Radial Basis Function Neural Network Method Research Articles

Optimal sizing and optimization of financial cost for EVs using SPOA-RBFNN technique

This study proposes a hybrid technique for optimal sizing and cost optimization of hybrid energy storage systems (HESS) integrated into electric vehicles (EVs). The proposed technique, SPOA-RBFNN, combines a student psychology-based optimization algorithm (SPOA) and a radial-basis function neural network (RBFNN). The study aims to minimize the overall cost of the HESS by evaluating two design variables: the super-capacitor (SC) and battery pack size. SPOA is employed to optimize the hybrid HESS design variables, ensuring efficient exploration of solution spaces. The RBFNN method is then used to predict the relationship between these design variables and the overall cost of the HESS in electric vehicles. The results show that the proposed technique is more effective than existing techniques, with an efficiency of 97.99039% compared to 82.137% for GA and 77.26589% for particle swarm optimization (PSO). This work offers a comprehensive and innovative approach to optimizing HESS sizing in EVs, connecting the gap between performance optimization and financial cost analysis.

Structural properties and diameter prediction of fine denier polyester fiber based on machine learning algorithms

Fine denier polyester fibers have attracted attention in electronic information industry owing to their unique structural properties and ultra fine diameters. Since there is a close connection between melt-spinning process parameters and their structural properties and diameters, the influence of process parameters on fiber structural properties and diameters is an issue worth further exploration. This study aims to construct prediction models based on the Gaussian process regression (GPR), radial basis function neural network (RBFNN) and extreme learning machine (ELM) algorithms to predict the structural properties and diameter of fine denier polyester fibers. For this purpose, firstly, fine denier polyester fibers with different structural properties (i.e., orientation degree and crystallinity) and diameters are produced by changing the key melt-spinning parameters, namely spinning temperature, take-up speed and metering pump speed. Then GPR, RBFNN and ELM methods are applied to predict the structural properties and diameter of fine denier polyester fibers based on the experimental data. Lastly, different predictive performance indicators, namely mean square error (MSE) and mean absolute error (MAE) are imported to evaluate the above three methods. The predicted results which the MSE values of GPR, RBFNN and ELM models are respectively 0.461, 0.358, 0.136, and the MAE values of GPR, RBFNN and ELM models are respectively 0.625, 0.564, 0.320 show that ELM model provided superior performance over the GPR and RBFNN models in predicting the structural properties and diameter of fine denier polyester fibers.

A Comparison of Ocean Wave Height Forecasting Methods for Ocean Wave Energy Conversion Systems

Ocean wave height plays an important role in the operation status of ocean wave energy conversion systems. In this paper, the future continuous ocean wave height within 2~3 s is forecasted by three methods, the autoregressive moving average model (ARMA) method, backpropagation (BP) neural network method, and radial basis function (RBF) neural network method. Then, the error between suggested forecast results and corresponding measured results are compared by the root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient R. The comparison result indicates that the RBF neural network method is preferred to the other two methods, having the advantage of high accuracy. Lastly, the reasons for the errors of the three forecasting methods are analyzed. This study signifies that the RBF neural network method is beneficial to the operation control and efficiency improvement of ocean wave energy conversion systems.

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.

Far-field identification of ice loads on ship structures by radial basis function neural network

The ice load is an environmental load that dominates the ice-resistant design of polar ship structures, and field measurement of ice-induced strains is an important approach to obtain ice loads. Constrained by narrow spaces and watertight structures in the ship-ice interaction area, the monitoring area where strain sensors are mounted sometimes has to be arranged separately from the loading area, which makes the classical influence coefficient matrix method no longer applicable. The far-field identification method for ice loads, based on the radial basis function neural network (RBFNN) with a simple structure and fast convergence, provides an alternative way to solve this problem. The potential mapping relationship between ice loads and far-field ice-induced strains is effectively established based on a generalised RBFNN. The influence of noise on the identification results of the ice loads on the bow shoulder of RV Xue Long 2 is thoroughly studied with finite element numerical analysis and effectively eliminated by noise injection learning algorithm. Under weak strain response and low signal-to-noise ratio, the accurate results of the subsequent scale model test indicate the possibility of engineering application. According to the rationality analysis of the identification results based on full-scale data, the applicability of the RBFNN method to field measurements is verified.

On the optimal design of radial basis function neural networks for the analysis of nonlinear stochastic systems

In this paper, an iterative selection strategy of Gaussian neurons for radial basis function neural networks (RBFNN) is proposed when the RBFNN method is applied to obtain the steady-state solution of the Fokker–Planck–Kolmogorov (FPK) equation. A performance index is introduced to rank neurons. Top rank neurons are selected, leading to a RBFNN with optimal number and locations of Gaussian neurons for the FPK equation under consideration. The statistical properties of the performance index are studied. It is found that the index assigned to the jth neuron is proportional to the probability of the system falling into the small neighborhood of the mean of this neuron as well as proportional to the weight of the neuron. The RBFNN method with the optimally selected neurons is then applied to several challenging examples of nonlinear stochastic systems in 2, 3 and 4 dimensional state space. The RBFNN solutions are also compared with the results of extensive Monte Carlo simulations. It is observed that the RBFNN method with optimally selected neurons by the proposed iterative algorithm is much more efficient than the RBFNN method with uniformly distributed neurons, and is very accurate in terms of the root mean squared (RMS) errors of the FPK equation or the RMS errors of the PDF solution compared with simulation results.

Multi-Objective Optimization Model for Uncertainty Consideration of RESs & Load Demands with the Optimal Design of Hybrid CCHP by DDAO-RBFNN Strategy

This manuscript proposes a hybrid system for an integrated solar and natural gas hybrid model with photovoltaic/thermal (PV/T) collectors and gas turbines (GT). The proposed optimization method combines both Dynamic Differential Annealed Optimizations (DDAO) and Radial Basis Function Neural Network (RBFNN), so it is called the DDAO-RBFNN approach. Natural gas, solar energy, coal, and geothermal energy are the sources of the system, while electricity, cooling, and heating are the energy needs of the system. A multi-objective stochastic model incorporates load and renewable energy uncertainty to obtain more efficient, economic, and environmental decisions. By utilizing an existing data set, the proposed approach is to forecast a new set. Some characteristics, such as historical weather data, building loads, and market information are required for modelling the energy hub and unpredictable factors. The proposed RBFNN method is used to model the energy hub through data collection, analysis, and initial sampling of uncertainty factors. To provide optimal outcomes with great computational time, the accuracy of DDAO approach is used. Smart operation managements consider both the energy supply and demand sides to achieve optimal state functioning of the hybrid CCHP scheme. Finally, the proposed system is performed in MATLAB/Simulink site and the performance of the proposed method is compared with existing methods.

Convolutional neural network for fast adaptive beamforming of phased array weather radar

PurposeThe purpose of this paper is to present a deep-learning-based beamforming method for phased array weather radars, especially whose antenna arrays are equipped with large number of elements, for fast and accurate detection of weather observations.Design/methodology/approachThe beamforming weights are computed by a convolutional neural network (CNN), which is trained with input–output pairs obtained from the Wiener solution.FindingsTo validate the robustness of the CNN-based beamformer, it is compared with the traditional beamforming methods, namely, Fourier (FR) beamforming and Capon beamforming. Moreover, the CNN is compared with a radial basis function neural network (RBFNN) which is a shallow type of neural network. It is shown that the CNN method has an excellent performance in radar signal simulations compared to the other methods. In addition to simulations, the robustness of the CNN beamformer is further validated by using real weather data collected by the phased array radar at Osaka University (PAR@OU) and compared to, besides the FR and RBFNN methods, the minimum mean square error beamforming method. It is shown that the CNN has the ability to rapidly and accurately detect the reflectivity of the PAR@OU with even less clutter level in comparison to the other methods.Originality/valueMotivated by the inherit advantages of the CNN, this paper proposes the development of a CNN-based approach to the beamforming of PAR using both simulated and real data. In this paper, the CNN is trained on the optimum weights of Wiener solution. In simulations, it is applied on a large 32 × 32 planar phased array antenna. Moreover, it is operated on real data collected by the PAR@OU.

Random vibration of hysteretic systems under Poisson white noise excitations

Hysteresis widely exists in civil structures, and dissipates the mechanical energy of systems. Research on the random vibration of hysteretic systems, however, is still insufficient, particularly when the excitation is non-Gaussian. In this paper, the radial basis function (RBF) neural network (RBF-NN) method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations. The solution to the reduced generalized Fokker-Planck-Kolmogorov (GFPK) equation is expressed in terms of the RBF-NNs with the Gaussian activation functions, whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition. A steel fiber reinforced ceramsite concrete (SFRCC) column loaded by the Poisson white noise is studied as an example to illustrate the solution process. The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated, and the obtained results are compared with those obtained by the Monte Carlo simulations (MCSs). The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.

Transient response of Bouc–Wen hysteretic system under random excitation via RBFNN method

Hysteresis normally exhibited by mechanical systems and materials is so prevalent that its response prediction under random excitation has been extensively investigated for decades. Nevertheless, the transient solution of the response, which is crucial for assessing the system’s reliability, is still a challenging topic that requires additional development. To this regard, this work proposes a semi-analytical method using the radial basis function neural network (RBFNN) to attain the transient probability density distribution of the randomly excited Bouc–Wen system. Specifically, the trial solution of the corresponding FPK equation is configured as the RBFNN with undetermined time-varying weight coefficients. By discretizing the time derivative with the Euler difference method, a loss function with time recurrence is derived and minimized to yield the time-varying optimal weight coefficients through the optimization method. Additionally, an optimized sampling strategy is adopted to reduce the burden of calculation. Finally, the Bouc–Wen hysteretic systems with softening and hardening nonlinearity are considered to investigate the performance of the adopted technique. The numerical results have shown that the evaluation process of the probability density functions(PDFs) can be captured well with sufficient accuracy and efficiency. The proposed efficient sampling technique can provide considerable efficiency improvement for the medium dimension system. The work of the paper will contribute to the reliability design of hysteretic structures in engineering.

Radial basis function neural networks solution for stationary probability density function of nonlinear stochastic systems

A radial basis function neural networks (RBF-NN) solution of the reduced Fokker–Planck-Kolmogorov (FPK) equation is proposed in this paper. The activation functions consist of normalized Gaussian probability density functions (PDFs). The use of normalized Gaussian PDFs leads to a simple constraint on the coefficients for normalization of the RBF-NN solution, which as a constraint is imposed with the help of the method of Lagrange multiplier. The relationship between the proposed RBF-NN PDF solution and the generalized cell mapping with short-time Gaussian approximation is discussed, which provides a justification for Gaussian PDFs with varying means and variances in the state space. The optimal number of neurons or activation functions, which leads to the smallest error, is investigated. Four examples are presented to show the effectiveness of the proposed solution method. The results indicate that the proposed solution method is a very efficient and accurate way to compute the stationary PDF of nonlinear stochastic systems. It is also found that the distribution of the optimal coefficients as a function of the mean of Gaussian activation functions is similar to the steady-state PDF solution. Finally, we should point out that an important advantage of the RBF-NN method over methods such as finite element and finite difference is its ability to obtain solutions of the FPK equation for multi-degree-of-freedom stochastic systems.

Prediction of suicidal ideation among Chinese college students based on radial basis function neural network.

Suicide is one of the leading causes of death for college students. The predictors of suicidal ideation among college students are inconsistent and few studies have systematically investigated psychological symptoms of college students to predict suicide. Therefore, this study aims to develop a suicidal ideation prediction model and explore important predictors of suicidal ideation among college students in China. We recruited 1,500 college students of Sichuan University and followed up for 4 years. Demographic information, behavioral and psychological information of the participants were collected using computer-based questionnaires. The Radial Basis Function Neural Network (RBFNN) method was used to develop three suicidal ideation risk prediction models and to identify important predictive factors for suicidal ideation among college students. The incidence of suicidal ideation among college students in the last 12 months ranged from 3.00 to 4.07%. The prediction accuracies of all the three models were over 91.7%. The area under curve scores were up to 0.96. Previous suicidal ideation and poor subjective sleep quality were the most robust predictors. Poor self-rated mental health has also been identified to be an important predictor. Paranoid symptom, internet addiction, poor self-rated physical health, poor self-rated overall health, emotional abuse, low average annual household income per person and heavy study pressure were potential predictors for suicidal ideation. The study suggested that the RBFNN method was accurate in predicting suicidal ideation. And students who have ever had previous suicidal ideation and poor sleep quality should be paid consistent attention to.

Random vibration analysis of vibro-impact systems: RBF neural network method

The recent success of the radial basis function neural networks (RBFNN) method for random vibration analysis of smooth systems fuels in speculations that this approach may be extended to non-smooth problems. However, very little is known on the applicability of this approach to non-smooth systems. This work generalizes the RBFNN method to the randomly excited non-smooth vibro-impact system (VI-S). We first transform the non-smooth VI-S system to a continuous nonlinear system. Then, the solution of the reduced Fokker–Planck–Kolmogorov (FPK) equation for the transformed VI-S is expressed in terms of the RBFNN with Gaussian activation functions. The weights of the RBFNN are determined by solving an optimization problem to minimize the reduced FPK equation residual subjected to the constraint of the normalization condition. Three examples are presented to demonstrate the validity of the suggested scheme. Several remarks on the solution process also presented. All the results confirm the applicability and validity of the RBFNN method in dealing with the randomly excited non-smooth VI-S.

Computational prediction of the drilling rate of penetration (ROP): A comparison of various machine learning approaches and traditional models

Rate of penetration (ROP) prediction, can assist precise planning of drilling operations and can reduce drilling costs. However, easy estimation of this key factor by traditional or experimental models is very difficult. This requires comparing available models for achieving the best prediction approach. In this study, four machine learning (ML) methods and two traditional ROP models were utilized to predict ROP. ML techniques include multilayer perceptron neural network (MLPNN), radial basis function neural network (RBFNN), adaptive neuro-fuzzy inference system (ANFIS), and support vector regression (SVR). MLPNN, ANFIS, and RBFNN methods were trained with four meta-heuristic algorithms including particle swarm optimization (PSO), ant colony optimization (ACO), differential evolution (DE), and genetic algorithm (GA). The backpropagation (BP) algorithm was also incorporated to train the ANFIS and MLPNN methods as a conventional method. For comparison purposes, the traditional ROP models of Bourgoyne and Young (BYM) and Bingham were also implemented in combination with four meta-heuristic algorithms. The required data were collected from the mud logging unit (MLU) and the final report of a drilled well located in southwestern of Iran. In the MLU, the information of different sensors is firstly collected through the data communications protocols and sent to a master unit to be processed into relevant dimensions (i.e. create operational variables). In order to accurately record information, the sensors are calibrated at regular intervals. After removing the outliers, the overall noise of data was reduced by Savitzky-Golay (SG) smoothing filter. Then, in order to simulate a drilling process in a realistic manner and also to evaluate the performance of the models in approximating the penetration rate at greater depth of hole, the available data were divided into 6 sections based on depth. After that, sections 2 Data collection and preprocessing , 3 Methodology , 4 Model development and ROP estimation , 5 Discussion and results , 6 Conclusion were separately used as a test dataset and all previous sections were considered as a training dataset. Results indicated that PSO-MLPNN achieved the highest performance in comparing with other developed models. The concluding remark is that ML models are more efficient and reliable than traditional models. In addition, combining ML models with meta-heuristic algorithms can achieve better results than conventional algorithms such as BP. The results of this study can be used as a practical guide for the management and planning of future well drilling. • Applying Savitzky-Golay (SG) filter to remove noise from data. • Data were divided into 6 sections. Section 2 to 6 were separately noted as test and the previous one(s) as training dataset. • Comparison of four machine learning (ML) methods and two traditional ROP models. • Coupling models with meta-heuristic algorithms and conventional algorithms. • PSO-MLPNNmodel showed the highest accuracy compared to others.

Comparative analysis of dynamic changes in forest resources with RBF neural network and regression method

Forest resources are the most important natural resources; their dynamic changes (growth or decline) are affected by socio-economic factors, and to study their linkage is of great significance. However, the relationship between forest resources and social economic factors is normally a multivariate nonlinear relationship. There are difficulties in accurately analyzing it by using traditional multivariate-statistical methods. Also, its explicit mathematical model is inconvenient for intelligent management. In this paper, the radial basis function (RBF) neural network was introduced to study the relationship between the changes of forest resources and socio-economic factors and was evaluated by comparison with the traditional multiple-linear regression model. The results showed that the RBF neural network method can be applied in modeling the dynamic changes of forest resources and showed a higher prediction accuracy over the traditional statistical modeling approaches. At the same time, the RBF neural network can analyze and evaluate the importance of influencing factors simply and conveniently. The results provide a new way and show an application potential for the analysis and intelligent management in forest resources.

Distribution Feeder Parameter Estimation Without Synchronized Phasor Measurement by Using Radial Basis Function Neural Networks and Multi-Run Optimization Method

In practice, the performance of distribution feeder parameter estimation is limited by the measurement conditions in distribution networks. An accurate mathematical model that considers limited phasor measurements in distribution networks is necessary to estimate feeder parameters. This paper presents a set of modified parameter estimation models for unbalanced three-phase distribution feeders that only require the measurements of voltage amplitudes and power flows. To simplify the calculation process and improve the estimated results, a method combined with a radial basis function neural network (RBFNN) and multi-run optimization method (MRO), namely RBFNN-MRO, is proposed to calculate the parameters of distribution feeders. The relationship between the feeder parameters and the measurement data from the two terminals of the feeder can be mapped perfectly using the RBFNN. Furthermore, the random errors in the measurement device were eliminated using the proposed RBFNN-MRO algorithm. The RBFNN-MRO algorithm can limit the number of neurons in the hidden layer and substantially reduce the training time for each RBFNN. The feasibility of the proposed method was verified using four IEEE test systems. The proposed RBFNN-MRO and RBFNN methods were compared using the maximum absolute percentage error (MAPE) curves. The results reveal that the proposed RBFNN-MRO method has excellent potential for improving the accuracy of feeder parameter estimation even without synchronized phasor measurement.

Investigation of spectrophotometric simultaneous absorption of Salmeterol and Fluticasone in Seroflo spray by continuous wavelet transform and radial basis function neural network methods

In this research, the simultaneous absorption of Salmeterol (SAL) and Fluticasone (FLU) in Seroflo spray was investigated using a spectrophotometric device via employing continuous wavelet transform (CWT) and radial basis function neural network (RBF-NN) methods. Root mean square error (RMSE) related to the RBF model was obtained 3.17 × 10-13 and 1.41 × 10-13 for SAL and FLU, respectively. Limit of detection (LOD) and limit of quantification (LOQ) corresponding to the CWT method were 0.004, 0.280 μg/mL, and 0.431, 0.479 μg/mL for SAL and FLU, respectively. Root mean square error (RMSE) of SAL and FLU was obtained 3.17 × 10-13 and 1.41 × 10-13, respectively in RBF-NN method. In the end, the results obtained from all methods were compared with the high-performance liquid chromatography (HPLC) as a reference method. According to the one-way analysis of variance with a 95% confidence level, there is no significant difference between the proposed techniques and HPLC. Therefore, chemometrics methods are sufficiently accurate, as the reference method for the analysis of drugs. The suggested methods are simple, fast, and cheap. Also, there is no need for pre-preparation steps. These methods can be used for quality control laboratories in the pharmaceutical industry.

THE USE OF AN RBF NEURAL NETWORK AND A GENETIC ALGORITHM FOR MULTI-OBJECTIVE OPTIMISATION OF A CENTRIFUGAL PUMP VOLUTE

When it comes to the construction of hydraulic structures, the hydraulic performance and acoustic performance of centrifugal pumps are connected and conflicting. In order to find a solution to this issue, a technique for optimising the design of a volute that is based on a radial basis function (RBF) neural network and a genetic algorithm (GA) has been developed. The effectiveness of the centrifugal pump as well as the total amount of sound pressure level are employed as the targets for optimisation. The factors that are used for optimisation purposes are the installation angle of the volute tongue, the height of the volute diffuser tube, the installation angle of the volute tongue, and the diameter of the base circle. The Latin hyper-cube sampling (LHS) method is used to construct the sample space. The RBF neural network method is used to develop the agent model between the optimisation variables and goals. Finally, the GA method is utilised to do multi-objective optimisation. In order to do a comparative investigation of the hydraulic and acoustic performance of the persons in the Pareto solution set under a variety of different working situations, the initial individuals and two individuals from the set's extremes are chosen. The findings indicate that under the rated working conditions, the efficiency of the optimal individual of efficiency increases by 3.79%, while the internal noise of the optimal individual of sound pressure level decreases by 5.5% and the external noise decreases by 2.3%. The results also show that the initial individual had a lower level of efficiency than the optimal individual.

Adaptive Neural-Network Boundary Control for a Flexible Manipulator With Input Constraints and Model Uncertainties

This article develops an adaptive neural-network (NN) boundary control scheme for a flexible manipulator subject to input constraints, model uncertainties, and external disturbances. First, a radial basis function NN method is utilized to tackle the unknown input saturations, dead zones, and model uncertainties. Then, based on the backstepping approach, two adaptive NN boundary controllers with update laws are employed to stabilize the like-position loop subsystem and like-posture loop subsystem, respectively. With the introduced control laws, the uniform ultimate boundedness of the deflection and angle tracking errors for the flexible manipulator are guaranteed. Finally, the control performance of the developed control technique is examined by a numerical example.

Image Reconstruction for Electrical Impedance Tomography Using Radial Basis Function Neural Network Based on Hybrid Particle Swarm Optimization Algorithm

A Hybrid Particle Swarm Optimization (HPSO) algorithm is proposed to optimize the Radial Basis Function Neural Network (RBFNN) for the image reconstruction of Electrical Impedance Tomography (EIT). This algorithm combines the non-linear approximation ability of RBFNN with the mutation ability of HPSO based on the simulated annealing, which has advantages of the strong global search ability and high robustness. A non-linear mapping relationship model between the boundary voltage and the conductivity distribution is established through HPSO-RBFNN to realize the image reconstruction, skipping the solution of the Jacobian matrix. The Structural similarity (SS) and correlation coefficient (CC) are used as the evaluation criteria for the quality of the reconstructed images in the simulations and experiments. Firstly, the HPSO-RBFNN method is compared with the Landweber and RBFNN methods through a single-target simulation, which verifies the accuracy of the image reconstruction. Secondly, the Gaussian noise is added to the ideal simulation data, the results show an anti-noise capability of the proposed method. Then, the multi-target simulation is conducted using the single-target training model, which verifies the generalization ability of the proposed method. Finally, the experiments with multiple fish eggs are performed to further verify the effectiveness of the HPSO-RBFNN method. The results show that the method proposed in this article has higher SS and CC, which indicates that the HPSO-RBFNN method has a higher accuracy.