Abstract: EEG signals are non-stationary, complex and non-linear signals. During major depressive disorder (MDD) or depression, any deterioration in the brain function is reflected in the EEG signals. In this paper, linear features (band power, inter hemispheric asymmetry) and non-linear features [relative wavelet energy (RWE) and wavelet entropy (WE)] and combination of linear and non-linear features were used to classify depression patients and healthy individuals. In this analysis the data set used is publicly available data set contributed by Mumtaz et al. (Biomed Signal Process Control 31:108–115, 2017b). The dataset consisted of 34 MDD patients and 30 healthy individuals. The classifiers used were multi layered perceptron neural network (MLPNN), radial basis function network (RBFN), linear discriminant analysis (LDA) and quadratic discriminant analysis. When linear feature was used, highest classification accuracy of 91.67% was obtained by alpha power with MLPNN classifier. When non-linear feature was used, both RWE and WE provided highest classification accuracy of 90% with RBFN and LDA classifier, respectively. The highest classification of 93.33% was achieved when combining linear and non-linear feature, i.e., combination alpha power and RWE with MLPNN as well as RBFN classifier. This paper also showed that the combination of non-linear features, i.e., RWE and WE also performed the best with highest classification accuracy of 93.33%. The study compared the accuracy, sensitivity and specificity of different classifiers along with linear and non-linear features and combination of both. The results indicated that combination alpha power and RWE showed the highest classification 93.33% accuracy in all the applied classifiers.

Abstract: The displacement at various measurement points is a critical indicator that can intuitively reflect the operational properties of a dam. It is important to analyse displacement monitoring data in a timely manner and make reliable predictions of dam safety. This paper proposes a GPR-based model for dam displacement forecasting. The input variables of the monitoring model consider hydraulic factors, thermal factors and irreversible factors, and the output variables are the observed displacements of the dam. An example analysis based on the proposed method is performed on a prototype gravity dam, and the performance of different simple/combined covariance functions is investigated to obtain the optimal choice. Compared to multiple linear regression, radial basis function network (RBFN) and support vector machine (SVM) methods, the results indicate that the GPR-based model with a combined covariance function significantly improves the prediction accuracy. The proposed model can effectively overcome the over-learning and poor robustness issues of approaches such as RBFN and SVM. In addition, the GPR-based forecasting model has the advantages of simplicity in the training process and the capacity to provide a probabilistic output.

Abstract: This paper deals with the problem of environmental monitoring by designing and analyzing a cooperative receding horizon temporal logic (CRH-TL) control approach for mobile robot networks. First, a radial basis function network is used to model the distribution of environmental attributes in the monitored environment. On the basis of the established environment model, the problem of environmental monitoring can be formulated as a dynamical optimization problem. Second, an acceptable node set is obtained by enforcing appropriate constraints from linear temporal logic (LTL) specifications on the task of environmental monitoring. Third, by designing a cooperative energy function and using the acceptable node set, the CRH-TL control approach is proposed to generate the movement trajectory of each robot, which satisfies the given LTL specifications while guiding mobile robot networks to trace the peaks of environmental attributes. Finally, the effectiveness of the proposed CRH-TL control approach is illustrated for the problem of environmental monitoring.

Abstract: In the previous work, the parameters of radial basis function network based autoregressive (RBF-AR) models are estimated offline and no longer updated afterward. In this letter, an adaptive learning algorithm is proposed for the RBF-AR models. The proposed strategy is that the nonlinear parameters are previously determined by an off-line variable projection method; and once new samples are available, the linear parameters are updated. The linear adaptive algorithm adopted in this letter is the multi-innovation least squares method, due to its high performance. The simulation results show that with the adaption of the linear parameters, the prediction performance of the RBF-AR models may be significantly improved, which demonstrates the effectiveness of the proposed algorithm.

Abstract: For many real-world engineering optimization applications, evolutionary algorithms require a large number of fitness evaluations via expensive simulations or experiments. However, in some particular cases, no expensive fitness evaluations are available during the optimization process, which is called offline data-driven optimization. As the offline data is very limited, high-quality surrogate models must be built to take full advantage of the data. In this paper, a new stochastic ranking-based surrogate-assisted evolutionary algorithm is proposed to deal with offline data-driven optimization problems. To manage multiple models, stochastic ranking is employed. The experiment results on benchmark problems with up to 500 decision variables demonstrate that the proposed algorithm is effective on high dimensional problems.

Abstract: The paper introduces an adaptive strategy to effectively control a nonlinear dual-arm robot under external disturbances and uncertainties. By the use of the backstepping sliding mode control (BSSMC) method, the proposed algorithm first allows the manipulators to be able to robustly track the desired trajectories. Furthermore, due to the nonlinear, uncertain and unmodeled dynamics of the dual-arm robot, it is proposed to employ the radial basis function network (RBFN) to adaptively estimate the robot’s dynamic model. Though the estimation of the dynamics is approximate, the adaptation law is derived from the Lyapunov theory, which provides the controller with ability to guarantee stability of the whole system in spite of its nonlinearities, parameter uncertainties and external load variations. The effectiveness of the proposed RBFN–BSSMC approach is demonstrated by implementation in a simulation environment with realistic parameters, where the obtained results are highly promising.

Abstract: The thermal predicting/evaluating model of data centers is pivotal in designing their thermal control systems. The existing modeling methods are based on the computational fluid dynamics (CFD) simulations, which is accurate in modeling for a steady-state flow pattern but considerably time-consuming. Besides, the corresponding parameters of CFD have to be re-identified with the deviation of the flow field, which makes it extremely inefficient in real-time thermal control system design of data centers. This paper proposed a machine learning method to derive the fast-temperature evaluation model with a constructed artificial neural network. It learns the relationship between the flow patterns and model parameters based on the system thermal–physical analysis, which replaces the time-consuming CFD-based parameter identifying process. Then, the temperature evaluation is implemented under different flow patterns with the proposed neural-network enhanced modeling method. In the learning process, multi-type of neural networks, i.e., backpropagation network, radial basis function network and extreme learning machine, are considered and compared. The accuracy of the proposed model is validated by comparing with the pure CFD results as the satisfactory standard. With the efficiency and accuracy, the proposed modeling method is more suitable to design real-time controllers for data centers with changing flow fields.

Abstract: Feedforward neural networks are those in which the input signal follows only one direction: from the input layer to the output layer, passing through all the hidden layers, in contrast with recurrent architectures. The main examples of this class are the Multilayer Perceptron (MLP) and the Radial Basis Function network (RBF). Recently, other model of this type has received significant attention: Extreme Learning Machines (ELMs). Nonlinear mapping problems, like time series forecasting, can be adequately solved by these methods. In this work, the aforementioned architectures are employed in the prediction of monthly seasonal streamflow series of important Brazilian hydroelectric plants, for different forecasting horizons. The results showed that all the proposals are efficient in solving the task, but, interestingly, the RBF achieved the best performance in most cases. However, the computational cost associated with the training process of the ELM is much smaller than the others.

Abstract: An increase in grid-connected photovoltaic arrays creates a need for efficient and reliable fault detection. In this paper, machine learning strategies for fault detection are presented. An Artificial Neural Network was studied with the goal of detecting three photovoltaic module conditions. In addition, an unsupervised approach was successfully implemented using the -means clustering algorithm, successfully detecting arc and ground faults. To distinguish and localize additional faults such as shading and soiling, a supervised approach is adopted using a Radial Basis Function Network. A solar array dataset with voltage, current, temperature, and irradiance was examined. This dataset had labeled data with normal conditions and faults due to soiling and shading. A radial basis network was trained to classify faults, resulting in an error rate below 2% on synthetic data with realistic levels of noise.

Abstract: In this paper, a novel temporally local recurrent radial basis function network for modeling and adaptive control of nonlinear systems is proposed. The proposed structure consists of recurrent hidden neurons having weighted self-feedback loops and a weighted linear feed-through from the input layer directly to the output layer neuron(s). The dynamic back-propagation algorithm is developed and used for updating the parameters of the proposed structure. To improve the performance of learning algorithm, discrete Lyapunov stability method is used to develop an adaptive learning rate scheme. This scheme ensures the faster convergence of the parameters and maintains the stability of the system. A total of 5 complex nonlinear systems are used to test and compare the performance of the proposed network with other neural network structures. The disturbance rejection tests are also carried out to check whether the proposed scheme is able to handle the external disturbance/noise signals effects or not. The obtained results show the efficacy of the proposed method.

Abstract: Characterization of the displacement response is critical for accurate chromatic confocal measurement. Current characterization methods usually provide a linear or polynomial relationship between the extracted peak wavelengths of the spectral signal and displacement. However, these methods are susceptible to errors in the peak extraction algorithms and errors in the selected model. In this paper, we propose a hybrid radial basis function network method to characterise the displacement response. With this method, the peak wavelength of the spectral signal is firstly extracted with a state-of-art peak extraction algorithm, following which, a higher-accuracy chromatic dispersion model is applied to determine the displacement-wavelength relationship. Lastly, a radial basis function network is optimized to provide a mapping between the spectral signals and the residual fitting errors of the chromatic dispersion model. Using experimental tests, we show that the hybrid radial basis function network method significantly improves the measurement accuracy, when compared to the existing characterizing methods.

Abstract: In recent decades, robot-assisted rehabilitation therapy has been widely researched and proven to be effective in the motor function recovery of disabled individuals. In this paper, an adaptive backstepping sliding mode control approach combined with neural uncertainty observer is developed for upper-limb exoskeleton, which can help the human operator perform repetitive rehabilitation training. Firstly, a comprehensive overview about the therapeutic exoskeleton hardware and real-time control system is introduced. Then, the neural adaptive backstepping sliding mode controller (NABSMC) is developed based on radial basis function network (RBFN) to improve the trajectory tracking accuracy with external disturbances and dynamics errors. Next, the closed-loop stability of the proposed controller is demonstrated according to the Lyapunov stability theory. Finally, further experimental investigation are conducted on three volunteers to compare the control performance of NABSMC strategy with an optimal backstepping sliding mode control (OBSMC) strategy. The comparison results show that the proposed NABSMC algorithm is capable of achieving higher trajectory tracking accuracy and better step response characteristic during repetitive passive rehabilitation training.

Abstract: In general, the online computation burden of robust model predictive control (RMPC) is very heavy, and the mechanical model of a plant, which is used in RMPC, is hard to obtain precisely in real industry. These issues may largely restrict the applicability of RMPC in real applications. This paper proposes a RBF-ARX (state-dependent Auto-Regressive model with eXogenous input and Radial Basis Function network type coefficients) model-based efficient robust predictive control (RBF-ARX-ERPC) approach to an inverted pendulum system, which is a complete and systematic method for designing robust MPC controller because it integrates the RBF-ARX modeling method and a fast RMPC approach. First, based on the offline identified RBF-ARX model without offset term, two convex polytopic sets are constructed to wrap the globally nonlinear behavior of the system. Then, the optimization problem of implementing a quasi-min-max MPC algorithm including several linear matrix inequalities (LMIs) is formulated, and it is solved offline to synthesize a sequence of explicit control laws that correspond to a sequence of asymptotically stable invariant ellipsoids, of which all the optimization results are stored in a look-up table. During the online real-time control, the controller only needs to carry out a simple state-vector computation and bisection search. The proposed approach is applied to an actual linear one-stage inverted pendulum (LOSIP), which is a fast-responding and nonlinear plant. The real-time control experiments demonstrate the effectiveness of the proposed RBF-ARX model-based efficient RMPC approach.

Abstract: A previously developed real-time forward collision warning system (RCWS) using a multi-layer perceptron neural network (MLPNN) with a single hidden layer aims to be implemented with in-vehicle sensor and smartphone under cloud-based communication environment. However, several issues exist concerning the communication delay between the smartphone and the cloud server, especially when uploading massive traffic information to the cloud server simultaneously. In order to mitigate the impact of the delay, this research proposes two modified RCWSs using an advanced feed-forward neural network (F2N2). One of them involves MLPNN with two hidden layers and the other includes radial basis function network. The modified RCWSs are evaluated by the real-time warning accuracy under different market penetration rates (MPRs) and delays. The evaluation shows that the warning performances of each RCWS increase when the MPR increases or the delay decreases overall. In addition, the modified RCWSs outperform the original one in all conditions. Furthermore, the performance gap between the modified RCWSs increases as the MPR decreases and the delay increases. These findings suggest that the advanced F2N2 model can be an effective alternative for uprating the performance of the RCWS, particularly under a large delay with low MPR.

Abstract: In this article, we have proposed a methodology for making a radial basis function network (RBFN) robust with respect to additive and multiplicative input noises. This is achieved by properly selecting the centers and widths for the radial basis function (RBF) units of the hidden layer. For this purpose, firstly, a set of self-organizing map (SOM) networks are trained for center selection. For training a SOM network, random Gaussian noise is injected in the samples of each class of the data set. The number of SOM networks is same as the number of classes present in the data set, and each of the SOM networks is trained separately by the samples belonging to a particular class. The weight vector associated with a unit in the output layer of a particular SOM network corresponding to a class is used as the center of a RBF unit for that class. To determine the widths of the RBF units, p-nearest neighbor algorithm is used class-wise. Proper selection of centers and widths makes the RBFN robust with respect to input perturbation and outliers present in the data set. The weights between the hidden and output layers of RBFN are obtained by pseudo inverse method. To test the robustness of the proposed method in additive and multiplicative noise scenarios, ten standard data sets have been used for classification. Proposed method has been compared with three existing methods, where the centers have been generated in three ways: randomly, using k-means algorithm, and based on SOM network. Simulation results show the superiority of the proposed method compared to those methods. Wilcoxon signed-rank test also shows that the proposed method is statistically better than those methods.

Abstract: Despite its significance, modulation classification of constant envelope modulations (CEM) has not gained worthy attention in AMC literature so far. Two neural network-based architectures, i.e., radial basis function network (RBFN) and sparse-autoencoder-based deep neural network (DNN) are proposed and analyzed for the classification of spectrally efficient CEM modulations. A blind classification method which does not require any a-priori information about the channel or CEM specifics is based on the effectiveness of proposed hybrid feature space (HFS), used to train the trending neural network classifiers. Classification performance of both networks is analyzed for the typical additive white Gaussian noise (AWGN) channel and less explored, unfriendly, frequency-selective fading environment under the impact of Doppler shift.

Abstract: Drowsiness detection is important since its strong relation with traffic accident. A study for drowsiness level detection using Artificial Neural Network (ANN) method has been conducted. It utilizes electrocardigraphic RR interval statistical features and Radial Basis Function Artificial Neural Network or RBF Network as classifier. Drowsiness levels are defined by Karonlinska Sleep Scale (KSS) which simplified into two classes, alert and drowsy classes. The main parameter of the RBFN are centers and width which are tuned using k-means clustering. A gradient descent is utilized to determine the output weight. The classifier is evaluated by using DROZY database which are collected from 14 subjects; each of them in different drowsiness levels. Feature extraction stage is conducted by segmenting the 10-min data into 30-seconds and it get the RR interval statistical feature. This study is conducted by varying the number of features as the input of RBFN. The method has been evaluated using 5fold cross validation with best performance 81.96%, 84.77%, 76.90% of accuracy, sensitivity, and specifity respectively.

Abstract: this work is a continuation of an ongoing effort to increase the robustness of the deep neural network, and thus mitigate possible adversarial examples. In our previous work, the emphasis was placed on denoising the input dataset by adding colored noise before processing. In that work, the evaluation made with the empirical robustness score, resulted in a 1% improvement on average for individual noise and a 3.74% improvement on average for ensemble noise. The aim of this paper is to demonstrate the effective robustness of a well-designed radial basis function neural network in tackling adversarial examples. With the empirical robustness as a metric, the results show a 72.5% increase with Fast Gradient Sign Method (FGSM) attack on the MNIST dataset in comparison to a simple deep network and a 6.4 % increase with FGSM on the CIFAR10 dataset.

Abstract: CO2 leakage from transmission pipelines in carbon capture and storage systems may seriously endanger the ecological environment and human health. Therefore, there is a pressing need of an accurate and reliable leak localization method for CO2 pipelines. In this study, a novel method based on the combination of a wavelet packet algorithm and a radial basis function network (RBFN) is proposed to realize the leak location. Multiple acoustic emission (AE) sensors are first deployed to collect leakage signals of CO2 pipelines. The characteristics of the leakage signals from the AE sensors under different pressures are then analyzed in both time and frequency domains. Further, leakage signals are decomposed into three layers using wavelet decomposition theory. Wavelet packet energy and maximum value, and time difference calculated by cross-correlation are selected as the input feature vectors of the RBFN. Experiments were carried out on a laboratory-scale test rig to verify the validity and correctness of the proposed method. Leakage signals at different positions under different pressures were obtained on the CO2 pipeline leakage test bench. Compared with the time difference of arrival method, the relative error obtained using the proposed method is less than 2%, which has certain engineering application prospects.

Abstract: In the new global economy, energy consumption has become a major issue for residential and commercial buildings. This paper discusses the accuracy of load forecasting for the aggregated load for residential and commercial buildings in the United States. The literature presents a plethora of different consumption forecasting approaches that vary in concept from conventional mathematical stochastic methods to the use of artificial neural network (ANN). The literature shows that ANN have many advantages over conventional techniques, hence the efficacy of ANN models to forecast energy consumptions are investigated. The objective of this paper is to compare recurrent ANN models with non-recurrent ANN models. The recurrent ANNs models used are the Long Short-Term Memory and Gated Recurrent Unit. The non-recursive ANNs studies are the Radial Basis Function Network and Multilayer Perceptron. The parameters examined are short and medium-term load forecasting. The study was made on historic data collected for individual buildings.

Abstract: The attitude of a human being involves with their emotions. Emotions can be observed in either verbally or visually or both. Verbal emotion recognition is a difficult task and an area of speech processing. It has a wide variety of applications in almost all fields. In this work, the authors have tried to recognize five types of emotion as anger, sadness, happiness, fear, and neutral. The work is focussed on the choice of spectral feature computation. For such purpose, Mel-frequency Cepstral coefficients (MFCC), spectral roll-off, spectral centroid and spectral flux are considered on frame-level extraction. Some of these features need to be reduced, combined, and balanced. The combined methods are verified and observed the effectiveness of results. The resulting features are used with neural network (NN) based models for recognition purpose. The models of multilayer perceptron (MLP), radial basis function network (RBFN), probabilistic neural network (PNN) and deep neural network (DNN) are considered and tested for the chosen features. It is observed that less amount of features provides reliable accuracy in case of PNN. The same utilizes less time for training and testing in case of MLP, RBFN, and PNN. However, DNN is not suitable for fewer amounts of features. It requires large data for better accuracy in the particular field. The results support the PNN with an average accuracy of 96.9% with low-dimensional feature sets, whereas the average accuracy of MLP, RBFN, DNN models found 90.1%, 92.7%, and 73.6% respectively.

Abstract: Recently, computer aided diagnosis and image processing have received considerable attention from a number of researchers. Mammography is the most effective method for exposure of early breast cancer to increase the survival rate. This paper presents the classification method for mammogram Image using Radial Basis Function Network (RBF) technique. This method is focused on features extracted from the breast cancer mammogram image processing algorithms. The actual decision about the presence of the disease is then made by RBF network classifiers. We conducted this study in five stages; collecting images, Region of Interest (ROI), features extracting, classification and end with testing and evaluating. The experimental results shown the classification accuracy results of the RBF neural network 79.166% while MLP algorithm was 54.1667%, that illustrate the capability of the RBF network to obtain better classification accuracy results.

Abstract: The present work brings two applications of the Lambert–Tsallis W q function in radial basis function networks (RBFN). Initially, an RBFN is used to discriminate between entangled and disentangled bipartite of qubit states. The kernel used is based on the Lambert–Tsallis W q function for q ∈ {1/2, 3/2, 2} and the quantum relative disentropy is used as a distance measure between quantum states. Entangled states with concurrence larger than 0.1 were correctly classified by the proposed RBFN in at least 97% of the cases. Following, a RBFN with the same kernel is used to estimate the probability density function of a set of data sampled according to Normal and Cauchy distributions.