Intelligent non-linear modelling of an industrial winding process using recurrent local linear neuro-fuzzy networks

This study deals with the neuro-fuzzy (NF) modelling of a real industrial winding process in which the acquired NF model can be exploited to improve control performance and achieve a robust fault-tolerant system. A new simulator model is proposed for a winding process using non-linear identification based on a recurrent local linear neuro-fuzzy (RLLNF) network trained by local linear model tree (LOLIMOT), which is an incremental tree-based learning algorithm. The proposed NF models are compared with other known intelligent identifiers, namely multilayer perceptron (MLP) and radial basis function (RBF). Comparison of our proposed non-linear models and associated models obtained through the least square error (LSE) technique (the optimal modelling method for linear systems) confirms that the winding process is a non-linear system. Experimental results show the effectiveness of our proposed NF modelling approach.     

Fixed-structure Gaussian process model

This article describes a method for modelling non-linear dynamic systems from measurement data. The method merges the linear local model blending approach in the velocity-based linearisation form with Bayesian Gaussian process (GP) modelling. The new Fixed-Structure GP (FSGP) model has a predetermined linear model structure with varying and probabilistic parameters represented by GP models. These models have several advantages for the modelling of local model parameters as they give us adequate results, even with small data sets. Furthermore, they provide a measure of the confidence in the prediction of the varying parameters and information about the dependence of the parameters on individual inputs. The FSGP model can be applied for the extended local linear equivalence class of non-linear systems. The obtained non-linear system model can be, for example, used for control-system design. The proposed modelling method is illustrated with a simple example of non-linear system modelling for control design.     

Modelling and multi-objective optimal control of batch processes using recurrent neuro-fuzzy networks

In this paper, the modelling and multi-objective optimal control of batch processes, using a recurrent neuro-fuzzy network, are presented. The recurrent neuro-fuzzy network, forms a "global" nonlinear long-range prediction model through the fuzzy conjunction of a number of "local" linear dynamic models. Network output is fed back to network input through one or more time delay units, which ensure that predictions from the recurrent neuro-fuzzy network are long-range. In building a recurrent neural network model, process knowledge is used initially to partition the processes non-linear characteristics into several local operating regions, and to aid in the initialisation of corresponding network weights. Process operational data is then used to train the network. Membership functions of the local regimes are identified, and local models are discovered via network training. Based on a recurrent neuro-fuzzy network model, a multi-objective optimal control policy can be obtained. The proposed technique is applied to a fed-batch reactor.     

Long Range Predictive Control of Nonlinear Processes Based on Recurrent Neuro-Fuzzy Network Models

A recurrent neuro-fuzzy network-based nonlinear long range model predictive control strategy is proposed in this paper. The process operation is partitioned into several fuzzy operating regions. Within each region, a local linear model is used to model the process. The global model output is obtained through the centre of gravity defuzzification. Based upon a neuro-fuzzy network model, a nonlinear model-based predictive controller can be developed by combining several local linear model-based predictive controllers which usually have analytical solutions. This strategy avoids the time consuming numerical optimisation procedure, and the uncertainty in convergence to the global optimum which are typically seen in conventional nonlinear model-based predictive control strategies. Furthermore, control actions obtained based on local incremental models contain integration actions which can nat-urally eliminate static control offsets. The technique is demonstrated by an application to the modelling and control of liquid level in a water tank.     

Using adaptive neuro-fuzzy inference system for hydrological time series prediction

Conventionally, the multiple linear regression procedure has been known as the most popular models in simulating hydrological time series. However, when the nonlinear phenomenon is significant, the multiple linear will fail to develop an appropriate predictive model. Recently, intelligence system approaches such as artificial neural network (ANN) and neuro-fuzzy methods have been used successfully for time series modelling. In most instances for neural networks, multi layer perceptrons (MLPs) that are trained with the back-propagation algorithm have been used. The major shortcoming of this approach is that the knowledge contained in the trained networks is difficult to interpret. Using neuro-fuzzy approaches, which enable the information that is stored in trained networks to be expressed in the form of a fuzzy rule base, would help to overcome this issue. In the present study, a time series neuro-fuzzy model is proposed that is capable of exploiting the strengths of traditional time series approaches. The aim of this article is to investigate the potential of a neuro-fuzzy system with a Sugeno inference engine, considering different numbers of membership functions. Three rivers have been selected and daily prediction for them was applied. For better judgment, outcomes of the network have been compared to an autoregressive model.     

A neuro-fuzzy multiple-model observer approach to robust fault diagnosis based on the DAMADICS benchmark problem

This paper presents a new framework for fault detection and isolation (FDI) based on neuro-fuzzy multiple modelling together with robust optimal de-coupling of observers. This new paradigm is called the ‘Neuro-Fuzzy and De-coupling Fault Diagnosis Scheme’ (NFDFDS). Multiple operating points are taken care of through the NF modelling framework. The structure also provides residuals that are de-coupled to ‘unknown inputs’, making use of the earlier research on unknown input de-coupling. The NF paradigm exploits the combined abilities of neural networks and fuzzy logic and is an efficient modelling tool for non-linear dynamic systems because of its approximation and reasoning capabilities. The paper also provides a comparative study of NFDFDS with the Extended Unknown Input Observer (EUIO) for FDI, using the DAMADICS benchmark example.     

Identification of low-order parameter-varying models for large-scale systems

In this paper we propose a novel procedure for obtaining low-dimensional models of large-scale multi-phase, non-linear, reactive fluid flow systems. Our approach is based on the combination of methods of proper orthogonal decompositions, black-box system identification techniques and non-linear spline based blending of local linear black-box models to create a reduced order linear parameter-varying model. The proposed method, which is of empirical nature, gives computationally very efficient low-order process models for large-scale processes. The proposed method does not need Galerkin type of projections on equation residuals to obtain the reduced order models and the proposed method is of generic nature. The efficiency of the proposed approach is illustrated on a benchmark problem of an industrial glass manufacturing process where the process non-linearity and non-linearity arising due to the corrosion of refractory materials is approximated using a linear parameter varying model. The results show good performance of the proposed framework.     

Recurrent neuro-fuzzy networks for nonlinear process modeling

A type of recurrent neuro-fuzzy network is proposed in this paper to build long-term prediction models for nonlinear processes. The process operation is partitioned into several fuzzy operating regions. Within each region, a local linear model is used to model the process. The global model output is obtained through the centre of gravity defuzzification which is essentially the interpolation of local model outputs. This modeling strategy utilizes both process knowledge and process input/output data. Process knowledge is used to initially divide the process operation into several fuzzy operating regions and to set up the initial fuzzification layer weights. Process I/O data are used to train the network. Network weights are such trained so that the long-term prediction errors are minimized. Through training, membership functions of fuzzy operating regions are refined and local models are learnt. Based on the recurrent neuro-fuzzy network model, a novel type of nonlinear model-based long range predictive controller can be developed and it consists of several local linear model-based predictive controllers. Local controllers are constructed based on the corresponding local linear models and their outputs are combined to form a global control action by using their membership functions. This control strategy has the advantage that control actions can be calculated analytically avoiding the time consuming nonlinear programming procedures required in conventional nonlinear model-based predictive control. The techniques have been successfully applied to the modeling and control of a neutralization process.     

Lazy learning for local modelling and control design

This paper presents local methods for modelling and control of discrete-time unknown non-linear dynamical systems, when only input-output data are available. We propose the adoption of lazy learning, a memory-based technique for local modelling. The modelling procedure uses a query-based approach to select the best model configuration by assessing and comparing different alternatives. A new recursive technique for local model identification and validation is presented, together with an enhanced statistical method for model selection. A lso, three methods to design controllers based on the local linearization provided by the lazy learning algorithm are described. In the first method the lazy technique returns the forward and inverse models of the system which are used to compute the control action to take. The second is an indirect method inspired by self-tuning regulators where recursive least squares estimation is replaced by a local approximator. The third method combines the linearization provided by the local learning techniques with optimal linear control theory, to control non-linear systems about regimes which are far from the equilibrium points. Simulation examples of identification and control of non-linear systems starting from observed data are given.     

Modeling and Optimal Control of Batch Processes Using Recurrent Neuro-Fuzzy Networks

A recurrent neuro-fuzzy network based strategy for batch process modeling and optimal control is presented in this paper. The recurrent neuro-fuzzy network allows the construction of a “global” nonlinear long-range prediction model from the fuzzy conjunction of a number of “local” linear dynamic models. In this recurrent neuro-fuzzy network, the network output is fed back to the network input through one or more time delay units. This particular structure ensures that predictions from a recurrent neuro-fuzzy network are long-range or multi-step-ahead predictions. Long-range predictions are particularly important for batch processes where the interest lies in the product quality and quantity at the end of a batch. To enhance batch process control and monitoring, a model capable of predicting accurately the product quality/quantity at the end of a batch is required. Process knowledge is used to initially partition the process nonlinear characteristics into several local operating regions and to aid in the initialization of the corresponding network weights. Process input output data is then used to train the network. Membership functions of the local regimes are identified and local models are discovered through network training. An advantage of this recurrent neuro-fuzzy network model is that it is easy to interpret. This helps process operators in understanding the process characteristics. The proposed technique is applied to the modeling and optimal control of a fed-batch reactor.     

A comparative study on modelling material removal rate by ANFIS and polynomial methods in electrical discharge machining process

Due to the controversy associated with modelling Electrical Discharge Machining (EDM) processes based on physical laws; this task is predominantly accomplished using empirical modelling methods. The modelling studies reported in the literature deal predominantly with quantitative parameters i.e. ones with numerical levels. In fact, modelling categorical parameters has been devoted a scant attention. This study reports the results of an EDM experiment conducted on the Ti–6Al–4V alloy. Its aim was to model the relationship between the Material Removal Rate (MRR) and the parameters of the process, namely, current, pulse on-time and pulse off-time along with a categorical factor (electrode material). The modelling process was accomplished using adaptive neuro-fuzzy inference system (ANFIS) and polynomial modelling approaches. In fact, one purpose of this study was to compare the performance of these modelling approaches as no study was found contrasting their prediction capability in the literature. Regarding the polynomial model, two numerical parameters (current and pulse on-time) were declared significant in the ANOVA together with the electrode material and its interaction with pulse on-time. Thus, they were all incorporated in the developed polynomial model. Furthermore, five ANFIS models with 6, 9, 19, 21 and 51 rules were developed utilizing the first order Sugeno fuzzy approach by back-propagation neural networks training algorithm. Of these, the ANFIS model with 21 rules was the best. This model also outperformed the polynomial model remarkably in terms of predicting error, residuals range and the correlation coefficient between the experimental and predicted MRR values. The study sheds light on the powerful learning capability of ANFIS models and its superiority over the conventional polynomial models in terms of modelling complex non-linear machining processes.     

Modelling the Security of Smart Cards by Hard and Soft Types for Higher-Order Mobile Embedded Resources

We provide a type system inspired by affine intuitionistic logic for the calculus of Higher-Order Mobile Embedded Resources (Homer), resulting in the first process calculus combining affine linear (non-copyable) and non-linear (copyable) higher-order mobile processes, nested locations, and local names. The type system guarantees that linear resources are neither copied nor embedded in non-linear resources during computation.We exemplify the use of the calculus by modelling a simplistic e-cash Smart Card system, the security of which depends on the interplay between (linear) mobile hardware, embedded (non-linear) mobile processes, and local names. A purely linear calculus would not be able to express that embedded software processes may be copied. Conversely, a purely non-linear calculus would not be able to express that mobile hardware processes cannot be copied.     

An adaptive multiscale basis method for modelling discrete-time non-linear dynamical systems

Based on locally applicable autoregressive moving average with exogenous (ARMAX) models this paper proposes two new adaptive modelling schemes for discrete-time non-linear dynamic systems based on the concept of a multiscale which originates in approximation theory. A general result on the convergence of modelling based on the multiscale basis functions with a least square estimated is derived. With the advantage of the multiresolution nature of the multiscale basis, the new modelling scheme can be used to capture both the global and local characteristics of a non-linear system over distinct scales. The algorithms also provide a trade-off between the model structure/model size and the modelling error, one of which emphasizes the modelling error with variable model structure whilst the other stresses a desired model size with better modelling error. Data-based modelling examples are used to demonstrate the effectiveness of the multiscale modelling schemes with different multiscale basis.     

Neuro-fuzzy modelling in support of knowledge management in social regulation of access to cigarettes by minors

In this paper a neuro-fuzzy modelling is proposed to support knowledge management in social regulation. The neuro-fuzzy learning process is based on tacit knowledge in order to highlight what specific steps local government should undertake to reach the outcome with an increase in compliance. An example is given to demonstrate the validity of the approach. Empirical results show the dependability of the proposed techniques.     

A neuro-fuzzy approach to fast ferry vertical motion modelling

In order to stabilise the motion of a high speed craft, and so to improve the comfort of the passengers and the crew while maintaining the speed, control-oriented model are needed. For this purpose, neuro-fuzzy systems have been used to obtain general models of the non-linear behaviour of a fast ferry. The sources of the available knowledge are the physical laws of the vertical dynamics of the craft, and some experimental and simulated data of the ship performance. Two non-linear models focused on the vertical motion of the craft, both heave and pitch, are proposed: an academic one and a predictive one. The modelling task is complex and the results are original as the problem has not been previously solved in a general way neither by applying artificial intelligence techniques. The models have been proved satisfactory with regular and also irregular waves, and they have been used for ship control purposes.     

State estimation and multi-sensor data fusion using data-based neurofuzzy local linearisation process models

Modelling unknown non-linear dynamic processes is an essential prerequisite for model-based state estimation and fusion. Fuzzy local linearisation (FLL) is a useful divide-and-conquer method for coping with complex problems such as data-based non-linear process modelling. In this paper, a hybrid learning scheme which combines a modified adaptive spline modelling (MASMOD) algorithm and the expectation-maximisation (EM) algorithm is developed for FLL modelling, based on which Kalman filter type algorithms for state estimation and multi-sensor data fusion are investigated. Two commonly used measurement fusion methods are analytically compared. A hierarchical multi-sensor data fusion architecture is proposed, with an example of non-linear trajectory estimation to validate the proposed method, which integrates the techniques for FLL modelling, neurofuzzy state estimation and multi-sensor data fusion. Whilst this paper mainly focuses on state estimation and data fusion for unknown non-linear dynamic processes, maneuvering targets are also briefly considered.     

On the interpretation of local models in blended multiple model structures

The construction of non-linear dynamics by means of interpolating the behaviour of locally valid models offers an attractive and intuitively pleasing method of modelling non-linear systems. The approach is used in fuzzy logic modelling, operating regime based models, and non-linear statistical models. The model structure suggests that the composite local models can be used to interpret, in some appropriate manner, the overall non-linear dynamics. In this paper we demonstrate that the interpretation of these local models, in the context of multiple model structures, is not as straightforward as it might initially appear. We argue that the blended multiple model system can be interpreted in two ways as an interpolation of linearizations, or as a full parameterization of the system. The choice of interpretation affects experiment design, parameter identification, and model validation. We then show that, in some cases, the local models give insight into full model behaviour only in a very small region of state space. More alarmingly, we demonstrate that for off-equilibrium behaviour, subject to some approximation error, a non-unique parameterization of the model dynamics exists. Hence, qualitative conclusions drawn from the behaviour of an identified local model, e.g. regarding stable, unstable, nodal or complex behaviour, must be treated with extreme caution. The example of muscle modelling is used to illustrate these points clearly.     

基于UKF的自适应模糊推理神经网络

如何生成最优的模糊规则数及模糊规则的自动生成和修剪是模糊神经网络训练算法研究的重点。针对这一问题,本文提出了基于UKF的自适应模糊推理神经网络(UKF-ANFIS)。首先,通过减法聚类确定UKF-ANFIS的模糊规则及其高斯隶属函数的中心和宽度参数;其次,分析了模糊神经网络的非线性动力系统表示,并用LLS和UKF分别学习线性和非线性的参数;然后,用误差下降率方法作为模糊规则修剪的策略,删除作用不大的规则;最后,通过典型的函数逼近和系统辨识实例,表明本文算法得到的模糊神经网络的结构更为紧凑,泛化性能也更佳。     

基于神经模糊系统的热工过程建模及预测

热工对象内部过程的物理性能比较复杂,其往往表现出非线性、严重时变、大迟延和不确定等特点,这就使得难以对其建立比较精确的模型。该文以自适应神经模糊推理系统(ANFIS)作为辨识器建立热工过程模型,用ANFIS分别建立锅炉-汽轮机的非线性模型、不同负荷工况点的线性模型,并根据现场采集的锅炉-汽轮机系统数据建立了ANFIS模型。对以上三个系统的建模仿真结果表明基于ANFIS建立的模型具有较高的模型精度和较好的预测能力,ANFIS可用于非线性系统、复杂系统的建模和预测,并具有较少的训练次数和较小的预测误差。