Nonlinear Dynamic Process Research Articles

NARX Deep Convolutional Fuzzy System for Modelling Nonlinear Dynamic Processes

This paper presents a new approach for modelling nonlinear dynamic processes (NDP). It is based on a nonlinear autoregressive with exogenous (NARX) inputs model structure and a deep convolutional fuzzy system (DCFS). The DCFS is a hierarchical fuzzy structure, which can overcome the deficiency of general fuzzy systems when facing high dimensional data. For relieving the curse of dimensionality, as well as improving approximation performance of fuzzy models, we propose combining the NARX with the DCFS to provide a good approximation of the complex nonlinear dynamic behavior and a fast-training algorithm with ensured convergence. There are three NARX DCFS structures proposed, and the appropriate training algorithm is adapted. Evaluations were performed on a popular benchmark—Box and Jenkin’s gas furnace data set and the four nonlinear dynamic test systems. The experiments show that the proposed NARX DCFS method can be successfully used to identify nonlinear dynamic systems based on external dynamics structures and nonlinear static approximators.

A penalty function-based greedy diffusion search algorithm for the optimization of constrained nonlinear dynamical processes with discrete-valued input

This paper considers an optimization problem of nonlinear dynamical processes with discrete-valued input and continuous-time inequality constraints. This problem requires to determine an order and some instants. Since the order is a discrete variable and the constraints are complex, classical optimal control approaches cannot be used directly to solve this problem. To tackle this issue, a penalty function-based greedy diffusion search algorithm is proposed based on a novel transformation for each discrete value, a novel second-order smoothing technique, a $ l_1 $ penalty function, and a novel greedy rule. In the novel greedy rule, there exist only two parameters, which can be set in advance. Thus, unlike existing hybrid approaches, no parameters is required adjusted in the penalty function-based greedy diffusion search algorithm. Following that, the global convergence results of the proposed algorithm are established. Finally, an energy management problem in an electrical vehicle is used to illustrate the effectiveness of the proposed algorithm. The numerical simulation results show that the algorithm proposed by this paper can obtain a better solution with less time-consuming, fewer iterations, and fewer errors compared with existing methods.

Soft Sensor Modeling Method for Sulfur Recovery Process Based on Long Short-Term Memory Artificial Neural Network (LSTM)

In the process of sulfur recovery, H2S and SO2 concentrations reflect the effectiveness and reliability of the recovery process. However, the concentration of H2S and SO2 in the process of sulfur recovery is difficult to be measured by online analysis instrument, so the soft sensing modeling method is often used to analyze the system. Because SRU system has strong nonlinear characteristics and dynamic process characteristics,traditional soft sensing modeling methods are often limited in use. Long Short-Term Memory (LSTM)Artificial neural networks show strong ability in processing nonlinear data and dynamic data. Therefore, LSTM soft sensing method is used in this paper to systematically analyze the sulfur recovery process.

ResNet and PolyNet Based Identification and (MPC) Control of Dynamical Systems: A Promising Way

This paper deals with model predictive control synthesis which take benefits from artificial neural networks to model (non-linear) dynamical system. More precisely, thanks to a systematic and rigorous methodology, it is shown that residual networks (ResNet) and PolyInception networks (PolyNet) neural network architectures, developed initially for image recognition, are very good candidate for i) identification of dynamical systems, ii) being used as embedded model in a model predictive control laws. Concretely, the widely used non-linear dynamical system quadruple tank process is used as a benchmark. The neural network architectures studied are i) feedforward networks as a reference point, and the two other linked to Euler integration method ii) residual networks and iii) PolyInception networks. Networks training is performed by mixing classical back-propagation algorithm and hyperparameters optimisation through heuristics. The identification results provided show that neural networks of types ii) and iii) perform better than the classical one i), with a better generalisation capability. Finally, model predictive controllers are synthesized based on the various networks trained. The simulation results obtained for controlling water levels of a 4 tanks system benchmark give interesting insights. They show that residual networks based model predictive control is better suited than feedforward networks and PolyInception networks based ones, both taking into account computation time and set point errors.

Nonlinear Dynamic Process Robust Monitoring Based on Spatiotemporal Preserving Projections With Rank-Order Distance

Nonlinear Dynamic Process Robust Monitoring Based on Spatiotemporal Preserving Projections With Rank-Order Distance

A data-driven nonlinear frequency response approach based on the Loewner framework: preliminary analysis

We propose a hybrid method based on the combination of computed-aided nonlinear frequency response analysis with the Loewner framework, for the characterization of nonlinear dynamical processes with application in electrochemistry. The method is data-driven, i.e., requiring only samples of the first two generalized transfer functions of the underlying system, given as values of the sampled nonlinear frequency response. Then, the established system fitting and complexity reduction approach (in the frequency domain), known as the Loewner framework, is used to extract the system's invariant quantities. In this analysis, we have used a nonlinear electrical circuit model as a test case, for which the new method provides good results.

Nonlinear Dynamic Process Monitoring Using Canonical Variate Kernel Analysis

Most industrial systems today are nonlinear and dynamic. Traditional fault detection techniques show their limits because they can hardly extract both nonlinear and dynamic features simultaneously. Canonical variate analysis (CVA) shows its excellent monitoring performance in fault detection for dynamic processes but is not applicable to nonlinear processes. Inspired by the CVA method, a novel nonlinear dynamic process monitoring method, namely, the “canonical variate kernel analysis” (CVKA), is proposed in this work. The way to extract nonlinear features is different from a traditional kernel canonical variate analysis (KCVA). In a sequential structure, the new approach firstly extracts the linear dynamic features from the data through the CVA method, followed by a kernel principal component analysis to extract nonlinear features from the CVA residual space. The new CVKA method is then applied to a TE process case study, proving the excellent performance of CVKA compared to other common approaches in dynamic nonlinear process monitoring for TE-like processes.

Расчет оптимальных параметров систем управления нелинейными динамическими процессами импульсных преобразователей напряжения

A technique for choosing the optimal control system parameters for DC voltage converters is proposed, based on the joint application of the theory of linear automatic control systems and the theory of nonlinear dynamic systems. A small-signal structural dynamic model of an open loop of an automatic control system based on a direct step-up voltage converter with a control system for nonlinear dynamic processes based on a delayed feedback method is considered. Applying this model makes it possible to carry out a scientifically substantiated choice of the control system parameters for nonlinear dynamic processes using the methods of linear automatic control system theory. Bode diagrams of an open loop system are calculated without additional control of nonlinear dynamic processes and with additional control. The efficiency of using control systems for nonlinear dynamic processes is shown, which allows eliminating undesirable dynamic modes without additional parametric synthesis of the controller and, consequently, without reducing the system performance as a whole. In addition, applying these methods allows adjusting the controller parameters to increase the system performance without switching the system to undesirable dynamic modes. The results obtained can be applied at the stage of designing wide-class DC voltage pulse converters

Dynamic network biomarker factors orchestrate cell-fate determination at tipping points during hESC differentiation

The generation of ectoderm, mesoderm, and endoderm layers is the most critical biological process during the gastrulation of embryo development. Such a differentiation process in human embryonic stem cells (hESCs) is an inherently nonlinear multi-stage dynamical process which contain multiple tipping points playing crucial roles in the cell-fate decision. However, the tipping points of the process are largely unknown, letting alone the understanding of the molecular regulation on these critical events. Here by designing a module-based dynamic network biomarker (M-DNB) model, we quantitatively pinpointed two tipping points of the differentiation of hESCs toward definitive endoderm, which leads to the identification of M-DNB factors (FOS, HSF1, MYCN, TP53, and MYC) of this process. We demonstrate that before the tipping points, M-DNB factors are able to maintain the cell states and orchestrate cell-fate determination during hESC (ES)-to-ME and ME-to-DE differentiation processes, which not only leads to better understanding of endodermal specification of hESCs but also reveals the power of the M-DNB model to identify critical transition points with their key factors in diverse biological processes, including cell differentiation and transdifferentiation dynamics.

Computational Method to Predict Three-Dimensional Chatter Vibration in Cold Rolling of Flat Metals

Abstract Introduced is a three-dimensional, physics-based mathematical model capable of efficiently predicting self-excited chatter vibration phenomena in the cold rolling of metal strip and sheet. The described nonlinear chatter model combines the 3D mill structural dynamics behavior with the elastic–plastic rolling process dynamics to predict conditions of instability in a single-stand 4-high mill that can lead to both third-octave and fifth-octave chatter. Formulation of the 3D chatter model is achieved by coupling the dynamic simplified-mixed finite element method with a nonlinear roll-bite process dynamics model to capture self-exciting feedback interactions. In contrast to prior approaches to model chatter in the cold rolling of flat metals, the presented method abandons several simplifying assumptions, including 1D or 2D linear lumped parameter analyses, vertical symmetry of the upper and lower halves of the roll-stack, and continuous contact between the rolls and strip. The model is demonstrated for a single-stand 4-high rolling mill considering the detrimental third-octave self-excited chatter condition. Detailed stability analyses that show time histories of the 3D mill behaviors are presented, respectively, for stable, marginally stable, and unstable rolling speeds, and for changes in the lower housing stiffness to reflect more realistic, asymmetric rolling mill conditions.

Root cause diagnosis for complex industrial process faults via spatiotemporal coalescent based time series prediction and optimized Granger causality

It is essential to conduct root cause diagnosis (RCD) to guarantee the safety of operations of chemical processes and suppress fault deterioration, yet RCD has encountered challenges in the context of the increasing complexity of industrial processes. Granger causality (GC) analysis is one of the most commonly used methods to construct process causal maps and identify root causes. However, its use is subject to a number of limitations for dynamic nonlinear industrial processes. Therefore, an optimized GC analysis is proposed to perform RCD in complex industrial processes based on the spatiotemporal coalescent-based prediction model (SCPM) and causality verification algorithm (CVA). The time series prediction model SCPM is presented as an alternative to GC’s conventional autoregressive model in order to avoid spurious regressive facing nonlinear processes, which stacks dilated convolutional neural networks (DCNN) and bidirectional gated recurrent unit (BiGRU) to coalesce time series nonlinear couplings and long-term dependence information. Moreover, considering data that may deviate from normal distribution after the fault occurs, a nonparametric causality test method CVA based on the Wilcoxon signed-rank test (WSRT) is constructed combined with SCPM to eliminate false causality discovery. Empirical results on the Tennessee Eastman process and the blast furnace process demonstrate the effectiveness of the proposed RCD method.

Knowledge: the good, the bad, and the ways for designer creativity

Design is a highly nonlinear chaotic dynamic process with many possible solutions, some of which can be creative. The chaotic nonlinearity of design dynamics triggers mental stresses in designers, whose creativity happens only when their mental stresses are at an optimal level. Following a deductive approach, this paper investigates how knowledge can contribute to designer creativity by uncovering knowledge's (good and bad) roles in the design process, based on which three ways are recommended to use knowledge properly in design. The assumption is that all designs follow one governing equation, which is a recursive integration of three basic design activities: formulation, evaluation and synthesis. The difference between designs of various fields and different kinds (routine, innovative and creative) lies in the range, content, size and nature of the design space in which the design governing equation works. The design governing equation implies a nonlinear chaotic design dynamics, whose solutions are sensitive to its initial conditions and can be routine, innovative or creative. The design governing equation is solved and reformulated by the designer's creativity capability. Therefore, design researchers, practitioners and educators should cohesively look at both designer's knowledge/experience and the designer's creative thinking process.

Research on Dynamic Nonlinearity of Materials Based on Tensile Test

The collision impact process of a structure is a complex nonlinear dynamic response process, and the key factor to ensure the accuracy of the calculation results when calculating the simulation collision problem is the definition of the dynamic nonlinear parameters of the material during the simulation analysis, and there is no uniform treatment for the collision impact problem. Based on Q235 steel, quasi-static tensile and high-speed tensile tests were carried out, and the material parameters were calibrated to meet the requirements of the collision simulation calculation based on the test data, considering the material strain rate sensitivity and material hardening properties. The research results can be used as a reference for the simulation of large structure impact problems.

Non-linear dynamic processes and their correlation with indicators of microcirculation in patients with obliterating atherosclerosis of the lower extremities arteries according to laser doppler flowmetry

Objective: To study features of nonlinear dynamic and oscillatory processes in the skin microcirculatory flow in patients with obliterating atherosclerosis in lower extremities arteries (OALEA).Material and methods. 56 male patients with obliterating atherosclerosis in the arteries of lower extremities and 15 practically healthy individuals were taken into the study. Microcirculation in the skin on feet with the assessment of nonlinear dynamic processes and spectral wavelet analysis of blood fl ow fl uctuations was studied by laser Doppler flowmetry, device “LACK-M” (firm Lazma, Russia). Normalized amplitude parameters of blood flow fluctuations in frequency ranges of hemocirculation tonus-forming factors were analyzed: endothelial, neurogenic, myogenic. Myogenic microvascular tone and capillary blood flow indices were calculated. To study nonlinear dynamic processes, the following parameters were assessed: fractal dimension, entropy and phase portrait analysis.Results. Spastic-atonic microcirculation disorders were revealed in patients with OALEA. They were characterized with metarteriole constriction and with restriction of capillary blood flow, with an increased myogenic tone and dilated arterioles. Statistically significant shifts in parameters of nonlinear dynamics in this case- in particular, decrease in entropy (–10.6 %) and in dimensions of phase portrait (–9.3%) under energy deficit in oscillatory microcirculation processes (–20.8 %) – can be interpreted as a decrease in complexity of laser Doppler flowmetric signal and better ordering in regulatory mechanisms of the peripheral blood flow.Conclusion. In patients with obliterating atherosclerosis in the arteries of lower extremities, the obtained results indicate significant functional microcirculation disorders of the spastic-atonic nature leading to the restriction of nutritive blood flow and accompanied by the lack of energy in oscillatory processes. These results have also shown the decrease in the system chaos severity which indicates limitation of connections of microcirculation control factors, simplification of the mechanisms of functioning of the microvascular bed and, as a consequence, decrease in the compensatory adaptive potential.

Virtual Sensor Modeling for Nonlinear Dynamic Processes Based on Local Weighted PSFA

Modern industrial processes are featured with complex dynamic, nonlinear, and noisy characteristics. It is of great significance to apply the probabilistic latent variable models (LVMs) to mine the pivotal features of the industrial processes. A probabilistic slow feature analysis (PSFA) can extract slowly varying features in rapidly changing data sequences as a dynamic LVM. However, the performance of PSFA is limited because of its linear assumption. In this article, a locally weighted PSFA (LWPSFA) is proposed for nonlinear dynamic modeling of industrial data with random noises. Two different kinds of weighting techniques are designed to approximate the nonlinear slow feature transition and emission functions. After that, the expectation maximum (EM) algorithm is adopted to estimate the parameters of LWPSFA with a weighted log-likelihood function (W-LLF). Eventually, a debutanizer column and a hydrocracking process are used to validate the effectiveness of LWPSFA.

Dynamic ramping for demand response of processes and energy systems based on exact linearization

The increasing share of volatile renewable electricity production motivates demand response. Substantial potential for demand response is offered by flexible processes and their local multi-energy supply systems. Simultaneous optimization of their schedules can exploit the demand response potential, but leads to numerically challenging problems for nonlinear dynamic processes. In this paper, we propose to capture process dynamics using dynamic ramping constraints. In contrast to traditional static ramping constraints, dynamic ramping constraints are a function of the process state and can capture high-order dynamics. We derive dynamic ramping constraints rigorously for the case of single-input single-output processes that are exactly input-state linearizable. The resulting scheduling problem can be efficiently solved as a mixed-integer linear program. In a case study, we study two flexible reactors and a multi-energy system. The proper representation of process dynamics by dynamic ramping allows for faster transitions compared to static ramping constraints and thus higher economic benefits of demand response. The proposed dynamic ramping approach is sufficiently fast for application in online optimization.

Combined Forecasting of Ship Heave Motion Based on Induced Ordered Weighted Averaging Operator

AbstractHeave motion of ships is a complex nonlinear dynamic process and cannot be accurately forecasted using a single prediction model. In this paper, an effective combined forecasting method is proposed to perform ship's heave motion prediction. The proposed method combines back propagation neural network (BPNN), autoregressive model (AR) and extreme learning machine (ELM) through an induced ordered weighted averaging (IOWA) operator. The prediction accuracy is selected as the induced variable and the prediction results are sorted according to prediction accuracy and IOWA operator assigns larger weights to the position with the smallest prediction error. The optimal weights are determined by maximizing the B‐mode relational degree. Experimental results demonstrate its effectiveness of the proposed method. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Calculation of high-order harmonic generation of atoms and molecules by combining time series prediction and neural networks.

High-order harmonic generation (HHG) from the interaction of ultra-intense laser pulses with atoms is an important tabletop short-wave coherent light source. Accurate quantum simulations of it present large computational difficulties due to multi-electron multidimensional effects. In this paper, the time-dependent response of hydrogen atoms is calculated using a time-series prediction scheme, the HHG spectrum is reconstructed very accurately. The accuracy of the forecasting is further improved by using a neural network scheme. This scheme is also applied to the simulation of the harmonic emission on multi-electron systems, and the applicability of the scheme is confirmed by the harmonic calculation of complex systems. This method is expected to simulate the nonlinear dynamic process of multi-electron atoms and molecules irradiated by intense laser pulses quickly and accurately.

Study on the regulation of amplitude for the optical soliton through nonlinear effects in the optical communication system

Optical communication system is a kind of communication system using the light wave as the carrier. It has been widely used in recent years with the advantages of the long distance. Optical solitons have some merits for high stability, amenable to generate and low cost, it is an ideal carrier of optical communication system. In this paper, the regulation of pulse characteristics of the optical soliton is studied theoretically. The influence of high-order dispersion and high-order nonlinear effects on the amplitude, shape and other transmission characteristics of the optical soliton is studied by using the bilinear method with the high-order variable coefficient nonlinear Schrödinger (NLS) equation in the nonuniform fibers, and the regulation problems such as the maintenance and excitation of the optical soliton are analyzed. The waveform and amplitude control of the optical soliton and the change of optical soliton characteristics with the dispersion management are studied profoundly, and the nonlinear dynamic processes in their respective intracavity are analyzed. A feasible scheme for avoiding and utilizing the optical soliton is proposed, which has the significance for the investigation of the parameter regulation and dynamic control of the optical soliton in practical inhomogeneous optical fiber communication systems.

A Hybrid Machine Learning Model Coupling Double Exponential Smoothing and ELM to Predict Multi-Factor Landslide Displacement

The deformation of landslides is a non-linear dynamic and complex process due to the impacts of both inherent and external factors. Understanding the basis of landslide deformation is essential to prevent damage to properties and losses of life. To forecast the landslides displacement, a hybrid machine learning model is proposed, in which the Variational Modal Decomposition (VMD) is implemented to decompose the measured total surface displacement into the trend and periodic components. The Double Exponential Smoothing algorithm (DES) and Extreme Learning Machine (ELM) were adopted to predict the trend and the periodic displacement, respectively. Particle Swarm Optimization (PSO) algorithm was selected to obtain the optimal ELM model. The proposed method and implementation procedures were illustrated by a step-like landslide in the Three Gorges Reservoir area. For comparison, Least Square Support Vector Machine (LSSVM) and Convolutional Neutral Network–Gated Recurrent Unit (CNN–GRU) were also conducted with the same dataset to forecast the periodic component. The application results show that DES-PSO-ELM outperformed the other two methods in landslide displacement prediction, with RMSE, MAE, MAPE, and R2 values of 1.295mm, 0.998 mm, 0.008%, and 0.999, respectively.