提出了模拟退火的 Gauss-Newton 算法的神经网络,克服了经典 BP 网络存在的一些缺陷。并以正弦函数的迭代收敛为例,证明了该方法的正确性,有效性和优越性。同时将该方法用于同乐坪大坝的渗流反分析,利用反演出的渗透系数进行渗流场计算...提出了模拟退火的 Gauss-Newton 算法的神经网络,克服了经典 BP 网络存在的一些缺陷。并以正弦函数的迭代收敛为例,证明了该方法的正确性,有效性和优越性。同时将该方法用于同乐坪大坝的渗流反分析,利用反演出的渗透系数进行渗流场计算。得到的水头预报值与观测值相吻合,可知反演结果是正确的,说明该方法用于实践工程的渗流参数识别是可行的。展开更多
Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization p...Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC.Taking this as motivation,this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM)algorithm in the framework of MUC.This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM)method along with its convergence properties.The proposed method is generalized for n number of variables,and all its theoretical concepts are authenticated by simulation results.Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions.From simulation results,it has been observed that proposed MGNM method converges for 12972 points,out of 19600 points considered while optimizing multiplicatively-linear exponential function,whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points,respectively.Furthermore,for a given set of initial value,the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods.A similar pattern is observed for multiplicatively-non-linear exponential function.Therefore,it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.展开更多
In the digital image correlation research of fatigue crack growth rate,the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor,thereby affecting the life predic...In the digital image correlation research of fatigue crack growth rate,the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor,thereby affecting the life prediction.This paper proposes a Gauss-Newton iteration method for solving the crack tip position.The conventional linear fitting method provides an iterative initial solution for this method,and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix.A noise-added artificial displacement field is used to verify the feasibility of the method,which shows that all parameters can be solved with satisfactory results.The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result,and the relative error between the two is only−0.621%;The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip,and the maximum relative error with the test plastic zone area is−11.29%.The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05%.The crack tip coordinates,stress intensity factors,and plastic zone contour changes in the loading and unloading phases are explored.The results show that the crack tip change during the loading process is faster than the change during the unloading process;the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process;under the same load,the theoretical plastic zone during the unloading process is higher than that during the loading process.展开更多
This paper presents the derivation of Gauss-Newton filter in linear cases and an analysis of its properties. Based on the minimum variance theorem, the Gauss-Newton filter is constructed and derived, including its sta...This paper presents the derivation of Gauss-Newton filter in linear cases and an analysis of its properties. Based on the minimum variance theorem, the Gauss-Newton filter is constructed and derived, including its state transition equation, observation equation and filtering process. Then, the delicate relationship between the Gauss-Aitken filter and the Kalman filter is discussed and it is verified that without process noise the two filters are equivalent. Finally, some simulations are conducted. The result shows that the Gauss-Aitken filter is superior to the Kalman filter in some aspects.展开更多
In this paper, a Gauss-Newton-based Broyden’s class method for parameters of regression problems is presented. The global convergence of this given method will be established under suitable conditions. Numerical resu...In this paper, a Gauss-Newton-based Broyden’s class method for parameters of regression problems is presented. The global convergence of this given method will be established under suitable conditions. Numerical results show that the proposed method is interesting.展开更多
Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real pla...Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.展开更多
文摘提出了模拟退火的 Gauss-Newton 算法的神经网络,克服了经典 BP 网络存在的一些缺陷。并以正弦函数的迭代收敛为例,证明了该方法的正确性,有效性和优越性。同时将该方法用于同乐坪大坝的渗流反分析,利用反演出的渗透系数进行渗流场计算。得到的水头预报值与观测值相吻合,可知反演结果是正确的,说明该方法用于实践工程的渗流参数识别是可行的。
文摘Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC.Taking this as motivation,this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM)algorithm in the framework of MUC.This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM)method along with its convergence properties.The proposed method is generalized for n number of variables,and all its theoretical concepts are authenticated by simulation results.Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions.From simulation results,it has been observed that proposed MGNM method converges for 12972 points,out of 19600 points considered while optimizing multiplicatively-linear exponential function,whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points,respectively.Furthermore,for a given set of initial value,the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods.A similar pattern is observed for multiplicatively-non-linear exponential function.Therefore,it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.
基金Supported by National Natural Science Foundation of China(Grant No.51675446)Independent Research Project of State Key Laboratory of Traction Power(Grant No.2019TPL-T13).
文摘In the digital image correlation research of fatigue crack growth rate,the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor,thereby affecting the life prediction.This paper proposes a Gauss-Newton iteration method for solving the crack tip position.The conventional linear fitting method provides an iterative initial solution for this method,and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix.A noise-added artificial displacement field is used to verify the feasibility of the method,which shows that all parameters can be solved with satisfactory results.The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result,and the relative error between the two is only−0.621%;The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip,and the maximum relative error with the test plastic zone area is−11.29%.The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05%.The crack tip coordinates,stress intensity factors,and plastic zone contour changes in the loading and unloading phases are explored.The results show that the crack tip change during the loading process is faster than the change during the unloading process;the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process;under the same load,the theoretical plastic zone during the unloading process is higher than that during the loading process.
文摘This paper presents the derivation of Gauss-Newton filter in linear cases and an analysis of its properties. Based on the minimum variance theorem, the Gauss-Newton filter is constructed and derived, including its state transition equation, observation equation and filtering process. Then, the delicate relationship between the Gauss-Aitken filter and the Kalman filter is discussed and it is verified that without process noise the two filters are equivalent. Finally, some simulations are conducted. The result shows that the Gauss-Aitken filter is superior to the Kalman filter in some aspects.
文摘In this paper, a Gauss-Newton-based Broyden’s class method for parameters of regression problems is presented. The global convergence of this given method will be established under suitable conditions. Numerical results show that the proposed method is interesting.
文摘Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.
