Multilayer perceptron network optimization for chaotic time series modeling

Chaotic time series are widely present in practice, but due to their characteristics—such as internal randomness, nonlinearity, and long-term unpredictability—it is difficult to achieve high-precision intermediate or long-term predictions. Multi-layer perceptron (MLP) networks are an effective tool for chaotic time series modeling. Focusing on chaotic time series modeling, this paper presents a generalized degree of freedom approximation method of MLP. We then obtain its Akachi information criterion, which is designed as the loss function for training, hence developing an overall framework for chaotic time series analysis, including phase space reconstruction, model training, and model selection. To verify the effectiveness of the proposed method, it is applied to two artificial chaotic time series and two real-world chaotic time series. The numerical results show that the proposed optimized method is effective to obtain the best model from a group of candidates. Moreover, the optimized models perform very well in multi-step prediction tasks.This research was funded in part by the NSFC grant numbers 61972174 and 62272192, the Science-Technology Development Plan Project of Jilin Province grant number 20210201080GX, the Jilin Province Development and Reform Commission grant number 2021C044-1, the Guangdong Universities’ Innovation Team grant number 2021KCXTD015, and Key Disciplines Projects grant number 2021ZDJS138

Recent Advances and Applications of Fractional-Order Neural Networks

This paper focuses on the growth, development, and future of various forms of fractional-order neural networks. Multiple advances in structure, learning algorithms, and methods have been critically investigated and summarized. This also includes the recent trends in the dynamics of various fractional-order neural networks. The multiple forms of fractional-order neural networks considered in this study are Hopfield, cellular, memristive, complex, and quaternion-valued based networks. Further, the application of fractional-order neural networks in various computational fields such as system identification, control, optimization, and stability have been critically analyzed and discussed

Bio-Inspired Approach to Modelling Retinal Ganglion Cells using System Identification Techniques

The processing capabilities of biological vision systems are still vastly superior to artificial vision, even though this has been an active area of research for over half a century. Current artificial vision techniques integrate many insights from biology yet they remain far-off the capabilities of animals and humans in terms of speed, power, and performance. A key aspect to modeling the human visual system is the ability to accurately model the behavior and computation within the retina. In particular, we focus on modeling the retinal ganglion cells (RGCs) as they convey the accumulated data of real world images as action potentials onto the visual cortex via the optic nerve. Computational models that approximate the processing that occurs within RGCs can be derived by quantitatively fitting the sets of physiological data using an input–output analysis where the input is a known stimulus and the output is neuronal recordings. Currently, these input–output responses are modeled using computational combinations of linear and nonlinear models that are generally complex and lack any relevance to the underlying biophysics. In this paper, we illustrate how system identification techniques, which take inspiration from biological systems, can accurately model retinal ganglion cell behavior, and are a viable alternative to traditional linear–nonlinear approaches

Measurements, Models, Systems and Design

531 s.

Machine Learning Methods for Better Water Quality Prediction

In any aquatic system analysis, the modelling water quality parameters are of considerable significance. The traditional modelling methodologies are dependent on datasets that involve large amount of unknown or unspecified input data and generally consist of time-consuming processes. The implementation of artificial intelligence (AI) leads to a flexible mathematical structure that has the capability to identify non-linear and complex relationships between input and output data. There has been a major degradation of the Johor River Basin because of several developmental and human activities. Therefore, setting up of a water quality prediction model for better water resource management is of critical importance and will serve as a powerful tool. The different modelling approaches that have been implemented include: Adaptive Neuro-Fuzzy Inference System (ANFIS), Radial Basis Function Neural Networks (RBF-ANN), and Multi-Layer Perceptron Neural Networks (MLP-ANN). However, data obtained from monitoring stations and experiments are possibly polluted by noise signals as a result of random and systematic errors. Due to the presence of noise in the data, it is relatively difficult to make an accurate prediction. Hence, a Neuro-Fuzzy Inference System (WDT-ANFIS) based augmented wavelet de-noising technique has been recommended that depends on historical data of the water quality parameter. In the domain of interests, the water quality parameters primarily include ammoniacal nitrogen (AN), suspended solid (SS) and pH. In order to evaluate the impacts on the model, three evaluation techniques or assessment processes have been used. The first assessment process is dependent on the partitioning of the neural network connection weights that ascertains the significance of every input parameter in the network. On the other hand, the second and third assessment processes ascertain the most effectual input that has the potential to construct the models using a single and a combination of parameters, respectively. During these processes, two scenarios were introduced: Scenario 1 and Scenario 2. Scenario 1 constructs a prediction model for water quality parameters at every station, while Scenario 2 develops a prediction model on the basis of the value of the same parameter at the previous station (upstream). Both the scenarios are based on the value of the twelve input parameters. The field data from 2009 to 2010 was used to validate WDT-ANFIS. The WDT-ANFIS model exhibited a significant improvement in predicting accuracy for all the water quality parameters and outperformed all the recommended models. Also, the performance of Scenario 2 was observed to be more adequate than Scenario 1, with substantial improvement in the range of 0.5% to 5% for all the water quality parameters at all stations. On validating the recommended model, it was found that the model satisfactorily predicted all the water quality parameters (R2 values equal or bigger than 0.9). © 201

Control of chaos in nonlinear circuits and systems

Nonlinear circuits and systems, such as electronic circuits (Chapter 5), power converters (Chapter 6), human brains (Chapter 7), phase lock loops (Chapter 8), sigma delta modulators (Chapter 9), etc, are found almost everywhere. Understanding nonlinear behaviours as well as control of these circuits and systems are important for real practical engineering applications. Control theories for linear circuits and systems are well developed and almost complete. However, different nonlinear circuits and systems could exhibit very different behaviours. Hence, it is difficult to unify a general control theory for general nonlinear circuits and systems. Up to now, control theories for nonlinear circuits and systems are still very limited. The objective of this book is to review the state of the art chaos control methods for some common nonlinear circuits and systems, such as those listed in the above, and stimulate further research and development in chaos control for nonlinear circuits and systems. This book consists of three parts. The first part of the book consists of reviews on general chaos control methods. In particular, a time-delayed approach written by H. Huang and G. Feng is reviewed in Chapter 1. A master slave synchronization problem for chaotic Lur’e systems is considered. A delay independent and delay dependent synchronization criteria are derived based on the H performance. The design of the time delayed feedback controller can be accomplished by means of the feasibility of linear matrix inequalities. In Chapter 2, a fuzzy model based approach written by H.K. Lam and F.H.F. Leung is reviewed. The synchronization of chaotic systems subject to parameter uncertainties is considered. A chaotic system is first represented by the fuzzy model. A switching controller is then employed to synchronize the systems. The stability conditions in terms of linear matrix inequalities are derived based on the Lyapunov stability theory. The tracking performance and parameter design of the controller are formulated as a generalized eigenvalue minimization problem which is solved numerically via some convex programming techniques. In Chapter 3, a sliding mode control approach written by Y. Feng and X. Yu is reviewed. Three kinds of sliding mode control methods, traditional sliding mode control, terminal sliding mode control and non-singular terminal sliding mode control, are employed for the control of a chaotic system to realize two different control objectives, namely to force the system states to converge to zero or to track desired trajectories. Observer based chaos synchronizations for chaotic systems with single nonlinearity and multi-nonlinearities are also presented. In Chapter 4, an optimal control approach written by C.Z. Wu, C.M. Liu, K.L. Teo and Q.X. Shao is reviewed. Systems with nonparametric regression with jump points are considered. The rough locations of all the possible jump points are identified using existing kernel methods. A smooth spline function is used to approximate each segment of the regression function. A time scaling transformation is derived so as to map the undecided jump points to fixed points. The approximation problem is formulated as an optimization problem and solved via existing optimization tools. The second part of the book consists of reviews on general chaos controls for continuous-time systems. In particular, chaos controls for Chua’s circuits written by L.A.B. Tôrres, L.A. Aguirre, R.M. Palhares and E.M.A.M. Mendes are discussed in Chapter 5. An inductorless Chua’s circuit realization is presented, as well as some practical issues, such as data analysis, mathematical modelling and dynamical characterization, are discussed. The tradeoff among the control objective, the control energy and the model complexity is derived. In Chapter 6, chaos controls for pulse width modulation current mode single phase H-bridge inverters written by B. Robert, M. Feki and H.H.C. Iu are discussed. A time delayed feedback controller is used in conjunction with the proportional controller in its simple form as well as in its extended form to stabilize the desired periodic orbit for larger values of the proportional controller gain. This method is very robust and easy to implement. In Chapter 7, chaos controls for epileptiform bursting in the brain written by M.W. Slutzky, P. Cvitanovic and D.J. Mogul are discussed. Chaos analysis and chaos control algorithms for manipulating the seizure like behaviour in a brain slice model are discussed. The techniques provide a nonlinear control pathway for terminating or potentially preventing epileptic seizures in the whole brain. The third part of the book consists of reviews on general chaos controls for discrete-time systems. In particular, chaos controls for phase lock loops written by A.M. Harb and B.A. Harb are discussed in Chapter 8. A nonlinear controller based on the theory of backstepping is designed so that the phase lock loops will not be out of lock. Also, the phase lock loops will not exhibit Hopf bifurcation and chaotic behaviours. In Chapter 9, chaos controls for sigma delta modulators written by B.W.K. Ling, C.Y.F. Ho and J.D. Reiss are discussed. A fuzzy impulsive control approach is employed for the control of the sigma delta modulators. The local stability criterion and the condition for the occurrence of limit cycle behaviours are derived. Based on the derived conditions, a fuzzy impulsive control law is formulated so that the occurrence of the limit cycle behaviours, the effect of the audio clicks and the distance between the state vectors and an invariant set are minimized supposing that the invariant set is nonempty. The state vectors can be bounded within any arbitrary nonempty region no matter what the input step size, the initial condition and the filter parameters are. The editors are much indebted to the editor of the World Scientific Series on Nonlinear Science, Prof. Leon Chua, and to Senior Editor Miss Lakshmi Narayan for their help and congenial processing of the edition

Recurrent neural networks and proper orthogonal decomposition with interval data for real-time predictions of mechanised tunnelling processes

A surrogate modelling strategy for predictions of interval settlement fields in real time during machine driven construction of tunnels, accounting for uncertain geotechnical parameters in terms of intervals, is presented in the paper. Artificial Neural Network and Proper Orthogonal Decomposition approaches are combined to approximate and predict tunnelling induced time variant surface settlement fields computed by a process-oriented finite element simulation model. The surrogate models are generated, trained and tested in the design (offline) stage of a tunnel project based on finite element analyses to compute the surface settlements for selected scenarios of the tunnelling process steering parameters taking uncertain geotechnical parameters by means of possible ranges (intervals) into account. The resulting mappings of time constant geotechnical interval parameters and time variant deterministic steering parameters onto the time variant interval settlement field are solved offline by optimisation and online by interval analyses approaches using the midpoint-radius representation of interval data. During the tunnel construction, the surrogate model is designed to be used in real-time to predict interval fields of the surface settlements in each stage of the advancement of the tunnel boring machine for selected realisations of the steering parameters to support the steering decisions of the machine driver