桥梁车辆移动载荷识别MFI(Moving Force Identification)是结构动力学领域中的一个典型反问题.针对现有基于共轭梯度方法的载荷识别方法对多轴车辆荷载识别效果不佳的问题,提出了一种基于改进分数阶共轭梯度算法IFCG(Improved Fractiona...桥梁车辆移动载荷识别MFI(Moving Force Identification)是结构动力学领域中的一个典型反问题.针对现有基于共轭梯度方法的载荷识别方法对多轴车辆荷载识别效果不佳的问题,提出了一种基于改进分数阶共轭梯度算法IFCG(Improved Fractional Conjugate Gradient)的载荷识别方法.基于车辆行驶过程在时域中建立车桥动力系统,通过模态叠加原理得到桥梁动态响应,将MFI问题转化为无约束优化问题;其次,引入新的搜索方向标量,使所提算法能够针对多轴以及高噪声情况下保持精度和识别效率;接着,通过识别两轴车辆移动载荷验证了所提方法的有效性;然后,对分数阶次进行定量对比研究,选择最优分数阶次;最后,通过识别多种工况下的三轴车辆载荷,将所提方法与现有方法进行对比,验证了IFCG方法在不同工况下的桥梁多轴车辆MFI都具有较高的识别精度和速度.展开更多
Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay di...Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.展开更多
文摘Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.
