scholarly journals Optimal Centers’ Allocation in Smoothing or Interpolating with Radial Basis Functions

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 59
Author(s):  
Pedro González-Rodelas ◽  
Hasan M. H. Idais ◽  
Mohammed Yasin ◽  
Miguel Pasadas

Function interpolation and approximation are classical problems of vital importance in many science/engineering areas and communities. In this paper, we propose a powerful methodology for the optimal placement of centers, when approximating or interpolating a curve or surface to a data set, using a base of functions of radial type. In fact, we chose a radial basis function under tension (RBFT), depending on a positive parameter, that also provides a convenient way to control the behavior of the corresponding interpolation or approximation method. We, therefore, propose a new technique, based on multi-objective genetic algorithms, to optimize both the number of centers of the base of radial functions and their optimal placement. To achieve this goal, we use a methodology based on an appropriate modification of a non-dominated genetic classification algorithm (of type NSGA-II). In our approach, the additional goal of maintaining the number of centers as small as possible was also taken into consideration. The good behavior and efficiency of the algorithm presented were tested using different experimental results, at least for functions of one independent variable.

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Muhammad Taimoor ◽  
Xiao Lu ◽  
Hamid Maqsood ◽  
Chunyang Sheng

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.


Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Xu-Qian Fan ◽  
Wenyong Gong

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.


Sign in / Sign up

Export Citation Format

Share Document