Nonstationary Systems Research Articles

Prediction of unobserved bifurcation by unsupervised extraction of slowly time-varying system parameter dynamics from time series using reservoir computing

IntroductionNonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Machine learning methods have advanced our ability to learn and predict such systems from observed time series data. However, predicting the behavior of systems with temporal parameter variations without knowledge of true parameter values remains a significant challenge.MethodsThis study uses reservoir computing framework to address this problem by unsupervised extraction of slowly varying system parameters from time series data. We propose a model architecture consisting of a slow reservoir with long timescale internal dynamics and a fast reservoir with short timescale dynamics. The slow reservoir extracts the temporal variation of system parameters, which are then used to predict unknown bifurcations in the fast dynamics.ResultsThrough experiments on chaotic dynamical systems, our proposed model successfully extracted slowly varying system parameters and predicted bifurcations that were not included in the training data. The model demonstrated robust predictive performance, showing that the reservoir computing framework can handle nonlinear, non-stationary systems without prior knowledge of the system's true parameters.DiscussionOur approach shows potential for applications in fields such as neuroscience, material science, and weather prediction, where slow dynamics influencing qualitative changes are often unobservable.

Seeing the Big‐ to Fine‐Grained Picture: Exploring the Baseline Status of Mammal Occupancy Across Myanmar Using Scale‐Optimised Modelling

ABSTRACTAimMyanmar, an Indo‐Burmese biodiversity hotspot, lacks baseline data on species occurrence and distribution. This hinders biodiversity monitoring and optimisation of conservation and development plans. We aim to document baseline mammal occupancy, interactions with environmental factors and scale‐dependent responses.LocationHkakaborazi National Park, Htamanthi Wildlife Sanctuary, Alaungdaw Kathapa National Park, Rakhine Yoma Elephant Range, Say Taung and Myinmoletkhat Key Biodiversity Areas distributed across Myanmar.MethodsCamera trap data throughout Myanmar were used to analyse species occupancy. We conducted a multiscale hierarchical spatial modelling process, using local and pooled data across Myanmar. We also optimised spatial scale across five scales and six predictors, using univariate occupancy models. We then selected scale‐optimised variables for multivariate modelling, repeating this process for each species across local, regional and national datasets.ResultsThe study identified 47 terrestrial species and observed strong scale‐dependent nonstationarity in occupancy estimates. Relationships with environmental variables differed among species and were highly scale dependent. Importantly, occupancy estimates produced by pooling data across sites were greatly different from any of the estimates for the individual sites, suggesting that high heterogeneity in occurrence and abundance across sites among species requires local or nested occupancy estimates to account for spatial heterogeneity and variation.Main ConclusionsFuture conservation efforts should focus on Northern Myanmar if range‐restricted and rare species are to be protected, while focus should still be given to common species which serve as potential indicators of overall community structure. The nonstationarity of occupancy results from different datasets underscores the potential for misleading interpretations from aggregated data in nonstationary ecological systems. Metareplicated analyses of local, geographically and ecologically proximal regional datasets provide an important view of spatial variation in occupancy patterns guiding conservation design and improving understanding of the drivers of biodiversity patterns and change across large regions, such as Southeast Asia.

МЕТОД ТА ДОСЛІДЖЕННЯ ТОЧНОСТІ ОБЧИСЛЮВАННЯ МАТЕМАТИЧНОЇ МОДЕЛІ ЕЛЕКТРОГІДРАВЛІЧНОГО ЕФЕКТУ

The mathematical model of the electrohydraulic effect (EHE) is a nonlinear non-stationary system of partial differential equations (PDE), which reflects the motion and contact interaction of two media, gaseous and liquid, under the action of pulsed thermal excitation. Such PDE systems generally do not have analytical solutions and are solved only by numerical methods, which are approximate in nature, i.e. they provide a solution with some error. The peculiarity of the motion of media in the case of EHE is large deformations in the form of flows and vortices. This feature imposes significant restrictions on the choice of the method for solving the PDE model. The widely known Lagrangian finite element method used to solve contact problems, in the case of EHE modeling leads to a pathological change in the shape of the finite elements, and therefore to instability of the calculation process and an unlimited increase in error. In calculation practice, a variant of the finite element method, FEM-ALE, has become widespread. It uses both Lagrangian and Eulerian grids of nodes and a special advection procedure, i.e., transfer by interpolation of the solution from the Lagrangian grid to the Eulerian one, and then vice versa from the Eulerian one to another new Lagrangian grid. Such an additional interpolation procedure, which is used repeatedly in the calculation, leads to additional (in comparison with the Lagrangian FEM) errors. If the causes and kinetics, as well as the methods of error control in the case of the Lagrangian FEM, have been sufficiently studied in the literature, then the kinetics of error development in the simulation of the EGE using the FEM-ALE method has been practically not studied. The article is devoted to the study of the development of errors in the numerical solution in this particular case. An analytical solution of the problem in the asymptotic case for a technological system with a rigid chamber is obtained. This solution is analyzed in comparison with the numerical solution using the FEM-ALE method. Conclusions are made regarding the errors in calculating pressure as the main factor of mechanical impact of EGE on the technological object and technological equipment, as well as errors in calculating deformations of gaseous and liquid media.The scientific novelty consists in the development of a method for determining the accuracy of EHE parameter calculations using the MSE-ALE method. The practical value lies in determining the accuracy of calculating the parameters of the EHE mathematical model, which makes it possible to justify the use of numerical modeling as a method of researching technological processes and systems using EHE

Control-Oriented Modeling of a Solid Oxide Fuel Cell Affected by Redox Cycling Using a Novel Deep Learning Approach

Abstract A solid oxide fuel cell (SOFC) is a multiphysics system that involves heat transfer, mass transport, and electrochemical reactions to produce electrical power. Reduction and re-oxidation (Redox) cycling is a destructive reaction that can occur during SOFC operation. Redox induces various degradation mechanisms, such as electrode delamination, nickel agglomeration, and microstructural changes, which should be mitigated. The interplay of these mechanisms makes a post-Redox SOFC a nonlinear, time-varying, nonstationary dynamic system. Physics-based modeling of these complexities often leads to computationally expensive equations that are not suitable for the control and diagnostics of SOFCs. Here, a data-driven approach based on dilated convolutions and a self-attention mechanism is introduced to effectively capture the dynamics underlying SOFCs affected by Redox. Controlled Redox cycles are designed to collect appropriate experimental data for developing deep learning models, which are lacking in the current literature. The performance of the proposed model is validated on diverse unseen data sets gathered from different fuel cells and benchmarked against state-of-the-art models, in terms of prediction accuracy and computation complexity. The results indicate 31% accuracy improvement and 27% computation speed enhancement compared to the benchmarks.

An algorithm for simplified recurrence analysis.

Recurrence analysis applications are hindered by several issues including the selection of critical parameters, noise sensitivity, computational complexity, or the analysis of non-stationary systems. Great progresses have been made by the community to address these issues individually, yet the diversity of resulting techniques with often additional parameters as well as a lack of consensus still impedes its use by nonspecialists. We present a procedure for simplified recurrence analysis based on compact recurrence plots with automatized parameter selection and enhanced noise robustness, and that are suited to the analysis of complex non-stationary systems. This approach aims at supporting the expansion of recurrence analysis for currently challenging or future applications such as for large systems, on-site studies, or using machine learning. The method is demonstrated on both synthetic and real data showing promising results.

Spectral incremental dynamic methodology for nonlinear structural systems endowed with fractional derivative elements subjected to fully non-stationary stochastic excitation

A novel spectral incremental dynamic analysis methodology for analysing structural response in nonlinear systems with fractional derivative elements is presented, aligning with modern seismic design codes, like Eurocode 8. Drawing inspiration from the concept of fully non-stationary stochastic processes, the vector of the imposed seismic excitations is characterised by time and frequency evolving power spectra stochastically compatible with elastic response spectra of specified damping ratio and ground acceleration. The proposed method efficiently determines the nonlinear system time-dependent probability density functions for the non-stationary system response amplitude by employing potent nonlinear stochastic dynamics concepts, such as stochastic averaging and statistical linearisation. Unlike traditional incremental dynamic analysis curves found in the literature, the herein proposed method introduces a three-dimensional alternative counterpart, that of stochastic engineering demand parameter surfaces, providing with higher-order statistics of the system response. An additional noteworthy aspect involves the derivation of response evolutionary power spectra as function of spectral acceleration, offering a deeper insight into the underlying system dynamics. Besides its capabilities, the method maintains the coveted element of a particularly low associated computational cost, increasing its attractiveness and practicality among diverse applications of engineering interest. Numerical examples comprising the bilinear hysteretic model endowed with fractional derivative elements subject to an Eurocode 8 elastic design spectrum demonstrate the capabilities and reliability of the proposed methodology. Its accuracy is assessed by juxtaposing the derived results with germane Monte Carlo Simulation data.

Synthesis of adaptive observer for nonlinear nonstationary systems

Synthesis of adaptive observer for nonlinear nonstationary systems

Smoothness of Solutions to the Damping Problem for Nonstationary Control System with Delay of Neutral Type on the Whole Interval

Smoothness of Solutions to the Damping Problem for Nonstationary Control System with Delay of Neutral Type on the Whole Interval

Episodic Visual Hallucinations, Inference and Free Energy.

Understandings of how visual hallucinations appear have been highly influenced by generative approaches, in particular Friston's Active Inference conceptualization. Their core proposition is that these phenomena occur when hallucinatory expectations outweigh actual sensory data. This imbalance occurs as the brain seeks to minimize informational free energy, a measure of the distance between predicted and actual sensory data in a stationary open system. We review this approach in the light of old and new information on the role of environmental factors in episodic hallucinations. In particular, we highlight the possible relationship of specific visual triggers to the onset and offset of some episodes. We use an analogy from phase transitions in physics to explore factors which might account for intermittent shifts between veridical and hallucinatory vision. In these triggered forms of hallucinations, we suggest that there is a transient disturbance in the normal one-to-one correspondence between a real object and the counterpart perception such that this correspondence becomes between the real object and a hallucination. Generative models propose that a lack of information transfer from the environment to the brain is one of the key features of hallucinations. In contrast, we submit that specific information transfer is required at onset and offset in these cases. We propose that this transient one-to-one correspondence between environment and hallucination is mediated more by aberrant discriminative than by generative inference. Discriminative inference can be conceptualized as a process for maximizing shared information between the environment and perception within a self-organizing nonstationary system. We suggest that generative inference plays the greater role in established hallucinations and in the persistence of individual hallucinatory episodes. We further explore whether thermodynamic free energy may be an additional factor in why hallucinations are temporary. Future empirical research could productively concentrate on three areas. Firstly, subjective perceptual changes and parallel variations in brain function during specific transitions between veridical and hallucinatory vision to inform models of how episodes occur. Secondly, systematic investigation of the links between environment and hallucination episodes to probe the role of information transfer in triggering transitions between veridical and hallucinatory vision. Finally, changes in hallucinatory episodes over time to elucidate the role of learning on phenomenology. These empirical data will allow the potential roles of different forms of inference in the stages of hallucinatory episodes to be elucidated.

Design and construction of a versatile test bench for non-stationary fluid systems

Con el propósito de establecer una plataforma versátil para la investigación y enseñanza en ingeniería y ciencia de fluidos, se diseñó y construyó un banco de pruebas especializado para la Universidad Metropolitana. Este banco se enfoca en evaluar sistemas de fluidos no estacionarios, priorizando la medición precisa de caudal, presión y nivel en tanques. El desarrollo se centró en la selección de sensores y materiales de bajo costo, destacando la importancia de mediciones confiables y precisas. Se formuló un algoritmo en Matlab® para el cálculo sistemático de parámetros. La automatización se logró mediante un Arduino Mega, con la interfaz Humano-Máquina en Matlab® para facilitar la operación. Rigurosas pruebas demostraron la capacidad del banco para simular condiciones reales de manera efectiva. Los resultados, obtenidos experimentalmente y mediante Matlab®, respaldaron la eficacia y fiabilidad del sistema desarrollado, contribuyendo a la investigación y enseñanza en ingeniería y ciencia de fluidos.

Parallel Distributed Architecture of Linear Kalman Filter for Non-stationary MIMO Communication Systems

Parallel Distributed Architecture of Linear Kalman Filter for Non-stationary MIMO Communication Systems

COMPUTER MODELLING OF AERODYNAMIC FLOW OF A COMPLEX OF UNIQUE BUILDINGS

The way large-sized buildings interact with wind flows cannot be analyzed when considering such objects in isolation from their environment. The paper proposes a model representing such objects from the point of view of hydrogasodynamics as a system of bodies united by aerodynamic medium. A quantitative and qualitative assessment of the mutual influence of system objects on aerodynamic characteristics at different locations was performed. The results of computer modeling of the aerodynamic characteristics of two unique buildings in an isolated mode, as well as for various mutual positions in the system, using the methods of a computational experiment based on the numerical solution of non-stationary systems of Navier-Stokes differential equations are presented. The accuracy of the results obtained was monitored by conducting a model experiment in a wind tunnel. For the qualitative assessment of the mutual influence of objects on each other, the characteristics of the vector of the wind pressure force equalizing vector on each of the objects and the value of the equalizing moment at the base of the object most sensitive to its influence were determined. In this way, a quantitative assessment has been made that allows us to judge the redistribution of wind loads and the static characteristics of the system. On the basis of changes in their values the conclusion about the way the objects interact with wind flows depending on their initial geometric parameters and mutual location within the system was given.

Surrogate modeling with non-stationary-noise based Gaussian process regression and K-Fold ANN for systems featuring uneven sensitivity distribution

In the realm of aircraft design, there is a prevalent need for surrogate modeling techniques capable of efficiently and accurately modeling objects with high evaluation costs and uneven sensitivity distributions, such as those encountered in the nonlinear buckling of thin-walled structures and aerodynamics at transonic speeds. However, the non-stationary Gaussian Process Regression (GPR) model requires extensive hyperparameters or judicious assumptions, limiting its applications in such tasks, and the commonly used K-Fold methodology suffers from inherent instability. Addressing these issues, this paper proposes an active learning method for surrogate modeling in systems featuring uneven sensitivity distribution, integrating non-stationary-noise GPR and K-Fold Artificial Neural Network (ANN) methodology, namely NSN-GPR-KF. Instead of relying on a non-stationary kernel function, the algorithm regards noise as a non-stationary factor within a stationary GPR framework, with noise levels estimated via the K-Fold ANN methodology, allowing GPR to efficiently adapt to non-stationary systems while avoiding the aforementioned requirements for non-stationary GPR. Case validations, performed on two test functions with pronounced uneven spatial sensitivity, demonstrate that NSN-GPR-KF outperforms commonly used stationary GPR and pure K-Fold methodology. It synthesizes the exploration capabilities of GPR with the exploitation proficiency of the K-Fold methodology, achieving comparable global accuracy with reduced sample sizes—up to 26 % and 22 % less than the other two algorithms, respectively. The algorithm was successfully applied to predict the buckling load of thin-walled pipe beams, demonstrating accelerated convergence and approximately 25 % greater accuracy compared to pure K-Fold model. These results suggest that NSN-GPR-KF can serve as an efficient and precise modeling tool for engineering tasks with high evaluation costs and complex sensitivity distributions.

Smooth least absolute deviation estimators for outlier-proof identification

The paper proposes to identify the parameters of linear dynamic models based on the original implementation of least absolute deviation estimators. It is known that the object estimation procedures synthesized in the sense of the least sum of absolute prediction errors are particularly resistant to occasional outliers and gaps in the analyzed system data series, while the classical least squares procedure unfortunately becomes of little use for reliably identifying systems in the presence of destructive measurement errors. Bearing in mind that the classic task of minimizing the quality functional of absolute deviations encounters fundamental analytical problems, it is proposed to use a dedicated iterative estimator for off-line evaluation of the parameters of the analyzed process. In addition, a simplified recursive version of the absolute deviation estimation procedure was developed, which allows for practical on-line tracking of the evolution of variable parameters of non-stationary systems. Importantly, a novel refinement of the discussed absolute deviation estimators was proposed to effectively overcome some inconvenient numerical effects. We also present an interesting comparison of the improved (by non-linear modification) iterative absolute-deviation estimator with the classical Gauss-Newton gradient algorithm, which leads to constructive conclusions. Finally, using computer simulations, the operation of the developed iterative and recursive estimators minimizing the absolute deviation is illustrated. The work ends with an indication of directions for further research.

Double capture of coordinated evaders in recurrent differential games

In finite-dimensional Euclidean space, a problem of pursuit of two evaders by a group of pursuers, which is described by a linear nonstationary system of differential equations, is considered under the assumption that the fundamental matrix of the homogeneous system is a recurrent function. It is assumed that the evaders use the same control. The pursuers use counterstrategies based on information about the initial positions and the prehistory of the control of the evaders. The set of admissible controls is a strictly convex compact with a smooth boundary, and the goal sets are the origin of coordinates. The goal of the group of pursuers is to catch at least one evader by two pursuers. In terms of initial positions and parameters of the game, a sufficient condition for capture is obtained. This study is based on the method of resolving functions, which makes it possible to obtain sufficient conditions for solvability of the problem of pursuit in some guaranteed time.

Identifying Characteristic Fire Properties with Stationary and Non-Stationary Fire Alarm Systems.

The article reviews issues associated with the operation of stationary and non-stationary electronic fire alarm systems (FASs). These systems are employed for the fire protection of selected buildings (stationary) or to monitor vast areas, e.g., forests, airports, logistics hubs, etc. (non-stationary). An FAS is operated under various environmental conditions, indoor and outdoor, favourable or unfavourable to the operation process. Therefore, an FAS has to exhibit a reliable structure in terms of power supply and operation. To this end, the paper discusses a representative FAS monitoring a facility and presents basic tactical and technical assumptions for a non-stationary system. The authors reviewed fire detection methods in terms of fire characteristic values (FCVs) impacting detector sensors. Another part of the article focuses on false alarm causes. Assumptions behind the use of unmanned aerial vehicles (UAVs) with visible-range cameras (e.g., Aviotec) and thermal imaging were presented for non-stationary FASs. The FAS operation process model was defined and a computer simulation related to its operation was conducted. Analysing the FAS operation process in the form of models and graphs, and the conducted computer simulation enabled conclusions to be drawn. They may be applied for the design, ongoing maintenance and operation of an FAS. As part of the paper, the authors conducted a reliability analysis of a selected FAS based on the original performance tests of an actual system in operation. They formulated basic technical and tactical requirements applicable to stationary and mobile FASs detecting the so-called vast fires.

Determination of the Speed and Surface Temperature of Aircraft Using the Second Approximation of the System of Moment Equations

This study focuses on solving the initial-boundary value problem for a one-dimensional non-stationary nonlinear system of moment equations in the second approximation. We prove the existence of a unique local in-time solution of the problem under consideration in the space of functions that are continuous in time and square integrable over the spatial variable x. To solve the direct and inverse problems for this system, we develop an iterative numerical method and reduce the system of moment equations to canonical form. Furthermore, we present the software implementation of the algorithms and their application for solving inverse problems related to determining the speed and surface temperature of an aircraft, as well as atmospheric parameters. We provide the results of numerical experiments conducted to validate our approach.

Parameters of the runge-kutta method with different order of accuracy in the integration of dynamics equations in the problems of modelling non-stationary systems

Parameters of the runge-kutta method with different order of accuracy in the integration of dynamics equations in the problems of modelling non-stationary systems

Synthesis of an observer of state variables and sinusoidal disturbance for a linear nonstationary system with unknown parameters

Synthesis of an observer of state variables and sinusoidal disturbance for a linear nonstationary system with unknown parameters

An efficient non-negative least mean squares algorithm based on q-gradient for system identification

The system identification under non-negative constraints problem is a common and important one in the real-life problems. A non-negative least mean squares algorithm was proposed to address such problems. However, it suffers from slow and unbalanced convergence. Motivated by the introduction of non-Newtonian gradient in least mean squares algorithm can accelerate the convergence. In this paper, an efficient non-negative least mean squares algorithm based on q-gradient is developed. At first, the q-gradient of the mean square error cost function is derived from the definition of Jackson's derivative. Then, the modified algorithm is developed by replacing the conventional gradient with the q-gradient on a fixed-point iteration scheme using Karush-Kuhn-Tucker condition. Simulations for stationary and non-stationary system identification are conducted to illustrate the effectiveness of the developed algorithm for constrain the system parameters to be non-negative and accelerate the convergence speed. Besides, it can balance the convergence rate for widely distributed parameters, especially for the convergence of small parameters. For practical application, the accuracy of system identification when the order of the adaptive filter is larger than the order of the system is also verified by the simulation.