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
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.
