Combined genetic algorithms and neural‐network approach for power‐system transient stability evaluation

Three learning phases for radial-basis-function networks

We propose a differential radial basis function (RBF) network termed RBF-DiffNet—whose hidden layer blocks are partial differential equations (PDEs) linear in terms of the RBF—to make the baseline RBF network robust to noise in sequential data. Assuming that the sequential data derives from the discretisation of the solution to an underlying PDE, the differential RBF network learns constant linear coefficients of the PDE, consequently regularising the RBF network by following modified backward-Euler updates. We experimentally validate the differential RBF network on the logistic map chaotic timeseries as well as on 30 real-world timeseries provided by Walmart in the M5 forecasting competition. The proposed model is compared with the normalised and unnormalised RBF networks, ARIMA, and ensembles of multilayer perceptrons (MLPs) and recurrent networks with long short-term memory (LSTM) blocks. From the experimental results, RBF-DiffNet consistently shows a marked reduction in the prediction error over the baseline RBF network (e.g., 41% reduction in the root mean squared scaled error on the M5 dataset, and 53% reduction in the mean absolute error on the logistic map); RBF-DiffNet also shows a comparable performance to the LSTM ensemble but requires 99% less computational time. Our proposed network consequently enables more accurate predictions—in the presence of observational noise—in sequence modelling tasks such as timeseries forecasting that leverage the model interpretability, fast training, and function approximation properties of the RBF network.

Radial Basis Function (RBF) Network is popularly used for solving pattern recognition problems. The training of RBF Network is faster compared to multi layer perceptron using error backpropagation. However, the RBF Network uses the pseudo inverse matrix to calculate weights from the hidden layer to the output layer. Thus calculation cost increases when the number of data and the number of hidden units increase. In addition, in RBF Network the decision of optimum number of hidden units is difficult. It is also more prone to overtraining, needing repeated train and test cycles to ascertain a proper number of the Network hidden units, so that generalization performance is good. In this work, we propose a technique to set up RBF network parameters which is fast, as well as the number of hidden units are automatically determined. We start with training a Self-Organizing Maps (SOM), which is a unsupervised training, though our samples are labeled. SOM can find the distribution of data in multidimensional space, and map it on a two dimensional display. The results of SOM network is used to calculate the RBF parameters. It is shown by experiments that using the proposed method, RBF network parameters can be determined much faster compared to existing technique. Moreover, the recognition rate for the test data was higher, showing better generalization performance.

In order to forecast missile storage reliability better, the paper researched a forecasting method based on neural network which is with the ability of actualizing multi-nonlinear mapping from input to output, and discussed steps of forecasting based on back propagation (BP) network and radial basis function (RBF) network respectively. At last, the storage reliability of one type ship-to-ship missile is forecasted based on BP network and RBF network respectively. The results show that both of the BP and RBF are suitable for Missile storage reliability forecasting, and the precision of the train goal is better by using RBF network. RBF network is more suitable for dealing with this problem.

The present work aims to study the development and application of Radial Basis Function (RBF) networks for predicting auger energy consumption based on input energy. The study utilized RBF networks and explored the input energy with treatments 2 (Soil moisture content), 2 (Rotary speeds), 2 (Hole depths) and 4 (Replication) based on field operations. As indicated by the results, energy input differed between the treatments but was not significant. The highest input value in transaction soil moisture content was 14.75 %, rotary speeds of 235 rpm, and hole depths of 40 cm. In comparison, the lower input energy at transaction soil moisture content was 7.9%, rotary speeds of 235 rpm, and hole depths of 20 cm. Input energy in treatment (14.75 %, 235 rpm, and 40 cm) and treatment (7.9 %,235 rpm, and 20 cm) were 100.204 and 57.135 MJ. ha-1, respectively. The highest input energy shares were recorded for diesel fuel at all treatments. Furthermore, the RBF network with one hidden layer had good convergence. The output results showed 10 and five hidden neurons in a hidden layer with high accuracy for treatment (14.75 %, 235 rpm, and 40 cm) and treatment (7.9%, 235 rpm, and 20 cm). In the treatment (14.75 %, 235 rpm, and 40 cm), the MSE for the training and testing sets was 0.0001 % and 0.01 % for data points with Ordinary RBF (ORBF type). The performance of the 3-10-1 architecture was better than other architectures. Finally, this research concluded that the RBF network method can forecast the input energy and energy expenditures related to the types of treatments.

The radial basis function (RBF) network is a type of neural network that uses a radial basis function as its activation function (Ou, Oyang & Chen, 2005). Because of the better approximation capabilities, simpler network structure and faster learning speed, the RBF networks have attracted considerable attention in many science and engineering field. Horng (2010) used the RBF for multiple classifications of supraspinatus ultrasonic images. Korurek & Dogan (2010) used the RBF networks for ECG beat classifications. Wu, Warwick, Jonathan, Burgess, Pan & Aziz (2010) applied the RBF networks for prediction of Parkinson’s disease tremor onset. Feng & Chou (2011) use the RBF network for prediction of the financial time series data. In spite of the fact that the RBF network can effectively be applied, however, the number of neurons in the hidden layer of RBF network always affects the network complexity and the generalizing capabilities of the network. If the number of neurons of the hidden layer is insufficient, the learning of RBF network fails to correct convergence, however, the neuron number is too high, the resulting over-learning situation may occur. Furthermore, the position of center of the each neuron of hidden layer and the spread parameter of its activation function also affect the network performance considerably. The determination of three parameters that are the number of neuron, the center position of each neuron and its spread parameter of activation function in the hidden layer is very important.

The power transient stability analysis is one of the basis for determining the control strategy of power system security and stability. Considering the influence of power grid topology on the transient stability of power system, the transient stability evaluation model is constructed based on the graph attention neural network. The electrical components and their transient operation data are mapped to the graph data with the spatial topology characteristics of power system for model training, so as to improve the topological generalization performance of the model. The marginal contribution of input characteristics to the output of transient power angle stability evaluation model is quantitatively calculated based on Shapley additive explanation (SHAP), so as to improve the interpretability of data-driven method for transient power angle stability evaluation. The effectiveness of the proposed method is verified by the IEEE 39-bus system.

This research work focuses on the development of meta-cognitive sequential learning algorithms in Radial Basis Function (RBF) network classiers, and their application to the early diagnosis of neurodegenerative diseases. The important issues in existing sequential learning algorithms are proper selection of training samples, nding minimal network structure and selection of an appropriate learning strategy. In addition, the random sequence of sample arrival inuences the performance signicantly. It has been reported in human learning that best learning strategies employ meta-cognition (metacognition means cognition about cognition) to address fundamental problems of what-tolearn, when-to-learn and how-to-learn. This thesis develops such meta-cognitive sequential learning algorithms in RBF network for classication problems. We call a RBF network employing meta-cognitive algorithm as `meta-cognitive RBF network' (McRBFN). McRBFN is developed based on Nelson and Narens model of meta-cognition for human learning. Accordingly, McRBFN has two components, namely cognitive and meta-cognitive components. A RBF network with evolving structure is the cognitive component and a self-regulatory learning mechanism is its meta-cognitive component. List of Figures 1.1 Nelson and Narens model of meta-cognition . . . . . . . . . . . . . . . .

Radial basis function (RBF) network can be viewed as a fuzzy rule base with specified membership functions and fuzzy inference operations. However, there is a trade-off between the approximation performance of RBF network and the number of hidden neurons. To tackle this problem, this paper proposes a dynamic RBF (DRBF) network with a constructive learning. This DRBF network not only can create the new hidden neurons, but also can prune the insignificant hidden neurons. Then, an adaptive dynamic RBF fuzzy neural control (ADRFNC) system, including a neural controller and a saturation compensator, is developed. The neural controller uses a DRBF network to on-line mimic an ideal controller and the saturation compensator is designed to dispel the approximation error introduced by the neural controller. Finally, the proposed ADRFNC system is applied to a chaotic circuit and a DC motor control system. Simulation and experimental results show the proposed ADRFNC system can achieve a favorable tracking performance when the controller’s parameters have been learned and the network structure has been constructed by the proposed learning algorithm.

Generalized [formula omitted]-sparse algorithms for constructing fault tolerant RBF networks

A new learning method of radial basis function (RBF) network based on fuzzy C-means (FCM) clustering and ant colony optimization (ACO) is presented in the paper. Generally, the crucial problem of learning RBF network is the selection of the unit number, the centers and widths of the Gaussian radial basis function in hidden layer, and the weights between hidden layer and output layer. In this work, the centers are determined by FCM clustering, and the weights are determined by least mean squares (LMS) method. In addition, ACO is introduced to optimize two important parameters of FCM including the weighting exponent which impacts its performance, and the clustering number that is equal to the hidden unit number which impacts the generalization of RBF network, by minimizing an objective function integrated the generalization error with the hidden unit number of RBF network. Simulation results of identifying a nonlinear system illustrate the effectiveness of designing the RBF network with smaller structure but stronger generalization ability, comparing with K-means and orthogonal least squares (OLS) based learning methods.

Use of a mixed structure consisting of a radial basis function (RBF) network and pole-shifting feedback controller for power system stabilizer application is presented in this paper. The RBF network is used to identify the time-varying parameters of the power system. The RBF has a simple structure with a nonlinear hidden layer which constructs local approximations to nonlinear input-output mapping and a linear output layer. The network is capable of fast learning and represents a nonlinear autoregressive moving average model with exogeneous inputs (NARMAX). The NARMAX model is transformed into a linear ARMA model every sampling period and the pole-shift controller is used to calculate the control signal. This process of linearizing a nonlinear system is important because of the widespread industrial acceptance of linear feedback controllers, availability of theoretical and practical results about robustness, and closed-loop stability. Simulation studies carried out on a single-machine infinite bus power system verify the effectiveness of the above approach.

The present paper proposes a novel non-intrusive model reduction approach based on Proper Orthogonal Decomposition (POD), the Discrete Empirical Interpolation Method (DEIM) and Radial Basis Function (RBF) networks to efficiently predict production of oil and gas reservoirs. Provided a representative set of training reservoir scenarios, either POD or DEIM allows for effectively projecting input parameters (e.g., permeability, porosity), states (e.g., pressure, saturations) and outputs (e.g., well production curves) into a much lower dimension that retains the main features contained in the simulation system. In this work, these projections are applied across multiple levels to be able to collapse a large number of spatio-temporal correlations. It is observed that these projections can be effectively performed at a large extent regardless of the underlying geological complexity and operational constraints associated with the reservoir model. The RBF network provides a powerful means for developing learning functions from input-output relationships described by the reservoir dynamics entailed by multiple combinations of inputs and controls. In order to achieve a high degree of predictability from the resulting reduced model, the RBF network exploits locality by a means of Gaussian basis functions that are maximal at the sampled point and decrease monotonically with distance. Compared to multilayer perceptron networks (i.e., traditional artificial neural networks) RBF networks require less training and are less sensitive to the presence of noise in the data. In this regard, POD or DEIM acts as a data filter that additionally aids at designing a more compact RBF network representation suitable for targeting fast reservoir predictions. Numerical results show significant accelerations with respect to running the original simulation model on a set of field-motivated cases.

This paper investigates the transient stability of power systems co-dominated\nby different types of grid-forming (GFM) devices. Synchronous generators (SGs\nand VSGs) and droop-controlled inverters are typical GFM devices in modern\npower systems. SGs/VSGs are able to provide inertia while droop-controlled\ninverters are generally inertialess. The transient stability of power systems\ndominated by homogeneous GFM devices has been extensively studied. Regarding\nthe hybrid system jointly dominated by heterogeneous GFM devices, the transient\nstability is rarely reported. This paper aims to fill this gap. It is found\nthat the synchronization behavior of the hybrid system can be described by a\nsecond-order motion equation, resembling the swing equation of SGs. Moreover,\ntwo significant differences from conventional power systems are discovered. The\nfirst is that the droop control dramatically enhances the damping effect,\ngreatly affecting the transient stability region. The second is that the\nfrequency state variable exhibits a jump at the moment of fault disturbances,\nthus impacting the post-fault initial-state location and stability assessment.\nThe underlying mechanism behind the two new characteristics is clarified and\nthe impact on the transient stability performance is analyzed and verified. The\nfindings provide new insights into transient stability of power systems hosting\nheterogeneous devices.\n

To group microcrystalline celluloses (MCCs) using a combination of artificial neural network (ANN) and data clustering. Radial basis function (RBF) network was used to model the torque measurements of the various MCCs. Output from the RBF network was used to group the MCCs using a data clustering technique known as discrete incremental clustering (DIC). Rheological or torque profiles of various MCCs at different combinations of mixing time and water:MCC ratios were obtained using mixer torque rheometry (MTR). Correlation analysis was performed on the derived torque parameter Torque(max) and physical properties of the MCCs. Depending on the leniency of the predefined threshold parameters, the 11 MCCs can be assigned into 2 or 3 groups. Grouping results were also able to identify bulk and tapped densities as major factors governing water-MCC interaction. MCCs differed in their water retentive capacities whereby the denser Avicel PH 301 and PH 302 were more sensitive to the added water. An objective grouping of MCCs can be achieved with a combination of ANN and DIC. This aids in the preliminary assessment of new or unknown MCCs. Key properties that control the performance of MCCs in their interactions with water can be discovered.