| There is a wide variety of positive and inverse analytical problems in civil engineering,and there have always been significant differences in the way they are solved.The emergence of physics-informed neural networks provides a unified framework for the treatment of both positive and inverse analysis problems,one of the cores of which lies in the introduction of boundary conditions.In this paper,based on this unified framework of physical information neural networks,a neural network method using the generalised multiplier method to impose boundary conditions is proposed for the positive analysis problem,and a self-programming procedure is used to solve common initial boundary value problems in the field of civil engineering,and the influencing factors of the method are analysed;for the inverse analysis problem,a reverse iterative correction inversion method is proposed for the inversion of shear strength parameters of geotechnical bodies of slopes.The main work and conclusions of the thesis are as follows:(1)A physically-informed neural network method using the generalized multiplier method to impose boundary conditions is proposed for solving a system of partial differential equations,a typical positive-analytic problem.The loss function of the neural network is constructed using the generalized multiplier method and the loss value is calculated.The gradient descent method is used to find the optimal parameters and determine whether the loss value satisfies the requirements;if not,the penalty factor and multiplier are updated and then solved until the loss meets the requirements.(2)The solution procedure of the physical information neural network method with boundary conditions imposed by the generalised multiplier method is prepared,and an example of a simply-supported beam under the action of a perimeter simply-supported rectangular Kirchhoff plate and a uniform load is used to verify the effectiveness of the method from two perspectives,namely the differentiation lifting method and the energy lifting method,respectively.In comparison with the physical information neural network using the classical penalty function method,the L1 exact penalty function method and the Lagrange multiplier method to impose boundary conditions,the calculation results of the numerical examples show that the method proposed in this paper does not need to determine the value of the penalty factor in advance,and has good numerical accuracy and higher solving efficiency.(3)In-depth analysis of the physical information neural network with boundary conditions imposed by the generalized multiplier method from the perspectives of neural network topology,activation function and optimizer selection reveals that blindly expanding the scale of the neural network will lead to a reduction in solution accuracy and computational efficiency.In addition,for the reasons of both computational accuracy and computational efficiency,using Tanh as the activation function and Adam as the optimizer is the best choice at this stage.(4)For groundwater seepage,which is a common initial boundary value problem in civil engineering,a physical information neural network with boundary conditions imposed by the generalised multiplier method is used to solve the horizontal and inclined pressurised water movement of the water barrier substrate and the pressurised groundwater seepage within the sand layer with a time term,which further verifies the solution capability of the method in this paper.(5)To address the inverse analysis problem of inversion of shear strength parameters of geotechnical bodies when sliding surfaces pass through multi-layered soils in the design of small slope protection projects,an inverse iterative correction inversion method is proposed based on physical information neural networks,and a neural network is constructed with shear strength of multi-layered geotechnical bodies as input and stability coefficients calculated by Geoslope and shear inlet and outlet locations of sliding surfaces as output.Based on the stability coefficients and the sliding surface shear inlet and shear outlet locations measured in the field,the inverse iterative correction of the shear strength of the geotechnical body is achieved by repeatedly performing "reverse inversion-error check-sample correction".The validation results of the engineering example show that the shear strength of the geotechnical body obtained by this method is basically reasonable,and the number of samples required for the sample library is low,which can be used as a reference for the design of small-scale slope protection projects. |
