Nonlinear Dynamic Process Research Articles

Model predictive control of nonlinear processes using neural ordinary differential equation models

Neural Ordinary Differential Equation (NODE) is a recently proposed family of deep learning models that can perform a continuous approximation of a linear/nonlinear dynamic system using time-series data by integrating the neural network model with classical ordinary differential equation solvers. Modeling nonlinear dynamic processes using data has historically been a critical challenge in the field of chemical engineering research. With the development of computer science and neural network technology, recurrent neural networks (RNN) have become a popular black-box approach to accomplish this task and have been utilized to design model predictive control (MPC) systems. However, as a discrete-time approximation model, RNN requires strictly uniform step sequence data to operate, which makes it less robust to an irregular sampling scenario, such as missing data points during operation due to sensor failure or other types of random errors. This paper aims to develop a NODE model and construct an MPC based on this novel continuous-time neural network model. In this context, closed-loop stability is established and robustness to noise is addressed using a variety of data analysis techniques. An example of a chemical process is utilized to evaluate the performance of NODE-based MPC. Furthermore, the performance of the NODE-based MPC under Gaussian and non-Gaussian noise is investigated, and the subsampling method is found to be effective in building models for MPC that are suitable for handling the presence of non-Gaussian noise in the data.

Real-time temperature distribution reconstruction via linear parameter-varying state-space model and Kalman filter in rack-based cooling data centers

Rapidly growing data centers (DCs) are facing challenges with energy consumption increase and thermal environmental security. Thus, this paper proposed a novel real-time temperature distribution prediction and reconstruction model for rack-based cooling DCs, in order to facilitate efficient energy consumption and thermal environment management. The parameter identification method coupling with inherent physical relationships was employed to obtain the linear parameter-varying state-space model, rapidly and approximately predicting the nonlinear thermal dynamic processes within rack-based cooling DC. Then, Kalman filter was adopted to reconstruct the temperature distribution in real-time based upon the developed linear parameter-varying state-space temperature prediction model and measurement information. This study comprehensively analyzed the temperature estimation performance of the proposed model under various model input biases, different sensor numbers and layouts. The results show that the input biases have significant impacts on the accuracy of the temperature prediction model, e.g., ±5% bias in IT workload resulting in an increase of 0.6 times in the mean absolute error (MAE) of the temperature prediction. The proposed temperature reconstruction model reveals excellent performance: compared to the original temperature prediction model, the MAE was decreased by about 5%, 10%, and 13% for reconstruction scenarios using one, two, and three sensors, respectively.

Monitoring Multimode Nonlinear Dynamic Processes: An Efficient Sparse Dynamic Approach With Continual Learning Ability

Industrial processes generally operate under multiple modes and a global monitoring approach, built upon combining local models which are aimed at each mode, requires complete data from all potential modes to be available. However, practical data are generated and collected in a steady stream, which makes it difficult if not impossible to process. This paper proposes an efficient sparse dynamic inner principal component analysis algorithm for multimode nonlinear dynamic process monitoring, which aims to build a single monitoring model with continual learning ability for successive modes. To reduce the storage and computational costs, only a few representative data from each mode are selected based on cosine similarity and replayed for retraining when a new mode arrives, which are sufficient to reflect the operating condition of each mode. Inspired by replay continual learning, data from all existing modes are preprocessed by its own statistics and then regarded as a whole data set, followed by building a single multimode monitoring model. The multimode dynamic latent variables are extracted from data in raw format, via a vector autoregressive model. Therefore, the proposed method is not constrained by the mode similarity, which makes it appropriate for diverse modes and convenient for long-term monitoring tasks. Besides, the proposed method can deal with nonlinearity and a regularization term is added to avoid the potential overfitting issue. Compared with state-of-the-art multimode monitoring methods, the effectiveness of the proposed approach is demonstrated by continuous stirred tank heater and a practical industrial system.

Nonlinear and periodic dynamics of chaotic hydro-thermal process of Skokomish river

Nonlinear and periodic dynamics of chaotic hydro-thermal process of Skokomish river

ENVIRONMENT-BASED DESIGN (EBD): USING ONLY NECESSARY KNOWLEDGE FOR DESIGNER CREATIVITY

AbstractDesign is a highly nonlinear chaotic dynamic process with many possible solutions, which requires enormous knowledge for designers. This paper investigates how environment-based design (EBD) methodology can help designers use only necessary knowledge for their creativity based on three methods: information search, knowledge acquisition and knowledge application. The methods are applied in an aircraft pylon design, which is evaluated by two aerospace design specialists. The paper discussed the different roles of EBD for novice and expert designers in regard to overcoming emotion and knowledge barriers to achieving designer creativity.

THEORETICAL AND METHODOLOGICAL ASPECTS FOR THE DEVELOPMENT OF A CREATIVE ECONOMY IN THE CONTEXT OF THE FORMATION OF AN INNOVATIVE BUSINESS ECOSYSTEM

The aim of the study is to analyze the theoretical basis of creative economy and its development trends in the context of innovative business ecosystems formation. The scientific novelty of the research consists in solving the most important scientific and applied problem - further development of theoretical provisions of creative economy, ecosystems, as well as substantiation of the conceptual approach to the formation of innovative business ecosystem as a coherent management model. In the process of research, general scientific and special methods were used: scientific abstraction, deduction, analysis and synthesis, system and critical analysis, structural-logical, ascending from the abstract to the concrete, and statistical analysis. It has been substantiated that the priority development of creative economy as a strategic driver of sustainable development is the formation of an ecosystem conducive to the development of complex non-linear dynamic innovation processes, development of value propositions and value chain. The analysis of theoretical and methodological aspects of formation and functioning of ecosystems indicates the lack of development of this problem and the need to develop scientific approaches to their identification. Generalization of the results of theoretical analysis allowed us to group ecosystems according to the identified attributes into five main types. It was substantiated that a sustainable business ecosystem is a favorable environment for innovation to increase its value and contribute to the achievement of sustainable development goals. It is proposed to consider a sustainable "business ecosystem" as a coherent management model with established characteristics, which describes an aggregate system of business ecosystem modules that interact with each other and are focused on co-creation and co-production of value.

A multi-scale transition matrix approach to chaotic time series

There exist rich patterns in nonlinear dynamical processes, but they merge into averages in traditional statistics-based time series analysis. Herein the multi-scale transition matrix is adopted to display the patterns and their evolutions in several typical chaotic systems, including the Logistic Map, the Tent Map, and the Lorentz System. Compared with Markovian processes, there appear rich non-trivial patterns. The unpredictability of transitions matches almost exactly with the Lyapunov exponent. The eigenvalues decay exponentially with respect to the time scale, whose decaying exponents give us the details in the curves of Lyapunov exponent versus dynamical parameters. The evolutionary behaviors differ with each other and do not saturate to the ones for the corresponding shuffled series.

Special Issue: Nonlinear Dynamics in Complex Systems via Fractals and Fractional Calculus

Advances in our knowledge of nonlinear dynamical networks, systems and processes (as well as their unified repercussions) currently allow us to study many typical complex phenomena taking place in nature, from the nanoscale to the extra-galactic scale, in an comprehensive manner [...]

Modeling of Nonlinear Dynamic Processes of Human Movement in Virtual Reality Based on Digital Shadows

In virtual reality (VR) systems, a problem is the accurate reproduction of the user’s body in a virtual environment using inverse kinematics because existing motion capture systems have a number of drawbacks, and minimizing the number of key tracking points (KTPs) leads to a large error. To solve this problem, it is proposed to use the concept of a digital shadow and machine learning technologies to optimize the number of KTPs. A technique for movement process data collecting from a virtual avatar is implemented, modeling of nonlinear dynamic processes of human movement based on a digital shadow is carried out, the problem of optimizing the number of KTP is formulated, and an overview of the applied machine learning algorithms and metrics for their evaluation is given. An experiment on a dataset formed from virtual avatar movements shows the following results: three KTPs do not provide sufficient reconstruction accuracy, the choice of five or seven KTPs is optimal; among the algorithms, the most efficient in descending order are AdaBoostRegressor, LinearRegression, and SGDRegressor. During the reconstruction using AdaBoostRegressor, the maximum deviation is not more than 0.25 m, and the average is not more than 0.10 m.

Stability of the RC Column under Horizontal Impacts

Approaches to assessment of stability of reinforced concrete columns in case of horizontal emergency impact have been investigated. For this purpose, finite-element modeling of the system in spatial formulation, calculation according to the deformed scheme in the scope of nonlinear static analysis and dynamic transient process have been implemented. When constructing the model, the hexahedral elements were used, working in accordance with the Drucker-Prager model for concrete, and the rebars deformed according to the Prandtl model were used to modelling the reinforcement.The impact action was considered as a short-term pulse of constant intensity. Dependence diagrams for critical force on various scenarios of emergency impacts on the column have been obtained. Results of researches can be used for an estimation of resistance to the progressive collapse of reinforced concrete structures at their variants design and optimization.

Changes in oscillatory and nonlinear dynamic processes of microcirculation in patients with obliterating atherosclerosis of lower limb arteries after revascularization

Aim: To study the nature of changes in oscillatory and nonlinear dynamic processes in the skin microcirculatory system by laser Doppler flowmetry in patients with obliterating atherosclerosis of the lower limbs arteries (OALLA) after limb revascularization.Material and Methods. 27 male patients with OALLA before and after endovascular revascularization of the affected limb (median age 63.0 [60.0; 69.0] years) were studied. Microcirculation (MC) of the foot skin with assessment of nonlinear dynamic processes and spectral wavelet analysis of blood flow fluctuations was studied by laser Doppler flowmetry. The normalized amplitude indices of blood flow fluctuations were determined in frequency ranges reflecting: endothelial, neurogenic, myogenic, respiratory, pulse factors of hemocirculation. Bypass parameters and nutritive blood flow were assessed. An occlusion test was performed to determine capillary blood flow reserve. The study of nonlinear dynamic processes included assessment of fractal dimension, entropy determination and phase portrait analysis.Results. Limb revascularization in patients with OALLA resulted in improvement of the clinical picture accompanied by statistically significant increase in nutritive blood flow (+9.7%) and reserved dilatation potential of microvessels (+43.2%), decrease in arteriolo-venular blood shunting (–5.0%) and venous plethora (–14.3%). The analysis of nonlinear dynamic processes of the MC showed that after angioplasty, along with the remaining deficit of oscillatory processes energy, there was a decrease in the fractal dimension index (–14.3%), indicating the limitation of lability of the functional system of the microvascular bed. At the same time, an increase in the chaotization of the regulatory mechanisms of the peripheral blood flow was established.Conclusions. The results showed positive functional changes of the MC system associated with the improved clinical picture in patients with OALLA after limb revascularization. At the same time, changes in the nonlinear dynamics parameters indicate a compensatory increase in the chaotization of the system together with the remaining limitation of its functional lability and the energy deficit of oscillatory processes.

Novel adaptive fault detection method based on kernel entropy component analysis integrating moving window of dissimilarity for nonlinear dynamic processes

Fault detection of nonlinear dynamic processes can ensure the safety of industrial production processes. Industrial process data are mostly autocorrelated along with strong nonlinear characteristics. And these significant characteristics interact with each other and limit the fault detection performance of traditional methods. Therefore, this paper presents a novel adaptive fault detection method for nonlinear dynamic processes based on kernel entropy component analysis (KECA) integrating the moving window of dissimilarity (DMW) (KECA-DMW). The KECA is used to map the raw data and capture the nonlinear features of the data, which combine with moving window techniques to build the fault detection model. In the process of updating the data in the moving window, the data information of the historical window is combined with that of the current window to obtain a more comprehensive judgment of the current moment. Then a dynamic update fusion method with adaptive weight allocation based on the dissimilarity index is proposed by analyzing the data characteristics of window information at different moments through the dissimilarity. Finally, three example studies with a numerical example, a closed-loop continuously stirred tank reactor and a Tennessee-Eastman process are used to validate the effectiveness of the proposed method. Compared with other nonlinear dynamic process fault detection methods, the results verify the effectiveness of the proposed method in the process monitoring performance of nonlinear dynamic processes in terms of false alarm rate and fault detection rate, where the false alarm rates of the proposed method are only 2%, 1.83%, and 4.33%, while the fault detection rates are 97.4%, 96.83%, and 86.25%, respectively.

A new hybrid approach for the prediction of corrosion due to DC stray currents emitted by electrical traction and nonlinear dynamic process monitoring

A new hybrid approach for the prediction of corrosion due to DC stray currents emitted by electrical traction and nonlinear dynamic process monitoring

A purely data-driven framework for prediction, optimization, and control of networked processes

Networks are landmarks of many complex phenomena where interweaving interactions between different agents transform simple local rule-sets into nonlinear emergent behaviors. While some recent studies unveil associations between the network structure and the underlying dynamical process, identifying stochastic nonlinear dynamical processes continues to be an outstanding problem. Here, we develop a simple data-driven framework based on operator-theoretic techniques to identify and control stochastic nonlinear dynamics taking place over large-scale networks. The proposed approach requires no prior knowledge of the network structure and identifies the underlying dynamics solely using a collection of two-step snapshots of the states. This data-driven system identification is achieved by using the Koopman operator to find a low-dimensional representation of the dynamical patterns that evolve linearly. Further, we use the global linear Koopman model to solve critical control problems by applying to model predictive control (MPC)–typically, a challenging proposition when applied to large networks. We show that our proposed approach tackles this by converting the original nonlinear programming into a more tractable optimization problem that is both convex (quadratic programming) and with far fewer variables.

Real-time measurement-driven reinforcement learning control approach for uncertain nonlinear systems

The paper introduces an interactive machine learning mechanism to process the measurements of an uncertain, nonlinear dynamic process and hence advise an actuation strategy in real-time. For concept demonstration, a trajectory-following optimization problem of a Kinova robotic arm is solved using an integral reinforcement learning approach with guaranteed stability for slowly varying dynamics. The solution is implemented using a model-free value iteration process to solve the integral temporal difference equations of the problem. The performance of the proposed technique is benchmarked against that of another model-free high-order approach and is validated for dynamic payload and disturbances. Unlike its benchmark, the proposed adaptive strategy is capable of handling extreme process variations. This is experimentally demonstrated by introducing static and time-varying payloads close to the rated maximum payload capacity of the manipulator arm. The comparison algorithm exhibited up to a seven-fold percent overshoot compared to the proposed integral reinforcement learning solution. The robustness of the algorithm is further validated by disturbing the real-time adapted strategy gains with a white noise of a standard deviation as high as 5%.

Optimal tracking control for blast furnace molten iron quality based on subspace identification and Krotov's method

SummaryBlast furnace ironmaking is a complex nonlinear dynamic process, which has strict requirements on the quality of final molten iron. To improve the control effect of molten iron quality, this paper proposes an optimal tracking control method for molten iron quality based on the bilinear subspace identification and Krotov's method. First, a state space model between key process variables and blast furnace molten iron quality, using the bilinear subspace identification method, is established based on actual industrial data. Then, an augmented system is established combining the state vector and the reference trajectory, and the improving feedback controller is designed by solving a set of Riccati equations, which are established based on Krotov's method. In combination with the designed controller and the established system, the specific implementation steps are proposed. Finally, the effectiveness and advancement of the proposed method are verified based on actual industrial data of a large blast furnace.

Earthquake fault slip and nonlinear dynamics

Earthquake fault slip under shear forcing can be envisioned as a nonlinear dynamical process dominated by a single slip plane. In contrast, nonlinear behavior in Earth materials (e.g., rock) is driven by a strain-induced ensemble activation and slip of a large number of distributed features—cracks and grain boundary slip across many scales in the volume. The bulk recovery of a fault post-failure and that of a rock sample post dynamic or static forcing (”aging” or the “slow dynamics”) is very similar with approximate log(time) dependence for much of the recovery. In our work, we analyze large amounts of continuous acoustic emission (AE) data from a laboratory “earthquake machine,” applying machine learning, with the task of determining what information regarding fault slip the AE signal may carry. Applying the continuous AE as input to machine learning models and using measured fault friction, displacement, etc., as model labels, we find that the AE are imprinted with information regarding the fault friction and displacement. We are currently developing approaches to probe stick-slip on Earth faults, those that are responsible for damaging earthquakes. A related goal is to quantitatively relate nonlinear elastic theory (e.g., PM space, Arrhenius) to frictional theory (e.g., rate-state).

Least Square Support Vector Machines Laguerre Hammerstein Model Identification and Non-linear Model Predictive Controller Design for pH Neutralization Process

The ability to describe the nonlinear process dynamics is an essential feature of the Hammerstein model that paved more research and application studies in system identification and control. Using the Hammerstein model, this study shows an alternative approach to identify and control the highly nonlinear pH neutralization process. This Hammerstein model called Laguerre Least Square Support Vector Machines (LLSSVM) models the static nonlinearity with LSSVM and the linear part with Laguerre filter. The identified LLSSVM Hammerstein model performance evaluation with Mean Squared Error (MSE) and Variance Accounted For (VAF) is better than the Linear Laguerre model. We apply the identified LLSSVM Hammerstein model to implement a Nonlinear Model Predictive Controller (NMPC) to control the pH neutralization process. Then evaluated NMPC performance in terms of Integral Squared Error (ISE), Integral Absolute Error (IAE), and Total Variation (TV) and Control Effort (CE) parameters to verify its effectiveness in set-point tracking and disturbance rejection problems. The comparison of the NMPC with the Linear Laguerre Model-based Predictive Controller (LMPC) shows better performance of the NMPC than the LMPC. Results show that the LLSSVM Hammerstein model replicates the pH neutralization process well than the Linear Laguerre model. Also, the identified LLSSVM Hammerstein model provides an efficient NMPC than the LMPC for the pH neutralization process.

Demand response for flat nonlinear MIMO processes using dynamic ramping constraints

Volatile electricity prices make demand response attractive for processes that can modulate their production rate. However, if nonlinear dynamic processes must be scheduled simultaneously with their local multi-energy system, the resulting scheduling optimization problems often cannot be solved in real time. For single-input single-output processes, the problem can be simplified without sacrificing feasibility by dynamic ramping constraints that define a derivative of the production rate as the ramping degree of freedom. In this work, we extend dynamic ramping constraints to flat multi-input multi-output processes by a coordinate transformation that gives the true nonlinear ramping limits. Approximating these ramping limits by piecewise affine functions gives a mixed-integer linear formulation that guarantees feasible operation. As a case study, dynamic ramping constraints are derived for a heated reactor-separator process that is subsequently scheduled simultaneously with its multi-energy system. The dynamic ramping formulation bridges the gap between rigorous process models and simplified process representations for real-time scheduling.

A data‐driven soft sensor based on weighted probabilistic slow feature analysis for nonlinear dynamic chemical processes

AbstractModeling high‐dimensional dynamic processes is a challenging task. In this regard, probabilistic slow feature analysis (PSFA) is revealed to be advantageous for dynamic soft sensor modeling, which can extract slowly varying intrinsic features from high‐dimensional data. However, nonlinearities prevalent in industrial processes are not considered, which could lead to unsatisfactory prediction performance. In this paper, a weighted PSFA (WPSFA)‐based soft sensor model is proposed for nonlinear dynamic chemical process. In WPSFA, a weighted log‐likelihood function of complete data is constructed to linearize the nonlinear state emission equation. Then, the expectation maximization algorithm is applied to estimate the model parameters and a locally weighted regression model is established for quality prediction. Finally, the feasibility and effectiveness of the proposed approach are well illustrated through a numerical example and a real industrial process.