Study on Weigh-in-Motion System Based on Chaos Immune Algorithm and RBF Network

This paper presents a hybrid algorithm which combines chaos, immune and genetic algorithm to design the radial basis function neural networks. We use the chaos variable which has the characters of pseudo-randomness and irregularity in chaos theory to generate the initial population, ensuring the initial solutions would map into the whole solution space. Moreover, by introducing the affinity calculated operation in immune algorithm to keep the diversity of population during the evolution. Finally, we use the trained RBF networks on an artificial problem with uniform input distribution, a real-world non-uniform with higher dimensional benchmark problem and Mackey-Glass time series problem. The results show a good generalization capability compared with other training methods.

In this paper, a novel radial basis function (RBF) neural network is proposed and applied successively for online stable identification and control of nonlinear discrete-time systems. The proposed RBF network has one hidden layer neural network (NN) with its all parameters being adaptable. The RBF network parameters are optimized by gradient descent method with stable learning rate whose stable convergence behavior is proved by Lyapunov stability approach. The aim of construction of the proposed RBF network is to combine power of the networks which have different mapping abilities. These networks are auto-regressive exogenous input model, nonlinear static NN model and nonlinear dynamic NN model. In simulations, the proposed network is applied for the direct inverse control of one benchmark nonlinear functioned system and Van de Vusse reaction in a CSTR discrete system even there exist large disturbances. From simulations, it is seen that the RBF network with stable learning rate identifies and controls nonlinear systems accurately.

An incremental neuronal-activity-based RBF neural network for nonlinear system modeling

این مطالعه به منظور بررسی پیش بینی شاخص های عملکرد تولیدی در مرغان تخم گذار با استفاده از شبکه های عصبی مصنوعی و رگرسیون غیرخطی چندگانه انجام شد. بررسی بر روی اطلاعات چهار دوره متوالی پرورش در یک واحد پرورش مرغ تخم گذار صورت گرفت. روش های داده-کاوی شامل رگرسیون خطی و غیر خطی، شبکه عصبی پرسپترون سه لایه، شبکه عصبی پرسپترون چهار لایه و شبکه عصبی با تابع پایه ای شعاعی بود. در این مدل ها از متغیرهای سن گله، میزان خوراک مصرفی و فصل تولید به عنوان متغیر پیشگو و شاخص های عملکرد تولیدی شامل درصد تخم-گذاری، وزن توده ای تخم مرغ تولیدی و ضریب تبدیل غذایی به عنوان متغیر پاسخ استفاده شد. نتایج نهایی رگرسیون های خطی نشان داد که برای تمامی متغیرهای وابسته مورد مطالعه متغیر مستقل سن گله معنی دار می باشد. بنابراین رگرسیون غیر خطی شاخص های عملکرد تولیدی در مقابل سن برای مقایسه با شبکه های عصبی مختلف مورد بررسی قرار گرفت و برای مقایسه کلیه مدل ها از ضریب تعیین (R2) و میانگین قدر مطلق خطا (MAE) استفاده شد. نتایج نشان داد بین شبکه های عصبی مصنوعی مختلف مورد مطالعه، شبکه با تابع پایه ای شعاعی بهتر از سایر مدل های در پیش‌بینی شاخص های عملکرد تولیدی مرغان تخم گذار عمل می کند.

Three learning phases for radial-basis-function networks

In this paper, a steady-state frequency-domain model of an uncontrolled rectifier bridge with capacitive dc smoothing, developed with radial basis function (RBF) networks, is presented. The nonlinear load model is incorporated in a balanced harmonic load-flow program in order to evaluate the harmonic distortion introduced in the networks by this device. The fundamental frequency load flow, used in the harmonic load-flow algorithm, is enhanced with the incorporation to the Jacobian matrix of active and reactive power sensitivities from nonlinear loads. These sensitivities can be computed easily from the nonlinear load model built with RBF networks.

Adaptive sliding mode control of maglev system based on RBF neural network minimum parameter learning method

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.

Weigh-in-motion (WIM) is the process of weighing vehicle tires or axles at normal roadway speeds ranging up to 130 km/h (80 mph). WIM systems consist of sensors embedded onto the pavement surface and a data acquisition system equipped with software capable of processing sensor signals into weight, computing additional traffic data elements, and summarizing them into various database formats. There is an urgent need for ensuring WIM data accuracy. This is accomplished through routine WIM system calibration and periodic WIM data quality control. The way these tasks are carried out varies widely between agencies. This study synthesizes the state of the practice in high speed WIM system calibration. The study is likely to be of interest to those responsible for long-term pavement performance, pavement design, bridge design, monitoring highway usage, highway cost allocation, and enforcement of truck loads. Two main tools were used in conducting this study—a thorough review of the European and North American literature on the subject and an on-line survey addressed to highway and load enforcement agencies administering WIM systems in the United States. The survey was supplemented by telephone interviews.

Systems for weighing vehicles while they are in motion are in widespread use in many countries. The accuracy of these weigh-in-motion (WIM) systems is strongly influenced by the road profile and vehicle dynamics. Systems based on sensors that are embedded in the pavement or placed on top of the road surface can measure the axle load only for the fraction of a second for which the wheels are present on the sensor. An alternative to pavement WIM systems that increases the length of the load-sensitive element is to use an existing bridge as a weighing scale (Bridge WIM). A major test of a Bridge WIM system at a test site near the Arctic Circle is described in this paper. The test was conducted along-side a larger test of pavement WIM systems. A large number of trucks from random traffic were weighed statically and the results compared to those from the Bridge WIM system. The accuracy of the system is assessed in accordance with the COST 323 WIM specification, which provides a standardized method of accuracy classification. The Bridge WIM system is proven to perform satisfactorily and consistently for a wide range of temperatures in near-Arctic climatic conditions.

In this paper, a novel adaptive control scheme that incorporates fully tuned radial basis function (RBF) neural network (NN) is proposed for the control of MEMS gyroscope with respect to external disturbances and model uncertainties. An adaptive fully tuned RBF neural network controller is used to compensate the external disturbances and model uncertainties, thus improving the dynamic characteristics and robustness of the MEMS gyroscope. The fully tuned RBF neural network compensating controller and the adaptive nominal controller are combined in the unified Lynapunov framework to ensure the stability of the control system. By using the proposed scheme, not only the effect of model uncertainties and external disturbances can be eliminated, but also satisfactory dynamic characteristics and strong robustness can be obtained. Simulation studies are implemented to verify the effectiveness of the proposed scheme and demonstrate that the fully tuned RBF network control has better robustness and dynamic characteristics than traditional RBF network control.

In June 1996, a trial of four portable WIM (weigh-in-motion) systems was performed on a heavily trafficked highway near Trappes. France. This site was equipped with a multiple sensor (MS-WIM) array consisting of 24 piezoceramic strip sensors built in the road at non-uniform spacing. Within three days, 116 runs were made with two pre-weighed test vehicles. Moreover 92 trucks in the traffic flow were stopped randomly and statically weighed on a weighing area upstream of the test site. They were used to check the accuracy of the MS-WIM and the four portable WIM systems, using the criteria of the draft European WIM Specifications. Furthermore, the axle loads and gross weights of almost 4,000 trucks were recorded in the traffic flow by the MS-WIM system. This large sample of data was used as a reference to assess the accuracy of the portable WIM systems.

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.

We discuss the application of a radial basis function (RBF) network to the channel equalization problem. In particular, the purpose of the paper is to improve the previously developed RBF equalizer with training using K-means and LMS methods; reducing the RBF network size by considering a lesser number of RBF centers, and developing new techniques for determining channel order which is required to specify the structure of an RBF equalizer. A linear regression model was used for estimating the channel order. The basic idea of reducing the network size is to select the centers, based on the channel lag. This work includes the comparison of the limits of mean square error (MSE) convergence of both a linear equalizer and an RBF equalizer.

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.