Global convergence and limit cycle behavior of weights of perceptron

In this paper, it is found that the weights of a perceptron are bounded for all initial weights if there exists a nonempty set of initial weights that the weights of the perceptron are bounded. Hence, the boundedness condition of the weights of the perceptron is independent of the initial weights. Also, a necessary and sufficient condition for the weights of the perceptron exhibiting a limit cycle behavior is derived. The range of the number of updates for the weights of the perceptron required to reach the limit cycle is estimated. Finally, it is suggested that the perceptron exhibiting the limit cycle behavior can be employed for solving a recognition problem when downsampled sets of bounded training feature vectors are linearly separable. Numerical computer simulation results show that the perceptron exhibiting the limit cycle behavior can achieve a better recognition performance compared to a multilayer perceptro

Incremental and stable training algorithm for wind turbine neural modeling

Training and topology design of artificial neuralnetworks are important issues with largeapplication. This paper deals with an improvedalgorithm for feed forward neural networks (FNN) straining. The association of an incrementalapproach and the Lyapunov stability theoryaccomplishes both good generalization and stabletraining process. The algorithm is tested on windturbine modeling. Compared to the incrementalapproach and to the Lyapunov stability basedmethod, the association of both strategies givesinteresting results

Adaptive Analytical Approach to Lean and Green Operations

Recent problems faced by industrial players commonly relates to global warming and depletion of resources. This situation highlights the importance of improvement solutions for industrial operations and environmental performances. Based on interviews and literature studies, manpower, machine, material, money and environment are known as the foundation resources to fulfil the facility's operation. The most critical and common challenge that is being faced by the industrialists is to perform continuous improvement effectively. The needs to develop a systematic framework to assist and guide the industrialist to achieve lean and green is growing rapidly. In this paper, a novel development of an adaptive analytic model for lean and green operation and processing is presented. The development of lean and green index will act as a benchmarking tool for the industrialist. This work uses the analytic hierarchy process to obtain experts opinion in determining the priority of the lean and green components and indicators. The application of backpropagation optimisation method will further enhance the lean and green model in guiding the industrialist for continuous improvement. An actual industry case study (combine heat and power plant) will be presented with the proposed lean and green model. The model is expected to enhance processing plant performance in a systematic lean and green manner

Adaptive Analytical Approach to Lean and Green Operations

Recent problems faced by industrial players commonly relates to global warming and depletion of resources. This situation highlights the importance of improvement solutions for industrial operations and environmental performances. Based on interviews and literature studies, manpower, machine, material, money and environment are known as the foundation resources to fulfil the facility's operation. The most critical and common challenge that is being faced by the industrialists is to perform continuous improvement effectively. The needs to develop a systematic framework to assist and guide the industrialist to achieve lean and green is growing rapidly. In this paper, a novel development of an adaptive analytic model for lean and green operation and processing is presented. The development of lean and green index will act as a benchmarking tool for the industrialist. This work uses the analytic hierarchy process to obtain experts opinion in determining the priority of the lean and green components and indicators. The application of backpropagation optimisation method will further enhance the lean and green model in guiding the industrialist for continuous improvement. An actual industry case study (combine heat and power plant) will be presented with the proposed lean and green model. The model is expected to enhance processing plant performance in a systematic lean and green manner

Models for time series prediction based on neural networks. Case study : GLP sales prediction from ANCAP.

A time series is a sequence of real values that can be considered as observations of a certain system. In this work, we are interested in time series coming from dynamical systems. Such systems can be sometimes described by a set of equations that model the underlying mechanism from where the samples come. However, in several real systems, those equations are unknown, and the only information available is a set of temporal measures, that constitute a time series. On the other hand, by practical reasons it is usually required to have a prediction, v.g. to know the (approximated) value of the series in a future instant t. The goal of this thesis is to solve one of such real-world prediction problem: given historical data related with the lique ed bottled propane gas sales, predict the future gas sales, as accurately as possible. This time series prediction problem is addressed by means of neural networks, using both (dynamic) reconstruction and prediction. The problem of to dynamically reconstruct the original system consists in building a model that captures certain characteristics of it in order to have a correspondence between the long-term behavior of the model and of the system. The networks design process is basically guided by three ingredients. The dimensionality of the problem is explored by our rst ingredient, the Takens-Mañé's theorem. By means of this theorem, the optimal dimension of the (neural) network input can be investigated. Our second ingredient is a strong theorem: neural networks with a single hidden layer are universal approximators. As the third ingredient, we faced the search of the optimal size of the hidden layer by means of genetic algorithms, used to suggest the number of hidden neurons that maximizes a target tness function (related with prediction errors). These algorithms are also used to nd the most in uential networks inputs in some cases. The determination of the hidden layer size is a central (and hard) problem in the determination of the network topology. This thesis includes a state of the art of neural networks design for time series prediction, including related topics such as dynamical systems, universal approximators, gradient-descent searches and variations, as well as meta-heuristics. The survey of the related literature is intended to be extensive, for both printed material and electronic format, in order to have a landscape of the main aspects for the state of the art in time series prediction using neural networks. The material found was sometimes extremely redundant (as in the case of the back-propagation algorithm and its improvements) and scarce in others (memory structures or estimation of the signal subspace dimension in the stochastic case). The surveyed literature includes classical research works ([27], [50], [52]) as well as more recent ones ([79] , [16] or [82]), which pretends to be another contribution of this thesis. Special attention is given to the available software tools for neural networks design and time series processing. After a review of the available software packages, the most promising computational tools for both approaches are discussed. As a result, a whole framework based on mature software tools was set and used. In order to work with such dynamical systems, software intended speci cally for the analysis and processing of time series was employed, and then chaotic series were part of our focus. Since not all randomness is attributable to chaos, in order to characterize the dynamical system generating the time series, an exploration of chaotic-stochastic systems is required, as well as network models to predict a time series associated to one of them. Here we pretend to show how the knowledge of the domain, something extensively treated in the bibliography, can be someway sophisticated (such as the Lyapunov's spectrum for a series or the embedding dimension). In order to model the dynamical system generated by the time series we used the state-space model, so the time series prediction was translated in the prediction of the next system state. This state-space model, together with the delays method (delayed coordinates) have practical importance for the development of this work, speci cally, the design of the input layer in some networks (multi-layer perceptrons - MLPs) and other parameters (taps in the TFLNs). Additionally, the rest of the network components where determined in many cases through procedures traditionally used in neural networks : genetic algorithms. The criteria of model (network) selection are discussed and a trade-o between performance and network complexity is further explored, inspired in the Rissanen's minimum description length and its estimation given by the chosen software. Regarding the employed network models, the network topologies suggested from the literature as adequate for the prediction are used (TLFNs and recurrent networks) together with MLPs (a classic of arti cial neural networks) and networks committees. The e ectiveness of each method is con rmed for the proposed prediction problem. Network committees, where the predictions are a naive convex combination of predictions from individual networks, are also extensively used. The need of criteria to compare the behaviors of the model and of the real system, in the long run, for a dynamic stochastic systems, is presented and two alternatives are commented. The obtained results proof the existence of a solution to the problem of learning of the dependence Input ! Output . We also conjecture that the system is dynamic-stochastic but not chaotic, because we only have a realization of the random process corresponding to the sales. As a non-chaotic system, the mean of the predictions of the sales would improve as the available data increase, although the probability of a prediction with a big error is always non-null due to the randomness present. This solution is found in a constructive and exhaustive way. The exhaustiveness can be deduced from the next ve statements: the design of a neural network requires knowing the input and output dimension,the number of the hidden layers and of the neurons in each of them. the use of the Takens-Mañé's theorem allows to derive the dimension of the input data by theorems such as the Kolmogorov's and Cybenko's ones the use of multi-layer perceptrons with only one hidden layer is justi ed so several of such models were tested the number of neurons in the hidden layer is determined many times heuristically using genetic algorithms a neuron in the output gives the desired prediction As we said, two tasks are carried out: the development of a time series prediction model and the analysis of a feasible model for the dynamic reconstruction of the system. With the best predictive model, obtained by an ensemble of two networks, an acceptable average error was obtained when the week to be predicted is not adjacent to the training set (7.04% for the week 46/2011). We believe that these results are acceptable provided the quantity of information available, and represent an additional validation that neural networks are useful for time series prediction coming from dynamical systems, no matter whether they are stochastic or not. Finally, the results con rmed several already known facts (such as that adding noise to the inputs and outputs of the training values can improve the results; that recurrent networks trained with the back-propagation algorithm don't have the problem of vanishing gradients in short periods and that the use of committees - which can be seen as a very basic of distributed arti cial intelligence - allows to improve signi cantly the predictions).Una serie temporal es una secuencia de valores reales que pueden ser considerados como observaciones de un cierto sistema. En este trabajo, estamos interesados en series temporales provenientes de sistemas dinámicos. Tales sistemas pueden ser algunas veces descriptos por un conjunto de ecuaciones que modelan el mecanismo subyacente que genera las muestras. sin embargo, en muchos sistemas reales, esas ecuaciones son desconocidas, y la única información disponible es un conjunto de medidas en el tiempo, que constituyen la serie temporal. Por otra parte, por razones prácticas es generalmente requerida una predicción, es decir, conocer el valor (aproximado) de la serie en un instante futuro t. La meta de esta tesis es resolver un problema de predicción del mundo real: dados los datos históricos relacionados con las ventas de gas propano licuado, predecir las ventas futuras, tan aproximadamente como sea posible. Este problema de predicción de series temporales es abordado por medio de redes neuronales, tanto para la reconstrucción como para la predicción. El problema de reconstruir dinámicamente el sistema original consiste en construir un modelo que capture ciertas características de él de forma de tener una correspondencia entre el comportamiento a largo plazo del modelo y del sistema. El proceso de diseño de las redes es guiado básicamente por tres ingredientes. La dimensionalidad del problema es explorada por nuestro primer ingrediente, el teorema de Takens-Mañé. Por medio de este teorema, la dimensión óptima de la entrada de la red neuronal puede ser investigada. Nuestro segundo ingrediente es un teorema muy fuerte: las redes neuronales con una sola capa oculta son un aproximador universal. Como tercer ingrediente, encaramos la búsqueda del tamaño oculta de la capa oculta por medio de algoritmos genéticos, usados para sugerir el número de neuronas ocultas que maximizan una función objetivo (relacionada con los errores de predicción). Estos algoritmos se usan además para encontrar las entradas a la red que influyen más en la salida en algunos casos. La determinación del tamaño de la capa oculta es un problema central (y duro) en la determinación de la topología de la red. Esta tesis incluye un estado del arte del diseño de redes neuronales para la predicción de series temporales, incluyendo tópicos relacionados tales como sistemas dinámicos, aproximadores universales, búsquedas basadas en el gradiente y sus variaciones, así como meta-heurísticas. El relevamiento de la literatura relacionada busca ser extenso, para tanto el material impreso como para el que esta en formato electrónico, de forma de tener un panorama de los principales aspectos del estado del arte en la predicción de series temporales usando redes neuronales. El material hallado fue algunas veces extremadamente redundante (como en el caso del algoritmo de retropropagación y sus mejoras) y escaso en otros (estructuras de memoria o estimación de la dimensión del sub-espacio de señal en el caso estocástico). La literatura consultada incluye trabajos de investigación clásicos ( ([27], [50], [52])' así como de los más reciente ([79] , [16] or [82]). Se presta especial atención a las herramientas de software disponibles para el diseño de redes neuronales y el procesamiento de series temporales. Luego de una revisión de los paquetes de software disponibles, las herramientas más promisiorias para ambas tareas son discutidas. Como resultado, un entorno de trabajo completo basado en herramientas de software maduras fue definido y usado. Para trabajar con los mencionados sistemas dinámicos, software especializado en el análisis y proceso de las series temporales fue empleado, y entonces las series caóticas fueron estudiadas. Ya que no toda la aleatoriedad es atribuible al caos, para caracterizar al sistema dinámico que genera la serie temporal se requiere una exploración de los sistemas caóticos-estocásticos, así como de los modelos de red para predecir una serie temporal asociada a uno de ellos. Aquí se pretende mostrar cómo el conocimiento del dominio, algo extensamente tratado en la literatura, puede ser de alguna manera sofisticado (tal como el espectro de Lyapunov de la serie o la dimensión del sub-espacio de señal). Para modelar el sistema dinámico generado por la serie temporal se usa el modelo de espacio de estados, por lo que la predicción de la serie temporal es traducida en la predicción del siguiente estado del sistema. Este modelo de espacio de estados, junto con el método de los delays (coordenadas demoradas) tiene importancia práctica en el desarrollo de este trabajo, específicamente, en el diseño de la capa de entrada en algunas redes (los perceptrones multicapa) y otros parámetros (los taps de las redes TLFN). Adicionalmente, el resto de los componentes de la red con determinados en varios casos a través de procedimientos tradicionalmente usados en las redes neuronales: los algoritmos genéticos. Los criterios para la selección de modelo (red) son discutidos y un balance entre performance y complejidad de la red es explorado luego, inspirado en el minimum description length de Rissanen y su estimación dada por el software elegido. Con respecto a los modelos de red empleados, las topologóas de sugeridas en la literatura como adecuadas para la predicción son usadas (TLFNs y redes recurrentes) junto con perceptrones multicapa (un clásico de las redes neuronales) y comités de redes. La efectividad de cada método es confirmada por el problema de predicción propuesto. Los comités de redes, donde las predicciones son una combinación convexa de las predicciones dadas por las redes individuales, son también usados extensamente. La necesidad de criterios para comparar el comportamiento del modelo con el del sistema real, a largo plazo, para un sistema dinámico estocástico, es presentada y dos alternativas son comentadas. Los resultados obtenidos prueban la existencia de una solución al problema del aprendizaje de la dependencia Entrada - Salida . Conjeturamos además que el sistema generador de serie de las ventas es dinámico-estocástico pero no caótico, ya que sólo tenemos una realización del proceso aleatorio correspondiente a las ventas. Al ser un sistema no caótico, la media de las predicciones de las ventas debería mejorar a medida que los datos disponibles aumentan, aunque la probabilidad de una predicción con un gran error es siempre no nula debido a la aleatoriedad presente. Esta solución es encontrada en una forma constructiva y exhaustiva. La exhaustividad puede deducirse de las siguiente cinco afirmaciones : el diseño de una red neuronal requiere conocer la dimensión de la entrada y de la salida, el número de capas ocultas y las neuronas en cada una de ellas el uso del teorema de takens-Mañé permite derivar la dimensión de la entrada por teoremas tales como los de Kolmogorov y Cybenko el uso de perceptrones con solo una capa oculta es justificado, por lo que varios de tales modelos son probados el número de neuronas en la capa oculta es determinada varias veces heurísticamente a través de algoritmos genéticos una sola neurona de salida da la predicción deseada. Como se dijo, dos tareas son llevadas a cabo: el desarrollo de un modelo para la predicción de la serie temporal y el análisis de un modelo factible para la reconstrucción dinámica del sistema. Con el mejor modelo predictivo, obtenido por el comité de dos redes se logró obtener un error aceptable en la predicción de una semana no contigua al conjunto de entrenamiento (7.04% para la semana 46/2011). Creemos que este es un resultado aceptable dada la cantidad de información disponible y representa una validación adicional de que las redes neuronales son útiles para la predicción de series temporales provenientes de sistemas dinámicos, sin importar si son estocásticos o no. Finalmente, los resultados experimentales confirmaron algunos hechos ya conocidos (tales como que agregar ruido a los datos de entrada y de salida de los valores de entrenamiento puede mejorar los resultados: que las redes recurrentes entrenadas con el algoritmo de retropropagación no presentan el problema del gradiente evanescente en periodos cortos y que el uso de de comités - que puede ser visto como una forma muy básica de inteligencia artificial distribuida - permite mejorar significativamente las predicciones)

Global parameter identification and control of nonlinearly parameterized systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2002.Includes bibliographical references (leaves 109-114).Nonlinearly parameterized (NLP) systems are ubiquitous in nature and many fields of science and engineering. Despite the wide and diverse range of applications, there exist relatively few results in control systems literature which exploit the structure of the nonlinear parameterization. A vast majority of presently applicable global control design approaches to systems with NLP, make use of either feedback-linearization, or assume linear parameterization, and ignore the specific structure of the nonlinear parameterization. While this type of approach may guarantee stability, it introduced three major drawbacks. First, they produce no additional information about the nonlinear parameters. Second, they may require large control authority and actuator bandwidth, which makes them unsuitable for some applications. Third, they may simply result in unacceptably poor performance. All of these inadequacies are amplified further when parametric uncertainties are present. What is necessary is a systematic adaptive approach to identification and control of such systems that explicitly accommodates the presence of nonlinear parameters that may not be known precisely. This thesis presents results in both adaptive identification and control of NLP systems. An adaptive controller is presented for NLP systems with a triangular structure. The presence of the triangular structure together with nonlinear parameterization makes standard methods such as back-stepping, and variable structure control inapplicable. A concept of bounding functions is combined with min-max adaptation strategies and recursive error formulation to result in a globally stabilizing controller.(cont.) A large class of nonlinear systems including cascaded LNL (linear-nonlinear-linear) systems are shown to be controllable using this approach. In the context of parameter identification, results are derived for two classes of NLP systems. The first concerns systems with convex/concave parameterization, where min-max algorithms are essential for global stability. Stronger conditions of persistent excitation are shown to be necessary to overcome the presence of multiple equilibrium points which are introduced due to the stabilization aspects of the min-max algorithms. These conditions imply that the min-max estimator must periodically employ the local gradient information in order to guarantee parameter convergence. The second class of NLP systems considered in this concerns monotonically parameterized systems, of which neural networks are a specific example. It is shown that a simple algorithm based on local gradient information suffices for parameter identification. Conditions on the external input under which the parameter estimates converge to the desired set starting from arbitrary values are derived. The proof makes direct use of the monotonicity in the parameters, which in turn allows local gradients to be self-similar and therefore introduces a desirable invariance property. By suitably exploiting this invariance property and defining a sequence of distance metrics, global convergence is proved. Such a proof of global convergence is in contrast to most other existing results in the area of nonlinear parameterization, in general, and neural networks in particular.by Aleksandar M. KojiÄ.Ph.D

Nuevo enfoque en el diseño y entrenamiento de redes neuronales para la clasificación

Tesis (Doctor en Ingeniería con Especialidad en Ingeniería de Sistemas) UANL, 2001.UANLhttp://www.uanl.mx

Optimal convergence of on-line backpropagation

Many researchers are quite skeptical about the actual behavior of neural network learning algorithms like backpropagation. One of the major problems is with the lack of clear theoretical results on optimal convergence, particularly for pattern mode algorithms. In this paper, we prove the companion of Rosenblatt's PC (perceptron convergence) theorem for feedforward networks (1960), stating that pattern mode backpropagation converges to an optimal solution for linearly separable patterns