This paper considers parameter estimation of superimposed exponential signals in multiplicative and additive noise which are all independent and identically distributed. A modified Newton–Raphson algorithm is used to estimate the frequencies of the considered model, which is further used to estimate other linear parameters. It is proved that the modified Newton–Raphson algorithm is robust and the corresponding estimators of frequencies attain the same convergence rate with Least Squares Estimators (LSEs) under the same noise conditions, but it outperforms LSEs in terms of the mean squared errors. Finally, the effectiveness of the algorithm is verified by some numerical experiments.
The problem of small-signal stability considering load uncertainty in power system is investigated. Firstly, this paper shows attempts to create a nonlinear optimization model for solving the upper and lower limits of the oscillation mode’s damping ratio under an interval load. Then, the effective successive linear programming (SLP) method is proposed to solve this problem. By using this method, the interval damping ratio and corresponding load states at its interval limits are obtained. Calculation results can be used to evaluate the influence of load variation on a certain mode and give useful information for improvement. Finally, the proposed method is validated on two test systems.
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Purpose: Improve the generalization capability and speed of back-propagation neural network (BPNN). Design/methodology/approach: In this paper, CCD cameras are calibrated implicitly using BP neural network by means of its ability to fit the complicated nonlinear mapping relation. Conventional BP algorithms easily fall into part-infinitesimal, slowing speed of convergence and exorbitance training that will influence the training result, delay convergence time and debase generalization capability. During our experiments, dense sample data are acquired by using high precisely numerical control platform, and the variances error (PVE) is adopted during training the neural network. Findings: Experiments indicate that the neural network used PVE has great generalization. The error percentages obtained from our set-up are limitedly better than those obtained through Mean Square Error (MSE). The system is generalization enough for most machine-vision applications and the calibrated system can reach acceptable precision of 3D measurement standard. Research limitations/implications: The value needs to be decided by experiments, and the reconstruction images will be distorted if the value is more than 6. Originality/value: The variances error is be adopted in BPNN first.
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