Radial Basis Function Neural Network Research Articles

Event-triggered fixed-time fault-tolerant attitude control for the flying-wing UAV using a Nussbaum-type function

This paper introduces an innovative adaptive event-triggered fault-tolerant attitude control framework designed for a flying-wing unmanned aerial vehicle (UAV) operating under constraints such as limited embedded resources, unknown actuator failures, system uncertainties, and external disturbances. The proposed scheme incorporates several noteworthy features: (i) Implementation of a relative threshold event-triggered mechanism to efficiently alleviate communication pressures and computational burdens inherent in the attitude control system. (ii) Utilization of a radial basis function neural network to approximate lumped disturbances, reducing dependence on prior knowledge. (iii) Adaptive compensation for sampling errors and actuator faults by employing the Nussbaum gain. (iv) Integration of a smooth function to address singularity issues and prevent Zeno behavior. Furthermore, Lyapunov analysis validates that all signals within the closed-loop system remain bounded and converge within a predetermined time frame. Comparative numerical simulations underscore the effectiveness and superiority of the proposed control approach.

Adaptive Multi-Surface Sliding Mode Control with Radial Basis Function Neural Networks and Reinforcement Learning for Multirotor Slung Load Systems

While using multirotor UAVs for transport of suspended payloads, there is a need for stability along the desired path, in addition to avoidance of any excessive payload oscillations, and a good level of precision in maintaining the desired path of the vehicle. However, due to the nonlinear and underactuated nature of the system, in addition to the presence of mismatched uncertainties, the development of a control system for this application poses an interesting research problem. This paper proposes a control architecture for a multirotor slung load system by integrating a Multi-Surface Sliding Mode Control, aided by a Radial Basis Function Neural Network, with a Deep Q-Network Reinforcement Learning agent. The former will be used to ensure asymptotic tracking stability, while the latter will be used to suppress payload oscillations. First, we will present the dynamics of a multirotor slung load system, represented here as a quadrotor with a single pendulum load suspended from it. We will then propose a control method in which a multi-surface sliding mode controller, based on an adaptive RBF Neural Network for trajectory tracking of the quadrotor, works in tandem with a Deep Q-Network Reinforcement Learning agent whose reward function aims to suppress the oscillations of the single pendulum slung load. Simulation results demonstrate the effectiveness and potential of the proposed approach in achieving precise and reliable control of multirotor slung load systems.

A multi-stage sub-structural damage localization approach using multi-label radial basis function neural network and auto-regressive model parameters

This paper proposes a Structural Health Monitoring (SHM) approach to detect localized damage by employing a Multi-Label Radial Basis Function Neural Network (ML-RBFNN). The proposed research methodology aims to identify structural damage more efficiently. This involves dividing the main structure into smaller sub-structures known as zones instead of employing a global search for damage across the entire structure. Each zone is further divided into smaller groups, including sub-zones, nodes, or elements. To reduce the complexities associated with feature extraction, auto-regressive (AR) model parameters extracted from raw time series are considered damage-sensitive features. Considering the simultaneous effects of multiple sensors can increase the number of inputs to the networks, making it challenging to reduce the complexity of the dataset. To address this problem, the principal component analysis (PCA) method is utilized to decrease the dimension of feature space. The effectiveness of the proposed approach is evaluated through a comprehensive comparative analysis against conventional single-stage damage detection methods, with a focus on computational costs and accuracy. Furthermore, the noise-sensitivity characteristics of the proposed method are explored, providing insights into their robustness under various conditions. The validation of the approach is carried out through numerical modeling using the ASCE benchmark structure and experimental data collected from the Qatar University Grandstand Simulator. The application of ML-RBFNN with AR parameters as features yielded a remarkable accuracy exceeding 98% in diagnosing damage occurrence and location for both multi-stage and single-stage SHM methods. Moreover, our proposed approach demonstrates enhanced computational efficiency compared to the single-stage method.

Susceptibility Mapping of Thaw Slumps Based on Neural Network Methods along the Qinghai–Tibet Engineering Corridor

Climate warming has induced the thawing of permafrost, which increases the probability of thaw slump occurrences in permafrost regions of the Qinghai–Tibet Engineering Corridor (QTEC). As a key and important corridor, thaw slump distribution is widespread, but research into effectively using neural networks to predict thaw slumping remains insufficient. This study automated the identification of thaw slumps within the QTEC and investigated their environmental factors and susceptibility assessment. We applied a deep learning-based semantic segmentation method, combining U-Net with ResNet101, to high spatial and temporal resolution images captured by the Gaofen-1 images. This methodology enabled the automatic delineation of 455 thaw slumps within the corridor area, covering 40,800 km², with corresponding precision, recall, and F1 scores of 0.864, 0.847, and 0.856, respectively. Subsequently, employing a radial basis function neural network model on this inventory of thaw slumps, we investigated environmental factors that could precipitate the occurrence of thaw slumps and generated sensitivity maps of thaw slumps along the QTEC. The model demonstrated high accuracy, and the area under the curve (AUC) value of the receiver operating characteristic (ROC) curve reached 0.95. The findings of the study indicate that these thaw slumps are predominantly located on slopes with gradients of 1–18°, distributed across mid-elevation regions ranging from 4500 to 5500 m above sea level. Temperature and precipitation were identified as the predominant factors that influenced the distribution of thaw slumps. Approximately 30.75% of the QTEC area was found to fall within high to extremely high susceptibility zones. Moreover, validation processes confirmed that 82.75% of the thaw slump distribution was located within areas of high or higher sensitivity within the QTEC.

Research on the Teaching Model of English Teaching Quality Evaluation under the Background of MOOC

In the context of informatization, online teaching is increasingly favored by people for its convenience and resource richness. Through the Open CourseWar (MOOC) platform, people can easily access learning resources and achieve efficient line length learning. However, currently MOOC online learning cannot provide targeted evaluation for the learning effectiveness of English learners, and there is relatively little research on online English quality assessment. Propose an intelligent MOOC online English teaching evaluation technology. Firstly, analyze the existing English teaching factors and construct a quality evaluation system for online English teaching using Principal Component Analysis (PCA) and expert evaluation method. Considering that the quality of English teaching is influenced by many factors, the evaluation of English teaching quality belongs to a complex nonlinear solving problem. Therefore, the advanced GA-RBF (Genetic Algorithm Radial Basis Function Neural Network, GA-RBF) model is adopted to solve the English teaching quality evaluation model. In teaching quality evaluation, BP and RBF are selected to participate in comparative testing of teaching quality evaluation. In the training loss test of multiple models, the GA-RBF model has the best convergence speed and training performance in the oral sample test, tends to converge after 270 iterations, with a loss value of 0.24. In the evaluation of English proficiency indicators, the BP model has a significant error in testing, with an error of 13 in the evaluation of reading ability scores. The error of RBF in reading ability score evaluation is 4, and the GA-RBF model performs the best. The reading ability evaluation error is 1, and the overall evaluation performance is the best. Through the above research, an intelligent method for evaluating the quality of English teaching is proposed, which will provide important technical references for MOOC online education evaluation and English teaching improvement.

Prediction of the shear strength of lightweight concrete beams without web reinforcement based on a machine learning model optimized by a genetic algorithm

The shear performance of concrete beams is affected by several factors, and some of effective variables and control mechanisms should be considered in predicting shear strength. Compared with ordinary concrete, lightweight concrete (LWC) is more unique, which greatly increases the difficulty of prediction. This is also why it is necessary to introduce machine learning (ML) technology with stronger data processing capabilities to predict the shear performance of LWC. Therefore, the aim of this study is to employ four well-known machine learning methods to predict the shear performance of LWC beams, namely, support vector machine (SVM), artificial neural network (ANN), radial basis function (RBF) neural network and random forest (RF). First, the shear test results of 220 LWC beams were collected, and the corresponding datasets were established based on possible influencing factors. Then, the optimal dataset partitioning methods for four different ML models were explored and determined. The parameter search process of the four models under the optimal dataset partitioning ratio was optimized using a genetic algorithm (GA), and four GA-ML prediction models were developed. The results show that the developed GA-RF model achieves a train set accuracy of 95.3 % and a test set accuracy of 93.3 %. The GA-ML technology significantly improves the accuracy of the prediction of shear strength compared to the formulaic model based on current international design standards. The prediction mechanism of the model is further analyzed to ensure that the model is reliable. The results indicate that it can be applied to predict the shear strength of LWC. In summary, the GA-RF model and importance analysis proposed in this article are practical methods for predicting and explaining the shear strength of LWC.

Predefined-Time Platoon Control of Unmanned Aerial Vehicle with Range-Limited Communication

In this paper, the predefined-time platoon control for multiple uncertain unmanned aerial vehicles (UAVs) under range-limited communication and external disturbance constraints is considered. A novel control scheme, which can guarantee communication connectivity, collision avoidance, and the predefined convergence time simultaneously, is proposed. To achieve disturbance robustness, an observer-based distributed control law is firstly proposed with a time-varying gain. Then, a radial basis function neural network (RBFNN) with an adaptive tuning law is applied to approximate uncertainties of the system. Under the time and error transformation techniques, uniformly ultimate boundedness (UUB) stability of the closed-loop system is guaranteed within predefined convergence time. Compared with the existing results, the proposed method allows the system to have UUB within any predefined time without depending on the initial conditions or system parameters. Finally, simulation results are presented to verify the derived theorem.

A novel data-driven reduced-order model for the fast prediction of gas-solid heat transfer in fluidized beds

Computational fluid dynamics − discrete element method (CFD-DEM) emerges as a promising tool to model dense gas–solid two-phase flow in fluidized beds, yet the numerical efficiency is still far from being satisfactory. Accordingly, this work develops a proper orthogonal decomposition (POD) reduced-order model (ROM) based on the CFD-DEM method for the fast prediction of gas–solid flow and heat transfer in a bubbling fluidized bed (BFB). The POD method is employed to decompose particle coordinates and temperature into spatial modes and time evolution coefficients. The radial basis function neural network (RBFNN) and temporal convolutional neural network (TCN) are utilized to predict the time evolution coefficients. Regarding the POD modes, the particle temperature exhibits an obvious monotonic or periodic characteristic compared to the particle coordinates, indicating the potential for long-term prediction. The RBFNN-ROM and TCN-ROM reconstruct the flow field effectively, achieving acceleration ratios of 2000 and 3000, respectively. The ROM developed in this study holds the potential to enable real-time prediction of industrial processes, thus paving the way for the realization of digital twins.

Shape optimization of autonomous underwater helicopters based on different parameter curves and various optimization algorithms

This study aimed to compare the non-uniform rational B-spline (NURBS) and Bezier curves to design the shape of an autonomous underwater helicopter (AUH). Currently, there is no established method for AUH shape design. The optimal solutions obtained from both curves were compared to evaluate their performance. A parametric model was constructed to determine the design variables of the two curves. Computational fluid dynamics was used to solve the resistance values of different shapes. Sample points were generated using the design of the experimental approach, and an approximate model was established using the radial basis function neural network method. Based on the combinatorial optimization strategy, three intelligent optimization algorithms were used for the global search. Then, the resulting solution was used as the starting point for a local search to obtain the global optimal solution. The resistance optimal solutions achieved by employing the NURBS and Bezier curves were 25.2% and 24.1% smaller than the initial values, respectively. These findings indicate that, within the design parameters of this study, the shape design approach using the NURBS curve yields superior performance for the AUH.

Enhancing secure transmission of ultra-high order QAM via delta-sigma modulation integrated with radial basis function neural network enhanced chaos.

This paper proposes and experimentally demonstrates an ultra-high order signal security enhancement method based on delta-sigma modulation (DSM). We employ a radial basis function neural network (RBFnn) to enhance Henon chaos, effectively avoiding the degradation of chaotic dynamics, and increasing the key space from 1054 to 10385. In the experimental demonstration, we achieved high-security transmission of 16384QAM over 25 km in an intensity-modulated direct detection (IMDD) system based on DSM. The experimental results show that the ultra-high order transmission scheme based on RBFNN-chaos and DSM has superior security, with a key sensitivity of up to 10-16.

Modeling of Gaseous Reduction of Iron Oxide Pellets Using Machine Learning Algorithms, Explainable Artificial Intelligence, and Hyperparameter Optimization Techniques

In this study, a novel application of machine learning (ML) is introduced to pellet modeling in the intricate non‐catalytic gas–solid reaction of direct reduction of iron oxide in the steel industry. Twenty ML models are developed using four algorithms: multilayer perceptron neural networks (MLPNN), radial basis function neural network (RBFNN), support vector regression, and random forest (RF). Hyperparameter optimization is conducted using Bayesian algorithms, random search, and grid search. The optimum model achieves a mean squared error test of 0.0052 with random RF for the larger dataset (872 samples), while smaller datasets (132, 225, and 242 samples) produce optimum models with MLPNN and RBFNN. Hyperparameters vary between the larger datasets and the smaller datasets. The models offer insight into the complex interactions among variables, including time, temperature, gas composition, hematite composition, pellet radius, and initial pellet porosity, influencing the metallization degree. In this study, the significant role of time and temperature is emphasized, as revealed by explainable artificial intelligence using Shapley additive explanation analysis that utilizes the game theory, and the effects of pellet modeling parameters are elucidated through 3D plots, particularly highlighting the impact of changing H2/CO proportion on metallization degree and carbon deposit.

Comparison of non-linear time series models (Beta-t-EGARCH and NARMAX models) with Radial Basis Function Neural Network using Real Data

This paper presents a comparison of three different non-linear time series modelling approaches: NARMAX (Non-linear Autoregressive Moving Average with Exogenous Inputs), Beta-t-EGARCH (Beta t Exponential Generalized Autoregressive Conditional Heteroscedasticity), and Radial Basis Function Neural Networks (RBFNN) applied to weekly stock market index data. We will explain three types of models and compare their compositions and structures. Then, we will show which model gives better predictions. To study series data, the comparison involved analysing the structure of the model and its errors in various time series models and summarising their findings. We divide the data into two parts: training data to structure the time series and testing. The training data tests the model's predictions. Then, we can analyse the model with the errors and the best deterrence predictions. After selecting the NARMAX and Beta-t-EGARCH models, we test them with specific criteria. The best choice is finding the model with the lowest average errors. For this study, we analysed the weekly average closing of the Aramco 2222 index from 15 December 2019 to 16 July 2023 and made 187 observations.

Adaptive finite-time neural control of nonstrict-feedback nonlinear systems with input dead-zone and output hysteresis

This paper explores the adaptive finite-time neural control issue for nonlinear systems with input dead zone and output hysteresis in nonstrict-feedback form. The unknown functions are estimated by employing the radial basis function neural networks (RBFNN) approach. A systematic adaptive finite-time control method is introduced using the backstepping technique and neural network approximation properties. The stability of the system is also examined by using semi-global practical finite-time stability theory. The established control approach guarantees the boundedness of all signals within the closed-loop system, enabling the system output to accurately follow the desired signal within a finite time framework while maintaining a small and bounded tracking error. Finally, simulation results are shown to demonstrate the efficacy of the suggested strategy.

Adaptive neural dynamic surface control for nonstrict feedback systems with state delays

AbstractThis article focuses on a class of nonstrict feedback systems with input delay, state delays and time‐varying full‐state constraints by proposing an adaptive neural control scheme. To overcome the problems of all state variables effected by time‐varying constraints, the asymmetric time‐varying barrier Lyapunov functions are constructed. The influence of state delays and input delay is eliminated by employing suitable Lyapunov–Krasovskii functionals. Additionally, the process of controller design is based on backstepping method and the unknown functions can be approximated by radial basis function neural networks. Moreover, the problem of repeated differentiations for nonlinear components during controller design is hugely simplified by taking advantage of the dynamic surface control method. The boundness of all the closed‐loop signals can be ensured by the designed controller. Finally, two numerical simulations illustrate that the proposed adaptive neural control scheme is effective.

Command Filter-Based Adaptive Neural Control for Nonstrict-Feedback Nonlinear Systems with Prescribed Performance

In this paper, a new command filter-based adaptive NN control strategy is developed to address the prescribed tracking performance issue for a class of nonstrict-feedback nonlinear systems. Compared with the existing performance functions, a new performance function, the fixed-time performance function, which does not depend on the accurate initial value of the error signal and has the ability of fixed-time convergence, is proposed for the first time. A radial basis function neural network is introduced to identify unknown nonlinear functions, and the characteristic of Gaussian basis functions is utilized to overcome the difficulties of the nonstrict-feedback structure. Moreover, in contrast to the traditional Backstepping technique, a command filter-based adaptive control algorithm is constructed, which solves the “explosion of complexity” problem and relaxes the assumption on the reference signal. Additionally, it is guaranteed that the tracking error falls within a prescribed small neighborhood by the designed performance functions in fixed time, and the closed-loop system is semi-globally uniformly ultimately bounded (SGUUB). The effectiveness of the proposed control scheme is verified by numerical simulation.

Variety classification and identification of jujube based on near-infrared spectroscopy and 1D-CNN

Jujube is an important economic crop in Xinjiang, China, and its related industry provides abundant employment opportunities and contributes positively to local economic development. Due to the high economic value and similar appearance of jujubes from different regions, there is a phenomenon of counterfeit products in the market. Therefore, it is necessary to trace the origin of jujubes to address these issues. In this study, we conducted traceability research on jujubes from four locations: Alaer, Hotan, Ruoqiang, and Zhangye. Near-infrared spectroscopy was used to extract non-destructive data from the jujubes for analysis. The extracted data was transformed into one-dimensional data, and six algorithms, including the Back Propagation Neural Network (BP), Radial Basis Function Neural Network(RBF), Convolutional Neural Networks (CNN), Long Short-Term Memory Network(LSTM), Support Vector Machine (SVM), and Random Forest (RF), were used for classification research on the obtained 4000 sets of one-dimensional data. The results showed that when sufficient data were available, the RBF, LSTM and CNN perform relatively better best with 93.50 %, 94.33 % and 94.25 % accuracy. The RF achieved an accuracy of 92.42 % and demonstrated good detection efficiency. However, the BP and SVM performed relatively poorly, with accuracies of 90.42 % and 80.42 % respectively. Considering the time-consuming nature of data collection for large datasets during the detection process, several sets of one-dimensional data were randomly selected for further experiments, through which 400 sets of data were found to be more prominent with 700 sets of data. The final experimental results demonstrate that, in the traceability detection of a small-scale dataset containing 400 instances, the CNN exhibits the best performance, achieving an accuracy of 86.67 %. The performance of the LSTM is slightly lower than that of the CNN, with an accuracy of 84.12 %. The accuracies of the BP, RBF, SVM, and RF were relatively lower at 82.5 %, 82.5 %, 74.12 %, and 74.18 % respectively. In the experiments with a dataset of 700 instances, the performance of CNN stands out prominently. In comparison to the CNN algorithm on the 400-instance dataset and the second-best LSTM algorithm, the accuracy, precision, recall, and F1-score have exhibited significant improvements by 53.13 %, 98.98 %, 481.43 %, and 140.36 %, respectively. The corresponding values are 0.9043, 0.9083, 0.9052, and 0.906. This study demonstrates the non-destructive traceability of jujube fruits using near-infrared spectroscopy data combined with neural network algorithms. Additionally, it reduces the need for additional preprocessing steps in data handling and achieves promising detection results. This research has positive implications for the traceability of jujube fruits and related crops.

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 formation control of second‐order nonlinear multi‐agent systems using the neural network dynamic sliding mode

AbstractThe problem of fixed‐time formation control for a class of second‐order nonlinear multi‐agent systems is studied. For a class of such systems, a control algorithm is proposed to maintain the connections among the agents while avoiding collisions. Furthermore, a radial basis function neural network is used in the design to precisely approximate the nonlinear function for the nonlinear terms in the model. Then, a dynamic sliding mode control method is proposed to suppress the chattering phenomenon that may arise due to the sliding mode control. A sufficient condition for the system to achieve fixed‐time formation is obtained by using different methods, such as Lyapunov stability. Finally, the effectiveness of the proposed algorithm is verified by example. Simulation experiments reveal that the proposed method has faster error convergence and better robust control than conventional algorithms.

Intelligent Sensing of Thermal Error of CNC Machine Tool Spindle Based on Multi-Source Information Fusion.

Aiming at the shortcomings of single-sensor sensing information characterization ability, which is easily interfered with by external environmental factors, a method of intelligent perception is proposed in this paper. This method integrates multi-source and multi-level information, including spindle temperature field, spindle thermal deformation, operating parameters, and motor current. Firstly, the internal and external thermal-error-related signals of the spindle system are collected by sensors, and the feature parameters are extracted; then, the radial basis function (RBF) neural network is utilized to realize the preliminary integration of the feature parameters because of the advantages of the RBF neural network, which offers strong multi-dimensional solid nonlinear mapping ability and generalization ability. Thermal-error decision values are then generated by a weighted fusion of different pieces of evidence by considering uncertain information from multiple sources. The spindle thermal-error sensing experiment was based on the spindle system of the VMC850 (Yunnan Machine Tool Group Co., LTD, Yunnan, China) vertical machining center of the Yunnan Machine Tool Factory. Experiments were designed for thermal-error sensing of the spindle under constant speed (2000 r/min and 4000 r/min), standard variable speed, and stepped variable speed conditions. The experiment's results show that the prediction accuracy of the intelligent-sensing model with multi-source information fusion can reach 98.1%, 99.3%, 98.6%, and 98.8% under the above working conditions, respectively. The intelligent-perception model proposed in this paper has higher accuracy and lower residual error than the traditional BP neural network perception and wavelet neural network models. The research in this paper provides a theoretical basis for the operation, maintenance management, and performance optimization of machine tool spindle systems.

Response of Gaussian white noise excited oscillators with inertia nonlinearity based on the RBFNN method

Although stochastic averaging methods have proven effective in solving the responses of nonlinear oscillators with a strong stiffness term under broadband noise excitations, these methods appear to be ineffective when dealing with oscillators that have a strong inertial nonlinearity term (also known as coordinate-dependent mass) or multiple potential wells. To address this limitation, a radial basis function neural network (RBFNN) algorithm is applied to predict the responses of oscillators with both a strong inertia nonlinearity term and multiple potential wells. The well-known Gaussian functions are chosen as radial basis functions in the model. Then, the approximate stationary probability density function (PDF) is expressed as the sum of Gaussian basis functions (GBFs) with weights. The squared error of the approximate solution for the Fokker-Plank-Kolmogorov (FPK) function is minimized using the Lagrange multiplier method to determine optimal weight coefficients. Three examples are presented to demonstrate how inertia nonlinearity terms and potential wells affect the responses. The mean square errors between Monte Carlo simulations (MCS) and RBFNN predictions are provided. The results indicate that RBFNN predictions align perfectly with those obtained from MCS.