Mathematical problems for complex networks

Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics

Adaptive Neuro-Fuzzy Inference System for Dynamic Load Balancing in 3GPP LTE

ANFIS is applicable in modeling of key parameters when investigating the performance and functionality of wireless networks. The need to save both capital and operational expenditure in the management of wireless networks cannot be over-emphasized. Automation of network operations is a veritable means of achieving the necessary reduction in CAPEX and OPEX. To this end, next generations networks such WiMAX and 3GPP LTE and LTE-Advanced provide support for self-optimization, self-configuration and self-healing to minimize human-to-system interaction and hence reap the attendant benefits of automation. One of the most important optimization tasks is load balancing as it affects network operation right from planning through the lifespan of the network. Several methods for load balancing have been proposed. While some of them have a very buoyant theoretical basis, they are not practically implementable at the current state of technology. Furthermore, most of the techniques proposed employ iterative algorithm, which in itself is not computationally efficient. This paper proposes the use of soft computing, precisely adaptive neuro-fuzzy inference system for dynamic QoS-aware load balancing in 3GPP LTE. Three key performance indicators (i.e. number of satisfied user, virtual load and fairness distribution index) are used to adjust hysteresis task of load balancing

Intelligent methods for complex systems control engineering

This thesis proposes an intelligent multiple-controller framework for complex systems that incorporates a fuzzy logic based switching and tuning supervisor along with a neural network based generalized learning model (GLM). The framework is designed for adaptive control of both Single-Input Single-Output (SISO) and Multi-Input Multi-Output (MIMO) complex systems. The proposed methodology provides the designer with an automated choice of using either: a conventional Proportional-Integral-Derivative (PID) controller, or a PID structure based (simultaneous) Pole and Zero Placement controller. The switching decisions between the two nonlinear fixed structure controllers is made on the basis of the required performance measure using the fuzzy logic based supervisor operating at the highest level of the system. The fuzzy supervisor is also employed to tune the parameters of the multiple-controller online in order to achieve the desired system performance. The GLM for modelling complex systems assumes that the plant is represented by an equivalent model consisting of a linear time-varying sub-model plus a learning nonlinear sub-model based on Radial Basis Function (RBF) neural network. The proposed control design brings together the dominant advantages of PID controllers (such as simplicity in structure and implementation) and the desirable attributes of Pole and Zero Placement controllers (such as stable set-point tracking and ease of parameters’ tuning). Simulation experiments using real-world nonlinear SISO and MIMO plant models, including realistic nonlinear vehicle models, demonstrate the effectiveness of the intelligent multiple-controller with respect to tracking set-point changes, achieve desired speed of response, prevent system output overshooting and maintain minimum variance input and output signals, whilst penalising excessive control actions

An Incremental Construction of Deep Neuro Fuzzy System for Continual Learning of Non-stationary Data Streams

Existing FNNs are mostly developed under a shallow network configuration having lower generalization power than those of deep structures. This paper proposes a novel self-organizing deep FNN, namely DEVFNN. Fuzzy rules can be automatically extracted from data streams or removed if they play limited role during their lifespan. The structure of the network can be deepened on demand by stacking additional layers using a drift detection method which not only detects the covariate drift, variations of input space, but also accurately identifies the real drift, dynamic changes of both feature space and target space. DEVFNN is developed under the stacked generalization principle via the feature augmentation concept where a recently developed algorithm, namely gClass, drives the hidden layer. It is equipped by an automatic feature selection method which controls activation and deactivation of input attributes to induce varying subsets of input features. A deep network simplification procedure is put forward using the concept of hidden layer merging to prevent uncontrollable growth of dimensionality of input space due to the nature of feature augmentation approach in building a deep network structure. DEVFNN works in the sample-wise fashion and is compatible for data stream applications. The efficacy of DEVFNN has been thoroughly evaluated using seven datasets with non-stationary properties under the prequential test-then-train protocol. It has been compared with four popular continual learning algorithms and its shallow counterpart where DEVFNN demonstrates improvement of classification accuracy. Moreover, it is also shown that the concept drift detection method is an effective tool to control the depth of network structure while the hidden layer merging scenario is capable of simplifying the network complexity of a deep network with negligible compromise of generalization performance.Comment: This paper has been published in IEEE Transactions on Fuzzy System

Multi-objective evolutionary–fuzzy augmented flight control for an F16 aircraft

In this article, the multi-objective design of a fuzzy logic augmented flight controller for a high performance fighter jet (the Lockheed-Martin F16) is described. A fuzzy logic controller is designed and its membership functions tuned by genetic algorithms in order to design a roll, pitch, and yaw flight controller with enhanced manoeuverability which still retains safety critical operation when combined with a standard inner-loop stabilizing controller. The controller is assessed in terms of pilot effort and thus reduction of pilot fatigue. The controller is incorporated into a six degree of freedom motion base real-time flight simulator, and flight tested by a qualified pilot instructor

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

Neuro-fuzzy software for intelligent control and education

Tese de mestrado integrado. Engenharia Electrotécnica e de Computadores (Major Automação). Faculdade de Engenharia. Universidade do Porto. 200