State Space Variables Research Articles

Second law and Liu relations: the no-reversible-direction axiom—revisited

AbstractA thermodynamic process is governed by balance equations in field-formulated thermodynamics. Especially the balance equation of entropy takes a prominent role: it introduces the Second Law in the form of a dissipation inequality via the non-negative entropy production. Balance equations and dissipation inequality are independent of the considered material which is described by additional constitutive equations which need the introduction of a state space which is spanned by the state space variables. Inserting these constitutive equations into the balance equations results in the balance equations on state space which include the first order time and position derivatives of the state space variables, called “higher derivatives” wich are directional derivatives in a mathematicle sense. Why do not appear the latter in the Liu Relations which pretend to describe material as well as the equations on state space do ? The answer is that the Liu Relations describe materials whose entropy production does not depend on the higher derivatives. Consequently, the Liu Relations are more specific than the balance equations on state space. A toy example concerning heat conduction in compressible fluids is in two different versions added for elucidation.

Iterative Mamba Diffusion Change-Detection Model for Remote Sensing

In the field of remote sensing (RS), change detection (CD) methods are critical for analyzing the quality of images shot over various geographical areas, particularly for high-resolution images. However, there are some shortcomings of the widely used Convolutional Neural Networks (CNNs) and Transformers-based CD methods. The former is limited by its insufficient long-range modeling capabilities, while the latter is hampered by its computational complexity. Additionally, the commonly used information-fusion methods for pre- and post-change images often lead to information loss or redundancy, resulting in inaccurate edge detection. To address these issues, we propose an Iterative Mamba Diffusion Change Detection (IMDCD) approach to iteratively integrate various pieces of information and efficiently produce fine-grained CD maps. Specifically, the Swin-Mamba-Encoder (SME) within Mamba-CD (MCD) is employed as a semantic feature extractor, capable of modeling long-range relationships with linear computability. Moreover, we introduce the Variable State Space CD (VSS-CD) module, which extracts abundant CD features by training the matrix parameters within the designed State Space Change Detection (SS-CD). The computed high-dimensional CD feature is integrated into the noise predictor using a novel Global Hybrid Attention Transformer (GHAT) while low-dimensional CD features are utilized to calibrate prior CD results at each iterative step, progressively refining the generated outcomes. IMDCD exhibits a high performance across multiple datasets such as the CDD, WHU, LEVIR, and OSCD, marking a significant advancement in the methodologies within the CD field of RS. The code for this work is available on GitHub.

Mathematical analysis and optimal control of age‐structured social interaction model with law enforcement

Optimal use of available resources is one of the major issues in many situations. Apart from this, age is also an important factor in modeling social interaction in a society. In this article, we consider an age‐dependent social interaction model and study the stability and optimal control. Law enforcement is an important factor in controlling crime, and the deployment of police to enforce it is important. Now cost is a major issue, so optimal deployment is very important to study. Stability results are derived in terms of threshold parameters. Basic reproduction number is calculated for stability analysis. Using the adjoint system, the form of the law enforcement factor is obtained in terms of state space variables. We see that the cost functional increases with the increase in the population density of criminal population. Numerical results are also added to visually illustrate our theoretical results.

Bearing degradation prediction based on deep latent variable state space model with differential transformation

Rolling bearings are a critical component of mechanical transmission equipment. Predicting their degradation trend is crucial for ensuring safe and stable equipment operation. Most existing bearing degradation prediction methods based on state space models (SSMs) use either linear functions or limited nonlinear functions (e.g., exponential/power laws) to construct the state and measurement equations. As such, these models fail to adapt to the complex and varied nonlinear degradation processes that occur in real-world environments. To address this limitation, we developed a deep latent variable-driven state space degradation model and employed it for bearing degradation prediction. Owing to the powerful nonlinear modeling ability of deep learning models, the proposed method extends the applicability of state space equations. In addition, it inherits the advantages of SSMs and can model uncertainties in a structured manner. Furthermore, the model was integrated with differential pre-transformation to improve its long-term prediction performance. Finally, to validate the effectiveness of the proposed model in predicting bearing degradation, experiments were conducted using a bearing dataset from the PRONOSTIA platform and real wind turbine bearing data. Results showed that the proposed method yielded higher bearing degradation prediction accuracy than existing methods, thus demonstrating the superior performance of the proposed model in predicting bearing degradation.

Steady state stability assessment of voltage source converter in a DC microgrid under weak grid conditions

Traditionally, steady-state assessment involves analyzing numerous variables using Eigen analysis. This paper presents a decision support application for diagnosing the steady-state assessment of droop-controlled voltage source inverters in islanded microgrid operations or weak grid operations with reduced input attributes. This paper proposes an approach using feature extraction from the state space variables of the droop-controlled voltage source inverter (VSI). Photovoltaic (PV) and wind energy sources are considered with their stipulated power-delivering capability considered. To improve the generalization of the predictive model, preprocessing techniques are employed to eliminate data distortions. Dimensionality reduction is achieved through principal component analysis (PCA) applied to the steady-state variables. The evaluation of the VSI's steady-state stability is conducted utilizing support vector classification algorithm. To ascertain the reliability of the steady-state stability classification, an assessment of the support vector machine (SVM) model's performance is carried out, which includes the examination of metrics like the area under the curve (AUC) and the receiver operating characteristics (ROC) curve. The findings from the assessment of VSI's steady-state stability indicate a commendable level of performance, achieving an accuracy rate of 93.5%.

Model-free low-power observer based robust trajectory tracking control of UAV quadrotor with unknown disturbances

PurposeThe purpose of this paper is to design an output-feedback algorithm based on low-power observer (LPO), robust chattering-free controller and nonlinear disturbance observer (DO) to achieve trajectory tracking of quadrotor in the Cartesian plane.Design/methodology/approachTo achieve trajectory tracking control, firstly the decoupled rotational and translational model of quadrotor are modified by introducing backstepped state-space variables. In the second step, robust integral sliding mode control is designed based on the proportional-integral-derivative (PID) technique. In the third step, a DO is constructed. In next step, the measurable outputs, i.e. rotational and translational state variables, are used to design the LPO. Finally, in the control algorithm all state variables and its rates are replaced with its estimates obtained using the state-observer.FindingsThe finding includes output-feedback control (OFC) algorithm designed by using a LPO. A modified backstepping model for rotational and rotational systems is developed prior to the design of integral sliding mode control based on PID technique. Unlike traditional high-gain observers (HGO), this paper used the LPO for state estimation of quadrotor systems to solve the problem of peaking phenomenon in HGO. Furthermore, a nonlinear DO is designed such that it attenuates disturbance with unknown magnitude and frequency. Moreover, a chattering reduction criterion has been introduced to solve the inherited chattering issue of controllers based on sliding mode technique.Practical implicationsThis paper presents input and output data-driven model-free control algorithm. That is, only input and output of the quadrotor model are required to achieve the trajectory tracking control. Therefore, for practical implementation, the number of on-board sensor is reduced.Originality/valueAlthough extensive research has been done for designing OFC algorithms for quadrotor, LPO has never been implemented for the rotational and translational state estimations of quadrotor. Furthermore, the mathematical model of rotational and translational systems is modified by using backstepped variables followed by the controller designed using PID and integral sliding mode control technique. Moreover, a DO is developed for attenuation of disturbance with unknown bound, magnitude and frequency.

A Deep Neural Network-Ensemble Adjustment Kalman Filter and Its Application on Strongly Coupled Data Assimilation

This paper introduces a novel ensemble adjustment Kalman filter (EAKF) that integrates a machine-learning approach. The conventional EAKF adopts linear and Gaussian assumptions, making it difficult to handle cross-component updates in strongly coupled data assimilation (SCDA). The new approach employs nonlinear variable relationships established by a deep neural network (DNN) during the analysis stage of the EAKF, which nonlinearly projects observation increments into the state variable space. It can diminish errors in estimating cross-component error covariance arising from insufficient ensemble members, therefore improving the SCDA analysis. A conceptual coupled model is employed in this paper to conduct twin experiments, validating the DNN–EAKF’s capability to outperform conventional EAKF in SCDA. The results reveal that the DNN–EAKF can make SCDA superior to WCDA with a limited ensemble size. The root-mean-squared errors are reduced up to 70% while the anomaly correlation coefficients are increased up to 20% when the atmospheric observations are used to update the ocean variables directly. The other model components can also be improved through SCDA. This approach is anticipated to offer insights for future methodological integrations of machine learning and data assimilation and provide methods for SCDA applications in coupled general circulation models.

Infinite-memory classical wave-particle entities, attractor-driven active particles, and the diffusionless Lorenz equations.

A classical wave-particle entity (WPE) can materialize as a millimeter-sized droplet walking horizontally on the free surface of a vertically vibrating liquid bath. This WPE comprises a particle (droplet) that shapes its environment by locally exciting decaying standing waves, which, in turn, guides the particle motion. At high amplitude of bath vibrations, the particle-generated waves decay very slowly in time and the particle motion is influenced by the history of waves along its trajectory. In this high-memory regime, WPEs exhibit hydrodynamic quantum analogs where quantum-like statistics arise from underlying chaotic dynamics. Exploration of WPE dynamics in the very high-memory regime requires solving an integrodifferential equation of motion. By using an idealized one-dimensional WPE model where the particle generates sinusoidal waves, we show that in the limit of infinite memory, the system dynamics reduce to a 3D nonlinear system of ordinary differential equations (ODEs) known as the diffusionless Lorenz equations (DLEs). We use our algebraically simple ODE system to explore in detail, theoretically and numerically, the rich set of periodic and chaotic dynamical behaviors exhibited by the WPE in the parameter space. Specifically, we link the geometry and dynamics in the phase-space of the DLE system to the dynamical and statistical features of WPE motion, paving a way to understand hydrodynamic quantum analogs using phase-space attractors. Our system also provides an alternate interpretation of an attractor-driven particle, i.e., an active particle driven by internal state-space variables of the DLE system. Hence, our results might also provide new insights into modeling active particle locomotion.

System for automated design of resonant inverters

In the MATLAB environment, with the help of author's code, a programming environment is developed in which the input parameters are entered, the type and structure of the inverter is selected, and the values of the circuit elements are automatically calculated. Finally, for the purpose of verification, the operation of the designed inverter is simulated. From the resulting simulation, the overall behavior of the state space variables is seen.

State-Spatial Viewpoint of Stress in Thermally Postbuckled and Nonlinearly Bent FG Saturated Poroelastic Circular Plates

A dimensionless discrete state-space mathematical model is proposed for stress analysis of an axially-symmetric saturated poroelastic circular plate being loaded by temperature rise of one of the flat faces. Computation of stress by means of this model is free from a need for differentiation. The curves of thermal postbuckling, thermal nonlinear bending, radial stress, circumferential stress and resultant radial force have been achieved by means of six state-space variables and differential quadrature procedure. The effects of loading temperature, boundary conditions, porosity, pore distribution and fluid pore pressure on the thermal post buckling and nonlinear bending phenomena have been investigated. The critical postbuckling thermal load has been determined by means of a numerical algorithm that does not converge to trivial solution because it starts from a relatively great numerical thermal load. Contrary to the governing equation in usual form, the governing equations in state space together with the state equations equalize the number of the governing assembled difference equations and that of the unknowns, and eventually do not require to apply the so-called auxiliary extra boundary conditions at the nodes adjacent to the boundary nodes. As another advantage, in state-spatial viewpoint, there is not any necessity for computing the coefficients of derivatives with order higher than unity.

Ecological dynamic regimes: Identification, characterization, and comparison

AbstractUnderstanding ecological dynamics has been a central topic in ecology since its origins. Yet, identifying dynamic regimes remains a research frontier for modern ecology. The concept of ecological dynamic regime (EDR) emerged to emphasize the dynamic property of steady states in nature and refers to the fluctuations of ecosystems around some trend or average. Identifying and characterizing EDRs is of utmost importance in the current context of global change since they form the reference against which post‐disturbance dynamics must be compared to assess ecological resilience. However, the implementation of EDRs in empirical science is still challenging given the high dimensionality and stochasticity of ecological data and the large volume of data required to distinguish stochastic dynamics from general and predictable dynamics. The era of big data and the recent advances in quantitative ecology and data science offer an opportunity to study dynamic regimes using empirical approaches from a new perspective. This paper presents a novel methodological framework to describe EDRs from a set of ecological trajectories defined by the temporal changes of state variables in a multidimensional state space. In our framework, we formally define EDRs and include analytical tools to identify, characterize, and compare EDRs based on their geometric characteristics. More specifically, we propose different ways to identify EDRs from empirical data, develop a new algorithm to identify representative trajectories summarizing the main dynamic patterns, propose a set of metrics to describe the internal distribution of ecological trajectories, and define a dissimilarity index to compare two or more dynamic regimes based on their shape and position in the state space. We used artificial data to illustrate the different elements of our framework and applied our analyses to real data, using permanent sampling plots of Canadian boreal forests as an example. Overall, our framework contributes to filling the gap between theoretical and empirical ecology by providing robust analytical tools to assess ecological resilience and study ecosystem dynamics from a multidimensional perspective and considering the variability of natural systems.

Component Analysis and Accuracy Improvement of Linear Power Flow Equation Based on Legendre Polynomial Expansion

The linearization of the power flow equation is widely used in power industry. Existing linearization approaches are generally regarded as nonlinear state variable space transformation, where the original power flow equation can be approximately reformulated as the linear forms in transformed state variable spaces. However, the optimality of linear power flow equations cannot be theoretically compared in different spaces and is only verified based on case studies. In this paper, based on Legendre polynomial expansion, power flow equations are uniformly transformed into a single state variable space, where dimensions correspond to certain orders of Legendre expansion. Through component analysis of power flow equations on each dimension, we find that the accuracy of the linear power flow equation can be improved by formulating an appropriate state variable space transformation to reduce Legendre component loss. Based on this, a linearization method minimizing Legendre component loss is formulated. Compared with the regular case-based linearization, the proposed method does not depend on empirical data, and can theoretically guide the selection of the linear power flow equation within the specified operating bound. The accuracy performance is verified in OPF calculation based on numerous IEEE and Polish test systems.

A New Class of Nonlinear Resonance Networks Modeled by Levinson–Smith and Liénard Equations

We propose a new class of nonlinear resonance networks which are modeled by standard second-order nonlinear differential equations of the Levinson-Smith type or its subset, the Liénard type. In particular, we modify series and parallel RLC resonance networks such that the passive resistor in these networks is composed of a fixed part and a variable voltage-or current-controlled part. The variable resistor is then made controllable by one of the circuit’s state-space variables leading to an embedded self feedback control mechanism. A possible discrete component circuit realizing the proposed concept is presented along with its simulations and experimental verification. The filter response behavior of one of the modified series resonance circuits is also experimentally verified using a Field Programmable Analog Array.

Non-Parametric and Robust Sensitivity Analysis of the Weather Research and Forecast (WRF) Model in the Tropical Andes Region

With the aim of understanding the impact of air pollution on human health and ecosystems in the tropical Andes region (TAR), we aim to couple the Weather Research and Forecasting Model (WRF) with the chemical transport models (CTM) Long-Term Ozone Simulation and European Operational Smog (LOTOS–EUROS), at high and regional resolutions, with and without assimilation. The factors set for WRF, are based on the optimized estimates of climate and weather in cities and urban heat islands in the TAR region. It is well known in the weather research and forecasting field, that the uncertainty of non-linear models is a major issue, thus making a sensitivity analysis essential. Consequently, this paper seeks to quantify the performance of the WRF model in the presence of disturbances to the initial conditions (IC), for an arbitrary set of state-space variables (pressure and temperature), simulating a disruption in the inputs of the model. To this aim, we considered three distributions over the error term: a normal standard distribution, a normal distribution, and an exponential distribution. We analyze the sensitivity of the outputs of the WRF model by employing non-parametric and robust statistical techniques, such as kernel distribution estimates, rank tests, and bootstrap. The results show that the WRF model is sensitive in time, space, and vertical levels to changes in the IC. Finally, we demonstrate that the error distribution of the output differs from the error distribution induced over the input data, especially for Gaussian distributions.

Unsupervised and supervised learning for the reliability analysis of complex systems

AbstractIn this paper, a strategy to deal with high‐dimensional reliability systems with multiple correlated components is proposed. The goal is to construct a state function that enables the classification of the states of components in one of two categories, that is, failure and operative, in case of dealing with a large number of units in the system. To this end, it is proposed a new algorithm that combines a factor analysis algorithm (unsupervised learning) with local‐logistic and isotonic regression (supervised learning). The reliability function is estimated and system failures are predicted in terms of the variables in the original state space. The dimensions in the latent state space are defined by blocks of units with a certain dependence structure. The flexibility of the model allows quantifying locally the effect that a particular unit has on the system performance and a ranking of components can be obtained under the philosophy of the Birnbaum importance measure. The good performance of the proposal is assessed by means of a simulation study. Also a real data case is considered to illustrate the method.

Comparing Explicit and Implicit Methods for Estimating the Region of Attraction

The region of attraction (ROA) is an important tool in investigating control and dynamic systems. Numerous computational methods have been proposed for estimating the ROA within the Mathematics, Power systems, and Control community. These methods employ different methods such as invariant manifolds, linear differential inclusion, level set methods, the sum of squares decomposition, and many others. This paper provides new insights into these methods and divides them into two classes: explicit and implicit. The explicit methods discretize the ROA (or the boundary of the ROA) into a finite union of geometric elements and store them directly. The essential idea of the implicit methods is to present the ROA implicitly, meaning that it is feasible to find the ROA as the level set of some function of the state space variables. The key point is the iteration and optimization of this implicit function. The explicit and implicit methods are compared and discussed by investigating some numerical examples. In particular, we consider the determination of the boundary of the ROA using the stable manifolds, and the estimation of the ROA as backward reachable sets using a Hamilton-Jacobi-Isaacs partial differential equation.

Observer-Based Robust Fault Predictive Control for Wind Turbine Time-Delay Systems with Sensor and Actuator Faults

This paper presents a novel observer-based robust fault predictive control (OBRFPC) approach for a wind turbine time-delay system subject to constraints, actuator/sensor faults, and external disturbances. The proposed approach is based on an augmented state-space representation that contains state-space variables and estimation errors. The proposed augmented representation is then used to synthesize a robust predictive controller. In addition, an observer is developed and used to estimate both state variables and actuator/sensor faults. To ensure that the proposed approach has disturbance rejection capabilities, the disturbance estimates were merged with the prediction model. In addition, the disturbance rejection capabilities and fault tolerance were insured by formulating the control process as an optimization problem subject to constraints in terms of linear matrix inequalities (LMIs). As a result, the controller gains are acquired by solving an LMI problem to guarantee input-to-state stability in the presence of sensor and actuator faults. A simulation example is conducted on a nonlinear wind turbine (1 MW) model with 3 blades, a horizontal axis, and upwind variable speed subject to actuator/sensor faults in the pitch system. The results demonstrate the ability of the proposed method in dealing with nonlinear systems subject to external disturbances and keeping the control performance acceptable in the presence of actuator/sensor faults.

Polyphase Permanent Magnet Synchronous Motors Direct Current Model Predictive Control with Long Prediction Horizons

This manuscript presents a novel direct current model predictive control with long prediction horizon for medium-voltage polyphase permanent magnet synchronous motor drives. By utilizing the proposed technique, we can reduce the armature current harmonics and torque ripples, minimize the electrical and mechanical losses, improve the torque and speed rendering quality, and achieve a highly reliable permanent magnet motor drive. The state-space model of a representative polyphase permanent magnet synchronous motor is derived with the armature current and flux linkage jointly chosen as the state-space variables. Leveraging completing the squares, the mixed-integer-quadratic-programming (MIQP) problem can be formulated and efficiently solved, which provides the optimal switching sequence for the IGBT inverter. The proposed control algorithm is also implemented and examined with computer simulation to show the robustness and effectiveness.

Data-driven varying state-space model based on thermal network for transient temperature field prediction of motorized spindles

• 1) Rapid prediction of the transient temperature distribution. • 2) Parameter estimation driven by FE simulation and experimental data. • 3) Accuracy validated by thermal images of undetectable regions. • 4) Real-time correction of temperature prediction bias. Analyzing and modeling the thermal characteristics of the spindle is crucial to improving the thermal stability and intelligence of CNC machine tools. However, there is a lack of accurate real-time prediction methods for the transient temperature distribution inside the spindle. In this study, a thermal network consisting of thermal capacitances and resistors is constructed based on the thermal structure of a motorized spindle, and a varying state-space (VSS) model varying with node temperature and rotational speed is proposed to solve the thermal network. The parameters of this model are determined by a two-step estimation process, driven by simulation data of a finite element (FE) model under specific boundary conditions and experimental sensor data obtained from a series of thermal tests. The validation based on thermal experiment shows that the VSS model has high prediction accuracy with the average root mean square (RMS) bias of 0.5141°C. Thermal images of the rotating shaft also show that the proposed VSS model maintains high accuracy in predicting the temperature of the undetectable regions. In addition, a temperature prediction system (TPS) with bias correction is constructed based on two built-in temperature sensors in the spindle to further improve prediction accuracy, with the RMS bias reduced by 10.4% to 0.4606°C. All the results show that the real-time temperature field distribution of motorized spindles can be rapidly, accurately, and completely inferred based on the rotational speed and a few temperature sensors. The proposed modeling approach has the potential to be integrated into edge computing devices of intelligent spindles.

Optimization approach to the design of nonlinear control system controllers

The optimization approach is applied to the synthesis and optimization of nonlinear real-time feedback optimal control system of a certain Maglev platform. To optimize the nonlinear control law, the integral functional criteria is minimized, which evaluates the quality of the dynamics of not one trajectory, but an ensemble of nonlinear trajectories of the system. The considered ensemble of trajectories covers the entire area of the engineering gap between the platform and the guide rails. In this area the magnetic forces provide highly nonlinear effects due to the considered design features of the object. At the same time, it is required to provide the stabilization within the entire engineering gap. It makes this statement to be a multi-input nonlinear control problem. The components of the feedback control law vector have a polynomial form of the state-space variables. As a result of computational optimization of trajectories ensemble, a class of Pareto-optimal polynomial regulators is constructed for considered control object. In the presented set, each Pareto-optimal point corresponds to a specific designed controller and investigated functional criteria which evaluates the entire ensemble of perturbed nonlinear trajectories. This allows a research engineer to choose various nonlinear regulators and achieve a compromise between stabilization accuracy and energy costs.