Nonstationary Systems Research Articles

The temporal correlation of fluctuation–variation in the non-stationary complex climate system

In this article we mainly focus on the temporal correlation between the past dynamic fluctuations and the future motion of the dynamic variables in the climate system by means of a new temporal correlation function. When the complex climate system is assumed to be in the stationary states, that is, the dynamic effects of the non-stationary states are not considered, the above correlation is weak or even non-existent. Unexpectedly, a good correlation is shown when the dynamic effects of the non-stationary states are taken into account. Subsequently, we analyze the main factors contributing to these results and conclude that the small fluctuations make a major contribution to this. At the same time, we also find that this correlation function is somewhat stable over time scales. Finally, we extend our analysis by using the persistence probabilities. Knowing these is of key importance for the study of climate analysis and prediction.

Meta-Schrödinger invariance

The Meta-Schrödinger algebra arises as the dynamical symmetry in transport processes which are ballistic in a chosen ‘parallel’ direction and diffusive in all other ‘transverse’ directions. The time-space transformations of this Lie algebra and its infinite-dimensional extension, the meta-Schrödinger-Virasoro algebra, are constructed. We also find the representations suitable for non-stationary systems by proposing a generalised form of the generator of time-translations. Co-variant two-point functions of quasi-primary scaling operators are derived for both the stationary and the non-stationary cases.

Time irreversibility analysis and abnormality detection based on Riemannian geometry for complex time series

Time irreversibility (TIR) is one of the basic properties of nonlinear systems, and it can be used as an effective way to explore the nonlinear complexity of dynamic systems. In this paper, we propose the TIR measure algorithm based on Riemannian geometry and apply this algorithm to abnormality detection tasks. The core idea is to calculate the positive definite covariance matrices of the forward sequence and its inverse sequence based on the theories of sliding window and phase space reconstruction, and compute the affine invariant Riemannian metric (AIRM) between them to characterize the TIR of the time series. The advantage of this algorithm is that the framework based on Riemannian geometry can more effectively use the spatial information of time series. In addition, compared with the traditional methods, the new method is suitable for nonstationary complex systems, which introduces a sliding window to make subsequences satisfy weak stationary conditions to measure local time irreversibility. The simulated and surrogate data are used to verify the effectiveness of the algorithm. Finally, we apply the algorithm to empirical analysis. The results show that, the algorithm detects the financial crisis period and stable period of the stock markets in the analysis of the financial system, and the loss degree of TIR of physiologic signals of different types of cardiac patients is detected in the study of physiologic signals. In the research of Parkinson’s gait, we verify that the walker is an effective tool to improve the gait of early Parkinson’s patients through statistical tests.

Numerical simulation of separated flow past a square cylinder based on a two-fluid turbulence model

The paper presents the numerical results of the transverse flow around an infinite square beam based on the two-fluid turbulence model for the Reynolds number Re = 21400. This problem has a periodic solution, so the non-stationary system of equations of the turbulence model was solved. For the difference approximation of the initial equations, the control volume method and the computational grid arranged in a checkerboard pattern were used. Coarse, fine, and condensed computational grids were used in the work. Their influence on the numerical results is shown. The SIMPLE procedure was applied to correct the velocity through pressure. For the numerical implementation of the equations of the two-fluid model, the two-step Peaceman-Rachford scheme was used. In the work, instantaneous and averaged results for longitudinal and transverse velocities, pressure, pressure coefficient and turbulent stresses are obtained. These results are presented in the form of profiles, as well as in the form of dependences on time and distance in the longitudinal direction. The instantaneous and averaged flow patterns are also presented. The obtained numerical results are compared with the experimental data and the results of other known turbulent models. It is shown that the two-fluid model describes this turbulent flow well.

Large Spillover Networks of Nonstationary Systems

This article proposes a vector error correction framework for constructing large consistent spillover networks of nonstationary systems grounded in the network theory of Diebold and Y ilmaz. We aim to provide a tailored methodology for the large nonstationary (macro)economic and financial system application settings avoiding technical and often hard to verify assumptions for general statistical high-dimensional approaches where the dimension can also increase with sample size. To achieve this, we propose an elementwise Lasso-type technique for consistent and numerically efficient model selection of VECM, and relate the resulting forecast error variance decomposition to the network topology representation. We also derive the corresponding asymptotic results for model selection and network estimation under standard assumptions. Moreover, we develop a refinement strategy for efficient estimation and show implications and modifications for general dependent innovations. In a comprehensive simulation study, we show convincing finite sample performance of our technique in all cases of moderate and low dimensions. In an application to a system of FX rates, the proposed method leads to novel insights on the connectedness and spillover effects in the FX market among the OECD countries.

Some Consequences of Mathematical Inaccuracies in Mechanics

The article is devoted to the study of some violations of the known laws of mathematics and classical mechanics in continuum mechanics and kinetics. The most common is open non-stationary systems. From the equations formulated earlier and some experiments, a connection traced between the gradients of physical quantities and the angular momentum (force). The use of Hamilton's formalism and the dependence of force only on the distance between particles limits the study. In the collision integral, for example, for a rarefied gas, the Lennard-Jones potential, which not related to the type under consideration, is often used. Hamilton's formalism traces the behavior of closed systems. The general form of boundary conditions and forces changes the theory proposed in the works of N.N. Bogolyubov. The results of the reformulation discussed. Even in the classical theory, after taking into account the moments, we come to the absence of symmetric stress tensor in Boltzmann theory. The symmetric tensor obtains after assumption of small influence from absence of symmetry at the condition of the forces balance. No symmetric tensor leads to the existence of two solutions. New examples of solving problems on hydromechanics, elasticity theory and kinetic theory are given. A correspondence between the terms of the Liouville equation with more general and traditional forces established for continues mechanics. Previously considered boundary layer problems, jet problems and the simplest problems of elasticity theory. The paper proposes a method for finding the second solution for no symmetric problems, if the solution of the symmetric problem we know. The mathematical inaccuracies of the theory of continuum mechanics and kinetics discussed.

Simple fluid with broken time-reversal invariance.

We characterize a system of hard spheres with a simple collision rule that breaks time-reversal symmetry but conserves energy. The collisions lead to an achiral, isotropic, and homogeneous stationary state whose properties are determined in simulations and compared to an approximate theory originally developed for elastic hard spheres. In the nonequilibrium fluid state, velocities are correlated, a phenomenon known from other nonequilibrium stationary states. The correlations are long-ranged decaying like 1/r^{D} in D dimensions. Such correlations are expected on general grounds far from equilibrium and had previously been observed in driven or nonstationary systems.

Systems of Vortices in a Binary Core–Shell Bose–Einstein Condensate

A trapped Bose--Einstein-condensed mixture of two types of cold atoms with significantly different masses has been simulated numerically within the coupled Gross--Pitaevskii equations. A configuration consisting of a vortex-free core and a shell penetrated by quantum vortices is possible in the phase separation regime. The dynamic properties of vortices in the shell are determined by several parameters. Physically implementable parametric domains corresponding to long-lived strongly nonstationary systems of several vortices attached to the core have been sought. A number of realistic numerical examples of three vortex pairs existing for many hundreds of characteristic times have been presented.

Intelligent decision support systems in the development of megalopolis infrastructure

From the point of view of the management theory, a megapolis is a complex non-stationary spatial system. The problem of making innovative decisions on the development of their infrastructure is caused by the presence of a large amount of information, its uncertainty and inconsistency. This article discusses the principles of building intelligent decision support systems of a situational type for the innovative development of the infrastructure of megacities. Solutions are formed by logico-analytical processing of data on the situation in general and special cases of situations for the considered subject of the megalopolis infrastructure. For the practical implementation of the decision-making mechanism, the article proposes a linguistic-numerical method for determining the potentially best alternative and a fuzzy situational algorithm for managing the subjects of the megalopolis infrastructure, based on the structural generality of the situations of a fuzzy situational network. The obtained results were tested on two real infrastructure subjects of Kyiv.

Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system

Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system

Analysis of the human error occurrence process in non-stationary system operation (1)

Analysis of the human error occurrence process in non-stationary system operation (1)

Analysis of the Human Error Occurrence Process in Non-stationary System Operation (2)

Analysis of the Human Error Occurrence Process in Non-stationary System Operation (2)

Index similarity assisted particle filter for early failure time prediction with applications to turbofan engines and compressors

The particle filter (PF) has been widely studied in the prognostics’ field due to its ability to deal with nonlinear and non-stationary systems. However, there is no update of the model parameters during the prediction, preventing PF to work in its traditional way to generate accurate long-term predictions. In order to solve this problem, we put forward an improved PF that is based on a novel health index (HI) similarity matching method. This method is employed to search for similar HIs in the training library and construct an optimal “similar HI” for the system under study. Finally, the obtained HI is consistently fed into the PF to deliver precise state-of-health (SoH) estimates. The effectiveness of the proposed PF was validated on the C-MAPSS datasets as well as data collected from an operational reciprocating compressor. We observed that the new similarity matching method demonstrated excellent performance in finding suitable HIs for failure time prediction. We also observed that the proposed PF framework had a superior prognostics performance over the standard PF. We obtained an averaged predictive accuracy of 96% (C-MAPSS data) and 92% (compressor data) when only the first 10% of the degradation data were used. This work highlights the promise of combining index similarity, Procrustes analysis and PF for complementing existing prognostic methods.

Nonstationary fuzzy neural network based on FCMnet clustering and a modified CG method with Armijo-type rule

Nonstationary fuzzy inference systems (NFISs) model the variation in opinions of individual experts and expert groups. They have the capability similar to type-2 fuzzy systems in some regards with less computational costs. This paper presents a nonstationary fuzzy neural network (NFNN) model by combining NFISs and neural networks (NNs). The proposed model synthesizes the logical inference and language expression abilities of NFIS with the learning mechanism of NNs. Hence, it makes NNs more translatable and also achieves self-learning of fuzzy rules. Besides, a fuzzy c-means network (FCMnet) clustering and a modified conjugate gradient method with constrained Armijo-type rule (MCGA) are proposed to initialize and train NFNN, respectively. The proposed FCMnet first combines the fuzzy c-means (FCM) algorithm with NNs. Thus, it not only improves the performance of FCM, but also makes NNs more interpretable. For MCGA, we construct a specific conjugate coefficient to ensure the sufficient descent property and propose a constrained Armijo-type rule to search a suitable learning rate in each iteration. By adopting these two techniques, MCGA achieves a fast convergence speed. In addition, both weak and strong convergence results are proven rigorously. Experiments on 14 datasets are carried out to illustrate the competitive performance of our models.

A control algorithm for a non-stationary batch service production system using Kalman filter

This paper presents a dynamically optimized control algorithm for a fully automated batch service production process, with non-stationary nature of order arrivals. The problem of interest is a non-stationary SELSP, i.e., stochastic economic lot sizing problem, with erratic order flow, where the objective is to continuously optimize the production lot size according to the real-time detection of demand fluctuations. Such a problem has a dual nature of being a planning problem, which used to be dealt with within the operational research (OR) community and a control problem, often dealt with within the control theory (CT) circle.To tackle the problem a Kalman Filter (KF) based approach has been employed, as one of the most reliable methods in CT, with an edge over its previously studied alternatives, i.e., Exponential Filter (EF) and its fuzzified version. It is illustrated that the adopted KF performs much better both in terms of efficiency metrics of OR, and responsiveness metrics of CT. The results advocate that the new generation of automated production planning and control systems may benefit from the concepts and methods from both communities of OR and CT, in an integrated fashion.

Dynamic Regret Minimization for Control of Non-stationary Linear Dynamical Systems

We consider the problem of controlling a Linear Quadratic Regulator (LQR) system over a finite horizon T with fixed and known cost matrices Q,R, but unknown and non-stationary dynamics At, Bt. The sequence of dynamics matrices can be arbitrary, but with a total variation, VT, assumed to be o(T) and unknown to the controller. Under the assumption that a sequence of stabilizing, but potentially sub-optimal controllers is available for all t, we present an algorithm that achieves the optimal dynamic regret of Õ(VT2/5 T3/5). With piecewise constant dynamics, our algorithm achieves the optimal regret of Õ(√ST) where S is the number of switches. The crux of our algorithm is an adaptive non-stationarity detection strategy, which builds on an approach recently developed for contextual Multi-armed Bandit problems. We also argue that non-adaptive forgetting (e.g., restarting or using sliding window learning with a static window size) may not be regret optimal for the LQR problem, even when the window size is optimally tuned with the knowledge of VT. The main technical challenge in the analysis of our algorithm is to prove that the ordinary least squares (OLS) estimator has a small bias when the parameter to be estimated is non-stationary. Our analysis also highlights that the key motif driving the regret is that the LQR problem is in spirit a bandit problem with linear feedback and locally quadratic cost. This motif is more universal than the LQR problem itself, and therefore we believe our results should find wider application.

The practical effects of friction for tuned mass dampers installed in tall buildings

In real-world applications, tuned mass dampers (TMDs) possess friction that must be overcome before they will increase the total effective damping of the structure. The performance of structure-TMD systems with unintended TMD friction is investigated in this study. A nonlinear time domain model is developed, which incorporates the TMD damping due to friction, and also exhibits TMD “lock-out” if the forces of friction are not overcome, a feature that existing studies have not considered. Comparisons with full-scale measurements indicate the model adequately captures the response of a TMD with friction. A linearized equivalent mechanical model is also presented, which represents the friction as amplitude-dependent viscous damping, but this model does not capture TMD lock-out. A parametric study is conducted to assess the effect of TMD friction on the performance of TMD systems with various TMD mass ratios, structure and TMD damping ratios, and the TMD damping form (linear or quadratic). In all cases, the TMD performance decreases markedly if the baseline peak structural acceleration is not at least an order of magnitude greater than the acceleration that causes the TMD to break free. If the baseline acceleration is less than five times the break-free acceleration, the TMD motion reduction performance may be negligible, and the linearized model predictions do not agree with the nonlinear simulations. TMD lock-out produces a non-stationary system response, in which the TMD reduces the peak structural accelerations slightly more than the RMS structural accelerations.

СТАТИСТИЧЕСКИЕ АСПЕКТЫ КОЛИЧЕСТВЕННОЙ ОЦЕНКИ ПОЛЯРНОГО УСИЛЕНИЯ. I. ОТНОШЕНИЕ ТРЕНДОВ

Statistical aspects of the quantitative estimation of the climate change polar amplification (PA) are considered. A theoretical study is provided of the distribution density for the PA sample coefficient defined as the ratio of the linear trend coefficients of spatially averaged surface air temperature. It is shown that heavy tails of the distribution lead to instability of the PA sample estimates. A statistically valid quantification of the PA can be obtained from the results of the ensemble modeling of climate change based on the Fieller’s method. The applicability of the method in the case of a non-stationary climate system response to external forcing is considered.

Boundary Lebesgue mixed-norm estimates for non-stationary Stokes systems with VMO coefficients

We consider Stokes systems with measurable coefficients and Lions-type boundary conditions. We show that, in contrast to the Dirichlet boundary conditions, local boundary mixed-norm -estimates hold for the spatial second-order derivatives of solutions, assuming the smallness of the mean oscillations of the coefficients with respect to the spatial variables in small cylinders. In the un-mixed norm case with the result is still new and provides local boundary Caccioppoli-type estimates. The main challenges in the work arise from the lack of regularity of the pressure and time derivatives of the solutions and from interaction of the boundary with the nonlocal structure of the system. To overcome these difficulties, our approach relies heavily on several newly developed regularity estimates for both divergence and non-divergence form parabolic equations with coefficients that are only measurable in the time variable and in one of the spatial variables.

Stability of the nonconstant stationary solution to the damped Poisson–Nernst–Planck–Euler equations

We study the stability of the stationary solution to the three‐dimensional damped Poisson–Nernst–Planck–Euler equations. We show that the stationary system has and only has a semitrivial solution under a general nonconstant doping profile. Under small initial data, we prove the existence and uniqueness of the global strong solution to the nonstationary system. We also obtain the optimal convergence rate of the norm of the solution toward the semitrivial stationary solution as time tends to infinity.