Parameters Of Radial Basis Function Neural Network Research Articles

Optimization of modeling and temperature control of air-cooled PEMFC based on TLBO-DE

The temperature control of the air-cooled proton exchange membrane fuel cell (PEMFC) is important for effective and safe operation. To develop a practical and precise controller, this study combines the Radial Basis Function (RBF) neural network with Back Propagation neural network adaptive Proportion Integration Differentiation (BP-PID), and then a metaheuristic algorithm is used to optimize the parameters of RBF-BP-PID for further improvement in temperature control. First, an air-cooled PEMFC system model is established. To match the simulation data with the experimental data, Teaching Learning Based Optimization–Differential Evolution (TLBO-DE) is proposed to identify the unknown parameters, and the maximum relative error is <3.5 %. Second, RBF neural network is introduced to identify the stack temperature and provide the accurate ∂y(k)∂u(k) for BP-PID, which solves the problem of using sign function sgn(∂y(k)∂u(k)) to approximate the ∂y(k)∂u(k) in BP-PID. Regarding the temperature control of air-cooled PEMFC, several controllers are compared, including PID, Fuzzy-PID, BP-PID and RBF-BP-PID. The proposed RBF-BP-PID achieves the best control effect, which reduces the integrated time and absolute error (ITAE) by 3.4 % and 15.8 % based on BP-PID in the startup and steady phases, respectively. Since the ∂y(k)∂u(k) provided by RBF changes softly and continuously during the control process, the parameters self-tuning ability of RBF-BP-PID is better than BP-PID. Third, to improve the control effect of RBF-BP-PID further, TLBO-DE is adopted to optimize the parameters of RBF neural network and BP neural network.

A flow inferential measurement of the independent metering multi-way valve based on an improved RBF neural network

The flow inferential measurement is a crucial way to conduct the electrohydraulic (EH) flow control of independent metering multi-way valves (IMMV). However, valve flow is nonlinearly and uncertainly affected by multiple parameters, which makes its estimation inaccurate. In this paper, a flow inferential measurement method based on an improved radial basis function neural network (RBFNN) is proposed. A three-input and one-output RBFNN is designed utilizing the Gaussian functions to train the flow mapping in terms of the tested flow data. A particle swarm optimization (PSO) combined with the least squares algorithm is presented to optimize the sensitive and irregular parameters of RBFNN, such as center, width, and weight. Furthermore, a linear time-varying factor (LTVF) strategy is adopted to enhance the global search capability of the particle swarm. Experiments demonstrate that compared with other neural network-based flow calculation methods, the proposed LTVF-PSO-RBF method achieves superior accuracy with improvements of 13.08 %-19.83%.

Dynamic analysis of a new 4D fractional-order financial system and its finite-time fractional integral sliding mode control based on RBF neural network

In this paper, considering the combined effect of interest rate and investment demand on the price index, a new 4D fractional-order financial system is established. Based on the local stability theory, the stability of equilibrium points and static bifurcation phenomena are discussed. Subsequently, to further analyze the dynamic behaviors of the new financial system, numerical tools such as bifurcation diagrams, Lyapunov exponents, phase diagrams, 0–1 test diagrams, and complexity diagrams are employed. It is found that, for a suitable selection of the differential order or system parameter, the proposed system can generate periodic oscillations with different period and chaotic attractors with different shapes. Furthermore, a new controller combining radial basis function (RBF) neural network with fractional-order integral sliding mode control is proposed to realize the finite-time synchronization for a class of fractional-order systems. Finally, the effectiveness of the presented control scheme is verified by numerical simulations and the influence of RBF neural network parameters on the control performance is analyzed.

An Efficient Reliability Analysis Method Based on the Improved Radial Basis Function Neural Network

Abstract This paper develops an efficient reliability analysis method based on the improved radial basis function neural network (RBFNN) to increase the accuracy and efficiency of structural reliability analysis. To solve the problems of low computational accuracy and efficiency of the RBFNN, an improved RBFNN method is developed by transferring the sampling center of Latin hypercube sampling (LHS) from the mean values of random variables to the most probable point (MPP) in the sampling step. Then, the particle swarm optimization algorithm is adopted to optimize the shape parameters of RBFNN, and the RBFNN model is assessed by the cross-validation method for subsequent reliability analysis using Monte Carlo simulation (MCS). Four numerical examples are investigated to demonstrate the correctness and effectiveness of the proposed method. To compare the computational accuracy and efficiency of the proposed method, the traditional radial basis function method, hybrid radial basis neural network method, first-order reliability method (FORM), second-order reliability method (SORM), and MCS method are applied to solve each example. All the results demonstrate that the proposed method has higher accuracy and efficiency for structural reliability analysis. Importantly, one practical example of an industrial robot is provided here, which demonstrates that the developed method also has good applicability and effectiveness for complex engineering problems.

Study on Thermal Error Modeling for CNC Machine Tools Based on the Improved Radial Basis Function Neural Network

The thermal error modeling technology of computer numerical control (CNC) machine tools is the core of thermal error compensation, and the machining accuracy of CNC machine tools can be improved effectively by the high-precision prediction model of thermal errors. This paper analyzes several methods related to thermal error modeling in the latest research applications, summarizes their deficiencies, and proposes a thermal error modeling method of CNC machine tool based on the improved particle swarm optimization (PSO) algorithm and radial basis function (RBF) neural network, named as IPSO-RBFNN. By introducing a compression factor to make the PSO algorithm balance between global and local search, the structure parameters of RBF neural network are optimized. Furthermore, in order to pick up the temperature-sensitive variables, an improved model, which combines the K-means clustering algorithm and correlation analysis method based on back propagation (BP) neural network is proposed. After the temperature-sensitive variables are selected, the IPSO-RBFNN method is adopted to establish the thermal error model for CNC machine tool. Based on the experimental data of the CNC machine tool under the name of DMG-DMU65, the predictive accuracy of the IPSO-RBFNN model in Z direction reaches 2.05 μm. Compared with other neural network method, it is improved by 10.48%, which indicates that it has better prediction ability. At last, the experiment verification for different thermal error terms at different velocities proves that this model has stronger robustness.

Hybrid prediction method of blast furnace gas generation considering multi-operation modes in steel plants near the city

Blast furnace gas (BFG) generated in blast furnace (BF) ironmaking process can be converted into steam and electricity to provide energy for the nearby cities. Accurate prediction of BFG generation is crucial for assessing BFG surplus, which is the difficult problem faced by steel plants. A hybrid prediction method is proposed to solve it, which is named Radial Basis Function Neural Network (RBFNN) Based on Improved Genetic Algorithm (IGA) and Grey Relation Analysis (GRA). BF’s operation modes, including smooth, blown-down, blow-down to 0, blow-in, were classified to exclude the unrelated feature factors and set the adaptive prediction horizon. Then feature factors related to BFG generation are quantitatively analyzed by GRA in different operation mode, which affects the structure of RBFNN. And the key parameters of RBFNN is optimized by IGA. Proposed method is validated by a case study from a China’s steel plant. The results show the hybrid method has the obvious advantage with the MAPE of 3.31 %, 3.22 % and RMSE of 337.57 m3 in blow down, blown-in and smooth operation mode, respectively. This paper helps steel plants assess how much steam and electricity converted from BFG can be sent to its nearby cities, and contributes to energy resources utilization.

Adaptive Hyperparameter Fine-Tuning for Boosting the Robustness and Quality of the Particle Swarm Optimization Algorithm for Non-Linear RBF Neural Network Modelling and Its Applications

A method is proposed for recognizing and predicting non-linear systems employing a radial basis function neural network (RBFNN) and robust hybrid particle swarm optimization (HPSO) approach. A PSO is coupled with a spiral-shaped mechanism (HPSO-SSM) to optimize the PSO performance by mitigating its constraints, such as sluggish convergence and the local minimum dilemma. Three advancements are incorporated into the hypothesized HPSO-SSM algorithms to achieve remarkable results. First, the diversity of the search process is promoted to update the inertial weight ω based on the logistic map sequence. Then, two distinct parameters are trained in the original position update algorithm to enhance the work efficiency of the successive generation. Finally, the proposed approach employs a spiral-shaped mechanism as a local search operator inside the optimum solution space. Moreover, the HPSO-SSM method concurrently improves the RBFNN parameters and network size, building a model with a compact configuration and higher precision. Two non-linear benchmark functions and the total phosphorus (TP) modelling issue in a waste water treatment process (WWTP) are utilized to assess the overall efficacy of the creative technique. The results of testing indicate that the projected HPSO-SSM-RBFNN algorithm performed very effectively.

GSM-R wireless field strength coverage prediction algorithm based on PSO-RBF neural network algorithm

In the wake of the successive construction of new railway lines, new lines and existing lines are adjacent, approached and surpassed. In the early stage of line construction, if the influence of adjacent lines is not considered in subsequent planning, the original lines need to be adjusted, and the reconstruction of the base station (BS) coverage along the railway increases the hardness of buliding and the invested funds. Therefore, a Global System for Mobile Communications – Railway (GSM-R) wireless field strength coverage prediction model based on particle swarm optimization (PSO) algorithm optimized radial basis function neural network (RBFNN) was proposed. Aiming at the problem of slow network convergence caused by improper selection of network parameters and structure of RBFNN, PSO algorithm is used to optimize the parameters of RBFNN, and combined with the actual measurement data on site, a PSO-RBFNN model is established to simulate and predict the field strength coverage. The results show that the prediction effect of PSO-RBFNN is the best, followed by RBFNN, and the worst of HATA model, which is very beneficial to the future railway GSM-R wireless network coverage and provides a feasible idea.

Prediction of photovoltaic power output based on similar day analysis using RBF neural network with adaptive black widow optimization algorithm and K-means clustering

Solar photovoltaic power generation has become the focus of the world energy market. However, weak continuity and variability of solar power data severely increase grid operating pressure. Therefore, it is necessary to propose a new refined and targeted forecasting method to broaden the forecasting channels. In this paper, a hybrid model (KM-SDA-ABWO-RBF) based on radial basis function neural networks (RBFNNs), adaptive black widow optimization algorithm (ABWO), similar day analysis (SDA) and K-means clustering (KM) has been developed. The ABWO algorithm develops adaptive factors to optimize the parameters of RBFNNs and avoid getting trapped in local optima. SDA and K-means clustering determine the similarity days and the optimal similarity day through meteorological factors and historical datasets. Nine models compared forecast accuracy and stability over four seasons. Experiments show that compared with other well-known models on the four indicators, the proposed KM-SDA-ABWO-RBF model has the highest prediction accuracy and is more stable.

Direct adaptive neural network-based sliding mode control of a high-speed, ultratall building elevator using genetic algorithm

A direct adaptive sliding mode controller (SMC) based on radial basis function neural network (RBFNN) approximation is proposed for a high-speed, ultratall building elevator system using genetic algorithm (GA) to optimise the control parameters. The nonlinear dynamic model of the elevator system is described, with the RBFNN used to approximate the elevator system functions and external disturbance uncertainties. The RBFNN parameters are optimised using GA. The RBFNN-SMC was compared with a traditional sliding mode controller, nonlinear pseudo-derivative feedback (NPDF) controller and a nonlinear proportional-integral-derivative controller. The Lyapunov stability theorem is applied to develop the adaptive law, thereby guaranteeing the system stability. Performance of the proposed RBFNN-SMC has been evaluated using numerical simulations. The RBFNN-SMC achieved effective control of the elevator system. Although the RBFNN-SMC system achieved comparable pre-re-levelling control to its competitors, problematic chattering was observed due to sensor noise, suggesting that the system must be coupled with a noise-attenuating filter to avoid actuator damage. Following arrival of the cabins, an adaptive re-levelling operation was applied to reduce the distance between the cabins and the arrival floor. Although both SMC variants accomplished successful re-levelling, the NPDF-based controller achieved the best performance—adjusting the final cabin position to within 1 mm of the target floor in both considered displacement overshoot cases.

Reference modification for trajectory tracking using hybrid offline and online neural networks learning

In this paper, we propose a hybrid offline/online neural networks learning method, which combines complementary advantages of two types of neural networks (NNs): deep NN (DNN) and single-layer radial basis function NN (RBFNN). Firstly, after analyzing the mechatronic system’s model, we select reasonable features as the input of the DNN to learn the inverse dynamic characteristics of the closed-loop system offline, so as to establish the mapping between the desired trajectory and the reference trajectory of the system. The trained DNN is used to generate a new reference trajectory and compensate for the tracking error in advance, which can speed up the convergence of online learning control based on RBFNN. This reference trajectory is further modified iteratively when the tracking task is repeated. For this purpose, a single-layer RBFNN model is established, and an online learning algorithm is developed to update the RBFNN parameters. The proposed hybrid offline/online NN method can improve the tracking performance of mechatronic systems by modifying the reference trajectory on top of the baseline controller without affecting the system stability. To verify the effectiveness of this method, we conduct experiments on a piezoelectric drive platform.

Prediction and Estimation of Book Borrowing in the Library: Machine learning

In the library, the prediction and estimation of book borrowing plays an important role in library work. Based on the data mining method, this paper analyzed the prediction and estimation of book borrowing. Firstly, the radial basis function neural network (RBFNN) was analyzed. Then, the improved ant colony algorithm (IACO) was used to obtain the optimal parameters of RBFNN, and then the IACO-RBFNN model was established to realize the prediction and estimation of book borrowing. The results showed that the improved model had advantages in training time, iteration times, and error compared with BPNN and RBFNN. The results of book prediction and estimation showed that the results obtained by the IACO-RBFNN model were closer to the actual book borrowing situation, with smaller error and higher precision (97.09%), and its precision was 11.18% and 4.74% higher than BPNN and RBFNN respectively. The training time and testing time of the IACO-RBFNN model were 5.12 s and 1.03 s, respectively, which were significantly shorter than the other two methods. The results show that the IACO-RBFNN model has a good performance in the prediction and estimation of book borrowing and can be further promoted and applied in practice.

Signal Recognition Based on APSO-RBF Neural Network to Assist Athlete's Competitive Ability Evaluation.

The advanced analysis and research methods of big data will provide theoretical support for the integration of athletes' talent training. The advanced technological methods of big data will also give full play to the advantages of tapping the potential of talents and actively improve the success rate of grassroots young athletes. This paper proposes an improved Adaptive Particle Swarm Optimization (APSO) algorithm for the optimization of radial basis function (RBF) neural network parameters. The basic structure of RBF neural network is introduced, and the influence of parameters on the performance of RBF neural network is analyzed. The optimization method of RBF neural network parameters is analyzed, and Particle Swarm Optimization (PSO) algorithm is selected as the parameter optimization method of RBF neural network. In addition, an improved APSO algorithm is proposed according to the advantages and disadvantages of PSO and compared with other PSO algorithms. Experimental results show that the improved PSO algorithm has better accuracy. The improved PSO algorithm is applied to the parameter optimization of RBF neural network, and the experimental results prove the superiority of the proposed method. By weighting the second-level indicators, the weights of the second-level indicators of athletes' competitive ability are in order of skill, athletic quality, psychological ability, and artistic expression. Skills are the main factors that determine the level of competitive ability. Sports quality and psychological ability are important guarantees for supporting the normal performance of skills. Artistic expressiveness is a supplementary factor for competitive ability. The various elements cooperate with each other and interact with each other. The indicators do not exist alone but cooperate with each other to support the formation of the entire athletic ability system. In the content of the competitive ability index of excellent athletes, technical ability is the core, and sports quality, psychological ability, and artistic performance ability ultimately exist to serve the improvement of technical ability. The competition scores of the 100 athletes counted in this article are all above 9.0 points. The difference between APSO-RBF's action quality scores of 100 athletes and the real value is less than 3%. In terms of movement difficulty, the APSO-RBF evaluated athletes' scores are close to 1.65 points, which is basically the same as the real value.

The Application of RBF Neural Network Optimized by K-means and Genetic-backpropagation in Fault Diagnosis of Power Transformer

Through the dissolved gas analysis (DGA) in transformer oil, the fault of the power transformer can be diagnosed. However, the DGA method has the disadvantage of low accuracy because it couldn’t exactly reflect the nonlinear relationship between the characteristic gases and fault types. Radial basis function neural network (RBFNN) has the advantage of dealing with complex nonlinear problems, so it can be applied to transformer fault diagnosis based on DGA. The centers, widths and weights has important effects on the performance of the RBFNN. However, it is difficult to find the global optimal solution of these parameters when RBFNN training. This paper creatively designs a method to improve these parameters of RBFNN, firstly using the K-means algorithm to optimize the centers and widths of RBFNN, then using the genetic algorithm-backpropagation (GA-BP) algorithm optimize the weights. Finally, establish the K-means RBF-genetic backpropagation (KRBF-GBP) algorithm model through a large amount of training data. The test results show that the fault diagnosis accuracy of the KRBF-GBP algorithm is 96.4%, higher than the unoptimized RBFNN with 71.43%.

Optimized neural network combined model based on the induced ordered weighted averaging operator for vegetable price forecasting

Vegetable price predictions are of great significance to vegetable growers, particularly regarding production and management to ensure a balance in the regional supply and demand of vegetables. In the current paper, in order to improve the accuracy and efficiency of vegetable price forecasting, we propose an optimized neural network combined model based on the induced ordered weighted averaging operator. Our frameworks integrate the fruit fly algorithm (FOA) with the induced ordered weighted averaging (IWOA) operator for an enhanced performance. In particular, the FOA is employed for the parameter optimization of the generalized regression neural network (GRNN) and radial basis function neural network (RBFNN), reducing the adverse influence of man-induced factors in the model construction process and improving the learning ability of both GRNN and RBFNN. The IWOA operator calculates the weights of the single GRNN and RBFNN to address the problem of fixed weights in combination forecasting models. Monthly vegetable price data in Beijing was used to compare our method with nine single forecasting models, revealing that the optimization of the GRNN and RBFNN parameters by the FOA, the prediction accuracy of the FOA-GRNN model and FOA-RBFNN model surpass those of GRNN and RBFNN, respectively. Furthermore, results from four evaluation indexes reveal that the IOWA-based optimized neural network model exhibited a stronger predictive ability than the other nine prediction models. Results demonstrate the effectiveness of our framework for the prediction of vegetable price series, with potential applications in agricultural products of similar characteristics.

Two novel combined systems for predicting the peak shear strength using RBFNN and meta-heuristic computing paradigms

Effective prediction of the peak shear strength (PSS) is of crucial importance in evaluating the stability of a rock slope with interlayered rocks and has both theoretical and practical significance. This paper offers two novel prediction tools for the PSS prediction based on radial basis function neural network (RBFNN) and meta-heuristic computing paradigms. For this work, the gray wolf optimization (GWO) and ant colony optimization (ACO) algorithms were used to select the optimal parameters of RBFNN. Then, these two new models were compared with the gene expression programming (GEP) model. A total of 158 experimental data were used to train and test the proposed models using three input parameters, i.e., normal stress, compressive strength ratio of joint walls, and joint roughness coefficient. Finally, the computational result revealed that the RBFNN-GWO model, with the coefficient of determination (R2) of 0.997, produced a better convergence speed and higher accuracy compared with RBFNN-ACO and GEP models, with the R2 of 0.995 and 0.996, respectively. The RBFNN-GWO model was found an efficient predictive tool that can help rock engineers in the slopes design processes.

Fuzzy Neural Network Q-Learning Method for Model Disturbance Change: A Deployable Antenna Panel Application

This paper addresses the disturbance change control problem with an active deformation adjustment mechanism on a 5-meter deployable antenna panel. A fuzzy neural network Q-learning control (FNNQL) strategy is proposed in this paper for the disturbance change to improve the accuracy of the antenna panel. In the proposed method, the error of the model disturbance is reduced by introducing the fuzzy radial basis function (RBF) neural network into Q-learning, and the parameters of the fuzzy RBF neural network were optimized and adjusted by a Q-learning method. This allows the FNNQL controller to have a strong adaptability to deal with the disturbance change. Finally, the proposed method has been adopted in the middle plate of a 5-meter deployable antenna panel, and it was found that the method could successfully adapt the model disturbance change in the antenna panel. Results of the simulation also show that the whole control system meets the required accuracy requirements.

Dispersion Model of Volatile Organic Compounds Based on RBF Neural Network

In this paper, we try to establish the dispersion model of Volatile Organic Compounds (VOCs). Whereas the mechanism dispersion model is too complicated and only suitable for the case where only one release source exists, we establish the black-box model based on data for the case where multiple release sources exist. After the input and output variables are determined, the Radial-Basis Function (RBF) neural network is used to describe the relationship between the inputs and the outputs because it can approximate arbitrary function with arbitrary precision. Considering the difficulty in selecting the parameters of RBF neural network, we use the Swarm Cuckoo Search (SCS) algorithm to obtain the suitable parameters. The simulation experiments demonstrate the effectiveness of the proposed model.

Non-negative Radial Basis Function Neural Network in Polynomial Feature Space

Radial basis function neural network (RBFNN) is an effective nonlinear learning model, which has a strong nonlinear fitting capability. The hidden neurons and the weight play important roles in the neural network. In the existing researches, the hidden neurons are computed in the form of a rigorous linear combination. And the weight is hard to be solved. To address these issues, in this paper a novel neural network named non-negative radial basis function neural network (NRBFNN) is proposed. The main thought of non-negative matrix factorization (NMF) is to be used to train the parameters of RBFNN. According to the structure of the neural network, the label information of the samples is decomposed into the weight matrix and the mapped feature by activation functions in polynomial feature space. And the proposed method is able to obtain the weight matrix and the hidden neurons implied in the activation functions iteratively. Furthermore, the proposed NRBFNN is able to improve the representability of the hidden neurons and the iterative formulas of the weight can ensure the solvability and interpretability of it. ORL, Yale and Caltech 101 face databases are selected for evaluations. Experimental results show that the proposed algorithm outperforms several related algorithms.

Biomass concentration prediction via an input-weighed model based on artificial neural network and peer-learning cuckoo search

Biomass concentration (BC) is considered as one of the most important biochemical parameters. Its reliable on-line estimation is crucial in the real-time status monitoring and quality control of fermentation processes. Considering that each input variable may have different influence on BC in actual fermentation processes, a novel input-weighted empirical model based on the radial basis function neural network (RBFN) and a new peer-learning cuckoo search (PLCS) algorithm, is proposed in this paper to predict BC. The determination of input variable weights and RBFN parameters for the proposed BC prediction model is framed as one and the same optimization problem. Inspired by a common social phenomenon that the mutual learning between team members (peers) would be extremely helpful for their team to accomplish a work efficiently, a PLCS algorithm is proposed to solve the resulting optimization (RO) problem, and thereby accomplish the development of the proposed BC prediction model. The effectiveness and superiority of this new prediction model is validated using the production data from a lab-scale nosiheptide fermentation process. Moreover, the performance of PLCS is also demonstrated on the RO problem with these data and some benchmark functions.