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

Entropy in Dynamic Systems

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed

Dynamic ridge polynomial neural network with Lyapunov function for time series forecasting

The ability to model the behaviour of arbitrary dynamic system is one of the most useful properties of recurrent networks. Dynamic ridge polynomial neural network (DRPNN) is a recurrent neural network used for time series forecasting. Despite the potential and capability of the DRPNN, stability problems could occur in the DRPNN due to the existence of the recurrent feedback. Therefore, in this study, a su cient condition based on an approach that uses adaptive learning rate is developed by introducing a Lyapunov function. To compare the performance of the proposed solution with the existing solution, which is derived based on the stability theorem for a feedback network, we used six time series, namely Darwin sea level pressure, monthly smoothed sunspot numbers, Lorenz, Santa Fe laser, daily Euro/Dollar exchange rate and Mackey-Glass time-delay di erential equation. Simulation results proved the stability of the proposed solution and showed an average 21.45% improvement in Root Mean Square Error (RMSE) with respect to the existing solution. Furthermore, the proposed solution is faster than the existing solution. This is due to the fact that the proposed solution solves network size restriction found in the existing solution and takes advantage of the calculated dynamic system variable to check the stability, unlike the existing solution that needs more calculation steps

Chaos Synchronization Based Novel Real-Time Intelligent Fault Diagnosis for Photovoltaic Systems

The traditional solar photovoltaic fault diagnosis system needs two to three sets of sensing elements to capture fault signals as fault features and many fault diagnosis methods cannot be applied with real time. The fault diagnosis method proposed in this study needs only one set of sensing elements to intercept the fault features of the system, which can be real-time-diagnosed by creating the fault data of only one set of sensors. The aforesaid two points reduce the cost and fault diagnosis time. It can improve the construction of the huge database. This study used Matlab to simulate the faults in the solar photovoltaic system. The maximum power point tracker (MPPT) is used to keep a stable power supply to the system when the system has faults. The characteristic signal of system fault voltage is captured and recorded, and the dynamic error of the fault voltage signal is extracted by chaos synchronization. Then, the extension engineering is used to implement the fault diagnosis. Finally, the overall fault diagnosis system only needs to capture the voltage signal of the solar photovoltaic system, and the fault type can be diagnosed instantly

Fault Analysis of Electromechanical Systems using Information Entropy Concepts

Fault analysis of mechanical and electromechanical systems has been a subject of considerable interest in the systems and control research community. Entropy, under its various formulations is an important variable, which is unrivaled when it comes to measuring order (or organization) and/or disorder (or disorganization). Researchers have successfully used entropy based concepts to solve various challenging problems in engineering, mathematics, meteorology, biotechnology, medicine, statistics etc. This research tries to analyze faults in electromechanical systems using information entropy concepts. The objectives of this research are to develop a method to evaluate signal entropy of a dynamical system using only input/output measurements, and to use this entropy measure to analyze faults within a dynamical system. Given discrete-time signals corresponding to the three-phase voltages and currents of an electromechanical system being monitored, the problem is to analyze whether or not this system is healthy. The concepts of Shannon entropy and relative entropy come from the field of Information Theory. They measure the degree of uncertainty that exists in a system. The main idea behind this approach is that the system's dynamics may have regularities hidden in measurements that are not obvious to see. The Shannon entropy and relative entropy measures are calculated by using probability distribution functions (PDF) that are formed by sampling the time series currents and voltages of a system. The system's health is monitored by, first, sampling the currents and voltages at certain time intervals, then generating the corresponding PDFs and, finally, calculating the information entropy measures. If the system dynamics are unchanged, or in other words, the system continues to be healthy, then the relative entropy measures will be consistently low or constant. But, if the system dynamics change due to damage, then the corresponding relative entropy and Shannon entropy measures will be increasing compared to the entropy of the system with less damage

Application of Wavelet Decomposition and Phase Space Reconstruction in Urban Water Consumption Forecasting: Chaotic Approach (Case Study)

The forecasting of future value of water consumption in an urban area is highly complex and nonlinear. It often exhibits a high degree of spatial and temporal variability. It is a crucial factor for long-term sustainable management and improvement of the operation of urban water allocation system. This chapter will study the application of two pre-processing phase space reconstruction (PSR) and wavelet decomposition transform (WDT) methods to investigate the behavior of time series to forecast short-term water demand value of Kelowna City (BC, Canada). The research proposes two pre-process technique to improve the accuracy of the models. Artificial neural networks (ANNs), gene expression programming (GEP) and multilinear regression (MLR) methods are the tools that considered for forecasting the demand values. Evaluation of the tools is based on two steps with and without applying the pre-processing methods. Moreover, autocorrelation function (ACF) is used to calculate the lag time. Correlation dimension is used to study the chaotic behavior of the dataset. The models’ relative performance is compared using three different fitness indexes; coefficient of determination (CD), root mean square error (RMSE) and mean absolute error (MAE). The results showed how pre-processing combination of WDT and PSR improved the performance of the models in forecasting short-term demand values

Computational Intelligence in Electromyography Analysis

Electromyography (EMG) is a technique for evaluating and recording the electrical activity produced by skeletal muscles. EMG may be used clinically for the diagnosis of neuromuscular problems and for assessing biomechanical and motor control deficits and other functional disorders. Furthermore, it can be used as a control signal for interfacing with orthotic and/or prosthetic devices or other rehabilitation assists. This book presents an updated overview of signal processing applications and recent developments in EMG from a number of diverse aspects and various applications in clinical and experimental research. It will provide readers with a detailed introduction to EMG signal processing techniques and applications, while presenting several new results and explanation of existing algorithms. This book is organized into 18 chapters, covering the current theoretical and practical approaches of EMG research

Filtering method in backlash phenomena analysis

The behavior of robotic manipulators with backlash is analyzed. Based on the pseudo-phase plane two indices are proposed to evaluate the backlash effect upon the robotic system: the root mean square error and the fractal dimension. For the dynamical analysis the noisy signals captured from the system are filtered through wavelets. Several tests are developed that demonstrate the coherence of the results