Weights Of Radial Basis Function Neural Network Research Articles

Real-time haptic characterisation of Hunt-Crossley model based on radial basis function neural network for contact environment

Dynamic soft tissue characterisation is an important element in robotic minimally invasive surgery. This paper presents a novel method by combining neural network with recursive least square (RLS) estimation for dynamic soft tissue characterisation based on the nonlinear Hunt-Crossley (HC) model. It develops a radial basis function neural network (RBFNN) to compensate for the error caused by natural logarithmic factorisation (NLF) of the HC model for dynamic RLS estimation of soft tissue properties. The RBFNN weights are estimated according to the maximum likelihood principle to evaluate the probability distribution of the neural network modelling residual. Further, by using the linearisation error modelled by RBFNN to compensate for the linearised HC model, an RBFNN-based RLS algorithm is developed for dynamic soft tissue characterisation. Simulation and experimental results demonstrate that the proposed method can effectively model the natural logarithmic linearisation error, leading to improved accuracy for RLS estimation of the HC model parameters.

Fixed-time command-filtered composite adaptive neural fault-tolerant control for strict-feedback nonlinear systems

The research investigates the fixed-time command-filtered composite adaptive neural fault-tolerant (FCCANF) control issue of strict-feedback nonlinear systems (SFNSs). There exist unknown functions and bounded disturbances in the considered systems. Radial basis function neural networks (RBFNNs) will be used in the estimate of the unknown functions. By the serial–parallel estimation models (SPEMs), the forecast biases and the track biases can change the weights of RBFNNs and the approximate characteristics of RBFNNs will be improved. Then, utilizing the novel fixed-time command filter and adaptive disturbance observers, the issue of complex explosion will be effectively solved and the external disturbance is effectively compensated. Subsequently, by utilizing the adaptive control technique, a novel FCCANF controller is developed. Additionally, we have that the system internal variables are bounded and the output variable inclines to a little interval around zero in fixed time which is not determined by the system initial variables. Eventually, numerical and practical examples are shown to prove the availability of the obtained control technique.

Nearly optimal fault-tolerant constrained tracking for multi-axis servo system via practical terminal sliding mode and adaptive dynamic programming

In this paper, a nearly optimal tracking control is proposed for n-links robotic manipulators subject to parameter uncertainties, time-profile failures, and input saturation constraints. Firstly, the practical terminal sliding-mode (PTSM) manifold with a linear additional term is proposed to combine the system states related to joint rotation, such that the controlled states quickly fall into a tiny neighborhood of the equilibrium once they reach the PTSM manifold. Secondly, a nearly optimal sliding-mode reaching law is designed by using the adaptive dynamic programming (ADP) technique. Benefiting from a non-quadratic positive defined mapping of the proposed performance index, which relates to the derivative of the sliding-mode function, reduced-order system dynamics can be constrained to a desired region. For the bounded actuator fault caused by various inducements such as the power supply fluctuation and the wear of parts, a radial basis function neural network (RBFNN) is introduced to compensate for this, and the input saturation constraints of the controlled plant are also compensated at the same time. Innovatively, the node weights of RBFNN are updated by the critic network of the ADP framework, such that the integrity of the proposed control strategy is improved. Simulations verify the main conclusions.

Deterministic Learning From Adaptive Neural Network Control for a 2-DOF Helicopter System With Unknown Backlash and Model Uncertainty

In this study, we develop a deterministic learning control approach using adaptive neural network (NN) for a two-degrees-of-freedom helicopter nonlinear system subject to unknown backlash and model uncertainty. First, by combining the backstepping and direct Lyapunov approaches, a novel adaptive NN control scheme with an inverse compensation method is proposed to address the input backlash nonlinearity, track specified trajectories, and stabilize the closed-loop system. Simultaneously, uncertain system dynamics are accurately identified and stored as learned knowledge in constant radial basis function NN weights, while satisfying partial persistent excitation. Subsequently, by extracting the learned knowledge, a learning-based controller is constructed to operate the same control tasks to achieve a superior control performance, less backlash nonlinearity, and minimal computational burden. Finally, the validity and efficacy of the proposed scheme are demonstrated through numerical examples and experiments.

Fault-tolerant attitude tracking control for carrier-based aircraft using RBFNN-based adaptive second-order sliding mode control

This paper proposes a fault-tolerant attitude tracking control for carrier-based aircraft with external disturbances and actuator faults, which is based on backstepping control, second-order sliding mode control (SOSMC) and the radial basis function neural network (RBFNN) adaptation algorithm. First, the generic attitude dynamic model of carrier-based aircraft is presented. Based on backstepping method, the attitude control system is divided into two simple and low-order subsystems. Then, the basic SOSMC using the type of proportional integral (PI) sliding mode variable are designed respectively for two subsystems, which can guarantee the system stable with no chattering in the finite time. To compensate for disturbances and faults more accurately, we design RBFNN-based adaptive second-order sliding mode control (RASOSMC) where RBFNN algorithm is utilized to approximate the lumped perturbation, which attenuates the impact of disturbances and faults more effectively and improves attitude tracking performance. Furthermore, the adaptive online algorithms for the RBFNN weights are proposed based on Lyapunov theory. Finally, numerical simulation results are given to indicate the effectiveness and robustness of the SOSMC scheme and RASOSMC scheme.

Flash-flood propagation susceptibility estimation using weights of evidence and their novel ensembles with multicriteria decision making and machine learning

The present study aims to enrich the specialized literature by proposing and calculating a new flash-flood propagation susceptibility index (FFPSI). Thus, firstly the Flash-Flood Potential Index (FFPI) using the ensembles of the next models was calculated: Weights of Evidence (WOE), Analytical Hierarchy Process (AHP), Logistic Regression (LR), Classification and Regression Trees (CART), and Radial Basis Function Neural Network-Weights of Evidence (RBFN-WOE). A number of 255 flash-flood locations, split into training (70%) and validating (30%) samples, along with 10 predictors were used as input in the five models. The Receiver Operating Characteristics (ROC) Curve and several statistical metrics were used to evaluate the Flash-Flood Potential Index results. LR-WOE and AHP-WOE were the most performant models. Nevertheless, all the applied models performed very well (AUC > 0.85). Further, the FFPSI was determined by integrating the FFPI results into a Flow Accumulation procedure. Over 55% of the valleys identified are characterized by high and very high values of FFPSI.

Global adaptive neural backstepping control of a flexible hypersonic vehicle with disturbance estimation

PurposeThis paper aims to discuss the precise altitude and velocity tracking control of a hypersonic vehicle, a global adaptive neural backstepping controller was studied based on a disturbance observer (DOB).Design/methodology/approachThe DOB combined with a radial basis function (RBF) neural network (NN) was used to estimate the disturbance terms that are generated by the flexible modes of the hypersonic vehicle system. A global adaptive neural method was introduced to approximate the unknown system dynamics, with robust control terms pulling the system transient states back into the neural approximation domain externally.FindingsThe globally uniformly ultimately bounded for all signals of a closed-loop system can be guaranteed by the proposed control algorithm. Additionally, the command filtered backstepping methods can avoid the explosion of the complexity problem caused by the backstepping design process. In addition, the effectiveness of the proposed controller can be verified by the simulation used in this study.Research limitations/implicationsNormally lateral dynamics issue should be discussed in the process of control system designed, the lateral dynamics are not included in the nonlinear dynamic model of hypersonic vehicle used in this paper, merely the longitudinal flight dynamics are discussed in this paper.Originality/valueThe flexible states in rigid modes are considered as the disturbance of the system, which is estimated by structuring DOB with NN approximations. The compensating tracking error and prediction error are used in the update law of RBF NN weight. The differential explosions complexity derived from the backstepping procedure is dealt with by using command filters.

RBF neural network modeling approach using PCA based LM–GA optimization for coke furnace system

Neural network prediction and data processing have been widely used in chemical industry, however, there exist many disturbance variables that will affect the system output, and traditional neural network prediction model has poor accuracy. In this paper, the dimensionality reduction of normalized input variables that affect the outputs is first implemented by using principal component analysis (PCA). Then, radial basis function (RBF) neural network model is established. Levenberg–Marquardt (LM) algorithm is used to initialize the weights of RBF neural network, which overcomes the influence of initial weights during the training process. Genetic algorithm (GA) is further introduced to train the centers, widths and weights to improve the modeling accuracy. Finally, the root mean square error (RMSE) is used to evaluate the prediction performances. Compared with two RBF neural network modeling methods, the proposed method can improve the prediction accuracy greatly.

Optimal Adaptive Robust Pitch Control with Load Mitigation for Uncertain Variable Speed Wind Turbines

In this paper, an optimal adaptive robust pitch controller is proposed for variable speed wind turbines (VSWTs). The proposed pitch controller has stability analysis, while it simultaneously keeps the generated power of the wind turbine at the rated power and mitigates the mechanical loads on the gearbox. The proposed pitch controller in this paper has two terms. The first term is a radial basis function neural network (RBFNN), to approximate unknown nonlinear functions of the wind turbine. Another term is a chattering-free continuous robust structure, which can cope with the approximation error. The weights of RBFNN and the gain of the robust structure are derived via the Lyapunov synthesis approach. It is proved that the closed-loop signals are semi-globally uniformed and ultimately bounded. The optimal parameters of the proposed controller are derived by solving a proposed multi-objective optimization problem using non-dominated sorting genetic algorithm-II (NSGA-II) and multi-objective particle swarm optimization (MOPSO) algorithm. The effectiveness of the proposed controller is compared to the baseline PI controller designed by NREL. First, both the proposed and the baseline PI controllers are applied to the general model (2-mass model) of the wind turbine, and then they are validated via a highly reliable simulator called FAST. The results demonstrate the effectiveness and applicability of the proposed pitch controller.

Gimbal control of inertially stabilized platform for airborne remote sensing system based on adaptive RBFNN feedback model

The attitude stabilization precision of inertially stabilized platform (ISP) directly affect the resolution of remote sensing image by stabilizing the airborne remote sensing system and holding the line of sight. Therefore, an adaptive control model based on radial basis function neural network (RBFNN) is designed to improve the attitude stabilization precision of ISP gimbal in this article. The adaptive control law and the RBFNN weight adaptive law are designed based on the Lyapunov stability theorem, and the inputs of state feedback control and disturbance observer are combined into the control input. Both simulation and experimental results indicate that the adaptive control based on RBFNN can improve the attitude stabilization precision of ISP gimbal compared to the state feedback control.

Anti‐disturbance adaptive sampled‐data observers for a class of nonlinear systems with unknown hysteresis

AbstractIn this article, based on radial basis function neural network (RBFNN) and disturbance estimator (DE), an adaptive sampled‐data observer design scheme is proposed for a class of nonlinear systems with unknown Prandtl–Ishlinskii (PI) hysteresis and unknown multiple disturbances. To begin with, we investigate a class of sampled‐data nonlinear systems and present corresponding sufficient conditions ensuring ultimate uniform boundedness (UUB). Subsequently, a sampled‐data observer and a DE are designed to estimate the unknown states and compounded disturbances, respectively. Additionally, the unknown hysteresis and the unknown unmatched disturbances are approximated by RBFNNs. Meanwhile, we also give the learning laws of the weights of RBFNNs. The estimation errors of the states and the weights are verified to be UUB in the light of the obtained sufficient conditions and a special constructing Lyapunov–Krasovskii function. Finally, the effectiveness of the proposed design method is verified by numerical simulations.

Adaptive Boundary Control of Flexible Manipulators with Parameter Uncertainty Based on RBF Neural Network

In this paper, nonlinear dynamical equations of the flexible manipulator with a lumped payload at the free end are derived from Hamilton's principle. The obtained model consists of both distributed parameters and lumped parameters, namely, partial differential equations (PDEs) governing the flexible motion of links and boundary conditions in the form of ordinary differential equations (ODEs). Considering the great nonlinear approximation ability of the radial basis function (RBF) neural network, we propose a combined control algorithm that includes two parts: one is a boundary controller to track the desired joint positions and suppress the vibration of flexible links; another is a RBF neural network designed to compensate for the parametric uncertainties. The iteration criterion of the RBF neural network weight matrix is derived from the extended Lyapunov function. Stabilization analysis is further carried out theoretically via LaSalle’s invariance principle. Finally, the results of the numerical simulation verify that the proposed control law can realize the asymptotic convergence of tracking error and suppression of the elastic vibration as well.

Matched-field geoacoustic inversion based on radial basis function neural network.

Multi-layer neural networks (NNs) are combined with objective functions of matched-field inversion (MFI) to estimate geoacoustic parameters. By adding hidden layers, a radial basis function neural network (RBFNN) is extended to adopt MFI objective functions. Specifically, shallow layers extract frequency features from the hydrophone data, and deep layers perform inverse function approximation and parameter estimation. A hybrid scheme of backpropagation and pseudo-inverse is utilized to update the RBFNN weights using batch processing for fast convergence. The NNs are trained using a large sample set covering the parameter interval. Numerical simulations and the SWellEx-96 experimental data results demonstrate that the proposed NN method achieves inversion performance comparable to the conventional MFI due to utilizing big data and integrating MFI objective functions.

Data classification based on fractional order gradient descent with momentum for RBF neural network

ABSTRACT The weight-updating methods have played an important role in improving the performance of neural networks. To ameliorate the oscillating phenomenon in training radial basis function (RBF) neural network, a fractional order gradient descent with momentum method for updating the weights of RBF neural network (FOGDM-RBF) is proposed for data classification. Its convergence is proved. In order to speed up the convergence process, an adaptive learning rate is used to adjust the training process. The Iris data set and MNIST data set are used to test the proposed algorithm. The results verify the theoretical results of the proposed algorithm such as its monotonicity and convergence. Some non-parametric statistical tests such as Friedman test and Quade test are taken for the comparison of the proposed algorithm with other algorithms. The influence of fractional order, learning rate and batch size is analysed and compared. Error analysis shows that the algorithm can effectively accelerate the convergence speed of gradient descent method and improve its performance with high accuracy and validity.

Automated design of a new integrated intelligent computing paradigm for constructing a constitutive model applicable to predicting rock fractures

Making a relation between strains and stresses is an important subject in the rock engineering field. Shear behaviors of rock fractures have been extensively investigated by different researchers. Literature mostly consists of constitutive models in the form of empirical functions that represent experimental data using mathematical regression techniques. As an alternative, this study aims to present a new integrated intelligent computing paradigm to form a constitutive model applicable to rock fractures. To this end, an RBFNN-GWO model is presented, which integrates the radial basis function neural network (RBFNN) with grey wolf optimization (GWO). In the proposed model, the hyperparameters and weights of RBFNN were tuned using the GWO algorithm. The efficiency of the designed RBFNN-GWO was examined comparing it with the RBFNN-GA model (a combination of RBFNN and the Genetic Algorithm). The proposed models were trained based on the results of a systematic set of 84 direct shear tests gathered from the literature. The finding of the current study demonstrated the efficiency of both the RBFNN-GA and RBFNN-GWO models in predicting the dilation angle, peak shear displacement, and stress as the rock fracture properties. Among the two models proposed in this study, the statistical results revealed the superiority of RBFNN-GWO over RBFNN-GA in terms of prediction accuracy.

Ship Traffic Flow Prediction Based on Fractional Order Gradient Descent with Momentum for RBF Neural Network

To prevent the maritime traffic accidents and make scientific decision, scientific and accurate prediction of the traffic flow is useful, which has often been made by neural network. The weight updating methods have played an important role in improving the performance of neural networks. To ameliorate the oscillating phenomenon in training radial basis function (RBF) neural network, a fractional order gradient descent (GD) with momentum method for updating the weights of RBF neural network (FOGDM-RBF) is proposed. Its convergence is proved. The new algorithm is used to predict vessel traffic flow at Xiamen Port. It performs stable and converges to zero as the iteration increases. The results verify the theoretical results of the proposed algorithm such as its monotonicity and convergence. The descending curve of error values by fractional order GDM is smoother than the GD and GDM method. Error analysis shows that the algorithm can effectively accelerate the convergence speed of the GD method and improve its performance with high accuracy and validity. The influence of fractional order, number of hidden layer neurons, tide peak hours, and ship size is analyzed and compared. 1. Introduction As the world shipping becomes more and more busy, the large ship traffic flow leads to frequent maritime traffic accidents, resulting in huge economic losses. Ship traffic flow is a basic system in marine traffic engineering and an important index to measure the construction of marine traffic infrastructure. Its prediction results can provide basis for formulating scientific Port management planning and ship navigation management. Therefore, to ensure the accuracy and rationality of ship traffic flow forecasting is of great significance for improving port infrastructure construction and formulating scientific port management strategies. Many advanced artificial intelligence optimization algorithms have been used for ship traffic flow forecasting, such as artificial neural network (Zhai 2013; Zhang 2015). Neural network can deal with complex nonlinear problems and has achieved some results. However, the neural network itself has some shortcomings, such as slow learning speed, easy to fall into the local extremum, learning and memory instability, etc.

Adaptive Sampled-Data Observer Design for a Class of Nonlinear Systems with Unknown Hysteresis

In this paper, a novel adaptive sampled-data observer design is studied for a class of nonlinear systems with unknown Prandtl–Ishlinskii hysteresis and unknown unmatched disturbances based on radial basis function neural networks (RBFNNs). To begin with, we investigate a sampled-data nonlinear system and present sufficient conditions such that the sampled-data nonlinear system is ultimately uniformly bounded (UUB). Then, an adaptive sampled-data observer is designed to estimate the unknown states of the nonlinear system. The unknown hysteresis and the unknown disturbances are approximated by RBFNNs. We also give the learning laws of the weights of RBFNNs, and prove that the estimation errors of the states and the weights are UUB, based on the obtained sufficient conditions and a special constructing Lyapunov–Krasovskii function. Finally, the effectiveness of the proposed design method is verified by numerical simulations.

Serial-Parallel Estimation Model-Based Sliding Mode Control of MEMS Gyroscopes

This article proposes a serial-parallel estimation model (SPEM)-based sliding mode control (SMC) of MEMS gyroscope. For the system nonlinearity, the linear-in-parameterized dynamics are formulated and the updating law of the parameter vector is given. For the system uncertainty, the radial basis function (RBF) neural network (NN) is utilized. To improve the approximation accuracy of the compound nonlinearity, the updating laws of the parameter vector and RBF NN weight are constructed by the tracking error and the filtered modeling error derived from SPEM. Furthermore, the fast terminal (FT) SMC is employed to achieve finite-time convergence. The simulation results show that the proposed controller obtains higher tracking accuracy and faster convergence, while the compound nonlinearity approximation is with higher precision.

Maximum Power Point Tracker Based on Fuzzy Adaptive Radial Basis Function Neural Network for PV-System

In this article, a novel maximum power point tracking (MPPT) controller for a photovoltaic (PV) system is presented. The proposed MPPT controller was designed in order to extract the maximum of power from the PV-module and reduce the oscillations once the maximum power point (MPP) had been achieved. To reach this goal, a combination of fuzzy logic and an adaptive radial basis function neural network (RBF-NN) was used to drive a DC-DC Boost converter which was used to link the PV-module and a resistive load. First, a fuzzy logic system, whose single input was based on the incremental conductance (INC) method, was used for a variable voltage step size searching while reducing the oscillations around the MPP. Second, an RBF-NN controller was developed to keep the PV-module voltage at the optimal voltage generated from the first stage. To ensure a real MPPT in all cases (change of weather conditions and load variation) an adaptive law based on backpropagation algorithm with the gradient descent method was used to tune the weights of RBF-NN in order to minimize a mean-squared-error (MSE) criterion. Finally, through the simulation results, our proposed MPPT method outperforms the classical P and O and INC-adaptive RBF-NN in terms of efficiency.

High-Gain Observer-Based Neural Adaptive Feedback Linearizing Control of a Team of Wheeled Mobile Robots

SummaryThis paper addresses the neural network (NN) output feedback formation tracking control of nonholonomic wheeled mobile robots (WMRs) with limited voltage input. A desired formation is achieved based on the leader–follower strategy utilizing hyperbolic tangent saturation functions to reduce the risk of actuator saturation. The controller is developed by incorporating the high-gain observer and radial basis function (RBF) NNs using the inverse dynamics control technique. The high-gain observer is introduced to estimate velocities of the followers. The RBF NN preserves the robustness of the proposed controller against uncertain nonlinearities. The adaptive laws are also combined by a robust control term to estimate the weights of RBF NN, approximation errors, and bounds of unknown time-variant environmental disturbances. A Lyapunov-based stability analysis proves that all signals of the closed-loop system are bounded, and tracking errors are uniformly ultimately bounded. Finally, some simulations are carried out to show the effectiveness of the proposed controller for a number of WMRs.