes. Thus, the waveform of the two points P

_{a}and P

_{b}on the X-axis is calculated as test data.

#### 3.2. Evaluation of the Prediction Result

_{t}is the predicted value output by the model at time t, y

_{t}is the true value corresponding to the trajectory data at time t, and N is the number of samples in the prediction set.

#### 3.3. Determination of LSTM Network

#### 3.4. Experimental Result

^{(R)}Xeon

^{(R)}Bronze 3106 processor with a main frequency of 1.7 GHz, 16 GB of running memory (RAM), NVIDIA GeForce RTX 2080 Ti graphics card, and 64-bit Microsoft Win10 professional operating system. The system includes data simulation and model construction. The programming language used in this experiment is Python 3.7.1 (64-bit), and the experimental operating environment is Spyder 3.3.6. During the construction of the LSTM-based vibration wave prediction model, multiple libraries were used for data processing and matrix operations between model nodes. The TensorFlow library version is 1.14.0, the Numpy library version is 1.16.5, and the Matplotlib library version is 2.2.2.

_{b}. Starting from the 0.05 s prediction point, the predicted trajectory curve and the real trajectory curve are in good agreement, as shown in Figure 6.

## 4. Field Application

#### 4.1. Engineering Background Overview

#### 4.2. Blasting Parameters

^{3}, Detonation distance: 7 cm). The specific explosive consumption is 0.255 to 0.301 kg t − 1. The blast area division and blasting sequence (I–VII) are shown in Figure 10.

#### 4.3. Blasting Vibration Monitoring Scheme

#### 4.4. Blasting Vibration Monitoring Data

#### 4.5. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 15.**Loss function curves when the number of hidden layers is (

**a**) 10, (

**b**) 20, (

**c**) 30, and (

**d**) 40.

**Figure 16.**Loss function curves when the optimisation function is (

**a**) Adam, (

**b**) RMSprop, (

**c**) Adamax, and (

**d**) Adagrad.

Channel Number | Maximum Velocity (cm/s) | Maximum Moment (ms) | Vibration Duration (s) | Dominate Frequency (Hz) |
---|---|---|---|---|

X-direction vibration | 3.06 | 20 | 0.539 | 285 |

Y-direction vibration | 4.11 | 20.4 | 0.518 | 243.726 |

Z-direction vibration | 8.07 | 62.2 | 0.654 | 305.62 |

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**MDPI and ACS Style**

Wang, Y.; Zheng, G.; Li, Y.; Zhang, F.
Full Waveform Prediction of Blasting Vibration Using Deep Learning. *Sustainability* **2022**, *14*, 8200.
https://doi.org/10.3390/su14138200

**AMA Style**

Wang Y, Zheng G, Li Y, Zhang F.
Full Waveform Prediction of Blasting Vibration Using Deep Learning. *Sustainability*. 2022; 14(13):8200.
https://doi.org/10.3390/su14138200

**Chicago/Turabian Style**

Wang, Yunsen, Guiping Zheng, Yuanhui Li, and Fengpeng Zhang.
2022. "Full Waveform Prediction of Blasting Vibration Using Deep Learning" *Sustainability* 14, no. 13: 8200.
https://doi.org/10.3390/su14138200