面向起重机械力学正反问题的深度学习求解方法

Deep learning method for solving the forward and inverse problems of hoisting machinery mechanics

传统数值方法在求解机械工程中的复杂偏微分方程及反问题时往往存在过程繁琐、时间成本高等问题。为解决这一问题,建立了基于物理信息的神经网络模型,通过深度学习求解偏微分方程的正反问题,并在损失函数中添加一项梯度增强项以进一步提高预测的精度。为验证该方法,将其应用到起重机械中两种常见模型的求解,即简支梁和矩形薄板简化模型的力学正反问题。与传统的数值方法在求解反问题中计算复杂、精度相对较差相比,深度学习在求解反问题时,仅需在正问题的基础上对简单的修改损失函数即可求解反问题,从而节省了时间成本,获得相对较高的数值精度。同时,对添加增强项前后的神经网络模型进行计算与对比分析。结果表明,在相同的参数设置下,添加梯度增强项的神经网络模型在求解机械工程的正反问题中均能获得更为准确的预测结果,可为起重机械力学中的方程求解问题提供新思路。

Traditional numerical methods are tedious and time-consuming in solving complex partial differential equations and inverse problems in mechanical engineering.In order to solve these problems,a neural network model based on physical information was established,and the forward and inverse problems of partial differential equations were solved by deep learning,and a gradient enhancement term was added to the loss function to further improve the prediction accuracy.For the purpose of verification,this method was applied to the solution of two common models in hoisting machinery,that is,the mechanical forward problem and inverse problem of the simplified model of simply supported beam and rectangular thin plate.The traditional numerical method is complex and has poor accuracy in solving the inverse problem.When solving the inverse problem,deep learning can solve the inverse problem by simply modifying the loss function on the basis of the forward problem,thus saving time and improving the numerical accuracy.Moreover,the neural network models before and after adding enhancement items were calculated and compared.The results show that with same parameters,the neural network model with gradient enhancement term can obtain more accurate prediction results in solving the forward and inverse problems of mechanical engineering,which can provide a new idea for solving the equations in hoisting machinery mechanics.