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Abstract In order to adapt to the intelligent development trend of solving the inverse problem of thin plate, this paper established a novel framework for solving the inverse problem of thin plate using physics-informed neural networks based on the hybrid driving idea of data and model. Inspired by the fine-tuning learning in few-shot learning method, a step-by-step training method for freezing parameters is proposed to solve the problem of long time for neural network to calculate higher order terms. To optimize the sampling area in view of the large error at the edge for supervised learning of the deflection of thin plate, an edge cutting method is proposed. The measured data of thin plate deflections are obtained by calculating the deflection partial differential equation based on the Kirchhoff thin plate theory combined with the analytical solution formula and superimposing random noise, thus a physics-informed neural networks model for solving the inverse problem of thin plate is constructed. In addition, ablation experiments are carried out to analyze and verify the effectiveness of the proposed improvement measures. The numerical results show that under the acceleration of NVIDIA RTX 3060 video card, the inversion time of the ratio of uniformly distributed load to flexural rigidity, uniformly distributed load and modulus of elasticity of simply supported and clamped rectangular thin plates is less than 30 seconds and the relative error is less than 3% in low noise environment. For rectangular thin plates with four edges clamped, the relative error of linear load inversion clamped under hydrostatic pressure is less than 11%. The results show that the inversion method of thin plate problem based on physics-informed neural networks is correct and effective, and can accurately invert the parameters of various mechanical models. The corresponding step-by-step training inversion algorithm of cutting edge-freezing parameters has the advantages of fast speed, high precision, strong robustness and small parameter redundancy. This research creates conditions for adaptive, efficient and accurate solution of thin plate inverse problem, and provides a useful reference for intelligent health monitoring of thin plate structures.
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Received: 06 November 2022
Published: 18 August 2023
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2023, Vol. 44 
