scholarly journals Neural-Network-Based Curve Fitting Using Totally Positive Rational Bases

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2197
Author(s):  
Rocio Gonzalez-Diaz ◽  
E. Mainar ◽  
Eduardo Paluzo-Hidalgo ◽  
B. Rubio
Keyword(s):  
Neural Network ◽  
Curve Fitting ◽  
Least Squares Method ◽  
Rational Bézier Curves ◽  
The Neural Network ◽  
Totally Positive ◽  
Gradient Based ◽  
Data Points ◽  
Satisfactory Approximation ◽  
And Control

This paper proposes a method for learning the process of curve fitting through a general class of totally positive rational bases. The approximation is achieved by finding suitable weights and control points to fit the given set of data points using a neural network and a training algorithm, called AdaMax algorithm, which is a first-order gradient-based stochastic optimization. The neural network presented in this paper is novel and based on a recent generalization of rational curves which inherit geometric properties and algorithms of the traditional rational Bézier curves. The neural network has been applied to different kinds of datasets and it has been compared with the traditional least-squares method to test its performance. The obtained results show that our method can generate a satisfactory approximation.

scholarly journals A Nonlinear System Identification Method Based on Adaptive Neural Network

2021 ◽  
Vol 28 (2) ◽  
pp. 111-123
Keyword(s):  
Neural Network ◽  
System Identification ◽  
Nonlinear System ◽  
Nonlinear System Identification ◽  
Generic Model ◽  
Control Engineering ◽  
The Neural Network ◽  
Adaptive Pso ◽  
And Control ◽  
Scientific Engineering

Nonlinear system identification (NSI) is of great significance to modern scientific engineering and control engineering. Despite their identification ability, the existing analysis methods for nonlinear systems have several limitations. The neural network (NN) can overcome some of these limitations in NSI, but fail to achieve desirable accuracy or training speed. This paper puts forward an NSI method based on adaptive NN, with the aim to further improve the convergence speed and accuracy of NN-based NSI. Specifically, a generic model-based nonlinear system identifier was constructed, which integrates the error feedback and correction of predictive control with the generic model theory. Next, the radial basis function (RBF) NN was optimized by adaptive particle swarm optimization (PSO), and used to build an NSI model. The effectiveness and speed of our model were verified through experiments. The research results provide a reference for applying the adaptive PSO-optimized RBFNN in other fields.

Weights Direct Determination of Feedforward Neural Networks without Iterative BP-Training

2010 ◽  
pp. 197-225 ◽  
Author(s):  
Yunong Zhang ◽  
Ning Tan
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Direct Determination ◽  
Bp Neural Networks ◽  
Learning Rates ◽  
The Neural Network ◽  
Gradient Based ◽  
Artificial Neural ◽  
Output Behavior

Artificial neural networks (ANN), especially with error back-propagation (BP) training algorithms, have been widely investigated and applied in various science and engineering fields. However, the BP algorithms are essentially gradient-based iterative methods, which adjust the neural-network weights to bring the network input/output behavior into a desired mapping by taking a gradient-based descent direction. This kind of iterative neural-network (NN) methods has shown some inherent weaknesses, such as, 1) the possibility of being trapped into local minima, 2) the difficulty in choosing appropriate learning rates, and 3) the inability to design the optimal or smallest NN-structure. To resolve such weaknesses of BP neural networks, we have asked ourselves a special question: Could neural-network weights be determined directly without iterative BP-training? The answer appears to be YES, which is demonstrated in this chapter with three positive but different examples. In other words, a new type of artificial neural networks with linearly-independent or orthogonal activation functions, is being presented, analyzed, simulated and verified by us, of which the neural-network weights and structure could be decided directly and more deterministically as well (in comparison with usual conventional BP neural networks).

scholarly journals Mind-Wave Controlled Robot: An Arduino Robot Simulating the Wheelchair for Paralyzed Patients

2018 ◽  
Vol 1 (1) ◽  
pp. 6
Author(s):  
Chi Hang Cheng ◽  
Shuai Li ◽  
Seifedine Kadry
Keyword(s):  
Neural Network ◽  
Low Cost ◽  
Eeg Signal ◽  
The Neural Network ◽  
Lead Electrode ◽  
Short Period ◽  
Specific Position ◽  
And Control

This project attempts to implement an Arduino robot to simulate a brainwave-controlled wheelchair for paralyzed patients with an improved controlling method. The robot should be able to move freely in anywhere under the control of the user and it is not required to predefine any map or path. An accurate and natural controlling method is provided, and the user can stop the robot any time immediately to avoid risks or danger. This project is using a low-cost and a brainwave-reading headset which has only a single lead electrode (Neurosky mind wave headset) to collect the EEG signal. BCI will be developed by sending the EEG signal to the Arduino Mega and control the movement of the robot. This project used the eye blinking as the robot controlling method as the eye blinking will cause a significant pulse in the EEG signal. By using the neural network to classify the blinking signal and the noise, the user can send the command to control the robot by blinking twice in a short period of time. The robot will be evaluated by driving in different places to test whether it can follow the expected path, avoid the obstacles, and stop in a specific position.

A Simple Heat Transfer Correlation for Three Inlet Configurations Using Artificial Neural Network in the Complex Transition Flow Regime

2003 ◽  
Author(s):  
A. J. Ghajar ◽  
L. M. Tam ◽  
S. C. Tam
Keyword(s):  
Neural Network ◽  
Heat Transfer ◽  
Artificial Neural Network ◽  
Least Squares Method ◽  
Transition Flow ◽  
Transfer Coefficients ◽  
Transition Flow Regime ◽  
Bell Mouth ◽  
Data Points ◽  
Artificial Neural

Local forced and mixed heat transfer coefficients were measured by Ghajar and Tam (1994) along a stainless steel horizontal circular tube fitted with reentrant, square-edged, and bell-mouth inlets under uniform wall heat flux condition. For the experiments the Reynolds, Prandtl, and Grashof numbers varied from about 280 to 49000, 4 to 158, and 1000 to 2.5×105, respectively. The heat transfer transition regions were established by observing the change in the heat transfer behavior. The data in the transition region were correlated by using the traditional least squares method. The correlation predicted the transitional data with an average absolute deviation of about 8%. However, 30% of the data were predicted with 10 to 20% deviation. The reason is due to the abrupt change in the heat transfer characteristic and its intermittent behavior. Since the value of heat transfer coefficient has a direct impact on the size of the heat exchanger, a more accurate correlation has been developed using the artificial neural network (ANN). A total of 1290 data points (441 for reentrant, 416 for square-edged, and 433 for bell mouth) were used. The accuracy of the new correlation is excellent with the majority of the data points predicted with less than 10% deviation.

Research of Oilfield Production Forecast Based on Least Squares Fitting and Improved BP Neural Network

2013 ◽  
Vol 333-335 ◽  
pp. 1456-1460 ◽  
Author(s):  
Wen Bo Na ◽  
Zhi Wei Su ◽  
Ping Zhang
Keyword(s):  
Neural Network ◽  
Least Squares ◽  
Curve Fitting ◽  
Bp Neural Network ◽  
Least Squares Method ◽  
Forecast Error ◽  
Production Forecast ◽  
Least Squares Fitting ◽  
Weak Points ◽  
Lm Algorithm

A new method which is least squares fitting combined with improved BP neural network based on LM algorithm was put forward. In order to overcome the weak points that easy to fall into local minimum, slow convergence of traditional BP neural network, we use LM algorithm to improve it. Least-squares curve fitting can be used to reflect the overall trend of the data changes, so we adopted least squares method firstly to make curve fitting for sample data firstly. Then, we corrected the fitting error by the improved BP Neural Network which has the advantages that reflecting external factors. Finally, the fitted values and error correction values were added to get oilfield production forecast. The results show that the oilfield production forecast error is significantly lower than the single curve fitting, BP Neural Network or LMBP.

Neural Network Based Constitutive Model for Rubber Material

2004 ◽  
Vol 77 (2) ◽  
pp. 257-277 ◽  
Author(s):  
Y. Shen ◽  
K. Chandrashekhara ◽  
W. F. Breig ◽  
L. R. Oliver
Keyword(s):  
Neural Network ◽  
Curve Fitting ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Phenomenological Approach ◽  
Neural Network Approach ◽  
Energy Functions ◽  
The Neural Network ◽  
Strain Energy Functions

Abstract Rubber hyperelasticity is characterized by a strain energy function. The strain energy functions fall primarily into two categories: one based on statistical thermodynamics, the other based on the phenomenological approach of treating the material as a continuum. This work is focused on the phenomenological approach. To determine the constants in the strain energy function by this method, curve fitting of rubber test data is required. A review of the available strain energy functions based on the phenomenological approach shows that it requires much effort to obtain a curve fitting with good accuracy. To overcome this problem, a novel method of defining rubber strain energy function by Feedforward Backpropagation Neural Network is presented. The calculation of strain energy and its derivatives by neural network is explained in detail. The preparation of the neural network training data from rubber test data is described. Curve fitting results are given to show the effectiveness and accuracy of the neural network approach. A material model based on the neural network approach is implemented and applied to the simulation of V-ribbed belt tracking using the commercial finite element code ABAQUS.

scholarly journals Deciphering anomalous heterogeneous intracellular transport with neural networks

2019 ◽  
Author(s):  
Daniel S Han ◽  
Nickolay Korabel ◽  
Runze Chen ◽  
Mark Johnston ◽  
Viki J. Allan ◽  
...  
Keyword(s):  
Neural Network ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Intracellular Transport ◽  
Time Series Data ◽  
Series Data ◽  
Range Analysis ◽  
The Neural Network ◽  
Rescaled Range Analysis ◽  
Data Points

AbstractBiological intracellular transport is predominantly heterogeneous in both time and space, exhibiting varying non-Brownian behaviour. Characterisation of this movement through averaging methods over an ensemble of trajectories or over the course of a single trajectory often fails to capture this heterogeneity adequately. Here, we have developed a deep learning feedforward neural network trained on fractional Brownian motion, which provides a novel, accurate and efficient characterization method for resolving heterogeneous behaviour of intracellular transport both in space and time. Importantly, the neural network requires significantly fewer data points compared to established methods, such as mean square displacements, rescaled range analysis and sequential range analysis. This enables robust estimation of Hurst exponents for very short time series data, making possible direct, dynamic segmentation and analysis of experimental tracks of rapidly moving cellular structures such as endosomes and lysosomes. By using this analysis, we were able to interpret anomalous intracellular dynamics as fractional Brownian motion with a stochastic Hurst exponent.

scholarly journals A Compact Gradient Based Neural Network for Capon Spectral Estimation

2020 ◽  
Vol 7 ◽  
Keyword(s):  
Neural Network ◽  
Network Architecture ◽  
Spectral Estimation ◽  
Original Method ◽  
Vector Product ◽  
Neural Network Architecture ◽  
Computational Burden ◽  
The Neural Network ◽  
Gradient Based ◽  
Simulation Results

This paper describes the use of a novel gradient based recurrent neural network to perform Capon spectral estimation. Nowadays, in the fastest algorithm proposed by Marple et al., the computational burden still remains significant in the calculation of the autoregressive (AR) Parameters. In this paper we propose to use a gradient based neural network to compute the AR parameters by solving the Yule-Walker equations. Furthermore, to reduce the complexity of the neural network architecture, the weights matrixinputs vector product is performed efficiently using the fast Fourier transform. Simulation results show that proposed neural network and its simplified architecture lead to the same results as the original method which prove the correctness of the proposed scheme.

scholarly journals An Islanding Detection and Control Strategy to Realize the Stable and Autonomous Operation of Microgrids Using the Virtual Synchronous Generator

2021 ◽  
Vol 9 (11) ◽  
pp. 1315-1333
Author(s):  
Illuru Sree Lakshmi
Keyword(s):  
Neural Network ◽  
Control Strategy ◽  
Synchronous Generator ◽  
Islanding Detection ◽  
Neural Network Approach ◽  
Autonomous Operation ◽  
The Neural Network ◽  
Control Stability ◽  
And Control ◽  
Virtual Synchronous Generator

Abstract: An islanding detection and based control strategy is created in this exploration to accomplish the steady and independent activity of microgrids using the neural network based Virtual Synchronous Generator (VSG) idea during unplanned grid reconfigurations . Maybe of utilizing a design-orientedmethodology, this paper gives a rigorous and extensive hypothetical investigation and reaches a concise conclusion that is easy to execute and successful even in complex situations. Based on the results of the mutation sequence and voltage wavering, a neural network based islanding identification calculation is proposed, which requires less constraint strategy. The proposed neural network approach outperforms the thefrequency measured passive detection method in terms of detection speed and reliability. Broad recreations affirm the reasonableness of the proposed islanding location and control methodology. Additionally, think about the results of the reproductions for the PI regulator, fluffy organizations, and neural organizations. Keywords: Virtual Synchronous Generator, Islanding detection, Islanding operation, Droop control, Stability, Microgrids.

scholarly journals Sensitivity analysis of the GTN damage parameters at different temperature for dynamic fracture propagation in X70 pipeline steel using neural network

2021 ◽  
Vol 15 (58) ◽  
pp. 442-452
Author(s):  
Abdelmoumin Ouladbrahim ◽  
Idir Belaidi ◽  
Samir Khatir ◽  
Erica Magagnini ◽  
Roberto Capozucca ◽  
...  
Keyword(s):  
Neural Network ◽  
Pipeline Steel ◽  
Fem Analysis ◽  
Maximum Load ◽  
Impact Testing ◽  
The Neural Network ◽  
Different Temperatures ◽  
Satisfactory Approximation ◽  
Artificial Neural Network Ann ◽  
Growth Of Voids

In this paper, the initial and maximum load was studied using the Finite Element Modeling (FEM) analysis during impact testing (CVN) of pipeline X70 steel. The Gurson-Tvergaard-Needleman (GTN) constitutive model has been used to simulate the growth of voids during deformation of pipeline steel at different temperatures. FEM simulations results used to study the sensitivity of the initial and maximum load with GTN parameters values proposed and the variation of temperatures. Finally, the applied artificial neural network (ANN) is used to predict the initial and maximum load for a given set of damage parameters X70 steel at different temperatures, based on the results obtained, the neural network is able to provide a satisfactory approximation of the load initiation and load maximum in impact testing of X70 Steel.            

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