Local Sub-models Research Articles

An adaptive neuro-fuzzy tracking control for multi-input nonlinear dynamic systems

An adaptive neuro-fuzzy control design is suggested in this paper, for tracking of nonlinear affine in the control dynamic systems with unknown nonlinearities. The plant is described by a Takagi–Sugeno (T–S) fuzzy model, where the local submodels are realized through nonlinear dynamical input–output mappings. Our approach relies upon the effective approximation of certain terms that involve the derivative of the Lyapunov function and the unknown system nonlinearities. The above task is achieved locally, using linear in the weights neural networks. A novel resetting scheme is proposed that assures validity of the control input. Stability analysis provides the control law and the adaptation rules for the network weights, assuring uniform ultimate boundedness of the tracking and the signals appearing in the closed-loop configuration. Illustrative simulations highlight the approach.

POP: Patchwork of Parts Models for Object Recognition

We formulate a deformable template model for objects with an efficient mechanism for computation and parameter estimation. The data consists of binary oriented edge features, robust to photometric variation and small local deformations. The template is defined in terms of probability arrays for each edge type. A primary contribution of this paper is the definition of the instantiation of an object in terms of shifts of a moderate number local submodels--parts--which are subsequently recombined using a patchwork operation, to define a coherent statistical model of the data. Object classes are modeled as mixtures of patchwork of parts POP models that are discovered sequentially as more class data is observed. We define the notion of the support associated to an instantiation, and use this to formulate statistical models for multi-object configurations including possible occlusions. All decisions on the labeling of the objects in the image are based on comparing likelihoods. The combination of a deformable model with an efficient estimation procedure yields competitive results in a variety of applications with very small training sets, without need to train decision boundaries--only data from the class being trained is used. Experiments are presented on the MNIST database, reading zipcodes, and face detection.

ADM1 application for tuning and performance analysis of a multi-model observer-based estimator

Anaerobic digestion model no.1 (ADM1) was used for tuning and performance analysis of the multi-model observer based estimator (mmOBE). The mmOBE was based on the variable structure model (VSM) of the anaerobic digestion model, which consists of several local submodels, each of which describes a typical process state. Depending on the hydraulic retention time, ADM1 simulated the methanogenic, organic overload, and acidogenic states of the process. These simulations allowed for optimising tunable parameters of the mmOBE. Owing to relatively slow process dynamics, a data acquisition interval as large as one day was sufficient to obtain acceptable accuracy. The simulations of mmOBE performance showed excellent rate of mmOBE convergence to ADM1 outputs. Moreover, mmOBE successfully estimated key kinetic parameters, such as maximal transformation rates of CODs, VFAs, and methane. These estimations can be used in the development of the advanced knowledge-based process system, which uses both available measurements and estimations of key kinetic parameters for extended diagnosis of failures and process trend analysis.

Fuzzy systems design: direct and indirect approaches

A systematic classification of the data-driven approaches for design of fuzzy systems is given in the paper. The possible ways to solve this modelling and identification problem are classified on the basis of the optimisation techniques used for this purpose. One algorithm for each of the two basic categories of design methods is presented and its advantages and disadvantages are discussed. Both types of algorithms are self-learning and do not require interaction during the process of fuzzy model design. They perform adaptation of both the fuzzy model structure (rule-base) and the parameters. The indirect approach exploits the dual nature of Takagi-Sugeno (TS) models and is based on recently introduced recursive clustering combined with Kalman filtering-based procedure for recursive estimation of the parameter of the local sub-models. Both algorithms result in finding compact and transparent fuzzy models. The direct approach solves the optimisation problem directly, while the indirect one decomposes the original problem into on-line clustering and recursive estimation problems and finds a sub-optimal solution in real-time. The later one is computationally very efficient and has a range of potential applications in real-time process control, moving images recognition, autonomous systems design etc. It is extended in this paper for the case of multi-input–multi-output (MIMO systems). Both approaches have been tested with real data from an engineering process.

Application of Kernel Trick to Fuzzy c-Means with Regularization by K-L Information

Support vector machines (SVM), kernel principal component analysis (KPCA), and kernel Fisher discriminant analysis (KFD), are examples of successful kernel-based learning methods. By the addition of a regularizer and the kernel trick to a fuzzy counterpart of Gaussian mixture models (GMM), this paper proposes a clustering algorithm in an extended high dimensional feature space. Unlike the global nonlinear approaches, GMM or its fuzzy counterpart is to model nonlinear structure with a collection, or mixture, of local linear sub-models of PCA. When the number of feature vectors and clusters are n and c respectively, this kernel approach can find up to c × n nonzero eigenvalues. A way to control the number of parameters in the mixture of probabilistic principal component analysis (PPCA) is adopted to reduce the number of parameters. The algorithm provides a partitioning with flexible shape of clusters in the original input data space.

Permeability prediction in shaly formations: The fuzzy modeling approach

This paper shows how fuzzy rule‐based systems help predict permeability in sedimentary rocks using well‐log responses. The fuzzy rule‐based approach represents a global nonlinear relationship between permeability and a set of input log responses as a smooth concatenation of a finite family of flexible local submodels. The fuzzy inference rules expressing the local input‐output relationships are obtained automatically from a set of observed measurements using a fuzzy clustering algorithm. This approach simplifies the process of constructing fuzzy systems without much computation effort. The benefits of the methodology are demonstrated with a case study in the Lake Maracaibo basin, Venezuela. Special core analyses from three early development wells provide the data for the learning task. Core permeability and well‐log data from a fourth well provide the basis for model validation. Numerical simulation results show that the fuzzy system is an improvement over conventional empirical methods in terms of predictive capability.

データのクラス振分けとクラス別モデルの同時推定法

A data classification method using a Boltzmann machine algorithm is proposed in this paper. The purpose of the classification is to determine local submodels which describe the data of each class. The Boltzmann machine is enabled to estimate both classification and submodel parameters at the same time. The method is also used in conjunction with a set of multilayer-perceptron class models, in which the relevant algorithm work on the basis of calculated expectations, rather than actual stochastic behaviors. The network is shown to be successful for classification of iris data and wine data.

Stress history generation for truss bridges using multi-level models

A technique is described for the automatic computation of numerical stress histories in the steel truss railway bridges, caused by the passage of pre-defined trains. The 3-D frame of the bridge is combined with finite element method plate/shell sub-models of selected details. The effects of joint rigidity and interaction of structural elements are taken into account by the global model. Joint geometry is introduced by the local sub-models. Connection nodes in the global beam model correspond to the end cross-section centroids of the sub-model. Their displacements are interpreted as imposed deformations on the sub-models. The load cases for the global model simulate the passage of two vertical unit forces along the stringers. The load cases for the sub-model are imposed unit deformations. Combining these, and applying train loads, numerical stress histories are obtained. The method is illustrated by test load results of an existing railway bridge.