scholarly journals A Meshless Method to Determine a Source Term in Heat Equation with Radial Basis Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Baiyu Wang ◽  
Anping Liao
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Radial Basis Functions ◽  
Meshless Method ◽  
Source Term ◽  
Initial Boundary ◽  
High Accuracy ◽  
Basis Functions ◽  
Unknown Source ◽  
Radial Basis

This paper considers a numerical method based on the radial basis functions for the inverse problem of heat equation; the inverse problem is determining an unknown source term subject to the overdetermination along with the usual initial boundary conditions, and the unknown source term is only time-dependent. The radial basis functions method is a meshless method with high accuracy for the inverse problem. Some numerical experiments using this method are presented and discussed.

scholarly journals Numerical method of identification of an unknown source term in a heat equation

2002 ◽  
Vol 8 (2) ◽  
pp. 161-168 ◽  
Author(s):  
Afet Golayoğlu Fatullayev
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Numerical Method ◽  
Minimization Problem ◽  
Unknown Function ◽  
Source Term ◽  
Numerical Procedure ◽  
Numerical Examples ◽  
Unknown Source

A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the overspecified data. Numerical examples are presented.

Adaptive rapid neural observer-based sensors fault diagnosis and reconstruction of quadrotor unmanned aerial vehicle

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Muhammad Taimoor ◽  
Xiao Lu ◽  
Hamid Maqsood ◽  
Chunyang Sheng
Keyword(s):  
Radial Basis Functions ◽  
Function Theory ◽  
Sliding Mode ◽  
High Accuracy ◽  
Basis Functions ◽  
Multi Layer Perceptron ◽  
Content Type ◽  
Radial Basis ◽  
Aerial Vehicle ◽  
A New Technique

Purpose The objective of this research is to investigate various neural network (NN) observer techniques for sensors fault identification and diagnosis of nonlinear system in consideration of numerous faults, failures, uncertainties and disturbances. For the importunity of increasing the faults diagnosis and reconstruction preciseness, a new technique is used for modifying the weight parameters of NNs without enhancement of computational complexities. Design/methodology/approach Various techniques such as adaptive radial basis functions (ARBF), conventional radial basis functions, adaptive multi-layer perceptron, conventional multi-layer perceptron and extended state observer are presented. For increasing the fault detection preciseness, a new technique is used for updating the weight parameters of radial basis functions and multi-layer perceptron (MLP) without enhancement of computational complexities. Lyapunov stability theory and sliding-mode surface concepts are used for the weight-updating parameters. Based on the combination of these two concepts, the weight parameters of NNs are updated adaptively. The key purpose of utilization of adaptive weight is to enhance the detection of faults with high accuracy. Because of the online adaptation, the ARBF can detect various kinds of faults and failures such as simultaneous, incipient, intermittent and abrupt faults effectively. Results depict that the suggested algorithm (ARBF) demonstrates more confrontation to unknown disturbances, faults and system dynamics compared with other investigated techniques and techniques used in the literature. The proposed algorithms are investigated by the utilization of quadrotor unmanned aerial vehicle dynamics, which authenticate the efficiency of the suggested algorithm. Findings The proposed Lyapunov function theory and sliding-mode surface-based strategy are studied, which shows more efficiency to unknown faults, failures, uncertainties and disturbances compared with conventional approaches as well as techniques used in the literature. Practical implications For improvement of the system safety and for avoiding failure and damage, the rapid fault detection and isolation has a great significance; the proposed approaches in this research work guarantee the detection and reconstruction of unknown faults, which has a great significance for practical life. Originality/value In this research, two strategies such Lyapunov function theory and sliding-mode surface concept are used in combination for tuning the weight parameters of NNs adaptively. The main purpose of these strategies is the fault diagnosis and reconstruction with high accuracy in terms of shape as well as the magnitude of unknown faults. Results depict that the proposed strategy is more effective compared with techniques used in the literature.

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