Nonlinear Output Research Articles

Relative Threshold-Based Event-Triggered Control for Nonlinear Constrained Systems With Application to Aircraft Wing Rock Motion

This article concentrates on the event-driven controller design problem for a class of nonlinear single input single output parametric systems with full state constraints. A varying threshold for the triggering mechanism is exploited, which makes the communication more flexible. Moreover, from the viewpoint of energy conservation and consumption reduction, the system capability becomes better owing to the contribution of the proposed event-triggered mechanism. In the meantime, the developed control strategy can avoid the Zeno behavior since the lower bound of the sample time is provided. The considered plant is in a lower triangular form, in which the match condition is not satisfied. To ensure that all the states retain in a predefined region, a barrier Lyapunov function (BLF) based adaptive control law is developed. Due to the existence of the parametric uncertainties, an adaptive algorithm is presented as an estimated tool. All the signals appearing in the closed-loop systems are then proven to be bounded. Meanwhile, the output of the system can track a given signal as far as possible. In the end, the effectiveness of the proposed approach is validated by an aircraft wing rock motion system.

Limit cycle periods in damage detection

This paper introduces a damage detection scheme based on changes in the period of limit cycles (LCs) realized by nonlinear output feedback. The parameterized feedback law is selected to make the dynamic equilibrium of the actuated coordinate approximate that of a generalized van der Pol oscillator and potential model-related difficulties are avoided by fixing the parameters from experimental results. It is found that not all sensor/actuator arrangements are suitable for generating a LC in closed loop, so a methodology to determine which arrangements are viable is presented. Numerical results show that LC periods are adequately stable with respect to noise and system changes from environmental effects and have sensitivity to localized damage that is often orders of magnitude larger than those of the modal frequencies.

Constrained Nonlinear Output Regulation Using Model Predictive Control

We present a model predictive control (MPC) framework to solve the constrained nonlinear output regulation problem. The main feature of the proposed framework is that the application does not require the solution to classical regulator (Francis-Byrnes-Isidori) equations or any other offline design procedure. In particular, the proposed formulation simply minimizes the predicted output error, possibly with some input regularization. Instead of using terminal cost/sets or a positive definite stage cost as is standard in MPC theory, we build on the theoretical results by Grimm et al. 2005 using a detectability notion. The proposed formulation is applicable if the constrained nonlinear regulation problem is (strictly) feasible, the plant is incrementally stabilizable and incrementally input-output to state stable (i-IOSS/detectable). We show that for minimum phase systems such a design ensures exponential stability of the regulator manifold. We also provide a design procedure in case of unstable zero dynamics using an incremental input regularization and a nonresonance condition. Inherent robustness properties for the noisy error/output-feedback case are established under simplifying assumptions (e.g. no state constraints). The theoretical results are illustrated with an example involving offset free tracking with noisy error feedback. The paper also contains novel results for MPC without terminal constraints with positive semidefinite input/output stage costs that are of independent interest.

A new meerkat optimization algorithm based maximum power point tracking for partially shaded photovoltaic system

The output power of solar photovoltaic (PV) system is intermittent in nature with a non-linear output voltage. This has peak power points in accordance with varying irradiation and temperature. Hence a Maximum Power Point Tracker (MPPT), which is power extraction technique is essential in PV power systems to ensure maximum power delivery for a given point of time. Thenonlinear power voltage curve gets more intense when shading of PV panels takes place, as the panels receive irregular and different solar irradiation, which alters the profile of power –voltage (P-V) curves. Due to the partial shading, the panels exhibit peculiar multiple power peaks instead of one single peak as in the case of uniform irradiation and as a result the conventional MPPT schemes could attain only local maxima and the global one. This research article proposes a new intelligent, bio inspired Meerkat optimization algorithm (MOA) which is capabale finding the global power peak and ensured maximum power delivery. ThisMOA MPPT technique is employed for a 120 W PV system and the versatility of the said scheme is tested by subjecting the PV panel for three different partially shaded conditions. The results reveal that the MOA exhibits fast tracking speed of with improved efficiencyof 99.8% when compared with particle swarm optimization (PSO) and differential evolution algorithm (DE)MPPT schemes.

Learning nonlinear state–space models using autoencoders

We propose a methodology for the identification of nonlinear state–space models from input/output data using machine-learning techniques based on autoencoders and neural networks. Our framework simultaneously identifies the nonlinear output and state-update maps of the model. After formulating the approach and providing guidelines for tuning the related hyper-parameters (including the model order), we show its capability in fitting nonlinear models on different nonlinear system identification benchmarks. Performance is assessed in terms of open-loop prediction on test data and of controlling the system via nonlinear model predictive control (MPC) based on the identified nonlinear state–space model.

Nonlinear Properties Analysis of Metallic Fatigue Damage Process Based on the Combined Nonlinear Parameter

To effectively extract the nonlinear properties of fatigue crack extension and evaluate the fatigue damage of metallic specimens, the chaos and fractal theory is applied to analyze the nonlinear output signal in a nonlinear ultrasonic experiment. A combined nonlinear parameter using the Lyapunov exponent, Kolmogorov entropy, and correlation dimension is proposed to evaluate the nonlinearity of fatigue damage. The nonlinear ultrasonic experiment is carried out on specimens with different stages of fatigue life, wherein the ultrasonic nonlinear output signal is collected and its combined nonlinear parameters are calculated. With the increase of fatigue damage in metallic specimens, the combined nonlinear parameter increases monotonically and tends to become saturated when a macroscopic crack appears, which indicates that complexity and randomness gradually increase during the accumulation of fatigue damage. According to microcrack propagation, the combined nonlinear parameter is very sensitive to the evolution of fatigue damage in metallic specimens, especially earlier fatigue damage. The relationship between the combined nonlinear parameter and the fatigue damage of specimens is established, which can provide an effective analytical method for evaluating fatigue damage and predicting the service life of specimens.

A software-hardware unit for studying the output characteristic of MEMS pressure sensors and its linearization

The paper presents the development of a linearization algorithm of the output parameters of the sensors based on the circuits that determine the static characteristics of the correction transducers, ensuring the linearity of the general conversion function with a given accuracy. Simulation modeling of correcting the output parameters of MEMS pressure sensors has been carried out. The qualitative characteristics of the measuring system are determined via providing the sensors with a means for determining the degree of reliability of their output data using a virtual exemplary tool. A technique for calibrating and linearizing the output characteristic of an analog MEMS pressure sensor has been developed. An algorithm for polynomial approximation of the nonlinear output characteristic of the sensor and a method for its implementation in Lab View software environment (by National Instruments) are presented. Virtual instruments developed in Lab View software environment have been the basis of software-hardware means for monitoring and processing of measuring data. The developed methodology and means of automation of measuring processes with the use of virtual devices made it possible to make the process of correcting the output parameters of sensors autonomous, independent of stationary measuring devices and debugging tools.

Model Predictive Control of Nonlinear MIMO Systems Based on Adaptive Orthogonal Polynomial Networks

This paper considers a new design of model predictive control based on specific models in the form of adaptive orthogonal polynomial networks, built around a specially tailored basis of generalized orthogonal functions. Polynomial model has a single layer structure and a smaller number of model parameters than classical neural networks, usually used for model predictive control design, leading to lower complexity and shorter calculation time. Desired property of adaptability of the model is achieved by using additional variable factors inside the orthogonal basis. The designed controller was applied in control of twin-rotor aero-dynamic system as a representative of nonlinear multiple input-multiple output systems and compared to the other state-of-the-art control algorithms.

Steep slope carbon nanotube tunneling field-effect transistor

Tunneling field-effect transistors (TFETs) have emerged as a potential candidate to outperform conventional metal-oxide-semiconductor FETs at low voltages, since their operation mechanism can overcome the fundamental subthreshold swing (SS) limit of 60 mV/decade at room temperature. We report carbon nanotube (CNT) based TFETs with abrupt p-i-n tunneling junctions controlled by electrostatic doping. Minimum SS (SSmin) of ∼41 mV/dec is observed with nearly no temperature dependence, as clear evidence of the TFET operation. We further investigate devices using CNTs with smaller bandgaps, reporting a record high band-to-band tunneling (BTBT) current of ∼100 nA for a single CNT. Non-linear output characteristics are observed as expected for devices operating outside of the quantum capacitance limit (QCL). Overall, electrostatically doped CNT TFETs shine a promising path for low-power electronic applications.

Magnetic position estimation using optimal sensor placement and nonlinear observer for smart actuators

This paper focuses on position estimation in smart actuators using non-contacting magnetic sensors. Magnetic position estimation in long-stroke actuators involves nonlinear non-monotonic measurement equations and the need to use more than one magnetic sensor. These challenges are addressed by developing a methodology for computing optimal sensor placement and an improved methodology for a LMI-based observer design technique. First, the lack of a constant gain observer with global stability for this application is shown due to the non-monotonic nature of the output nonlinearity. A switched-gain observer is therefore designed to ensure global stability. Second, the minimum singular values of the observability matrix over the range of actuator positions are utilized as a metric for optimizing sensor location and deciding on the number of sensors that need to be utilized. While a zero-norm problem formulation is non-convex and computationally expensive, the optimization problem is relaxed into a convex form and solved using a randomized rounding algorithm. Extensive experimental results are presented on the performance of the developed estimation algorithms. A nonlinear observer with two sensors placed at reasonable but non-optimal locations is shown to provide ∓ 2% error in position estimation and superior robustness properties compared to an extended Kalman filter. The use of optimal sensor locations with two sensors reduces the estimation error to less than 1% and helps meet desired performance specifications. Utilizing three sensors with optimal locations results in less than 0.5% peak position errors.

An Enhanced Equivalent Circuit Model With Real-Time Parameter Identification for Battery State-of-Charge Estimation

This article introduces an efficient modeling approach based on the Wiener structure to reinforce the capacity of classical equivalent circuit models (ECMs) in capturing the nonlinearities of lithium-ion (Li-ion) batteries. The proposed block-oriented modeling architecture is composed of a simple linear ECM followed by a static output nonlinearity block, which helps achieving a superior nonlinear mapping property while maintaining the real-time efficiency. The observability of the established battery model is analytically proven. This article also introduces an efficient parameter estimator based on extended-kernel iterative recursive least squares algorithm for real-time estimation of the parameters of the proposed Wiener model. The proposed approach is applied for state-of-charge (SoC) estimation of 3.4-Ah 3.6-V nickel-manganese-cobalt-based Li-ion cells using the extended Kalman filter (EKF). The results show about 1.5% improvement in SoC estimation accuracy compared with the EKF algorithm based on the second-order ECM. A series of real-time tests are also carried out to demonstrate the computational efficiency of the proposed method.

Linear and Nonlinear Optical Properties of CuO NPs for Photonics

The optical properties of various nanomaterials make them quite interesting and play a vital role in the fabrication of devices used in the optoelectronic and photonic fields. The research community around the world is curios to understand the physical phenomena behind such nanomaterials. In this study, copper oxide (CuO) nanoparticles (NPs) were prepared by a sonochemical method and their detailed optical properties analyzed by ultraviolet–visible (UV–Vis) spectroscopy. The normal dispersion of the refractive index of the CuO NPs was illustrated by the Wemple–DiDomenico single-oscillator method to yield the oscillator strength, static refractive index, dispersion energy (Ed), energy of effective dispersion oscillator (Eo), carrier concentration, and N/m* values. In addition, nonlinear optical parameters such as the refractive index, third-order nonlinear susceptibility, and optical polarization were also estimated. The nonlinear optical performance of the CuO NPs was simulated by using optiFDTD software, and the acceptance angle, spectral bandwidth, and nonlinear output power obtained. The findings could be used in optoelectronic device applications.

Prediction of temperature distribution around fusion zone in fiber dissimilar laser welding of AISI 304 and AISI 420: A wavelet network nonlinear ARX model

This paper has proposed a parameter estimation method for a laser welding process inherently highly nonlinear as a result of the highly nonlinear inputs and outputs of the system. Hence, a nonlinear system identification method was developed for the laser welding process using the wavelet network nonlinear autoregressive exogenous (ARX) model. The advantage of ARX over the standard nonlinear models is that it not only considers the delayed input and output regressors but also uses nonlinear functions for mapping, thus making ARX a better candidate for the prediction of nonlinear behaviors. In total, nine available datasets for the training and test phases at pulse durations, pulse frequencies, focal lengths, currents, and welding speeds were considered. Five inputs including pulse duration, pulse frequency, focal length, current and welding speed, and temperature as one output were considered. The first eight datasets were utilized for the training phase and one was used for the testing phase. The results showed that the ARX model had an acceptable performance in training and test phases, and it was capable of identifying the nonlinear and time-variant phenomenon of the laser welding process examined in this paper. For instance, most fitness values for austenitic and ferritic steel samples in the training time histories were 97.13 and 97.95, respectively.

Feature learning for stacked ELM via low-rank matrix factorization

Extreme-learning-machine based auto-encoder (ELM-AE) is regarded as a useful architecture with fast learning speed and general approximation ability, and stacked ELM is used to develop efficient and effective deep learning networks. However, considering features learned from conventional ELM-AEs have issues of weak nonlinear representation ability and random factors in feature projection, this paper proposes an improved ELM-AE architecture which utilize low-rank matrix factorization to learn optimal low-dimensional features. Two superiorities can be obtained compared to conventional ELM-AEs. One is the dimensionality of the hidden layer in ELM-AE could be set arbitrarily, e.g. a higher-dimension hidden layer could lower the random effect in feature learning and enhance features representation ability. The other is enhancing features nonlinear ability, since features are learned directly from the nonlinear outputs of hidden layer. Finally, comparison experiments on numerical and image datasets are implemented in this paper to verify the superior performance of the proposed ELM-AE in this paper.

Scaled conjugate gradient ANN for industrial sensors calibration

In this paper, artificial neural network is used to calibrate sensors that are commonly used in industry. Usually, such sensors have nonlinear input output characteristic that makes their calibration process rather inaccurate and unsatisfied. Artificial neural network is utilized in an inverse model learning mode to precisely calibrate such sensors. The scaled conjugate gradient (SCG) algorithm is used in the learning process. Three types of industrial sensors which are gas concentration sensor, force sensors and humidity sensors are considered in this work. It is found that the proposed calibration technique gives fast, robust and satisfactory results.

A grasshopper optimization algorithm aided maximum power point tracking for partially shaded photovoltaic systems

Photovoltaic (PV) systems exhibit non-linear output power voltage (P-V) characteristics for varying input irradiation and temperature. Due to this, the Maximum Power Point Tracker (MPPT), a widely used optimization technique is indispensable in PV power systems. This non-linearity gets more complicated when PV panels experience partial shading in an array. During partial shading, the panels receive non-uniform irradiance and, due to this the current-voltage (I-V) curve is multimodal and so are P-V curves. Therefore, PV array which is partially shaded will exhibit multiple power peaks which are termed global maxima and local maxima. The most prevalent algorithms like Perturb and Observe (P&O) and Incremental Conductance (INC) experiences a unique issue by getting stuck at local maxima and not grasping the global power peak. This research article proposes a new Grasshopper Optimization Algorithm (GOA) which is capable of extracting maximum power even during terrible shading conditions. This algorithm is validated by comparing its performance with both conventional and other most prominent global search counterparts. The results demonstrate the effectiveness of the proposed algorithm.

Research on a new diagnosis index for fixed-point rub-impact of rotor system

A model for a rotor system simulated with finite element method and a test bench are established in this paper. The fixed-point rub-impact fault on rotor system is studied (There are six clearances to be discussed). It is found that the nonlinear compositions are contained in the output responses by analyzing these vibration signals of the rotor system with fixed-point rub-impact, which implies that a nonlinear term appears in the system. In order to extract these compositions, a nonlinear method, named weighted contribution rate of nonlinear output frequency response functions (WNOFRFs), is adopted for analyzing the mechanism of these nonlinear problems in frequency domain. Furthermore, the Clenshaw-Curtis numerical integration method and the minimum mutual entropy principle (MMEP) are used to extract the fault diagnosis index J for identifying the fixed-point rub-impact fault of the system. At last, according to the simulation and experiment research, WNOFRFs can improve these higher-order nonlinear characteristics. And these findings prove that the index J has certain advantages compared with other indexes in the diagnosis of the rotor rub-impact fault.

Bitcoin closing price movement prediction with optimal functional link neural networks

Bitcoin prediction is a recent area of research interest and growing fast. Since its inception, in a short period of time Bitcoin got wide popularity and considered as an investment asset. At present it is the most successful cryptocurrency compared to other altcoins dispersed in the world economy. The Bitcoin prices fluctuate like other stock markets due to inherent volatility. The investors’ confidence on Bitcoin rising fast and have been reflected on its prices. Though few computational intelligence methods are available, sophisticated methodologies for accurate prediction of Bitcoin are still lacking and need to be explored. Functional link neural network (FLN) is a flat network, offers lower computational complexity, and achieves enhanced input–output nonlinearity mapping through functional expansion of input signals. Basis functions such as Legendre, Trigonometric, Laguerre, and Chebyshev are commonly used polynomials in FLN for expansion of input signal dimension. In this article along with the weight and bias vector of FLNs, optimal number of polynomial functions for each category of basis function is selected by genetic algorithm during training process rather fixing them earlier. Therefore, an optimal FLN structure is crafted on fly from exploitation of training data. The optimal FLN models are used to predict the daily, weekly, and monthly closing prices of Bitcoin. A comparative study among optimal FLNs is carried out using evaluation metrics such as MAPE, NMSE, ARV, and U of Theil’s statistics. Finally, outcomes from experimental and comparative studies suggested the superiority of optimal FLN models for Bitcoin closing price prediction.

Tensor product‐based model transformation approach to tower crane systems modeling

AbstractThis paper presents the application of the tensor product (TP)‐based model transformation approach to produce Tower CRrane (TCR) systems models. The modeling approach starts with a nonlinear model of TCR systems as representative multi‐input–multi‐output controlled processes. A linear parameter‐varying model is next derived, and the modeling steps specific to TP–based model transformation are proceeded to obtain the TP model. The TP model is tested on TCR laboratory equipment in two open‐loop scenarios considering chirp signals and pseudorandom binary step signals applied to the three model inputs (control inputs). The nonlinear and TP model outputs in the two scenarios are the payload position, the cart position, and the arm angular position. The nonlinear and TP model outputs are collected, measured, and compared. The simulation results prove that the derived TP model approximately mimics the behavior of the nonlinear model; both system responses and numerical approximation errors are illustrated.

Parameter identification for Wiener‐finite impulse response system with output data of missing completely at random mechanism and time delay

SummaryIn this paper, the parameter estimation issue of Wiener system with random time delay and missing output data is studied. The linear part of Wiener system is described by Finite Impulse Response (FIR) model. The mathematical formula of the Expectation Maximum algorithm to identify Wiener‐FIR system that contains the random time delay and the nonlinear output data in missing completely at random mechanism is derived, which is never considered before. To obtain the unmeasurable intermediate variable in Wiener‐FIR system, the idea of auxiliary model is adopted. The time delay and system parameters can be estimated simultaneously by this method. Numerical example and the identification of water tank system example are carried out, the effectiveness of the algorithm is proved.