An Integration-Implemented Newton-Raphson Iterated Algorithm With Noise Suppression for Finding the Solution of Dynamic Sylvester Equation

Wang, Guancheng; Huang, Haoen; Yan, Jingkun; Cheng, Yihang; Fu, Dongyang

doi:10.1109/access.2020.2974753

Cited by 15 publications

(4 citation statements)

References 36 publications

(24 reference statements)

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“…Since the internal force F(u, v) of the soft tissue is a non-linear function of position and velocity, it can be calculated iteratively using Newton-Raphson iteration [13]:…”

Section: Deformation Calculationmentioning

confidence: 99%

A Real-time Cutting Model Based on Finite Element and Order Reduction

Zhang¹,

Zhang²,

Sun³

et al. 2022

Computer Systems Science and Engineering

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Telemedicine plays an important role in Corona Virus Disease 2019 . The virtual surgery simulation system, as a key component in telemedicine, requires to compute in real-time. Therefore, this paper proposes a realtime cutting model based on finite element and order reduction method, which improves the computational speed and ensure the real-time performance. The proposed model uses the finite element model to construct a deformation model of the virtual lung. Meanwhile, a model order reduction method combining proper orthogonal decomposition and Galerkin projection is employed to reduce the amount of deformation computation. In addition, the cutting path is formed according to the collision intersection position of the surgical instrument and the lesion area of the virtual lung. Then, the Bezier curve is adopted to draw the incision outline after the virtual lung has been cut. Finally, the simulation system is set up on the PHANTOM OMNI force haptic feedback device to realize the cutting simulation of the virtual lung. Experimental results show that the proposed model can enhance the real-time performance of telemedicine, reduce the complexity of the cutting simulation and make the incision smoother and more natural.

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“…Since the internal force F(u, v) of the soft tissue is a non-linear function of position and velocity, it can be calculated iteratively using Newton-Raphson iteration [13]:…”

Section: Deformation Calculationmentioning

confidence: 99%

A Real-time Cutting Model Based on Finite Element and Order Reduction

Zhang¹,

Zhang²,

Sun³

et al. 2022

Computer Systems Science and Engineering

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show abstract

“…Originally, researchers studied many methods to solve the Sylvester equation [5], [6]. The most classical approach is Bartels-Stewart method.…”

Section: Introductionmentioning

confidence: 99%

Residual Error Feedback Zeroing Neural Network for Solving Time-Varying Sylvester Equation

Jiang

Xiao

et al. 2022

IEEE Access

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In many fields, the issue of solving the time-varying Sylvester equation (TVSE) is commonly encountered. Consequently, finding its exact solution has become a research hotspot. In general, the ZNN and IEZNN models are the most useful algorithms that are frequently utilized to solve the TVSE problem. However, the ZNN model is borned with noise susceptibility and the IEZNN model loses the adaptive performance due to its constant coefficient in solving the TVSE problem. In this paper, a residual error feedback zeroing neural network (REFZNN) is proposed to adaptively solve the TVSE problem. The REFZNN model feeds back the residual error to the solution system, which forms a feedback regulation to reduce the residual error between the system output and the system target. Then, the convergence and noise patience of the REFZNN model is proved by theoretical analyses. Finally, the validity of the proposed model is verified by designing computer simulation experiments and its superiority is confirmed by the performance comparisons with the ZNN and IEZNN models.INDEX TERMS Time-varying problems, Residual error, feedback, Zeroing neural network (ZNN), Sylvester equation.

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“…In recent years, the neural network has become a research hotspot [18][19][20][21]. Prediction methods based on the neural network are efficient and accurate, and can improve the shortcomings of traditional prediction methods.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid ARIMA-GABP Model for Predicting Sea Surface Temperature

Chen

Zeng

et al. 2022

Electronics

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Sea surface temperature (SST) is one of the most important parameters in air–sea interaction, and its accurate prediction is of great significance in the study of global climate change. However, SST is affected by heat flux, ocean dynamic processes, cloud coverage, and other factors, which means it contains linear and nonlinear components. Existing prediction models, especially single prediction models, cannot effectively handle these linear and nonlinear components in the meantime, degrading their accuracy concerning the prediction of SST. To remedy this weakness, this paper proposes a novel prediction model by the Lagrange multiplier method to combine the auto-regressive integrated moving average (ARIMA) model and the back propagation (BP) neural network model, where these two models have superior prediction performance for linear and nonlinear components, respectively. Moreover, the genetic algorithm is exploited to construct the genetic algorithm BP (GABP) neural network to further improve the performance of the proposed model. To verify the effectiveness of the proposed model, experiments predicting the SST based on historic time-series data are performed. The experiment results indicate that the mean absolute error (MAE) of the ARIMA-GABP model is only 0.3033 °C and the root mean square error (RMSE) is 0.3970 °C, which is better than the ARIMA model, BP neural network model, long short-term memory (LSTM) model, GABP neural network model, and ensemble empirical model decomposition BP model among various datasets. Therefore, the proposed model has superior and robust performance concerning predicting SST.

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An Integration-Implemented Newton-Raphson Iterated Algorithm With Noise Suppression for Finding the Solution of Dynamic Sylvester Equation

Cited by 15 publications

References 36 publications

A Real-time Cutting Model Based on Finite Element and Order Reduction

A Real-time Cutting Model Based on Finite Element and Order Reduction

Residual Error Feedback Zeroing Neural Network for Solving Time-Varying Sylvester Equation

A Hybrid ARIMA-GABP Model for Predicting Sea Surface Temperature

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