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This work employs the principles of time-variant systems theory to investigate the unsteady aerodynamics of rotary-wing configurations under periodic equilibrium conditions. Their application enables an extension of the pulse technique for system identification, as well as the adaptation of the linear-frequency-domain formulation commonly utilized in fixed-wing to rotary-wing scenarios. These methodologies effectively incorporate the aerodynamic nonlinearities associated with the equilibrium state into an efficient time-variant linearized representation of the unsteady aerodynamics. To promote its application in the context of rotary-wing aeroelasticity, a state-space realization based on a periodic autoregressive model with exogenous input is subsequently employed. Upon transformation from discrete to continuous time, the resulting aerodynamic model adopts a linear continuous-time periodic state-space formulation, offering compatibility for its coupling with a wide range of structural models. The proposed aerodynamic framework tailored to rotary-wing aeroelasticity holds applicability across a spectrum of aerodynamic models of arbitrary complexity, spanning from incompressible potential flow approximations to potentially more sophisticated methods. Showcasing the potential of this framework, the widely studied lossy Mathieu equation and the aerodynamic response to a flap perturbation about the periodic equilibrium condition of a prototypical rotor blade section, incorporating nonlinearities through an analytical dynamic stall model, are considered. [ABSTRACT FROM AUTHOR]

Hysteresis is a fundamental characteristic of magnetic materials. The Jiles–Atherton (J-A) hysteresis model, which is known for its few parameters and clear physical interpretations, has been widely employed in simulating hysteresis characteristics. To better analyze and compute hysteresis behavior, this study established a state space representation based on the primitive J-A model. First, based on the five fundamental equations of the J-A model, a state space representation was established through variable substitution and simplification. Furthermore, to address the singularity problem at zero crossings, local linearization was obtained through an approximation method based on the actual physical properties. Based on these, the state space model was implemented using the S-function. To validate the effectiveness of the state space model, the hysteresis loops were obtained through COMSOL finite element software and tested on a permalloy toroidal sample. The particle swarm optimization (PSO) method was used for parameter identification of the state space model, and the identification results show excellent agreement with the simulation and test results. Finally, a closed-loop control system was constructed based on the state space model, and trajectory tracking experiments were conducted. The results verify the feasibility of the state space representation of the J-A model, which holds significant practical implications in the development of magnetically shielded rooms, the suppression of magnetic interference in cold atom clocks, and various other applications. [ABSTRACT FROM AUTHOR]

In this paper we derive the Beveridge–Nelson (BN) decomposition and the state space representation for various multivariate (co)integrated time series subject to Markov switching in regime. Then we provide explicit expressions for the BN trend and cyclical components in terms of the matrices involved in the state space representation of the considered process. Our matrix expressions in closed form improve computational performance since they are readily programmable and greatly reduce the computational cost. Then we develop impulse-response function analysis and represent the BN trend component as a random walk. An empirical application on the world economy illustrates the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

Hysteresis is a fundamental characteristic of magnetic materials. The Jiles–Atherton (J-A) hysteresis model, which is known for its few parameters and clear physical interpretations, has been widely employed in simulating hysteresis characteristics. To better analyze and compute hysteresis behavior, this study established a state space representation based on the primitive J-A model. First, based on the five fundamental equations of the J-A model, a state space representation was established through variable substitution and simplification. Furthermore, to address the singularity problem at zero crossings, local linearization was obtained through an approximation method based on the actual physical properties. Based on these, the state space model was implemented using the S-function. To validate the effectiveness of the state space model, the hysteresis loops were obtained through COMSOL finite element software and tested on a permalloy toroidal sample. The particle swarm optimization (PSO) method was used for parameter identification of the state space model, and the identification results show excellent agreement with the simulation and test results. Finally, a closed-loop control system was constructed based on the state space model, and trajectory tracking experiments were conducted. The results verify the feasibility of the state space representation of the J-A model, which holds significant practical implications in the development of magnetically shielded rooms, the suppression of magnetic interference in cold atom clocks, and various other applications.

Real-time Kinematic (RTK) positioning provides centimeter-level positioning accuracy within several seconds, but it has to rely on a nearby base station. Although Precise Point Positioning (PPP) supplies precise positions with one receiver, its convergence time takes several tens of minutes, which makes PPP not well suited for real-time kinematic applications where a rapid convergence is required. PPP-RTK integrates the benefits of PPP and RTK, which actually is PPP augmented by a ground GNSS network. The satellite orbit, clock offsets, signal biases, ionospheric and tropospheric corrections are determined based on this GNSS network, modeled as state space information and transmitted to PPP users. By applying these State Space Representation (SSR) corrections, a real-time kinematic PPP-RTK approach is developed and implemented, which can instantly resolve the ambiguities to integers and realize rapid convergence. In a static scenario, it realized an instant ambiguity resolution and a rapid convergence within 2 s in more than 90% of 120 hourly sessions. The PPP-RTK has been applied and evaluated in a kinematic scenario on the highway. The horizontal positioning errors are almost lower than 0.1 m except for the time of passing through bridges. After passing bridges, the PPP-RTK successfully resolved ambiguities within 2 s in 90.6% of the cases and achieved convergence in horizontal within 5 s in more than 90% of the cases. The PPP-RTK with a precision of 0.1 m and rapid convergence of several seconds benefits the precise navigation of automobile on the highway, which will support the development of autonomous driving in future. [ABSTRACT FROM AUTHOR]

Data-driven parametric reduced-order models (ROMs) in state-space form are valuable tools for rapid aeroelastic (AE) analysis and aerostructure control synthesis. However, the issue of state inconsistence (significant variations in model parameters over tradespaces) makes ROMs noninterpolatable, and therefore unable to accommodate use over broad flight parameter space. This paper presents a holistic framework that combines a system identification technique with state-consistence enforcement (SCE) and a genetic algorithm (GA) for the automated development of interpolatable AE ROMs across broad flight regimes. The SCE technique introduces a regularization term to the AutoRegressive model with eXogenous inputs (ARX) to specifically penalize model parameter variation between flight conditions. The GA autonomously guides the ROM development process toward optimal SCE-ARX hyperparameter selection that balances between model parameter variations and ROM accuracy. The GA-guided SCE-ARX approach is applied to build a parametric AE-ROM database at selected flight conditions, which, because of its state consistence, can be interpolated to create ROMs at any interstitial conditions, where training data or ROMs are not initially available, hence rapidly establishing the full coverage of the entire parameter space. The ROMs generated by the proposed method are compared with those by ARX, SCE, and GA-guided ARX in prediction accuracy. The individual and combined effects of SCE and GA on model parameter variation and ROM interpolatability are thoroughly investigated. The present method demonstrates the most accurate and robust performance for parametric ROM construction across the broad flight envelope. [ABSTRACT FROM AUTHOR]

This paper presents a summary of system identification flight testing and results for a variety of large and small fixed-wing and multirotor unmanned air systems at Texas A&M University from 1999 to 2023. The six different types of vehicles range from a large powered parafoil, to a fixed-wing vehicle with synthetic jet-actuated roll control effectors, to a radially asymmetric multirotor, to large and small fixed-wing vehicles, and to a Steppe eagle. The observer/Kalman filter identification algorithm is used to generate linear time-invariant state-space models, and the results for both near-real-time online model generation and postflight offline model generation are presented. The use and efficacy of a variety of test input types and their sensitivity to exogenous inputs such as turbulence, in addition to identified model evaluation and selection criteria, are discussed. Several generations of low size, weight, power, and cost flight-test instrumentation including the Developmental Flight-Test Instrumentation data acquisition package are also presented. Challenges that arose from the flight-testing campaigns along with solutions are highlighted in the paper. [ABSTRACT FROM AUTHOR]

Real-time Kinematic (RTK) positioning provides centimeter-level positioning accuracy within several seconds, but it has to rely on a nearby base station. Although Precise Point Positioning (PPP) supplies precise positions with one receiver, its convergence time takes several tens of minutes, which makes PPP not well suited for real-time kinematic applications where a rapid convergence is required. PPP-RTK integrates the benefits of PPP and RTK, which actually is PPP augmented by a ground GNSS network. The satellite orbit, clock offsets, signal biases, ionospheric and tropospheric corrections are determined based on this GNSS network, modeled as state space information and transmitted to PPP users. By applying these State Space Representation (SSR) corrections, a real-time kinematic PPP-RTK approach is developed and implemented, which can instantly resolve the ambiguities to integers and realize rapid convergence. In a static scenario, it realized an instant ambiguity resolution and a rapid convergence within 2 s in more than 90% of 120 hourly sessions. The PPP-RTK has been applied and evaluated in a kinematic scenario on the highway. The horizontal positioning errors are almost lower than 0.1 m except for the time of passing through bridges. After passing bridges, the PPP-RTK successfully resolved ambiguities within 2 s in 90.6% of the cases and achieved convergence in horizontal within 5 s in more than 90% of the cases. The PPP-RTK with a precision of 0.1 m and rapid convergence of several seconds benefits the precise navigation of automobile on the highway, which will support the development of autonomous driving in future.

The main continuous time Leech problems considered in this paper are based on stable rational finite dimensional operator-valued functions G and K. Here stable means that G and K do not have poles in the closed right half plane including infinity, and the Leech problem is to find a stable rational operator solution X such that G (s) X (s) = K (s) (s ∈ C +) and sup { ‖ X (s) ‖ : ℜ s ≥ 0 } < 1. In the paper the solution of the Leech problem is given in the form of a state space realization. In this realization the finite dimensional operators involved are expressed in the operators of state space realizations of the functions G and K. The formulas are inspired by and based on ideas originating from commutant lifting techniques. However, the proof mainly uses the state space representations of the rational finite dimensional operator-valued functions involved. The solutions to the discrete time Leech problem on the unit circle are easier to develop and have been solved earlier; see, for example, Frazho et al. (Indagationes Math 25:250–274 2014). [ABSTRACT FROM AUTHOR]

A novel global parametric system identification framework is introduced in this work for aeroelastic modeling under varying flight states. The presented framework is based on the functionally pooled (FP) time-series models that enable explicit analytical inclusion of any admissible flight states into the model parameters and thus the system dynamics. In this paper, the autoregressive (AR) type of the FP model, which is designated as the FP-AR, is employed to interpret the aerodynamics of a wing structure. The data were recorded by accelerometers during a dedicated wind-tunnel flutter test with the airspeed increasing all the way to the flutter boundary. Including the varying flight states defined by the increasing airspeed into the system modeling via the FP technique, the global framework provides a more sophisticated identification results compared with the traditional nonparametric Welch-based spectral estimation. Flutter occurrence is indicated by the stability margin of the aeroelastic system evaluated by the estimated FP-AR parameters based on Jury's stability criterion. For online application purpose, an iterative state-based FP-AR process is also proposed in this paper. Compared with the standard FP-AR modeling, the iterative realization is a developing process that provides a global approximation of the system dynamics at each flight state. Experimental evaluation demonstrates the feasibility and effectiveness of the proposed global framework in aeroelastic modeling while facilitating an accurate flutter boundary prediction. [ABSTRACT FROM AUTHOR]

High impedance faults present unique challenges for power system protection engineers. The first challenge is the detection of the fault, given the low current magnitudes. The second challenge is to locate the fault to allow corrective measures to be taken. Corrective actions are essential as they mitigate safety hazards and equipment damage. The problem of high impedance fault detection and location is not a new one, and despite the safety and reliability implications, relatively few efforts have been made to find a general solution. This work presents a hybrid data driven and analytical-based model for high impedance fault detection in distribution systems. The first step is to estimate a state space model of the power line being monitored. From the state space model, eigenvalues are calculated, and their dynamic behavior is used to develop zones of protection. These zones of protection are generated analytically using machine learning tools. High impedance faults are detected as they drive the eigenvalues outside of their zones. A metric called eigenvalue drift coefficient was formulated in this work to facilitate the generalization of this solution. The performance of this technique is evaluated through case studies based on the IEEE 5-Bus system modeled in Matlab. Test results are encouraging indicating potential for real-life applications. [ABSTRACT FROM AUTHOR]

When analyzing and synthesizing digital filters with different structures, their representation in the state space is most often used. But this is not the only way to describe the filter. A digital filter with an arbitrary structure is most adequately described by a topological matrix, the elements of which are transfer coefficients between nodes of a block diagram. This paper allows us to expand the capabilities of the mathematical model of a digital filter in the form of a topological matrix.

Micro turbojets can be used for propulsion of civilian and military aircraft, consequently their investigation and control is essential. Although these power plants exhibit nonlinear behaviour, their control can be based on linearized mathematical models in a narrow neighbourhood of a selected operating point and can be extended by using robust control laws like H∞ or Linear Quadratic Integrating (LQI). The primary aim of the present paper is to develop a novel parametric linear mathematical model based on state space representation for micro turbojet engines and the thrust parameter being Turbofan Power Ratio (TPR). This parameter is used by recent Rolls-Royce commercial turbofan engines but can be applied for single stream turbojet power plants as well, as it has been proven by the authors previously. An additional goal is to perform the identification for a particular type based on measurements of a real engine. This model has been found suitable for automatic control of the selected engine with respect of TPR, this has been validated by simulations conducted in MATLAB® Simulink® environment using acquired data from transient operational modes.

High impedance faults present unique challenges for power system protection engineers. The first challenge is the detection of the fault, given the low current magnitudes. The second challenge is to locate the fault to allow corrective measures to be taken. Corrective actions are essential as they mitigate safety hazards and equipment damage. The problem of high impedance fault detection and location is not a new one, and despite the safety and reliability implications, relatively few efforts have been made to find a general solution. This work presents a hybrid data driven and analytical-based model for high impedance fault detection in distribution systems. The first step is to estimate a state space model of the power line being monitored. From the state space model, eigenvalues are calculated, and their dynamic behavior is used to develop zones of protection. These zones of protection are generated analytically using machine learning tools. High impedance faults are detected as they drive the eigenvalues outside of their zones. A metric called eigenvalue drift coefficient was formulated in this work to facilitate the generalization of this solution. The performance of this technique is evaluated through case studies based on the IEEE 5-Bus system modeled in Matlab. Test results are encouraging indicating potential for real-life applications.

• Purely data-driven surrogate model for rapid seismic response modeling. • Better model interpretability with novel parameter-free physics-informed mechanism. • Superior performance in both prediction accuracy and robustness. • Fully-demonstrated numerical and experimental validations using diverse field record datasets. • Web program development and API integration of involved algorithms and models. Artificial neural networks have been proven promisingly powerful in developing a data-driven surrogate model for rapid seismic response modeling, while very few of them embody a physical mechanism with explicit interpretability. Herewith, this study proposes a novel physics-informed deep 1D convolutional neural network compiled in extended state space fusion (SSM-CNN) for enhanced seismic response modeling. In the SSM-CNN, an innovative parameter-free physics-constrained mechanism is designed and embedded for performance enhancement by construing the differential nexus of state variables derived from the state-space representation of initial structural response. Both the designing philosophy and mechanism translating of the SSM-CNN are elaborated exhaustively. To fully demonstrate the capability and superiority of proposed model compared to normal CNN, two groups of filed records of earthquake events with different sources from PEER and CESMD dataset were allocated for numerical and experimental validations, respectively. The validation results confirmed the effectiveness and superiority of physics-informed SSM-CNN in seismic response prediction. The sensitivity analysis and generalization analysis were also performed on the models for better understanding their interpretability. Involved algorithms and models in present study were integrated and developed into a web program, which affirmed a promising engineering applicability for rapid seismic response prediction. [ABSTRACT FROM AUTHOR]

This paper describes a method for statistically estimating five components included in the time series of vertical track geometry measured at the same point on a railway track. We have developed a statistical model to represent the change of vertical track geometry. The model decomposes the time series into five components: seasonality, trend, effects of maintenance works, short-term variation, and noise. The vertical geometry in the near future is also forecasted with the components. Two features of the model are as follows: first, the model extracts the effects of seasonal variations. We actually identified track geometry that changes seasonally at some fixed points. The seasonal variations are found to be relevant to rather air temperature than train loads. This finding is contrary to a general belief that track geometry changes monotonically due to daily train loads. Second, the Kalman filter algorithm is applicable to this model. The parameters included in the model are thus estimated effectively according to the maximum likelihood method. In addition, the five components are obtained according to the fixed-interval smoothing algorithm. The goals of this study are to help the scheduling of railway track maintenance with forecasted track geometry and to obtain new information on changes of track geometry.

Summary: Lithium‐ion battery state‐of‐health estimation is one of the vital issues for electric vehicle safety. In this work, a joint model‐based and data‐driven estimator is developed to achieve accurate and reliable state‐of‐health estimation. In the estimator, an increase in ohmic resistance extracted from the Thevenin model is defined as the health indicator to quantify the capacity degradation. Then, a linear state‐space representation is constructed based on the data‐driven linear regression. Furthermore, the Kalman filter is introduced to trace capacity degradation based on the novel state space representation. A series of battery aging datasets with different dynamic loading profiles and temperatures are obtained to demonstrate the accuracy and robustness of the proposed method. Results show that the maximum error of the Kalman filter is 2.12% at different temperatures, which proves the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Modal properties of the primary structure and tuned mass dampers are basic parameters for in situ tuned mass damper frequency tuning and periodic condition assessment of the structure–tuned mass damper system. In this study, a state space technique is developed for identifying the respective modal properties of structure and tuned mass damper device from the dynamic responses of the coupled structure–tuned mass damper systems. The coupled structure–tuned mass damper system is represented by a reduced two-degree-of-freedom model which characterizes the coupled dynamics of the structural mode under control and tuned mass damper. A simple expression is derived for calculating the respective modal properties of the structural mode and tuned mass damper from the modal properties of the coupled two-degree-of-freedom model. Stochastic subspace identification is employed to estimate the modal properties of the combined system from ambient or free vibration responses. Numerical simulation of two structures and experimental validation of a laboratory steel frame equipped with a tuned mass damper are carried out to verify the proposed method. It is shown the proposed method successfully identifies the modal properties of both the structural mode under control and the tuned mass damper. Compared to the ambient vibration data, the identification results are superior when using the free decay responses. When the tuned mass damper is not perfectly tuned to the primary structure, much accurate identification results can be obtained, especially for the damping ratios of the primary structure and the tuned mass damper. [ABSTRACT FROM AUTHOR]

Micro turbojets can be used for propulsion of civilian and military aircraft, consequently their investigation and control is essential. Although these power plants exhibit nonlinear behaviour, their control can be based on linearized mathematical models in a narrow neighbourhood of a selected operating point and can be extended by using robust control laws like H∞ or Linear Quadratic Integrating (LQI). The primary aim of the present paper is to develop a novel parametric linear mathematical model based on state space representation for micro turbojet engines and the thrust parameter being Turbofan Power Ratio (TPR). This parameter is used by recent Rolls-Royce commercial turbofan engines but can be applied for single stream turbojet power plants as well, as it has been proven by the authors previously. An additional goal is to perform the identification for a particular type based on measurements of a real engine. This model has been found suitable for automatic control of the selected engine with respect of TPR, this has been validated by simulations conducted in MATLAB® Simulink® environment using acquired data from transient operational modes. [ABSTRACT FROM AUTHOR]

This paper states wireless power transfer (WPT) from an AC power supply to a micro implant device in human body. At first, an equivalent circuit of WPT which contains biomedical tissue is constructed with an AC power supply, parasitic components, load resistance, and inductances. Then a state equation which stands for the behavior of circuit is found, and the expression of efficiency is derived as the ratio of the power of power supply and load. Finally an experiment is conducted based on the theoretical calculation, and the error between experimental and calculated result is computed and examined. [ABSTRACT FROM AUTHOR]

This paper presents a modified differential operator multiplication (DOM) method for solving a certain class of fractional differential equations (FDEs), with emphasis on linear oscillators subjected to periodic excitation. The main idea of DOM is to transform the considered FDEs with rational order r/m into rth-order ordinary differential equations (ODEs), herein r and m are positive integers. The transformation is realized by differentiating the FDEs stepwise with fractional-order r/m, until the rth-order derivative is reached due to the accumulative property for FDs. In the modified method, differently, first-order ODEs are deduced by transforming the FDEs with order r/m into 1/m. In addition, we introduce auxiliary state space variables to represent the FDs of inhomogeneous terms such as triangle functions. Exact and explicit first-order ODEs are deduced and solved by the Runge–Kutta algorithm. To validate the modified DOM, we solve the fractional Kelvin-Voigt equation and harmonically excited oscillators with visco-elastic dampings. The presented method can provide highly accurate solution, at the expense of linearly increasing computational resources as the solution domain expands. Such high computation accuracy and efficiency would potentially enable the presented method to become a benchmark comparison for solving certain FDEs, especially harmonically excited fractional oscillators. [ABSTRACT FROM AUTHOR]

We develop and discuss a parameterization of vector autoregressive moving average processes with arbitrary unit roots and (co)integration orders. The detailed analysis of the topological properties of the parameterization—based on the state space canonical form of Bauer and Wagner (2012)—is an essential input for establishing statistical and numerical properties of pseudo maximum likelihood estimators as well as, e.g., pseudo likelihood ratio tests based on them. The general results are exemplified in detail for the empirically most relevant cases, the (multiple frequency or seasonal) I(1) and the I(2) case. For these two cases we also discuss the modeling of deterministic components in detail.