Fuzzy rule based multiwavelet ECG signal denoising

Since different multiwavelets, pre- and post-filters have different impulse responses and frequency responses, different multiwavelets, pre- and post-filters should be selected and applied at different noise levels for signal denoising if signals are corrupted by additive white Gaussian noises. In this paper, some fuzzy rules are formulated for integrating different multiwavelets, pre- and post-filters together so that expert knowledge on employing different multiwavelets, pre- and post-filters at different noise levels on denoising performances is exploited. When an ECG signal is received, the noise level is first estimated. Then, based on the estimated noise level and our proposed fuzzy rules, different multiwavelets, pre- and post-filters are integrated together. A hard thresholding is applied on the multiwavelet coefficients. According to extensive numerical computer simulations, our proposed fuzzy rule based multiwavelet denoising algorithm outperforms traditional multiwavelet denoising algorithms by 30%

Further Study on Observer Design for Continuous-Time Takagi-Sugeno Fuzzy Model with Unknown Premise Variables via Average Dwell Time

This article further studies the problem of observer design for the continuous-time Takagi-Sugeno (T-S) fuzzy system with unmeasurable premise variables. A membership function-dependent Lyapunov function is designed to obtain the observer-based controller. Different from the existing results, a switching method is proposed to deal with the time derivative of membership functions. Several problems such as, too many parameters, and the small local stabilization region in the existing papers are solved by applying the switching method. In addition, two algorithms are designed to obtain the controller gains and observer gains. In the end, two examples are provided to demonstrate the effectiveness of the proposed approach. </p

Properties of an invariant set of weights of perceptrons

In this paper, the dynamics of weights of perceptrons are investigated based on the perceptron training algorithm. In particular, the condition that the system map is not injective is derived. Based on the derived condition, an invariant set that results to a bijective invariant map is characterized. Also, it is shown that some weights outside the invariant set will be moved to the invariant set. Hence, the invariant set is attracting. Computer numerical simulation results on various perceptrons with exhibiting various behaviors, such as fixed point behaviors, limit cycle behaviors and chaotic behaviors, are illustrated

Fuzzy Remote Tracking Control for Randomly Varying Local Nonlinear Models Under Fading and Missing Measurements

This paper proposes a novel remote tracking control strategy for a class of discrete-time Takagi-Sugeno fuzzy systems with randomly occurring uncertainties and randomly varying local nonlinear models. The outputs of the fuzzy system are collected through an unreliable sensor subject to missing measurements. Simultaneously, the outputs of the remote models are transmitted to the controller through wireless channels, in which the fading measurements may inevitably happen. By considering the Rice fading model and the Markovian packet dropouts model, an output-feedback controller is designed such that the closed-loop fuzzy tracking system is robustly stochastically stable and a prescribed H∞ remote tracking performance is achieved. Furthermore, sufficient conditions are obtained for the existence of admissible tracking controllers in terms of nonstrict linear matrix inequalities. To overcome the difficulty in computation, a modified cone-complementarity linearization algorithm is employed to cast the tracking controller design problem into a sequential minimization one, which can be readily solved by using standard numerical software. Simulation results demonstrate the effectiveness of the developed control algorithm for fuzzy remote tracking controller.</p

H_∞ fuzzy control of semi-Markov jump nonlinear systems under σ-error mean square stability

This paper is concerned with the problem of time-varying H∞ fuzzy control for a class of semi-Markov jump nonlinear systems in the sense of σ-error mean square stability. The nonlinear plant is described via the Takagi–Sugeno fuzzy model. By defining a time-varying mode-dependent Lyapunov function, a set of sufficient stability and stabilisation criteria for non-disturbance case is first derived and then applied to the investigation of H∞ performance analysis and H∞ fuzzy controller design problems of semi-Markov jump nonlinear systems. Different from the traditional stochastic switching system framework, the probability density function of sojourn time is exploited to circumvent the complex computation of transition probabilities. The derived conditions can cover the time-invariant mode-dependent and time-invariant mode-independent H∞ fuzzy control schemes as special cases. A classic cart-pendulum system is presented to demonstrate the effectiveness and advantages of the proposed theoretical results.</p

State estimation over non-acknowledgment networks with Markovian packet dropouts

In this paper, we investigate state estimation for systems with packet dropouts. According to whether there are acknowledgment (ACK) signals sent by the actuator to the estimator indicating the status of control packet dropouts or not, the systems are classified into two types: ACK systems, those with ACK signals, and non-ACK (NACK) systems, those without. We first obtain the optimal estimator (OE) for NACK systems with Markovian packet dropouts. However, the number of the components in the OE grows exponentially, making its stability analysis complicated and its computation time-consuming. Therefore, we proceed to design a computationally efficient approximate optimal estimator (AOE) using a relative-entropy-based approach. We prove that the proposed AOE has the same stability as the OE. We show that, even the separation principle does not hold for NACK systems, the stability of the OE can also be investigated separately; and discover that the OE for an NACK system has the same stability as the OE for the corresponding ACK system, even their structures are quite different. Finally, for strongly observable NACK systems, we establish a necessary and sufficient condition for the stability of the OE and the AOE.</p

Variable Weight Algorithm for Convolutional Neural Networks and its Applications to Classification of Seizure Phases and Types

Deep learning techniques have recently achieved impressive results and raised expectations in the domains of medical diagnosis and physiological signal processing. The widely adopted methods include convolutional neural networks (CNNs) and recurrent neural networks (RNNs). However, the existing models possess static connection weights between layers, which might limit the generalization capability and the classification performance of the models as the weights of different layers are fixed after training. Furthermore, to deal with a large amount of data, a neural network with a sufficiently large size is required. This paper proposes the variable weight convolutional neural networks (VWCNNs), which are a type of network structure employing dynamic weights instead of static weights in their convolutional layers and fully-connected layers. VWCNNs are able to adapt to different characteristics of input data and can be viewed as an infinite number of traditional, fixed-weight CNNs. We will show that the proposed VWCNN structure outperforms the conventional CNN in terms of the classification accuracy, generalization capability, and robustness when the inputs are contaminated by noise. In this paper, VWCNNs are applied to the classification of three seizure phases (seizure-free, pre-seizure and seizure) based on measured electroencephalography (EEG) data. VWCNNs achieve 100% test accuracy and show strong robustness in the classification of the three seizure phases, and thus show the potential to be a useful classification tool for medical diagnosis. Furthermore, the classification of seven types of seizures is investigated in this paper using the world’s largest open source database of seizure recordings, TUH EEG seizure corpus. Comparisons with conventional CNNs, RNN, MobileNet, ResNet, DenseNet and traditional machine learning methods including random forest, decision tree, support vector machine, K-nearest neighbours, standard neural networks, and Naïve Bayes are being conducted using realistic test data sets. The results demonstrate that VWCNNs have advantages over other classifiers in terms of classification accuracy and robustness

Fuzzy-Affine-Model-Based Sliding-Mode Control for Discrete-Time Nonlinear 2-D Systems via Output Feedback

This work investigates the issue of output-feedback sliding-mode control (SMC) for nonlinear 2-D systems by Takagi-Sugeno fuzzy-affine models. Via combining with the sliding surface, the sliding-mode dynamical properties are depicted by a singular piecewise-affine system. Through piecewise quadratic Lyapunov functions, new stability and robust performance analysis of the sliding motion are carried out. An output-feedback dynamic SMC design approach is developed to guarantee that the system states can converge to a neighborhood of the sliding surface. Simulation studies are given to verify the validity of the proposed scheme

Hierarchical fuzzy model-agnostic explanation: framework, algorithms and interface for XAI

Artificial intelligence (AI) has made remarkable achievements in extensive fields while its black box nature limited applications in many critical areas. Against this drawback, explainable AI (XAI), has emerged as a focal point of current research. Recently, fuzzy logic systems (FLSs) attract increasing attention in XAI because of their linguistic representation, which can be naturally understood by humans. However, the focus of these works is limited by simply relying on inherent rule-based structures for explanation. Motivated by further exploring the potential of FLS to overcome the challenges of XAI in terms of comprehensibility, scalability and transferability, in this work we propose Fuzzy Model-Agnostic Explanation (FMAE) as a post-hoc paradigm to explain the behavior of black box models. The innovations and contributions of this work provide a unified framework offering four levels of explanation, develop the associated algorithms to present the hidden knowledge behind the black box model in human-understandable form at different levels of granularity and create the interface to deliver explanations to users. First, we introduce the hierarchical FMAE framework to formulate explanations into four levels including sample, local, domain and universe. Second, the learning and explaining algorithms are developed to systematically construct FLS to model the behavior of black box models in the four levels where downscaling is performed by simplification to facilitate explanations with concise rules and upscaling is performed by aggregation to integrate explanations at a higher level. Third, the proposed explanation interface unifies two typical forms of expression in XAI by fuzzy rules: the semantic inference explanation revealing the decision mechanism of the black box model and the feature salience explanation reflecting the attribution and interaction of input features. Simulated user experiments are designed on the comprehensive explanatory metrics. Compared with mainstream methods, the result shows outstanding explanation performance on real-world datasets for both regression and classification tasks