An intelligent prediction method for blasting craters of cylindrical blastholes based on Wavelet-Augmented Physics-Informed Neural Networks

Ting Zhu; Hongyu Zhang; Yongsheng Jia; Yingkang Yao; Fan Yong; Nan Jiang; Jinshan Sun; Ting Zhu; Hongyu Zhang; Yongsheng Jia; Yingkang Yao; Fan Yong; Nan Jiang; Jinshan Sun

doi:10.3934/math.2026590

AIMS Mathematics

2026, Volume 11, Issue 5: 14374-14411. doi: 10.3934/math.2026590

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Research article

An intelligent prediction method for blasting craters of cylindrical blastholes based on Wavelet-Augmented Physics-Informed Neural Networks

1.
State Key Laboratory of Precision Blasting, Jianghan University, Wuhan, 430056 Hubei, China
2.
Hubei Key Laboratory of Blasting Engineering, Jianghan University, Wuhan 430056, Hubei, China
3.
Key Laboratory of Hydroelectric Engineering Construction and Management in Hubei Province, Three Gorges University, Yichang, Hubei 443002, China

Received: 31 March 2026 Revised: 26 April 2026 Accepted: 28 April 2026 Published: 21 May 2026
MSC : 74-xx

Blasting crater prediction is critical for optimizing charge design and ensuring safety in engineering practice; however, traditional theoretical models suffer from idealized assumptions, numerical simulations are hindered by empirical parameter calibration and high computational cost, and physical experiments are constrained by scalability and repeatability. To address these challenges, a novel Wavelet-Augmented Physics-Informed Neural Networks (WA-PINNs) framework for accurately and efficiently predicting the diameter and volume of blasting craters induced by cylindrical charges is proposed. By leveraging Starfield's superposition method to equivalently model cylindrical charges as a series of spherical sources, a partial differential equation (PDE) system governing the tensile stress field responsible for crater formation was established. Comprehensive validation against high-fidelity numerical simulations and field experiments at Baima Iron Mine demonstrated that the WA-PINNs (Dog) achieves superior accuracy in predicting crater diameter and volume compared to conventional PINNs, with relative errors as low as 0.01 and markedly reduced training time. The results confirmed that the proposed WA-PINNs (Dog) is a robust, efficient, and physics-consistent intelligent solution for complex blasting problems, offering significant potential for real-world blasting design optimization.
- physics-informed neural networks,
- wavelets,
- blasting crater,
- charge mass,
- charge burial depth
Citation: Ting Zhu, Hongyu Zhang, Yongsheng Jia, Yingkang Yao, Fan Yong, Nan Jiang, Jinshan Sun. An intelligent prediction method for blasting craters of cylindrical blastholes based on Wavelet-Augmented Physics-Informed Neural Networks[J]. AIMS Mathematics, 2026, 11(5): 14374-14411. doi: 10.3934/math.2026590

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Abstract

Blasting crater prediction is critical for optimizing charge design and ensuring safety in engineering practice; however, traditional theoretical models suffer from idealized assumptions, numerical simulations are hindered by empirical parameter calibration and high computational cost, and physical experiments are constrained by scalability and repeatability. To address these challenges, a novel Wavelet-Augmented Physics-Informed Neural Networks (WA-PINNs) framework for accurately and efficiently predicting the diameter and volume of blasting craters induced by cylindrical charges is proposed. By leveraging Starfield's superposition method to equivalently model cylindrical charges as a series of spherical sources, a partial differential equation (PDE) system governing the tensile stress field responsible for crater formation was established. Comprehensive validation against high-fidelity numerical simulations and field experiments at Baima Iron Mine demonstrated that the WA-PINNs (Dog) achieves superior accuracy in predicting crater diameter and volume compared to conventional PINNs, with relative errors as low as 0.01 and markedly reduced training time. The results confirmed that the proposed WA-PINNs (Dog) is a robust, efficient, and physics-consistent intelligent solution for complex blasting problems, offering significant potential for real-world blasting design optimization.

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