Nonstationary Systems Research Articles

A Deep Learning Neural Network Method Using Linear Eigenvalue Statistics for Schizophrenic EEG Data Classification

Electroencephalography (EEG) signals can be used as a neuroimaging indicator to analyze brain-related diseases and mental states, such as schizophrenia, which is a common and serious mental disorder. However, the main limiting factor of using EEG data to support clinical schizophrenia diagnosis lies in the inadequacy of both objective characteristics and effective data analysis techniques. Random matrix theory (RMT) and its linear eigenvalue statistics (LES) can provide an effective mathematical modeling method for exploring the statistical properties of non-stationary nonlinear systems, such as EEG signals. To obtain an accurate classification and diagnosis of schizophrenia, this paper proposes a LES-based deep learning network scheme in which a series of random matrixes, consisting of EEG data sliding window sampling and their eigenvalues, are employed as features for deep learning. Due to the fact that the performance of the LES-based scheme is sensitive to the LES’s test function, the proposed LES-based deep learning network is embedded with two ways of combining LES’s test functions with learning techniques: the first is to have the LES’s test function assigned, while, using the second way, the optimal LES’s test function should be solved in a functional optimization problem. In this paper, various test functions and different optimal learning methods were coupled in experiments. Our results revealed a binary classification accuracy of nearly 90% in distinguishing between healthy controls (HC) and patients experiencing the first episode of schizophrenia (FES). Additionally, we achieved a ternary classification accuracy of approximately 70% by including clinical high risk for psychosis (CHR). The LES-embedded approach yielded notably higher classification accuracy compared to conventional machine learning methods and standard convolutional neural networks. As the performance of schizophrenia classification is strongly influenced by test functions, a functional optimization problem was proposed to identify an optimized test function, and an approximated parameter optimization problem was introduced to limit the search area of suitable basis functions. Furthermore, the parameterization test function optimization problem and the deep learning network were coupled to be synchronously optimized during the training process. The proposal approach achieved higher classification accuracy rates of 96.87% between HC and FES, with an additional 89.06% accuracy when CHR was included. The experimental studies demonstrated that the proposed LES-based method was significantly effective for schizophrenic EEG data classification.

Khronometric Theories of Modified Newtonian Dynamics

In 2011 Blanchet and Marsat suggested a fully relativistic version of Milgrom's modified Newtonian dynamics in which the dynamical degrees of freedom consist of the spacetime metric and a foliation of spacetime, the khronon field. This theory is simpler than the alternative relativistic formulations. We show that the theory has a consistent nonrelativistic or slow-motion limit. Blanchet and Marsat showed that in the slow motion limit, the theory reproduces stationary solutions of modified Newtonian dynamics. We show that these solutions are stable to khronon perturbations in the low acceleration regime, for the cases of spherical, cylindrical, and planar symmetry. For nonstationary systems in the low acceleration regime, we show that the khronon field generally gives an order unity correction to the modified Newtonian dynamics. In particular, there will be an order unity correction to the MOND version of Kepler's third law, potentially relevant to ongoing efforts to test MOND using GAIA observations of wide binaries.

GVFs in the real world: making predictions online for water treatment

In this paper we investigate the use of reinforcement-learning based prediction approaches for a real drinking-water treatment plant. Developing such a prediction system is a critical step on the path to optimizing and automating water treatment. Before that, there are many questions to answer about the predictability of the data, suitable neural network architectures, how to overcome partial observability and more. We first describe this dataset, and highlight challenges with seasonality, nonstationarity, partial observability, and heterogeneity across sensors and operation modes of the plant. We then describe General Value Function (GVF) predictions—discounted cumulative sums of observations–and highlight why they might be preferable to classical n-step predictions common in time series prediction. We discuss how to use offline data to appropriately pre-train our temporal difference learning (TD) agents that learn these GVF predictions, including how to select hyperparameters for online fine-tuning in deployment. We find that the TD-prediction agent obtains an overall lower normalized mean-squared error than the n-step prediction agent. Finally, we show the importance of learning in deployment, by comparing a TD agent trained purely offline with no online updating to a TD agent that learns online. This final result is one of the first to motivate the importance of adapting predictions in real-time, for non-stationary high-volume systems in the real world.

On the сontrollability, observability, and optimization of discrete nonstationary linear Volterra systems

In this article, we study discrete nonstationary linear dynamic systems of Volterra type. An essential feature of such kind of systems is that their current states depend on the previous states of this system. The formula Cauchy, which gives us the solution of linear Volterra systems with the control inputs, is obtained. The necessary and sufficient conditions of the pointwise controllability, pointwise output controllability, and observability are proven. Also the linear-quadratic optimization problem for the nonstationary Volterra control systems is studied.

Weighted Dynamic Time Warping for Time Series

Recurrence network is a typical time series analysis method. However, irregular sampling may overshadow the dynamic features characterized by traditional recurrence network method, which makes the method ineffective. This paper introduces dynamic time warping method to determine the distance between time series segments. The method can match the features of time series segments and reduce the distortion of distances caused by irregular sampling. For points in sparse sampling area, many characteristics may not be collected and thus the matching results are unreliable. To overcome this problem, we further propose weighted dynamic time warping method which assigns small weights to matching points with sparse local sampling so as to reduce their influence on distance. A recurrence network constructed by weighted dynamic time warping method can effectively capture underlying nonlinear and nonstationary system dynamics from irregular sampling time series. The effectiveness of the proposed method is illustrated by two case studies: the discrimination of different dynamic behaviors and detection of system parameter perturbation from time series of Rössler system.

Algorithm for Calculating Noise Immunity of Cognitive Dynamic Systems in the State Space

The research method consists in applying the state space method, widely used in the study of automatic dynamical systems, to describe the behavior of cognitive systems. It is assumed, that at the input of the cognitive system, there is a signal and interference described by Poisson point processes, modeling the amount of information, the amount of emotional stress, etc., corresponding to each event. The cognitive properties of the system in the paper are taken into account by two circumstances. Firstly, events localized in time are characterized in the paper not only by the Poisson distribution of the times of their occurrence, but also by some random variables that characterize the importance (significance) events for the system. A typical example is the attribution of a certain amount of information to each event, if an information processing system is modeled. Another example is the emotional reaction of a person to the appearance of stress, described in a classic work on psychology. In this case, the point is the event that causes stress, and the effects of stress on the system are modeled by the relative magnitude of stress in accordance with the Holmes and Rahe scale. Secondly, the cognitive system processes, assimilates, adapts to the impact that each event has on it with its inherent speed. In this paper, this phenomenon is modeled as the passage of a point process through a dynamic system described by differential equations. Such processes are called filtered point processes. Examples of impacts are given and, for simplicity, an assumption is made about the magnitude of the impact as the amount of information received by the system when an event occurs. Thus, the model of a cognitive system is a dynamic system described by a differential equation in the state space, at the input of which messages with a certain information load appear at random discrete moments of time.As for any technical system, the cognitive system faces the task of evaluating the quality of its work. In this regard, the paper substantiates the use of a convenient quality index from an engineering point of view and an appropriate criterion in the form of a signal – interference ratio. The new results are differential equations in the state space for the mathematical expectations of the signal and interference, as well as an algorithm for calculating the noise immunity of the cognitive system. As an example, a graph of the noise immunity of a particular cognitive system is calculated and presented, confirming an intuitive idea of its behavior.In conclusion, it is noted that the main result of the paper is an algorithm for calculating the noise immunity of cognitive systems using differential equations that allow calculating the behavior of non-stationary cognitive systems under any point impacts described by a non-stationary function of the intensities of the appearance of points. The equations of behavior of the mathematical expectation of the processed information are reduced to a canonical form, which allows them to be applied to a variety of practical tasks, for example, to the description of hierarchical cognitive structures when the output of one level is the input of another.

Adaptive observer of state variables of a nonlinear nonstationary system with unknown constant parameters

Adaptive observer of state variables of a nonlinear nonstationary system with unknown constant parameters

Wind Speed Modeling for Wind Farms Based on Deterministic Broad Learning System

As the penetration rate of wind power in the grid continues to increase, wind speed forecasting plays a crucial role in wind power generation systems. Wind speed prediction helps optimize the operation and management of wind power generation, enhancing efficiency and reliability. However, wind speed is a nonlinear and nonstationary system, and traditional statistical methods and classical intelligent algorithms struggle to cope with dynamically updating operating conditions based on sampled data. Therefore, from the perspective of optimizing intelligent algorithms, a wind speed prediction model for wind farms was researched. In this study, we propose the Deterministic Broad Learning System (DBLS) algorithm for wind farm wind speed prediction. It effectively addresses the issues of data saturation and local minima that often occur in continuous-time system modeling. To adapt to the continuous updating of sample data, we improve the sample input of the Broad Learning System (BLS) by using a fixed-width input. When new samples are added, an equivalent number of old samples is removed to maintain the same input width, ensuring the feature capture capability of the model. Additionally, we construct a dataset of wind speed samples from 10 wind farms in Gansu Province, China. Based on this dataset, we conducted comparative experiments between the DBLS and other algorithms such as Random Forest (RF), Support Vector Regression (SVR), Extreme Learning Machines (ELM), and BLS. The comparison analysis of different algorithms was conducted using Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). Among them, the DBLS algorithm exhibited the best performance. The RMSE of the DBLS ranged from 0.762 m/s to 0.776 m/s, and the MAPE of the DBLS ranged from 0.138 to 0.149.

A Tutorial on the Basics of Time-Varying Electromagnetic Systems and Circuits: Historic overview and basic concepts of time-modulation

During the last decade, possibilities to realize new phenomena and create new applications by varying system properties in time have gained increasing attention in many research fields. Although the interest in using time-modulation techniques for engineering electromagnetic (EM) response has become revitalized only in recent years, the field originates from the middle of the previous century, and a multitude of works have been published ever since. In this tutorial article, we provide a historical picture and review the basic concepts in this field. In particular, we introduce the general theory of linear time-varying (LTV) systems and discuss the means to properly account for frequency dispersion of nonstationary systems. Also, we elucidate models of time-varying electrical circuits and materials and discuss some useful effects that can be achieved by time modulation of circuit or material parameters.

Research on CNN-LSTM Brake Pad Wear Condition Monitoring Based on GTO Multi-Objective Optimization

As the core component of the automobile braking system, brake pads have a complex structure and high failure rate. Their accurate and effective state monitoring can help to evaluate the safety performance of brake pads and avoid accidents caused by brake failure. The wear process of automobile brake pads is a gradual, nonlinear, and non-stationary time-varying system, and it is difficult to extract its features. Therefore, this paper proposes a CNN-LSTM brake pad wear state monitoring method. This method uses a Convolutional Neural Network (CNN) to complete the deep mining of brake pad wear characteristics and realize data dimensionality reduction, and a Long Short-Term Memory (LSTM) network to capture the time dependence of the brake pad wear sequence, so as to construct the nonlinear mapping relationship between brake pad wear characteristics and brake pad wear values. At the same time, the artificial Gorilla Troops Optimization (GTO) algorithm is used to perform multi-objective optimization of the network structure parameters in the CNN-LSTM model, and its powerful global search ability improves the monitoring effect of the brake pad wear status. The results show that the CNN-LSTM model based on GTO multi-objective optimization can effectively monitor the wear state of brake pads, and its coefficient of determination R2 value is 0.9944, the root mean square error RMSE value is 0.0023, and the mean absolute error MAE value is 0.0017. Compared with the BP model, CNN model, LSTM model, and CNN-LSTM model, the value of the coefficient of determination R2 is the closest to 1, which is increased by 8.29%, 5.52%, 4.47%, 3.30%, respectively, which can more effectively realize the monitoring and intelligent early warning of the brake pad wear state.

State space model-based harmonic decomposition of pseudo-periodic non-stationary multivariate signals

This work is concerned with the harmonic decomposition of pseudo-periodic non-stationary multivariate signals. In this framework, a signal component corresponds to a single sinusoid with time-dependent amplitude and frequency. Thus, in the proposed harmonic decomposition, all the signal components are bound to share the same fundamental time-dependent frequency. Here, we establish a procedure to yield such decomposition by casting the multivariate signal into a block-diagonal state-space representation with multiple outputs. The harmonic components and instantaneous frequency are estimated using Kalman filtering. In addition, we provide an optimisation framework for the hyperparameters of the state space representation based on the Expectation-Maximisation algorithm. The proposed method provides an accurate, compact and physically explainable procedure for analysing pseudo-periodic non-stationary multiple-output systems, as demonstrated in the case of a simulated unbalanced rotor system and on real electrocardiographic records.

APPLICATION OF SPLINE FUNCTIONS AND WALSH FUNCTIONS IN PROBLEMS OF PARAMETRIC IDENTIFICATION OF LINEAR NONSTATIONARY SYSTEMS

Context. In this article, a generalized parametric identification procedure for linear nonstationary systems is proposed, which uses spline functions and orthogonal expansion in a series according to the Walsh function system, which makes it possible to find estimates of the desired parameters by minimizing the integral quadratic criterion of discrepancy based on solving a system of linear algebraic equations for a wide class of linear dynamical systems. The accuracy of parameter estimation is ensured by constructing a spline with a given accuracy and choosing the number of terms of the Walsh series expansion when solving systems of linear algebraic equations by the A. N. Tikhonov regularization method. To improve the accuracy of the assessment, an algorithm for adaptive partitioning of the observation interval is proposed. The partitioning criterion is the weighted square of the discrepancy between the state variables of the control object and the state variables of the model. The choice of the number of terms of the expansion into the Walsh series is carried out on the basis of adaptive approximation of non-stationary parameters in the observation interval, based on the specified accuracy of their estimates. The quality of the management of objects with variable parameters is largely determined by the accuracy of the evaluation of their parameters. Hence, obtaining reliable information about the actual nature of parameter changes is undoubtedly an urgent task.
 Objective. Improving the accuracy of parameter estimation of a wide class of linear dynamical systems through the joint use of spline functions and Walsh functions.
 Method. A generalized parametric identification procedure for a wide class of linear dynamical systems is proposed. The choice of the number of terms of the expansion into the Walsh series is made on the basis of the proposed algorithm for adaptive partitioning of the observation interval.
 Results. The results of modeling of specific linear non-stationary systems confirm the effectiveness of using the proposed approaches to estimating non-stationary parameters.
 Conclusions. The joint use of spline functions and Walsh functions makes it possible, based on the proposed generalized parametric identification procedure, to obtain analytically estimated parameters, which is very convenient for subsequent use in the synthesis of optimal controls of real technical objects. This procedure is applicable to a wide class of linear dynamical systems with concentrated and distributed parameters.

Stability analysis of nonstationary mechanical systems with time delay via averaging method

A linear mechanical system with constant matrix of dissipative forces and continuous and bounded matrices of positional forces is studied. It is assumed that there are a large positive multiplier at the vector of dissipative forces and a constant delay in positional forces. The case is considered where the associated delay-free averaged system is asymptotically stable. With the aid of the Lyapunov direct method and the averaging method, conditions are derived under which neither delay nor timevarying perturbations with zero mean values disturb the asymptotic stability. The developed approach is used in the problem of monoaxial stabilization of a rigid body.

Достаточные условия существования Н∝ -наблюдателя состояния линейных непрерывных динамических систем

<p>The article deals with the problem of finding the observer of the state vector of linear continuous non-stationary dynamical systems with uncertainty of the initial conditions, limited external influences and measurement errors over a finite time interval. Sufficient conditions for the existence of an observer are formulated and proved on the basis of the expansion principle. Relationships are obtained for finding the parameters of the observer and the worst laws of change in external influences and measurement errors. As a limiting case, the problem of observer synthesis for stationary linear dynamical systems on a semi-infinite time interval is considered. Two applied problems of estimating the aircraft state vector based on the results of incomplete and inaccurate measurements are solved.</p>

AdapSafe: Adaptive and Safe-Certified Deep Reinforcement Learning-Based Frequency Control for Carbon-Neutral Power Systems

With the increasing penetration of inverter-based renewable energy resources, deep reinforcement learning (DRL) has been proposed as one of the most promising solutions to realize real-time and autonomous control for future carbon-neutral power systems. In particular, DRL-based frequency control approaches have been extensively investigated to overcome the limitations of model-based approaches, such as the computational cost and scalability for large-scale systems. Nevertheless, the real-world implementation of DRLbased frequency control methods is facing the following fundamental challenges: 1) safety guarantee during the learning and decision-making processes; 2) adaptability against the dynamic system operating conditions. To this end, this is the first work that proposes an Adaptive and Safe-Certified DRL (AdapSafe) algorithm for frequency control to simultaneously address the aforementioned challenges. In particular, a novel self-tuning control barrier function is designed to actively compensate the unsafe frequency control strategies under variational safety constraints and thus achieve guaranteed safety. Furthermore, the concept of meta-reinforcement learning is integrated to significantly enhance its adaptiveness in non-stationary power system environments without sacrificing the safety cost. Experiments are conducted based on GB 2030 power system, and the results demonstrate that the proposed AdapSafe exhibits superior performance in terms of its guaranteed safety in both training and test phases, as well as its considerable adaptability against the dynamics changes of system parameters.

Imprecise Probabilistic Model Checking for Stochastic Multi-agent Systems

Standard techniques for model checking stochastic multi-agent systems usually assume the transition probabilities describing the system dynamics to be stationary and completely specified. As a consequence, neither non-stationary systems nor systems whose stochastic behaviour is partially unknown can be treated. So far, most of the approaches proposed to overcome this limitation suffer from complexity issues making them poorly efficient in the case of large state spaces. A fruitful but poorly explored way out is offered by the formalism of imprecise probabilities and the related imprecise Markov models. The aim of this paper is to show how imprecise probabilities can be fruitfully involved to model-check multi-agent systems characterised by non-stationary behaviours. Specifically, the paper introduces a new class of multi-agent models called Imprecise Probabilistic Interpreted Systems and their relative extensions with rewards. It also introduces a proper logical language to specify properties of such models and corresponding model checking algorithms based on iterative procedures to compute probabilistic and epistemic inferences over imprecise Markov models.

Order release optimisation for time-dependent and stochastic manufacturing systems

Order release optimisation is essential in production planning, especially in discrete manufacturing. Order release planning models with load-dependent lead times must anticipate the time-dependent work-in-process and output for any given release schedule and thus require an anticipation model that approximates the time-dependent behaviour of queueing systems. We present a generic optimisation model for order release planning in stochastic, non-stationary manufacturing systems that includes a well-defined interface for the anticipation model. We develop two stationary backlog carryover (SBC) approaches to approximate time-dependent queueing behaviour and prove their consistency with the order release model. The resulting nonlinear programming model is shown to be a special case of the well-known clearing function models. A numerical study demonstrates that the optimised order releases for different demand patterns are close to the optimum that results from simulation-based optimisation even for extreme demand and release patterns. The resulting output closely matches the simulated output with some deviations.

A Pattern Classification Distribution Method for Geostatistical Modeling Evaluation and Uncertainty Quantification

Geological models are essential components in various applications. To generate reliable realizations, the geostatistical method focuses on reproducing spatial structures from training images (TIs). Moreover, uncertainty plays an important role in Earth systems. It is beneficial for creating an ensemble of stochastic realizations with high diversity. In this work, we applied a pattern classification distribution (PCD) method to quantitatively evaluate geostatistical modeling. First, we proposed a correlation-driven template method to capture geological patterns. According to the spatial dependency of the TI, region growing and elbow-point detection were launched to create an adaptive template. Second, a combination of clustering and classification was suggested to characterize geological realizations. Aiming at simplifying parameter specification, the program employed hierarchical clustering and decision tree to categorize geological structures. Third, we designed a stacking framework to develop the multi-grid analysis. The contribution of each grid was calculated based on the morphological characteristics of TI. Our program was extensively examined by a channel model, a 2D nonstationary flume system, 2D subglacial bed topographic models in Antarctica, and 3D sandstone models. We activated various geostatistical programs to produce realizations. The experimental results indicated that PCD is capable of addressing multiple geological categories, continuous variables, and high-dimensional structures.

On the Existence of Solutions of Degenerate Discrete-Time Systems

We consider a nonstationary linear discrete-time descriptor system with rectangular matrix coefficients defined on a finite horizon. An answer is obtained to the question as to what the largest number of unknown vectors that can be found from a given finite number of equations is. In a similar way, the solvability of nonstationary linear continuous- or discrete-time systems, as well as (in the local sense) nonlinear discrete-time systems, is studied. It is shown that in cases where the considered linear (or nonlinear) system retains its internal structure, it is possible to find its solutions on an infinite horizon. The proposed approach has sufficient generality and automatically solves the problem of consistency of the initial data.

Game-theoretical problems for fractional-order nonstationary systems

Nonstationary fractional-order systems represent a new class of dynamic systems characterized by time-varying parameters as well as memory effect and hereditary properties. Differential game described by system of linear nonstationary differential equations of fractional order is treated in the paper. The game involves two players, one of which tries to bring the system’s trajectory to a terminal set, whereas the other strives to prevent it. Using the technique of set-valued maps and their selections, sufficient conditions for reaching the terminal set in a finite time are derived. Theoretical results are supported by a model example.