State-space Approach Research Articles

Levy solution and state-space approach for hygro-thermo-magnetic bending of a cross-ply laminated plate on Kerr foundation under various loadings

Levy solution and state-space approach for hygro-thermo-magnetic bending of a cross-ply laminated plate on Kerr foundation under various loadings

State-Space Approach to the Time-Fractional Maxwell’s Equations under Caputo Fractional Derivative of an Electromagnetic Half-Space under Four Different Thermoelastic Theorems

This paper introduces a new mathematical modelling method of a thermoelastic and electromagnetic half-space in the context of four different thermoelastic theorems: Green–Naghdi type-I, and type-III; Lord–Shulman; and Moore–Gibson–Thompson. The bunding plane of the half-space surface is subjected to ramp-type heat and traction-free. We consider that Maxwell’s time-fractional equations have been under Caputo’s fractional derivative definition, which is the novelty of this work. Laplace transform techniques are utilized to obtain solutions using the state-space approach. Laplace transform’s inversions were calculated using Tzou’s iteration method. The temperature increment, strain, displacement, stress, induced electric field, and induced magnetic field distributions were obtained numerically and are illustrated in figures. The time-fraction parameter of Maxwell’s equations had a major impact on all the studied functions. The time-fractional parameter of Maxwell’s equations worked as resistant to the changing of temperature, particle movement, and induced magnetic field, while it acted as a catalyst to the induced electric field through the material. Moreover, all the studied functions have different values in the context of the four studied theorems.

Environment-mediated long-ranged correlations in many-body system

Quantum states in complex aggregates are unavoidably affected by environmental effects, which typically cannot be accurately modeled by simple Markovian processes. As system sizes scale up, nonperturbative simulation becomes thus unavoidable, but they are extremely challenging due to the intimate interplay of intrinsic many-body interaction and time-retarded feedback from environmental degrees of freedom. In this work, we utilize the recently developed quantum dissipation with minimally extended state space approach to address reservoir induced long-ranged temporal correlations in finite size Ising-type spin chains. For thermal reservoirs with ohmic and subohmic spectral density, we simulate the quantum time evolution from finite to zero temperature. The competition between thermal fluctuations, quantum fluctuations, and anti-/ferromagnetic interactions reveals a rich pattern of dynamical phases, including dissipative induced phase transitions and spatiotemporal correlations.

A state-space relational event modeling approach for learning dynamic social interaction behavior

Relational event models (REMs) are the primary choice for the analysis of relational-event network data. However, the standard REM assumes static parameters, which hinders the modeling of time-varying dynamics. This assumption might be too restrictive in real-life scenarios, making a model that allows for time-varying parameters more valuable. We introduce a state-space extension of the relational event model as a way to tackle this problem. The model has three main attributes. First, it provides a statistical framework of the temporal change of the parameters. Second, it enables the forecasting of future parameter values (which can be utilized to simulate new networks that can account for temporal dynamics in out-of-sample predictions). Third, it requires smaller data structures to be loaded into computer memory compared to the standard REM; this makes the model easily scalable to large networks. We conduct empirical analyses on bike-sharing data, corporate communications, and interactions among socio-political actors to illustrate model usage and applicability.

Endogenous cycles in heterogeneous agent models: a state-space approach

Endogenous cycles in heterogeneous agent models: a state-space approach

Improved State-Space Approach Based on Lumped Mass Matrix for Transient Analysis of Large-Scale Locally Nonlinear Structures

Due to the assumption of acceleration variation in traditional step-by-step integration methods such as Newmark, sufficiently small time steps are required to ensure numerical stability and accuracy in dynamic systems. In contrast, the state-space approach, based on piecewise interpolation of discrete load functions, does not rely on predetermined acceleration assumptions and has demonstrated high efficiency in terms of stability and accuracy. The original state-space method requires the calculation of the inverse of the structural mass in the transition matrix. However, when a lumped mass matrix is used, this computation renders the entire mass matrix singular, resulting in an invalid solution expression. To address this issue, this study proposes an improved state-space approach for the transient analysis of large-scale structural systems with local nonlinearities. In this approach, a nonlinear force corrector is introduced as an external force term applied to the linear elastic system to account for the nonlinear behavior of locally yielding components. Consequently, the original nonlinear dynamic system can be transformed into an equivalent linear elastic transient system. Furthermore, based on the lumped mass matrix, a first-order ordinary differential state-space equation for such an equivalent linear elastic transient system is derived. Simulation results from three transient system examples show that the state-space approach outperforms the Newmark method in terms of accuracy and stability for dynamic systems characterized by high frequency and low damping. The prediction results show that the state-space approach appears to be insignificantly affected by the choice of the consistent or lumped mass matrix. The numerical results show that the root-mean-square errors between the consistent and lumped matrices in the top displacement time histories of a 15-storey plane frame under various seismic intensities are all less than 1%, and in the base reaction time histories responses the discrepancies are only about 0.5%, indicating that the use of lumped mass matrices is quite reliable. When many nodes or degrees of freedom have no assigned mass, the dimensionality of the state-space equation can be significantly reduced using the lumped mass approach. Therefore, the simulation of large-scale systems can be simplified by employing the improved state-space approach with lumped mass matrices, yielding results nearly identical to those obtained using traditional methods. In conclusion, the improved state-space approach has great potential for the simulation of transient behavior in large-scale systems with local nonlinearities.

The Impacts of COVID-19 Lockdowns on Road Transport Air Pollution in London: A State-Space Modelling Approach.

The emergence of the COVID-19 pandemic in 2020 led to the implementation of legal restrictions on individual activities, significantly impacting traffic and air pollution levels in urban areas. This study employs a state-space intervention method to investigate the effects of three major COVID-19 lockdowns in March 2020, November 2020, and January 2021 on London's air quality. Data were collected from 20 monitoring stations across London (central, ultra-low emission zone, and greater London), with daily measurements of NOx, PM10, and PM2.5 for four years (January 2019-December 2022). Furthermore, the developed model was adjusted for seasonal effects, ambient temperature, and relative humidity. This study found significant reductions in the NOx levels during the first lockdown: 49% in central London, 33% in the ultra-low emission zone (ULEZ), and 37% in greater London. Although reductions in NOx were also observed during the second and third lockdowns, they were less than the first lockdown. In contrast, PM10 and PM2.5 increased by 12% and 1%, respectively, during the first lockdown, possibly due to higher residential energy consumption. However, during the second lockdown, PM10 and PM2.5 levels decreased by 11% and 13%, respectively, and remained unchanged during the third lockdown. These findings highlight the complex dynamics of urban air quality and underscore the need for targeted interventions to address specific pollution sources, particularly those related to road transport. The study provides valuable insights into the effectiveness of lockdown measures and informs future air quality management strategies.

Seismic assessment of cylindrical storage tanks to records with different frequency contents considering fluid–structure–soil/foundation interaction

This study aims to primarily assess the dynamic behavior of ground-supported cylindrical tanks to real near-fault earthquake records with different frequency contents including soil-structure interaction effects. A cylindrical tank’s fluid-tank-soil interaction is modeled using a three-degree-of-freedom lumped mass model for the fluid. A mass-spring-dashpot model with frequency independence is used to model the soil/foundation system. Broad, medium, and slender tank models are developed considering and ignoring the soil flexibility effect. An algorithm based on discrete-time state-space approaches is developed for performing numerical simulations of the modeled tanks excited by the low-, medium-, and high-frequency contents. The obtained results for the modeled tanks in terms of base shear, overturning moment, and connective and impulsive mass displacements incorporating the influence of supporting soils as well as the frequency contents of excitation records are evaluated and compared with the corresponding results for modeled tanks with a fixed base. In addition, the liquid sloshing height for all aspect ratios is also evaluated and compared. The study’s findings clearly indicate that records with low-frequency contents require significantly more seismically demanding than other records for the considered soil types. Remarkably, soil-tank interaction under earthquake motions substantially amplifies the induced response.

Maximum-correntropy-based sequential method for fast neural population activity reconstruction in the cortex from incomplete abnormally-disturbed noisy measurements

This paper continues to explore the membrane potential reconstruction and pattern recognition problem in a neural tissue modeled by Stochastic Dynamic Neural Field (SDNF) equation. Although recent research has suggested an efficient solution based on the state-space approach through nonlinear Bayesian filtering framework, it is becoming extremely difficult to ignore the existence of non-Gaussian uncertainties in the SDNFs as well as the stability problem of neuronal population dynamics to outliers. Motivated by recent events in signal processing and mathematical neuroscience, this paper explores the SDNFs in a presence of non-Gaussian uncertainties, which is the shot noise case, where the corrupted data might appear due to broken sensors. We derive the “distributionally robust” state estimator for the membrane potential reconstruction process that is the Maximum Correntropy Criterion Extended Kalman Filter (MCC-EKF) as well as its fast and numerically robust (to roundoff) implementation method by using the sequential principle of processing the measurement vectors. The numerical experiments are provided to illustrate the performance of the novel estimation methods.

Medical Image Classification with a Hybrid SSM Model Based on CNN and Transformer

Medical image classification, a pivotal task for diagnostic accuracy, poses unique challenges due to the intricate and variable nature of medical images compared to their natural counterparts. While Convolutional Neural Networks (CNNs) and Transformers are prevalent in this domain, each architecture has its drawbacks. CNNs, despite their strength in local feature extraction, fall short in capturing global context, whereas Transformers excel at global information but can overlook fine-grained details. The integration of CNNs and Transformers in a hybrid model aims to bridge this gap by enabling simultaneous local and global feature extraction. However, this approach remains constrained in its capacity to model long-range dependencies, thereby hindering the efficient extraction of distant features. To address these issues, we introduce the MambaConvT model, which employs a state-space approach. It begins by locally processing input features through multi-core convolution, enhancing the extraction of deep, discriminative local details. Next, depth-separable convolution with a 2D selective scanning module (SS2D) is employed to maintain a global receptive field and establish long-distance connections, capturing the fine-grained features. The model then combines hybrid features for comprehensive feature extraction, followed by global feature modeling to emphasize on global detail information and optimize feature representation. This paper conducts thorough performance experiments on different algorithms across four publicly available datasets and two private datasets. The results demonstrate that MambaConvT outperforms the latest classification algorithms in terms of accuracy, precision, recall, F1 score, and AUC value ratings, achieving superior performance in the precise classification of medical images.

Relay feedback identification and PI-PD control of asymmetrical heating and cooling processes

A common type of nonlinear system in the field of process industry is asymmetrical heating and cooling processes. These systems have two operating modes, heating and cooling, each with a particular dynamic feature. This study deals with identifying and controlling such processes. The relay feedback identification method based on the state-space approach, which results in exact estimates, is used in the identification procedure to achieve two first-order plus dead time (FOPDT) process models. Following process identification, two sets of PI-PD controller parameters are acquired in line with the user-defined gain and phase margin specifications, and the system is controlled using a gain-scheduled PI-PD control method. Some simulation examples are provided to demonstrate the use and profitability of the suggested identification and control approaches. Comparisons with a similar study are provided for both identification and control approaches to clearly demonstrate the benefits of the suggested procedures.

Trend and Variance Adaptive Bayesian Changepoint Analysis and Local Outlier Scoring

We adaptively estimate both changepoints and local outlier processes in a Bayesian dynamic linear model with global-local shrinkage priors in a novel model we call Adaptive Bayesian Changepoints with Outliers (ABCO). We use a state-space approach to identify a dynamic signal in the presence of outliers and measurement error with stochastic volatility. We find that global state equation parameters are inadequate for most real applications and we include local parameters to track noise at each time-step. This setup provides a flexible framework to detect unspecified changepoints in complex series, such as those with large interruptions in local trends, with robustness to outliers and heteroscedastic noise. Finally, we compare our algorithm against several alternatives to demonstrate its efficacy in diverse simulation scenarios and two empirical examples on the U.S. economy.

A modified Green-Naghdi fractional order model for analyzing thermoelectric MHD

PurposeWhereas, the classical Green-Naghdi Type II (GN-II) model struggles to accurately represent the thermo-mechanical behavior of thermoelectric MHD due to its inability to account for the memory effect. A new mathematical model of the GN-II theory incorporates a fractional order of heat transport to address this issue.Design/methodology/approachThe employment of the matrix exponential method, which forms the basis of the state-space approach in contemporary theory, is central to this strategy. The resulting formulation, together with the Laplace transform techniques, is applied to a variety of problems. Solutions to a thermal shock problem and to a problem of a layer media both without heat sources are obtained. Also, a problem with the distribution of heat sources is considered. The numerical technique is used to achieve the Laplace transform inversion.FindingsAccording to the numerical results and its graphs, the influences of the fractional order parameters, figure-of-merit factor, thermoelectric power and Peltier coefficient on the behavior of the field quantities are investigated in the new theory.Originality/valueThe new modeling of thermoelectric MHD has advanced significantly as a result of this work, providing a more thorough and precise tool for forecasting the behavior of these materials under a range of thermal and magnetic conditions.

State-Space Modeling Approach to Exploring the Index of Production in Construction for Türkiye

In recent years, researchers and statisticians have increasingly used econometric techniques to generate timely, high-quality, and detailed official statistics. This study presents a modified form of regression-based temporal disaggregation model to compile the index of production in construction for Türkiye, employing a state-space modeling approach. The model incorporates the twelve-month moving sum of deflated turnover as an observed variable and the number of employees as an exogenous variable. Finally, four alternative models—three assuming constant labor productivity and one assuming time-varying labor productivity—are compared.

A novel approach to model nance drying considering its shrinkage

Air drying is a viable preservation method to boost the accessibility of nance, a seasonal drupe with very short shelf life; however, information about nance drying is scarce, especially from a mass transfer (MT) standpoint. Besides, the lack of simple models considering the stone fraction (radius of inner stone/radius of nance) and the mesocarp shrinkage in drupes has caused most investigations rely on sphere and cube geometries, contributing to the unreliable estimation of MT properties. This study developed a discrete state-space (SS) formulation with analytical solution to describe nance drying which, unlike a variable separation (VS) solution, can consider a variable stone fraction, caused by outer boundary moving while flesh-pit interface remains still. Nance fruits were air dried (60, 70 and 80 °C) to obtain their moisture kinetics and shrinking behavior. Drying data were used to estimate water diffusivity (D) under rigid (VS and SS solutions) and shrinkable (SS and numerical solution) mesocarp assumptions. Nances lost about 60% of their initial volume at the end of drying, while stone fraction increased from 0.44 to 0.62. D values ranged from 5.3 to 6.7 (×10–10) m2/s with SS approach and variable stone fraction. The major source of error in D was not the formulation (SS or VS) when a rigid mesocarp was considered, but the values assigned to the nance radius (length for diffusion) and stone fraction, an initial or average value along process. SS diffusivities did not differ to those estimated with the full numerical solution under variable stone fraction (p>0.05), while VS parameters were overestimated by 44–46 % as a minimum. SS formulation can be applied to hollow cylinders and other geometries with 2D or 3D MT, while able to include non-isotropic shrinkage and evolving external conditions, a problem normally reserved to pure numerical implementations, offering substantial advantages over VS equations.

Data-driven state-space and Koopman operator models of coherent state dynamics on invariant manifolds

The accurate simulation of complex dynamics in fluid flows demands a substantial number of degrees of freedom, i.e. a high-dimensional state space. Nevertheless, the swift attenuation of small-scale perturbations due to viscous diffusion permits in principle the representation of these flows using a significantly reduced dimensionality. Over time, the dynamics of such flows evolves towards a finite-dimensional invariant manifold. Using only data from direct numerical simulations, in the present work we identify the manifold and determine evolution equations for the dynamics on it. We use an advanced autoencoder framework to automatically estimate the intrinsic dimension of the manifold and provide an orthogonal coordinate system. Then, we learn the dynamics by determining an equation on the manifold by using both a function-space approach (approximating the Koopman operator) and a state-space approach (approximating the vector field on the manifold). We apply this method to exact coherent states for Kolmogorov flow and minimal flow unit pipe flow. Fully resolved simulations for these cases require $O(10^3)$ and $O(10^5)$ degrees of freedom, respectively, and we build models with two or three degrees of freedom that faithfully capture the dynamics of these flows. For these examples, both the state-space and function-space time evaluations provide highly accurate predictions of the long-time dynamics in manifold coordinates.

Enhancing predictive capabilities in data-driven dynamical modeling with automatic differentiation: Koopman and neural ODE approaches.

Data-driven approximations of the Koopman operator are promising for predicting the time evolution of systems characterized by complex dynamics. Among these methods, the approach known as extended dynamic mode decomposition with dictionary learning (EDMD-DL) has garnered significant attention. Here, we present a modification of EDMD-DL that concurrently determines both the dictionary of observables and the corresponding approximation of the Koopman operator. This innovation leverages automatic differentiation to facilitate gradient descent computations through the pseudoinverse. We also address the performance of several alternative methodologies. We assess a "pure" Koopman approach, which involves the direct time-integration of a linear, high-dimensional system governing the dynamics within the space of observables. Additionally, we explore a modified approach where the system alternates between spaces of states and observables at each time step-this approach no longer satisfies the linearity of the true Koopman operator representation. For further comparisons, we also apply a state-space approach (neural ordinary differential equations). We consider systems encompassing two- and three-dimensional ordinary differential equation systems featuring steady, oscillatory, and chaotic attractors, as well as partial differential equations exhibiting increasingly complex and intricate behaviors. Our framework significantly outperforms EDMD-DL. Furthermore, the state-space approach offers superior performance compared to the "pure" Koopman approach where the entire time evolution occurs in the space of observables. When the temporal evolution of the Koopman approach alternates between states and observables at each time step, however, its predictions become comparable to those of the state-space approach.

Control of linear instabilities in two-dimensional airfoil boundary layers

The present study deals with the control of linear, modal and non-modal growth of perturbations in a trapezoidal wing boundary layer. The asymmetric NACA 2515 airfoil is chosen for the analysis. The boundary layer velocity profiles, at different locations on the airfoil, are obtained using the Falkner–Skan equations. The non-modal linear stability theory is used to obtain the amplification of the initial perturbations, for which the state-space approach is adopted. The control is brought about using a Linear Quadratic Regulator (LQR) controller by the means of addition of fluid momentum in the wall-normal direction from the wing surface. Maximum transient energy growth is calculated across a range of wavenumber pairs, and control is applied to the pair with the highest energy growth. In this numerical analysis, we show that the transient growth is higher towards the trailing edge because of the adverse pressure gradient of the flow. Upon control actuation, the reduction in the transient energy growth of perturbations is achieved up to a maximum of 54.6%.

Spectral dynamic causal modeling: A didactic introduction and its relationship with functional connectivity.

We present a didactic introduction to spectral dynamic causal modeling (DCM), a Bayesian state-space modeling approach used to infer effective connectivity from noninvasive neuroimaging data. Spectral DCM is currently the most widely applied DCM variant for resting-state functional MRI analysis. Our aim is to explain its technical foundations to an audience with limited expertise in state-space modeling and spectral data analysis. Particular attention will be paid to cross-spectral density, which is the most distinctive feature of spectral DCM and is closely related to functional connectivity, as measured by (zero-lag) Pearson correlations. In fact, the model parameters estimated by spectral DCM are those that best reproduce the cross-correlations between all measurements-at all time lags-including the zero-lag correlations that are usually interpreted as functional connectivity. We derive the functional connectivity matrix from the model equations and show how changing a single effective connectivity parameter can affect all pairwise correlations. To complicate matters, the pairs of brain regions showing the largest changes in functional connectivity do not necessarily coincide with those presenting the largest changes in effective connectivity. We discuss the implications and conclude with a comprehensive summary of the assumptions and limitations of spectral DCM.

Developing Dynamic System Responses Model Based on Nanotechnology by Incorporating the Finite Element Analysis

The dynamic model of complex structure has set incredible progression with the use of finite element analysis (FEA), especially in the field of vibration control and nanotechnology. Main focus of this research is to conduct a frequency analysis in ANSYS and a state space model of the beam under the platform of MATLAB. This allowed a system to develop an active dynamic model for vibration control. To enhance test and analysis of the cantilever beam of Aluminium 6061T6, a new method has been proposed to predict the dynamic response of a cantilever beam under sinusoidal base excitation. This was achieved by creating an analytical model for the cantilever beam using moment and force equilibrium equations. The authenticity of the proposed method was made by comparing the results with experimental data. Additionally, to control vibration, a Proportional-Integral-Derivative (PID) controller was developed using the system model. The FEA in the ANSYS platform provided a cantilever beam model. Also, its mathematical modelling has been done. The proposed method utilizes a novel disturbance rejection control scheme that eliminates an unknown disturbance. Experimental results indicate that the control system results in gradually decreased beam vibration amplitude. The state space approach discussed in the work could be a valuable tool for studying the behaviours of nanomaterials.