Generalized Delta Rule Research Articles

An evolutionary intelligent control system for a flexible joints robot

In this paper, we present a model for a serial robotic system with flexible joints (RFJ) using Euler–Lagrange equations, which integrates the oscillatory dynamics generated by the flexible joints at specific operating points, using a pseudo-Ornstein-Uhlenbeck process with reversion to the mean. We also propose a Stochastic Flexible - Adaptive Neural Integrated System (SF-ANFIS) to identify and control the RFJ with two degrees of freedom. For the configuration of the model, we use two adaptive strategies. One strategy is based on the Generalised Delta Rule (GDR). In contrast, a second strategy is based on the EDA-MAGO algorithm (Estimation Distribution Algorithms - Multi-dynamics Algorithm for Global Optimisation), improving online learning. We considered three stages for analysing and validating the proposed SF-ANFIS model: a first identification stage, a second stage defined by the adaptive control process, and a final stage or cancellation of oscillations. Results show that, for the identification stage, the SF-ANFIS model showed better statistical indices than the MADALINE model in control for the second joint, which presents the greatest oscillations; among those that stand out, the IOA (0.9955), VG (1.0012) and UAPC2 (-0.0003). For the control stage, The SF-ANFIS model showed, in a general way, the best behaviour in the system’s control for both joints, thanks to the capacity to identify and cancel oscillations based on the advanced sampling that defines the EDA algorithm. For the cancellation of the oscillations stage, the SF-ANFIS achieved the best behaviour, followed by the MADALINE model, where it is highlighted the UAPC2 (0.9525) value.

Predictive Model of Lyme Disease Epidemic Process Using Machine Learning Approach

Lyme disease is the most prevalent tick-borne disease in Eastern Europe. This study focuses on the development of a machine learning model based on a neural network for predicting the dynamics of the Lyme disease epidemic process. A retrospective analysis of the Lyme disease cases reported in the Kharkiv region, East Ukraine, between 2010 and 2017 was performed. To develop the neural network model of the Lyme disease epidemic process, a multilayered neural network was used, and the backpropagation algorithm or the generalized delta rule was used for its learning. The adequacy of the constructed forecast was tested on real statistical data on the incidence of Lyme disease. The learning of the model took 22.14 s, and the mean absolute percentage error is 3.79%. A software package for prediction of the Lyme disease incidence on the basis of machine learning has been developed. Results of the simulation have shown an unstable epidemiological situation of Lyme disease, which requires preventive measures at both the population level and individual protection. Forecasting is of particular importance in the conditions of hostilities that are currently taking place in Ukraine, including endemic territories.

APPLICATION OF COMPUTATIONAL TECHNOLOGIES FOR SOLUTION OF PROBLEM OF STOCK MARKET

The article discusses a method for forecasting the exchange rate. Artificial neural networks act as a forecasting tool. As a currency for the numerical testing of the proposed approach, the oil price in dollars, USD (value in rubles and tenge) was chosen as the most common currency in the world. The data will be processed from 2000 to 2019. In the course of the study, the indicators of the General exchange rate were identified with each other by day. When determining the dollar exchange rate using a single-layer neural network, the Adeline algorithm and the generalized Delta rule were used. Based on the prediction algorithm, the program code is written in Python. It is obvious that the quality of neural network training can be used to further predict the dynamics of the exchange rate.

Backpropagation – Artificial Neural Network (BP-ANN): Understanding gender characteristics of older driver accidents in West Midlands of United Kingdom

Older people are vulnerable road users with higher rate of casualties in traffic accidents. The commonly cited causes of accidents for older people are poor attention and decision making at critical locations of road, poor visibility in extreme weather, poor road surface condition and unpredictability of other road users, particularly young drivers. Female drivers are often labelled as being precarious drivers and having higher accident risk comparing to male drivers. This paper applies Backpropagation - Artificial Neural Network (BP-ANN) with a Generalized Delta Rule (GDR) learning algorithm to model the factors affecting traffic accidents of both older female and male drivers. The BP-ANN can construct the causation model of traffic accidents with greater accuracy and define the proportion of errors contributed by each factor to traffic accidents. This paper studies a total of 95,092 accident records in West Midlands of the United Kingdom during the period of 2006 to 2016. This paper determines journey purpose, lighting condition, pedestrian crossing with physical interventions, complex roadway geometry, extreme weather and time severity as the most significant factors of older driver accidents. The accident risk of older drivers can be improved by providing accessible routes, affordable, reliable and convenient public transport, timely warning of unexpected situations and changes in roadway geometry; increasing use of assistive technology in cars, driverless cars and encouraging active transports into sociable activities. The findings help the transport authorities and city councils to develop strategies and measures promoting public and active transports to ensuring the safety of older drivers.

Perceptrón memoria de correlación multicapa para predecir la violencia sistemática contra la mujer por su pareja en la Sierra del Perú

Perceptrón memoria de correlación multicapa para predecir la violencia sistemática contra la mujer por su pareja en la Sierra del Perú Multilayer Perceptron correlation memory to predict systematic violence against woman by their partner in the Sierra of Peru María Estela Ponce Aruneri y Erwin Kraenau Espinal Universidad Nacional Mayor de San Marcos, Facultad de Ciencias Matemáticas. Lima 01 DOI: https://doi.org/10.33017/RevECIPeru2013.0008/ Resumen En este trabajo se muestra que el modelo perceptrón memoria de correlación multicapa permite predecir el tipo de violencia que sufren las mujeres mayores de 14 años unidas o alguna vez unidas, residentes habituales en las viviendas circundantes de los Centros de Emergencia Mujer ubicados en la sierra del Perú; así como asociaciones importantes entre algunos estilos de crianza, relaciones familiares y percepciones acerca de los roles de género, con el tipo de violencia que ejerce el esposo/ compañero. Utilizamos 1126 casos de la base de datos proporcionada por el Ministerio de la Mujer y Poblaciones Vulnerables (MIMP); para los que se construyeron catorce variables de entrada, una que se refieren a estilo de crianza recibido, tres a relaciones familiares, nueve sobre percepciones acerca de los roles de género y una referida al ámbito geográfico; siete variables de salida que se refieren al tipo de violencia contra la mujer por parte de su pareja o ex –pareja. Para la etapa de diseño del modelo perceptrón memoria de correlación y entrenamiento de la red aplicamos el algoritmo de retropropagación (backpropagation), la función de activación utilizada para este caso fue sigmoidal (logística), calculamos el error cuadrático para evaluar el error cometido por la red en cada patrón(observación); y finalmente regla delta generalizada para modificar pesos y umbrales. Se elaboraron dos programas en Matlab, para aplicar el modelo perceptrón memoria de correlación multicapa con una y dos capas ocultas. El modelo perceptrón memoria de correlación multicapa, con dos capas ocultas proporciono mejores resultados, 80.34% de predicciones correctas; y muestra que la violencia familiar y la percepción acerca del rol de género son factores importantes en la predicción del tipo de violencia que padece la mujer unida o alguna vez unida por su pareja, y que reside en la sierra del Perú. Descriptores: Memorias de Correlación, perceptrón multicapa, predicciones, violencia contra la mujer. Abstract In this research shows that the correlation model memory multilayer perceptron to predict the type of violence experienced by women over 14 have ever joined or united, ordinarily resident in the houses surrounding the Women's Emergency Centers located in the sierra del Peru, as well as significant associations between certain parenting styles, family relationships and perceptions about gender roles, with the kind of violence exercised by the husband / partner. We use 1126 cases of women from the database provided by the Ministry of Women and Vulnerable Populations (MIMP); for which fourteen input variables were built, one relating to parenting style received, three family relationships, nine out of perceptions about gender roles and one referring to the geographical, seven output variables relate to the type of violence against women by their partner or ex-partner. For the design stage memory model and correlation perceptron network training apply the backpropagation algorithm, the activation function used in this case was sigmoidal (logistic), we calculated the mean square error to evaluate the error committed by the network in each pattern (observation), and finally generalized delta rule to change weights and thresholds. Two programs were developed in Matlab to implement the memory mapping model multilayer perceptron with one and two hidden layers. The model multilayer perceptron correlation memory with two hidden layers I provide better results, 80.34% of correct predictions, and shows that family violence and perceptions about gender roles are important factors in predicting the type of violence that women have ever joined or united by their partner, and reside in the sierra of Peru. Keywords: Correlation memories, multilayer perceptron, predictions, violence against women

Evaluating the Learning of Automata through the Use of Recurrent Neural Networks

This paper presents the computational potentialities, demonstrating the learning capacity and extrapolation of recurrent neural networks (RNN) through the learning study of finite automata. Initially, the generalized delta rule is presented for a recurrent network. In addition, the theoretical basis on Finite Automata, Moore Machine and Mealy Machine are presented, showing the equivalence between them. We formalized the problem of parity using a Moore Machine and its equivalent Mealy Machine. We proceeded simulation and the results are presented for the problem and simulation of Tomita languages 1 and 2, testing the extrapolation capacity of each RNN. The results indicated that the neural networks with recurrent architectures have a good capacity of extrapolation for the simulated problems.

Backpropagation Neural Network to estimate pavement performance: dealing with measurement errors

The objective of this study is to apply the Backpropagation Neural (BPN) network with Generalised Delta Rule learning algorithm for reducing the measurement errors of pavement performance modelling. The Multi-Layer Perceptron network and sigmoid activation function are applied to build the BPN network of Pavement Condition Index (PCI). Collector and arterial roads of both flexible and rigid pavements in Montreal City are taken as a case study. The input variables of the PCI are Average Annual Daily Traffic (AADT), Equivalent Single Axle Loads (ESALs), Structural Number (SN), pavement age, slab thickness and difference in the PCI between the current and preceding year (ΔPCI). The BPN networks estimate that the PCI has inverse relationships with AADT, ESALs and pavement age. The PCI has positive relationships with these variables for roads that have recent treatment operations. The PCI has positive relationships with SN and slab thickness that imply the increase in pavement condition with increasing structural strength and slab thickness. The ΔPCI significantly influences the estimation of PCI values. The AADT and ESALs have considerable importance; however, pavement age and structural characteristics of the pavement have an insignificant influence in determining the PCI values, except in the case of flexible arterial roads.

Pavement management with dynamic traffic and artificial neural network: a case study of Montreal

This study improves the pavement management system by developing a linear programming optimization for the road network of the City of Montreal with simulated traffic for a period of 50 years and deals with the uncertainty of pavement performance modeling. Travel demand models are applied to simulate annual average daily traffic (AADT) every 5 years. A backpropagation neural network (BPN) with a generalized delta rule learning algorithm is applied to develop pavement performance models without uncertainties. Linear programming of life-cycle optimization is applied to develop maintenance and rehabilitation strategies to ensure the achievement of good levels of pavement condition subject to a given maintenance budget. The BPN network estimated that PCI values were predominantly determined by the differences in pavement condition index, AADT, and equivalent single axle loads. Dynamic linear programming optimization estimated that CAD$150 million is the minimum annual budget required to keep most of the arterial and local roads in good condition in Montreal.

Software reliability modelling using neural network with compounded decreased error rate

The main task for the software management is to predict the reliability of a software by using an appropriate software reliability growth model (SRGM). The accuracy of the mechanism adopted for reliability prediction is also an important factor. In this study, a software reliability growth modelling problem has been solved using artificial neural networks (ANNs), as ANNs based models are competitive with traditional statistical models for software testing effort estimation. In the first phase, a software reliability growth model has been proposed with compounded decreased error rate to predict the software reliability. The model is further extended by incorporating Cobb-Douglas production function to model the combined effect of time and resources used. Multi-layer feed-forward neural network is used to solve the problems. The weights associated with various input parameters are updated using generalised delta rule and Levenberg-Marquardt method. A comparison is then made with the results from existing models in the literature. The work is validated by using two famous real data sets. Numerical results show that the proposed models perform better in comparison to others existing in the literature.

A Comparative Study of the RSM and ANN Models for Predicting Surface Roughness in Roller Burnishing

In this paper the comparison of the surface roughness prediction models based on response surface methodology (RSM) and artificial neural networks (ANN) is described. The models were developed based on five-level design of experiments conducted on Aluminum alloy 6061 work material with spindle speed, interference, feed, and number of tool pass as the roller burnishing process parameters. The ANN predictive models of surface roughness was developed using a multilayer feed forward neural network and trained with the help of an error back propagation learning algorithm based on the generalized delta rule. Mathematical models of second order RSM and developed ANN models were compared for surface roughness. The comparison evidently indicates that the prediction capabilities of ANN models are far better as compared to the RSM models. The minutiae of experimentation, development of model, testing, and performance comparison are presented in the paper.

Software reliability modelling using neural network with compounded decreased error rate

The main task for the software management is to predict the reliability of a software by using an appropriate software reliability growth model (SRGM). The accuracy of the mechanism adopted for reliability prediction is also an important factor. In this study, a software reliability growth modelling problem has been solved using artificial neural networks (ANNs), as ANNs based models are competitive with traditional statistical models for software testing effort estimation. In the first phase, a software reliability growth model has been proposed with compounded decreased error rate to predict the software reliability. The model is further extended by incorporating Cobb-Douglas production function to model the combined effect of time and resources used. Multi-layer feed-forward neural network is used to solve the problems. The weights associated with various input parameters are updated using generalised delta rule and Levenberg-Marquardt method. A comparison is then made with the results from existing models in the literature. The work is validated by using two famous real data sets. Numerical results show that the proposed models perform better in comparison to others existing in the literature.

Time Series Prediction with Neural Networks for the Athens Stock Exchange Indicator

1. Introduction The common characteristic of all stock exchange indicators have the term of uncertainty, which is related with their short and long-term future state. This feature is undesirable for the investor but it is also unavoidable whenever the stock exchange indicator is selected as an investment tool. Among the best possible alterations that the researcher desires to make is to reduce this uncertainty. Stock exchange prediction or forecasting is one of the interesting issues in this process as it is also referred in other works (Helstrom T. & Holmstrom K., 1998, Tsibouris G. & Zeidenberg M., 1996, White H., 1993). Time series forecasting, or time series prediction, takes an existing series of data [x.sub.t-n],...,[x.sub.t-2], [x.sub.t-1], [x.sub.t] and forecasts the [x.sub.t+1], [x.sub.t+2],..., data values. The goal is to observe or model the existing data series to enable future unknown data values to be forecasted accurately. Examples of data series include financial data series (stocks, indices, rates, etc.), physically observed data series (sunspots, weather, etc.), and mathematical data series (Fibonacci sequence, integrals of differential equations, etc.). A neural network (Tsibouris G. & Zeidenberg M., 1996) is a computational model that is loosely based on the neuron cell structure of the biological nervous system. Given a training set of data, the neural network can learn the data with a learning algorithm; in this research the most common algorithm, back propagation, is used. Through back propagation, the neural network forms a mapping between inputs and desired outputs from the training set by altering weighted connections within the network. The origin of neural networks dates back to the 1940s. McCulloch and Pitts (1943) and Hebb (1949) researched networks of simple computing devices that could model neurological activity and learning within these networks, respectively. Later, the work of Rosenblatt (1962) focused on computational ability in perceptrons, or single-layer feed-forward networks. Proofs showing that perceptrons, trained with the Perceptron Rule on linearly separable pattern class data, could correctly separate the classes generated excitement among researchers and practitioners. This excitement waned with the discouraging analysis of perceptrons presented by Minsky and Papert (1969). The analysis pointed out that perceptrons could not learn the class of linearly inseparable functions. It also stated that the limitations could be resolved if networks contained more than one layer, however no effective training algorithm for multi-layer networks was available. Rumelhart, Hinton, and Williams (1986) revived interest in neural networks by introducing the generalized delta rule for learning by back propagation, which is today the most commonly used training algorithm for multi-layer networks. 2. Athens Stock Exchange Indicator Time Series The Athens Stock Exchange Indicator is presented as a signal x=x(t) as it shown in Figure 1. It covers data from the period 1998 to 2005. The sampling rate is [DELTA]t=1 day. [FIGURE 1 OMITTED] 3. Neural Network Constructions In order to predict the time series for the Athens Stock Exchange Indicator we construct a back propagation network (Wan A.E., 1990, Widrow B., and Lehr M., 1990, Rumelhart D., McClelland J. et al., 1986) that consists of 1 input layer 1 middle or hidden layer and 1 output layer. The input layer has 3 processing elements (PE) neurons; the middle layer has 2x3+1=7 neurons according to Kolmogorov theorem (Kolmogorov N. A., 1950, Blackwell D., 1947). We choose the input layer to have 3 inputs because of minimum embedding dimension 3, and the attractor is embedded at a three -dimensional phase space (Hanias P.M., Curtis G.P., and Thalassinos E.J., 2006). Beginning with the first value of the time series, the first set of inputs data is x1, x2, x3 and our outputs are x4, x5, x6, x7, x8, x9, x10, x11, x12. …

Backpropagation generalized delta rule for the selective attention Sigma-if artificial neural network

Backpropagation generalized delta rule for the selective attention Sigma-if artificial neural networkIn this paper the Sigma-if artificial neural network model is considered, which is a generalization of an MLP network with sigmoidal neurons. It was found to be a potentially universal tool for automatic creation of distributed classification and selective attention systems. To overcome the high nonlinearity of the aggregation function of Sigma-if neurons, the training process of the Sigma-if network combines an error backpropagation algorithm with the self-consistency paradigm widely used in physics. But for the same reason, the classical backpropagation delta rule for the MLP network cannot be used. The general equation for the backpropagation generalized delta rule for the Sigma-if neural network is derived and a selection of experimental results that confirm its usefulness are presented.

Backpropagation generalized delta rule for the selective attention Sigma-if artificial neural network

Backpropagation generalized delta rule for the selective attention Sigma-if artificial neural networkIn this paper the Sigma-if artificial neural network model is considered, which is a generalizat...

On the characteristics of the coefficients in the sea surface temperature estimation functions due to the split-window method

This paper presents an application of a neural network to the trophic state mapping of Deachung reservoir. Landsat TM data acquired on 20 June, 1995 was used as an image data, and fifteen water sampling measurements were acquired during the satellite overpass. From the water sample measurements, trophic state of the fifteen sampling points were determined. These point data of trophic state and DN values were used as input pattern for training the network. A simple three layer feed forward network was trained by generalized delta rule using the input patterns of trophic state. It was possible for the trained artificial neural network to classify the image data accurately even though there were very small number of training data. The finally produced trophic state map of Deachung reservoir showed synoptic geographic coverage of water quality which can not be expected from the traditional water sampling surveys.

A comparative study of the ANN and RSM modeling approaches for predicting burr size in drilling

This paper describes the comparison of the burr size predictive models based on artificial neural networks (ANN) and response surface methodology (RSM). The models were developed based on three-level full factorial design of experiments conducted on AISI 316L stainless steel work material with cutting speed, feed, and point angle as the process parameters. The ANN predictive models of burr height and burr thickness were developed using a multilayer feed forward neural network, trained using an error back propagation learning algorithm (EBPA), which is based on the generalized delta rule. The performance of the developed ANN models were compared with the second-order RSM mathematical models of burr height and thickness. The comparison clearly indicates that the ANN models provide more accurate prediction compared to the RSM models. The details of experimentation, model development, testing, and performance comparison are presented in the paper.

Weld line detection and process control for welding automation

Welding has been widely used as a process to join metallic parts. But because of hazardous working conditions, workers tend to avoid this task. Techniques to achieve the automation are the recognition of joint line and process control. A CCD (charge coupled device) camera with a laser stripe was applied to enhance the automatic weld seam tracking in GMAW (gas metal arc welding). The adaptive Hough transformation having an on-line processing ability was used to extract laser stripes and to obtain specific weld points. The three-dimensional information obtained from the vision system made it possible to generate the weld torch path and to obtain information such as the width and depth of the weld line. In this study, a neural network based on the generalized delta rule algorithm was adapted to control the process of GMAW, such as welding speed, arc voltage and wire feeding speed. The width and depth of the weld joint have been selected as neurons in the input layer of the neural-network algorithm. The input variables, the width and depth of the weld joint, are determined by image information. The voltage, weld speed and wire feed rate are represented as the neurons in the output layer. The results of the neural-network learning applied to the welding are as follows: learning ratio 0.5, momentum ratio 0.7, the number of hidden layers 2 and the number of hidden units 8. They have significant influence on the weld quality.

Generalized delta rule (GDR) algorithm with generalized predictive control (GPC) for optimum temperature tracking of batch polymerization

The generalized delta rule (GDR) algorithm with generalized predictive control (GPC) control was implemented experimentally to track the temperature on a set point in a batch, jacketed polymerization reactor. An equation for optimal temperature was obtained by using co-state Hamiltonian and model equations. To track the calculated optimal temperature profiles, controller used should act smoothly and precisely as much as possible. Experimental application was achieved to obtain the desired comparison. In the design of this control system, the reactor filled with styrene–toluene mixture is considered as a heat exchanger. When the reactor is heated by means of an immersed heater, cooling water is passed through the reactor-cooling jacket. So the cooling water absorbs the heat given out by the heater. If this is taken into consideration, this reactor can be considered to be continuous in terms of energy. When such a mixing chamber was used as a polymer reactor with defined values of heat input and cooling flow rate, system can reach the steady-state condition. The heat released during the reaction was accepted as a disturbance for the heat exchanger. Heat input from the immersed heater is chosen as a manipulated variable. The neural network model based on the relation between the reactor temperature and heat input to the reactor is used. The performance results of GDR with GPC were compared with the results obtained by using nonlinear GPC with NARMAX model. The reactor temperature closely follows the optimal trajectory. And then molecular weight, experimental conversion and chain lengths are obtained for GDR with GPC.

Identification of oxalotrophic bacteria by neural network analysis of numerical phenetic data

A new approach with artificial neural network (ANN) was applied to numerical taxonomy of bacteria using the oxalate as carbon and energy source. For this aim the characters effective in differentiating separate groups were selected from morphological, physiological and biochemical test results. Fourteen aerobic, Gram-negative, oxalate-utilizing isolates and four oxalate-utilizing reference strains (Ralstonia eutropha DSM 428, Methylobacterium extorquens DSM 1337T, Ralstonia oxalatica DSM 1105T, Oxalicibacterium flavum DSM 15506T) were included in the study. ANN program used here was developed in Borland C++ language. Iterations were performed on an IBM compatible PC computer. ANN architecture having feed-forward backpropagation algorithm was used for teaching generalized delta rule. The results show that ANN can have a large potential in solving the taxonomic problems of oxalate-utilizing bacteria.

Computer Evaluation of Weld Lines in Injection-molded Parts

Computer simulation packages of injection molding have had success in predicting filling behavior in extremely complicated geometries, capable of predicting weld lines’ location exactly. But none of the current packages can predict weld lines’ properties qualitatively. An evaluation model based on artificial neural network method is presented in this paper. Initially, for identifying the input of the network, the affecting factors of weld lines’ properties are discussed in detail, which are orientation coefficient of the material, the meeting angle, and the melt mobility history coefficient. And then a 3-4-1 three-layer back-propagation network is constructed, which is trained using MATLAB. In order to reduce extra-or over-fitting, a value of 0.9 is used for both momentum factor and rate of learning with generalized delta rule method. Comparison with experimental results shows that this presented model is capable of predicting weld lines’ properties quantitatively for engineering design.