Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.Comment: 31 page

Soft computing for tool life prediction a manufacturing application of neural - fuzzy systems

Tooling technology is recognised as an element of vital importance within the manufacturing industry. Critical tooling decisions related to tool selection, tool life management, optimal determination of cutting conditions and on-line machining process monitoring and control are based on the existence of reliable detailed process models. Among the decisive factors of process planning and control activities, tool wear and tool life considerations hold a dominant role. Yet, both off-line tool life prediction, as well as real tune tool wear identification and prediction are still issues open to research. The main reason lies with the large number of factors, influencing tool wear, some of them being of stochastic nature. The inherent variability of workpiece materials, cutting tools and machine characteristics, further increases the uncertainty about the machining optimisation problem. In machining practice, tool life prediction is based on the availability of data provided from tool manufacturers, machining data handbooks or from the shop floor. This thesis recognises the need for a data-driven, flexible and yet simple approach in predicting tool life. Model building from sample data depends on the availability of a sufficiently rich cutting data set. Flexibility requires a tool-life model with high adaptation capacity. Simplicity calls for a solution with low complexity and easily interpretable by the user. A neural-fuzzy systems approach is adopted, which meets these targets and predicts tool life for a wide range of turning operations. A literature review has been carried out, covering areas such as tool wear and tool life, neural networks, frizzy sets theory and neural-fuzzy systems integration. Various sources of tool life data have been examined. It is concluded that a combined use of simulated data from existing tool life models and real life data is the best policy to follow. The neurofuzzy tool life model developed is constructed by employing neural network-like learning algorithms. The trained model stores the learned knowledge in the form of frizzy IF-THEN rules on its structure, thus featuring desired transparency. Low model complexity is ensured by employing an algorithm which constructs a rule base of reduced size from the available data. In addition, the flexibility of the developed model is demonstrated by the ease, speed and efficiency of its adaptation on the basis of new tool life data. The development of the neurofuzzy tool life model is based on the Fuzzy Logic Toolbox (vl.0) of MATLAB (v4.2cl), a dedicated tool which facilitates design and evaluation of fuzzy logic systems. Extensive results are presented, which demonstrate the neurofuzzy model predictive performance. The model can be directly employed within a process planning system, facilitating the optimisation of turning operations. Recommendations aremade for further enhancements towards this direction

Neuro-Fuzzy Based Intelligent Approaches to Nonlinear System Identification and Forecasting

Nearly three decades back nonlinear system identification consisted of several ad-hoc approaches, which were restricted to a very limited class of systems. However, with the advent of the various soft computing methodologies like neural networks and the fuzzy logic combined with optimization techniques, a wider class of systems can be handled at present. Complex systems may be of diverse characteristics and nature. These systems may be linear or nonlinear, continuous or discrete, time varying or time invariant, static or dynamic, short term or long term, central or distributed, predictable or unpredictable, ill or well defined. Neurofuzzy hybrid modelling approaches have been developed as an ideal technique for utilising linguistic values and numerical data. This Thesis is focused on the development of advanced neurofuzzy modelling architectures and their application to real case studies. Three potential requirements have been identified as desirable characteristics for such design: A model needs to have minimum number of rules; a model needs to be generic acting either as Multi-Input-Single-Output (MISO) or Multi-Input-Multi-Output (MIMO) identification model; a model needs to have a versatile nonlinear membership function. Initially, a MIMO Adaptive Fuzzy Logic System (AFLS) model which incorporates a prototype defuzzification scheme, while utilising an efficient, compared to the Takagi–Sugeno–Kang (TSK) based systems, fuzzification layer has been developed for the detection of meat spoilage using Fourier transform infrared (FTIR) spectroscopy. The identification strategy involved not only the classification of beef fillet samples in their respective quality class (i.e. fresh, semi-fresh and spoiled), but also the simultaneous prediction of their associated microbiological population directly from FTIR spectra. In the case of AFLS, the number of memberships for each input variable was directly associated to the number of rules, hence, the “curse of dimensionality” problem was significantly reduced. Results confirmed the advantage of the proposed scheme against Adaptive Neurofuzzy Inference System (ANFIS), Multilayer Perceptron (MLP) and Partial Least Squares (PLS) techniques used in the same case study. In the case of MISO systems, the TSK based structure, has been utilized in many neurofuzzy systems, like ANFIS. At the next stage of research, an Adaptive Fuzzy Inference Neural Network (AFINN) has been developed for the monitoring the spoilage of minced beef utilising multispectral imaging information. This model, which follows the TSK structure, incorporates a clustering pre-processing stage for the definition of fuzzy rules, while its final fuzzy rule base is determined by competitive learning. In this specific case study, AFINN model was also able to predict for the first time in the literature, the beef’s temperature directly from imaging information. Results again proved the superiority of the adopted model. By extending the line of research and adopting specific design concepts from the previous case studies, the Asymmetric Gaussian Fuzzy Inference Neural Network (AGFINN) architecture has been developed. This architecture has been designed based on the above design principles. A clustering preprocessing scheme has been applied to minimise the number of fuzzy rules. AGFINN incorporates features from the AFLS concept, by having the same number of rules as well as fuzzy memberships. In spite of the extensive use of the standard symmetric Gaussian membership functions, AGFINN utilizes an asymmetric function acting as input linguistic node. Since the asymmetric Gaussian membership function’s variability and flexibility are higher than the traditional one, it can partition the input space more effectively. AGFINN can be built either as an MISO or as an MIMO system. In the MISO case, a TSK defuzzification scheme has been implemented, while two different learning algorithms have been implemented. AGFINN has been tested on real datasets related to electricity price forecasting for the ISO New England Power Distribution System. Its performance was compared against a number of alternative models, including ANFIS, AFLS, MLP and Wavelet Neural Network (WNN), and proved to be superior. The concept of asymmetric functions proved to be a valid hypothesis and certainly it can find application to other architectures, such as in Fuzzy Wavelet Neural Network models, by designing a suitable flexible wavelet membership function. AGFINN’s MIMO characteristics also make the proposed architecture suitable for a larger range of applications/problems

Sistemas granulares evolutivos

Orientador: Fernando Antonio Campos GomideTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Recentemente tem-se observado um crescente interesse em abordagens de modelagem computacional para lidar com fluxos de dados do mundo real. Métodos e algoritmos têm sido propostos para obtenção de conhecimento a partir de conjuntos de dados muito grandes e, a princípio, sem valor aparente. Este trabalho apresenta uma plataforma computacional para modelagem granular evolutiva de fluxos de dados incertos. Sistemas granulares evolutivos abrangem uma variedade de abordagens para modelagem on-line inspiradas na forma com que os humanos lidam com a complexidade. Esses sistemas exploram o fluxo de informação em ambiente dinâmico e extrai disso modelos que podem ser linguisticamente entendidos. Particularmente, a granulação da informação é uma técnica natural para dispensar atenção a detalhes desnecessários e enfatizar transparência, interpretabilidade e escalabilidade de sistemas de informação. Dados incertos (granulares) surgem a partir de percepções ou descrições imprecisas do valor de uma variável. De maneira geral, vários fatores podem afetar a escolha da representação dos dados tal que o objeto representativo reflita o significado do conceito que ele está sendo usado para representar. Neste trabalho são considerados dados numéricos, intervalares e fuzzy; e modelos intervalares, fuzzy e neuro-fuzzy. A aprendizagem de sistemas granulares é baseada em algoritmos incrementais que constroem a estrutura do modelo sem conhecimento anterior sobre o processo e adapta os parâmetros do modelo sempre que necessário. Este paradigma de aprendizagem é particularmente importante uma vez que ele evita a reconstrução e o retreinamento do modelo quando o ambiente muda. Exemplos de aplicação em classificação, aproximação de função, predição de séries temporais e controle usando dados sintéticos e reais ilustram a utilidade das abordagens de modelagem granular propostas. O comportamento de fluxos de dados não-estacionários com mudanças graduais e abruptas de regime é também analisado dentro do paradigma de computação granular evolutiva. Realçamos o papel da computação intervalar, fuzzy e neuro-fuzzy em processar dados incertos e prover soluções aproximadas de alta qualidade e sumário de regras de conjuntos de dados de entrada e saída. As abordagens e o paradigma introduzidos constituem uma extensão natural de sistemas inteligentes evolutivos para processamento de dados numéricos a sistemas granulares evolutivos para processamento de dados granularesAbstract: In recent years there has been increasing interest in computational modeling approaches to deal with real-world data streams. Methods and algorithms have been proposed to uncover meaningful knowledge from very large (often unbounded) data sets in principle with no apparent value. This thesis introduces a framework for evolving granular modeling of uncertain data streams. Evolving granular systems comprise an array of online modeling approaches inspired by the way in which humans deal with complexity. These systems explore the information flow in dynamic environments and derive from it models that can be linguistically understood. Particularly, information granulation is a natural technique to dispense unnecessary details and emphasize transparency, interpretability and scalability of information systems. Uncertain (granular) data arise from imprecise perception or description of the value of a variable. Broadly stated, various factors can affect one's choice of data representation such that the representing object conveys the meaning of the concept it is being used to represent. Of particular concern to this work are numerical, interval, and fuzzy types of granular data; and interval, fuzzy, and neurofuzzy modeling frameworks. Learning in evolving granular systems is based on incremental algorithms that build model structure from scratch on a per-sample basis and adapt model parameters whenever necessary. This learning paradigm is meaningful once it avoids redesigning and retraining models all along if the system changes. Application examples in classification, function approximation, time-series prediction and control using real and synthetic data illustrate the usefulness of the granular approaches and framework proposed. The behavior of nonstationary data streams with gradual and abrupt regime shifts is also analyzed in the realm of evolving granular computing. We shed light upon the role of interval, fuzzy, and neurofuzzy computing in processing uncertain data and providing high-quality approximate solutions and rule summary of input-output data sets. The approaches and framework introduced constitute a natural extension of evolving intelligent systems over numeric data streams to evolving granular systems over granular data streamsDoutoradoAutomaçãoDoutor em Engenharia Elétric

Dynamic non-linear system modelling using wavelet-based soft computing techniques

The enormous number of complex systems results in the necessity of high-level and cost-efficient modelling structures for the operators and system designers. Model-based approaches offer a very challenging way to integrate a priori knowledge into the procedure. Soft computing based models in particular, can successfully be applied in cases of highly nonlinear problems. A further reason for dealing with so called soft computational model based techniques is that in real-world cases, many times only partial, uncertain and/or inaccurate data is available. Wavelet-Based soft computing techniques are considered, as one of the latest trends in system identification/modelling. This thesis provides a comprehensive synopsis of the main wavelet-based approaches to model the non-linear dynamical systems in real world problems in conjunction with possible twists and novelties aiming for more accurate and less complex modelling structure. Initially, an on-line structure and parameter design has been considered in an adaptive Neuro- Fuzzy (NF) scheme. The problem of redundant membership functions and consequently fuzzy rules is circumvented by applying an adaptive structure. The growth of a special type of Fungus (Monascus ruber van Tieghem) is examined against several other approaches for further justification of the proposed methodology. By extending the line of research, two Morlet Wavelet Neural Network (WNN) structures have been introduced. Increasing the accuracy and decreasing the computational cost are both the primary targets of proposed novelties. Modifying the synoptic weights by replacing them with Linear Combination Weights (LCW) and also imposing a Hybrid Learning Algorithm (HLA) comprising of Gradient Descent (GD) and Recursive Least Square (RLS), are the tools utilised for the above challenges. These two models differ from the point of view of structure while they share the same HLA scheme. The second approach contains an additional Multiplication layer, plus its hidden layer contains several sub-WNNs for each input dimension. The practical superiority of these extensions is demonstrated by simulation and experimental results on real non-linear dynamic system; Listeria Monocytogenes survival curves in Ultra-High Temperature (UHT) whole milk, and consolidated with comprehensive comparison with other suggested schemes. At the next stage, the extended clustering-based fuzzy version of the proposed WNN schemes, is presented as the ultimate structure in this thesis. The proposed Fuzzy Wavelet Neural network (FWNN) benefitted from Gaussian Mixture Models (GMMs) clustering feature, updated by a modified Expectation-Maximization (EM) algorithm. One of the main aims of this thesis is to illustrate how the GMM-EM scheme could be used not only for detecting useful knowledge from the data by building accurate regression, but also for the identification of complex systems. The structure of FWNN is based on the basis of fuzzy rules including wavelet functions in the consequent parts of rules. In order to improve the function approximation accuracy and general capability of the FWNN system, an efficient hybrid learning approach is used to adjust the parameters of dilation, translation, weights, and membership. Extended Kalman Filter (EKF) is employed for wavelet parameters adjustment together with Weighted Least Square (WLS) which is dedicated for the Linear Combination Weights fine-tuning. The results of a real-world application of Short Time Load Forecasting (STLF) further re-enforced the plausibility of the above technique

Forecasting the stock market index using artificial intelligence techniques

The weak form of Efficient Market hypothesis (EMH) states that it is impossible to forecast the future price of an asset based on the information contained in the historical prices of an asset. This means that the market behaves as a random walk and as a result makes forecasting impossible. Furthermore, financial forecasting is a difficult task due to the intrinsic complexity of the financial system. The objective of this work was to use artificial intelligence (AI) techniques to model and predict the future price of a stock market index. Three artificial intelligence techniques, namely, neural networks (NN), support vector machines and neuro-fuzzy systems are implemented in forecasting the future price of a stock market index based on its historical price information. Artificial intelligence techniques have the ability to take into consideration financial system complexities and they are used as financial time series forecasting tools. Two techniques are used to benchmark the AI techniques, namely, Autoregressive Moving Average (ARMA) which is linear modelling technique and random walk (RW) technique. The experimentation was performed on data obtained from the Johannesburg Stock Exchange. The data used was a series of past closing prices of the All Share Index. The results showed that the three techniques have the ability to predict the future price of the Index with an acceptable accuracy. All three artificial intelligence techniques outperformed the linear model. However, the random walk method outperfomed all the other techniques. These techniques show an ability to predict the future price however, because of the transaction costs of trading in the market, it is not possible to show that the three techniques can disprove the weak form of market efficiency. The results show that the ranking of performances support vector machines, neuro-fuzzy systems, multilayer perceptron neural networks is dependent on the accuracy measure used