The novel information criterion （NIC） algorithm can find the principal subspace quickly, but it is not an actual principal component analysis （PCA） algorithm and hence it cannot find the orthonormal eigen-space wh...The novel information criterion （NIC） algorithm can find the principal subspace quickly, but it is not an actual principal component analysis （PCA） algorithm and hence it cannot find the orthonormal eigen-space which corresponds to the principal component of input vector. This defect limits its application in practice. By weighting the neural network＇s output of NIC, a modified novel information criterion （MNIC） algorithm is presented. MNIC extractes the principal components and corresponding eigenvectors in a parallel online learning program, and overcomes the NIC＇s defect. It is proved to have a single global optimum and nonquadratic convergence rate, which is superior to the conventional PCA online algorithms such as Oja and LMSER. The relationship among Oja, LMSER and MNIC is exhibited. Simulations show that MNIC could converge to the optimum fast. The validity of MNIC is proved.展开更多
为了提高风电机组的实时可靠性,避免维修不足及维修过剩问题,降低风场运维成本,基于监控与数据采集(supervisory control and data acquisition,SCADA)系统得出的监测数据,应用主元评价和非线性自回归(non-linear auto-regressive,NAR)...为了提高风电机组的实时可靠性,避免维修不足及维修过剩问题,降低风场运维成本,基于监控与数据采集(supervisory control and data acquisition,SCADA)系统得出的监测数据,应用主元评价和非线性自回归(non-linear auto-regressive,NAR)时间序列神经网络,通过建立评价及预测模型。通过实际数据验证模型有效性。结果表明:采用PCA-NAR的方法对风电机组的健康状况进行评估及预测有较好的效果,有助于帮助风场运营人员提前识别故障趋势并作出具体决策,以免机组遭受更为严重的故障。展开更多
The authors present their analysis of the differential equation d X(t)/ d t = AX(t)-X T (t)BX(t)X(t) , where A is an unsymmetrical real matrix, B is a positive definite symmetric real matrix, X ∈...The authors present their analysis of the differential equation d X(t)/ d t = AX(t)-X T (t)BX(t)X(t) , where A is an unsymmetrical real matrix, B is a positive definite symmetric real matrix, X ∈R n; showing that the equation characterizes a class of continuous type full feedback artificial neural network; We give the analytic expression of the solution; discuss its asymptotic behavior; and finally present the result showing that, in almost all cases, one and only one of following cases is true. 1. For any initial value X 0∈R n, the solution approximates asymptotically to zero vector. In this case, the real part of each eigenvalue of A is non positive. 2. For any initial value X 0 outside a proper subspace of R n, the solution approximates asymptotically to a nontrivial constant vector (X 0) . In this case, the eigenvalue of A with maximal real part is the positive number λ=‖(X 0)‖ 2 B and (X 0) is the corresponding eigenvector. 3. For any initial value X 0 outside a proper subspace of R n, the solution approximates asymptotically to a non constant periodic function (X 0,t) . Then the eigenvalues of A with maximal real part is a pair of conjugate complex numbers which can be computed.展开更多
To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which inte...To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.展开更多
In this paper, we are concerned with the inverse transmission eigenvalue problem to recover the shape as well as the constant refractive index of a penetrable medium scatterer. The linear sampling method is employed t...In this paper, we are concerned with the inverse transmission eigenvalue problem to recover the shape as well as the constant refractive index of a penetrable medium scatterer. The linear sampling method is employed to determine the transmission eigenvalues within a certain wavenumber interval based on far-field measurements. Based on a prior information given by the linear sampling method, the neural network approach is proposed for the reconstruction of the unknown scatterer. We divide the wavenumber intervals into several subintervals, ensuring that each transmission eigenvalue is located in its corresponding subinterval. In each such subinterval, the wavenumber that yields the maximum value of the indicator functional will be included in the input set during the generation of the training data. This technique for data generation effectively ensures the consistent dimensions of model input. The refractive index and shape are taken as the output of the network. Due to the fact that transmission eigenvalues considered in our method are relatively small,certain super-resolution effects can also be generated. Numerical experiments are presented to verify the effectiveness and promising features of the proposed method in two and three dimensions.展开更多
文摘The novel information criterion （NIC） algorithm can find the principal subspace quickly, but it is not an actual principal component analysis （PCA） algorithm and hence it cannot find the orthonormal eigen-space which corresponds to the principal component of input vector. This defect limits its application in practice. By weighting the neural network＇s output of NIC, a modified novel information criterion （MNIC） algorithm is presented. MNIC extractes the principal components and corresponding eigenvectors in a parallel online learning program, and overcomes the NIC＇s defect. It is proved to have a single global optimum and nonquadratic convergence rate, which is superior to the conventional PCA online algorithms such as Oja and LMSER. The relationship among Oja, LMSER and MNIC is exhibited. Simulations show that MNIC could converge to the optimum fast. The validity of MNIC is proved.
文摘为了提高风电机组的实时可靠性,避免维修不足及维修过剩问题,降低风场运维成本,基于监控与数据采集(supervisory control and data acquisition,SCADA)系统得出的监测数据,应用主元评价和非线性自回归(non-linear auto-regressive,NAR)时间序列神经网络,通过建立评价及预测模型。通过实际数据验证模型有效性。结果表明:采用PCA-NAR的方法对风电机组的健康状况进行评估及预测有较好的效果,有助于帮助风场运营人员提前识别故障趋势并作出具体决策,以免机组遭受更为严重的故障。
文摘The authors present their analysis of the differential equation d X(t)/ d t = AX(t)-X T (t)BX(t)X(t) , where A is an unsymmetrical real matrix, B is a positive definite symmetric real matrix, X ∈R n; showing that the equation characterizes a class of continuous type full feedback artificial neural network; We give the analytic expression of the solution; discuss its asymptotic behavior; and finally present the result showing that, in almost all cases, one and only one of following cases is true. 1. For any initial value X 0∈R n, the solution approximates asymptotically to zero vector. In this case, the real part of each eigenvalue of A is non positive. 2. For any initial value X 0 outside a proper subspace of R n, the solution approximates asymptotically to a nontrivial constant vector (X 0) . In this case, the eigenvalue of A with maximal real part is the positive number λ=‖(X 0)‖ 2 B and (X 0) is the corresponding eigenvector. 3. For any initial value X 0 outside a proper subspace of R n, the solution approximates asymptotically to a non constant periodic function (X 0,t) . Then the eigenvalues of A with maximal real part is a pair of conjugate complex numbers which can be computed.
基金Project (No. 60074008) supported by the National Natural Science Foundation of China
文摘To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.
基金supported by the Jilin Natural Science Foundation,China(No.20220101040JC)the National Natural Science Foundation of China(No.12271207)+2 种基金supported by the Hong Kong RGC General Research Funds(projects 11311122,12301420 and 11300821)the NSFC/RGC Joint Research Fund(project N-CityU 101/21)the France-Hong Kong ANR/RGC Joint Research Grant,A_CityU203/19.
文摘In this paper, we are concerned with the inverse transmission eigenvalue problem to recover the shape as well as the constant refractive index of a penetrable medium scatterer. The linear sampling method is employed to determine the transmission eigenvalues within a certain wavenumber interval based on far-field measurements. Based on a prior information given by the linear sampling method, the neural network approach is proposed for the reconstruction of the unknown scatterer. We divide the wavenumber intervals into several subintervals, ensuring that each transmission eigenvalue is located in its corresponding subinterval. In each such subinterval, the wavenumber that yields the maximum value of the indicator functional will be included in the input set during the generation of the training data. This technique for data generation effectively ensures the consistent dimensions of model input. The refractive index and shape are taken as the output of the network. Due to the fact that transmission eigenvalues considered in our method are relatively small,certain super-resolution effects can also be generated. Numerical experiments are presented to verify the effectiveness and promising features of the proposed method in two and three dimensions.
