State-space Method Research Articles

Dynamic analysis of segmental linings of shield tunnels using a state space method and its application in physical test interpretation

Based on the state space method and D'Alembert's principle, a new analytical method is established to study the dynamic response of circular segmental linings of shield tunnels. The tunnel lining segments are considered to be curved Euler–Bernoulli beams, the joints connecting the segments are modeled by a series of distributed springs, and the lining–surrounding soil interaction is represented by distributed reaction springs with viscous dampers. With the state space method, the governing equations can be concisely expressed in matrix form, and a separate variable method in conjunction with a frequency scanning strategy is employed to obtain the natural frequencies and corresponding modal shapes of the free vibration of the linings. The orthogonality of the vibration modes of the linings is demonstrated using a symplectic inner product, and the response of the linings under arbitrary dynamic loads is solved using the modal superposition method. Numerical and model experimental examples are presented to verify the efficiency and robustness of the proposed method. We prove that the proposed method can solve the dynamic response of segmental linings by considering the effect of joint and asymmetric loading conditions with high efficiency and accuracy.

A Two-Switch SEPIC-Based Nonisolated Three-Port Converter Featuring High Step-Up Gain for Solar PV Applications

A two-switch nonisolated DC–DC three-port converter (TPC) based on a modified SEPIC circuit with a high voltage gain is introduced and a unified power control strategy is proposed in this article. The proposed TPC is integrated with one low-voltage input and one high-voltage port and is suitable for photovoltaic (PV) applications. The operating principle of this TPC is analyzed in detail and then its static voltage gain is determined. In addition, the advantage of using a modified SEPIC circuit is that fewer components are employed compared to a similar topology. Furthermore, the state space method is adopted to analyze this multiple-input multiple-output (MIMO) system and then a small signal model is built to design an appropriate control strategy. Finally, the proposed 100 W TPC connects a solar PV energy storage system to a load demonstrating efficiency ranging from 85% to 94%. Moreover, the steady- and dynamic-state performances of this TPC are verified in the SimStar MT3200 HIL platform, which illustrates the feasibility of the proposed TPC and its power control strategy for solar PV applications.

Research on Transient Over-Voltages of High-Speed Train Passing Articulated Split-Section Insulator

The electromagnetic transient processes generated as a high-speed train (HST) passes the articulated split-section insulator cause over-voltages on the train roof and train body (TB), and thereby, an adverse effect is exerted on the electronic equipment. By this view, this article focuses on identifying the root causes and influencing factors pertinent to over-voltages. To begin with, the state-space analysis method is adopted to examine the probability and characteristics of arcing. Subsequently, the integrated vehicle-grid models associated with the split-section arcing are established to precisely simulate the over-voltage phenomenon in the independent transient processes of entering and leaving the insulator. The obtained results indicate that the hazardous over-voltages can be easily produced, and the behaviors of surges on the TB are very similar to that in the processes of rising and dropping pantograph. The influences of different variables, including the feeder phase, vehicle speed, lifting height, TB grounding pattern, and other HST’s simultaneous arcing impacts, are further revealed to discuss possible over-voltage suppression measures.

RCS Diagnostic Imaging Using Parameter Extraction Technique of State Space Method

AbstractThe signature extraction and processing are the key aspects of enhancing recognition ability for radar target characteristics. In this paper, to reveal the intrinsic property of the target and improve the accuracy of radar cross section (RCS), we proposed RCS diagnostic imaging technique, extracting the parameters of scattering center model by state space method (SSM), to analyze the signature of GTD‐based returns. To demonstrate the effectiveness of SSM, the comparison with estimating signal parameter via rotational invariance techniques method by the analysis of goodness‐of‐fit and root mean square error, reconstructing the RCS profile through original signal model, and employing SSM to extract the signature of specular and creeping wave from the PEC sphere. Furthermore, the RCS diagnostic imaging by SSM extracting position and amplitude is discussed, and range‐isolated pole technique specific to the creeping wave extraction is addressed the advantage of SSM.

Dynamics of axially moving beams: A finite difference approach

In this paper, a finite difference approach is being presented as the most reliable technique to investigate the non-linear transverse vibration of an axially moving beam. Firstly, Hamilton’s principle is used to derive the governing hyperbolic partial differential equation (HPDE) of free transverse vibration. Then finite difference along with state space method is used to convert the partial differential equation into a system of coupled first-order ordinary differential equations (ODE’s). Comparison of the proposed finite difference model is made with both the numerical and analytical models. It is noted that the finite difference model is in excellent agreement with the modal analysis approach (analytical solutions) as compared to the generalized integral transform technique GITT (numerical method). A parametric study was also presented to examine the impact of system parameters, such as axial translation speed and flexure rigidities of the beam on the transverse response amplitude, frequencies and instabilities. The transverse vibration of the beam at selected points along its length demonstrates higher-frequency oscillations that corresponds to a lower axial speed. With the increase of beam flexural rigidity, the divergence critical speed increases. Coupled effect of axially moving beam and rotating rolls is also considered.

An Analytical Solution for the Dynamics of a Functionally Graded Plate resting on Viscoelastic Foundation

This paper deals with the dynamic response of Functionally Graded Material (FGM) plates resting on a viscoelastic foundation under dynamic loads. The governing equations are derived by using Hamilton’s principle using the classical plate theory and the higher-order shear deformation plate theory. Using state-space methods to find the closed-form solution of the dynamic response of functionally graded rectangular plates resting on a viscoelastic foundation. Numerical examples are given for displacement and stresses in the plates with various structural parameters and the effects of these parameters are discussed. The result of the numerical example shows a marked decrease in displacement and stresses as the coefficient of viscous damping is increased.

Comprehensive analysis of the effects of magnetic field gradient on the performance of the SERF co-magnetometer.

The magnetic field gradient affects the improvement of sensitivity and magnetic field suppression ability of the spin-exchange relaxation-free co-magnetometer. This paper proposes a response model of a co-magnetometer considering magnetic field gradient based on state-space method. The effects of transverse and longitudinal magnetic field gradients on the system's scale factor, bandwidth and magnetic field response are analyzed. The analysis shows that transverse gradient affects the whole frequency band of system response, including steady-state and dynamic performance, while longitudinal gradient only affects steady-state response. With the increase of the gradient, the effect becomes more significant. The test results are in agreement with the theory, proving the accuracy of the theoretical analysis. The rotational sensitivity at 1 Hz decreases from 6.51 ×10-6 °/s/Hz1/2 to 5.05×10-5 °/s/Hz1/2 in the presence of a magnetic field gradient of -40 nT/cm, so the effect of the magnetic field gradient is critical. This work provides an accurate model for evaluating the effects of magnetic field gradients and provides a method for suppressing gradients using gradient coils, which are important for improving the sensitivity and accuracy of co-magnetometers.

Acoustic insulation characteristics improvement of a thick CNT-reinforced doubly-curved shell by using GPLRC and MEE composite layers

Noise reduction in structures and human living environments is one of the most important issues in engineering that is always given special attention. Sound insulation has always been improved using different methods, one of which is to use the properties of materials. Herewith, the aim of this paper is to take advantage of graphene-platelet reinforced composites and magneto-electro-elastic (MEE) material properties for sound attenuation. The present paper deals with the analysis of sound transmission loss (STL) through a three-layer sandwich doubly-curved shell where an MEE sheet is integrated with two nanocomposite sheets. In addition, these two nanocomposite sheets are reinforced by functionally graded (FG) distributions of CNT and graphene platelet (GPL)-reinforced composites, respectively. Firstly, the three-dimensional elasticity theory is employed to derive the governing equations of motion. Then, the vibroacoustic analysis for the resultant equations is completed according to the state space and transfer matrix method. Comparing the obtained results with the available literature discloses that the offered procedure has a high precision for structural acoustic problems. In the next step, in addition to inspecting two kinds of MEE composites, the effective parameters, such as layup configuration, FG distribution, volume fraction, weight fraction, radii of curvature, electromagnetic boundary conditions, and interphase thickness, are assessed on the STL. This assessment shows that the parameters involved in this paper are highly interdependent. Accordingly, the analysis of these parameters is done simultaneously with the aid of three- and four-dimensional plots in order that the optimal value for each parameter can be realized. As seen clearly in the outcomes, the electromagnetic boundary conditions parameters, compared to the other parameters, can much more alter the STL trend, so that a slight change in electric potential results in great change in the STL.

Analysis Multivariate Time Series Using State Space Model for Forecasting Inflation in Some Sectors of Economy in Indonesia

Many analytical methods can be utilized for multivariate time series modeling. One of the analytical models for modeling time series data with multiple variables is the State Space Model. The data to be analyzed in this study is inflation data from expenditure groups such as processed foods, beverages, cigarettes, and tobacco; and housing inflation for water, electricity, gas, and fuel from January 2001 to December 2021. The aim is to determine the best State Space Model that fits the data for forecasting. In this study, the State Space method will be utilized further with multivariate time series data and represent State Space in Vector Autoregressive (VAR) to determine the relationship between groups of observed variables.

Wave propagation in a porous functionally graded curved viscoelastic nano-size beam

In this paper, wave propagation analysis of a viscoelastic system of curved nanobeams made of porous functionally graded materials (P-FGM) is studied, for the first time. The displacement fields for the curved nanobeam are obtained via a higher-order shear deformation beam theory which contains curvilinear axial, rotation, transverse, and thickness stretching effects, while size effects are considered using nonlocal strain gradient theory. The effective material properties for P-FGMs are expressed by modified model of power-law variation which is connected with cosine functions to estimate the effect of porosity and Kelvin–Voigt viscoelastic model for estimating viscoelastic behavior on mechanics of nanostructures. The Hamilton’s principle is applied to find governing equations of motion of the viscoelastic curved nanobeam. The state space method and a set of mathematical series are developed to find response. The Influence of porosity value and types of distributions, viscosity coefficient, power-law index, geometry, and opening angle (related to curvature radius) on phase velocity of curved viscoelastic nanobeams is investigated.

Subspace State-Space Identification of Nonlinear Dynamical System Using Deep Neural Network with a Bottleneck

This paper proposes a new type of subspace state-space system identification method for nonlinear dynamical systems, which generates a model consisting of a state estimator and a predictor that can be directly used for model predictive control (MPC). The main feature of the proposed method is that it uses a neural network with a bottleneck layer between the state estimator and predictor to represent the input-output dynamics, and it is proven that the state of the dynamical system can be extracted from the bottleneck layer based on the observability of the target system. The training of the network is shown to be a natural nonlinear extension of the subspace state-space system identification method established for linear dynamical systems. This correspondence provides interpretability and optimality to the resulting model based on linear control theory. The usefulness of the proposed method and the interpretability of the model are demonstrated through an illustrative example of MPC.

Harmonic State-Space Based AC-Side Impedance Model of MMC and High Frequency Oscillation Characteristics Analysis

Recently, high-frequency oscillation of the modular multilevel converter (MMC) based high-voltage direct current (HVDC) projects has attracted great attentions. In order to analyze the small-signal stability, this paper uses the harmonic state-space (HSS) method to establish a detailed frequency domain impedance model of the AC-side of the HVDC transmission system, which considers the internal dynamic characteristics. In addition, the suggested model is also used to assess the system's high-frequency oscillation mechanism, and the effects of the MMC current inner loop control, feedforward voltage links, and control delay on the high-frequency impedance characteristics and the effect of higher harmonic components. Finally, three oscillation suppression schemes are analyzed for the oscillation problems occurring in actual engineering, and a simplified impedance model considering only the high-frequency impedance characteristics is established to compare the suppression effect with the detailed impedance model to prove its reliability.

Hybrid Decoders for Marked Point Process Observations and External Influences.

Internal physiological processes govern multiple state variables within the human body. Estimating these from point process-type bioelectric and biochemical observations is a challenge. Here we seek to estimate cortisol-related energy production and sympathetic arousal based on point process and continuous-valued data while permitting an external influence to affect the state estimates. Traditional point process state-space methods, such as those used for estimating the aforementioned quantities from cortisol and skin conductance measurements respectively, suffer from the inability to permit the state estimates to also fit to an external influence (e.g. labels) or be guided by it. Here we modify an existing recurrent neural network (RNN) approach for state-space estimation through a weighted cost-function to enable a hybrid estimator that has this capability. Results on cortisol data based on a hypothetical sleep-wake influence term show how energy production can be estimated by permitting the estimates to fit to the external influence as much as desired. We further show how overfitting may be reduced by using circadian rhythm-based influence terms. Results on skin conductance data also indicate how the method can be used to estimate sympathetic arousal in an experiment containing stressors and relaxation, and permit an external influence as well. The RNN-based hybrid method is thus able to recover internal physiological states from point process and continuous-valued observations while permitting an external influence to guide the estimates. The hybrid estimator could be embedded within wearable monitors that can be tailored based on domain expertise or individual feedback.

Low-Frequency Oscillation Analysis of Grid-Connected VSG System Considering Multi-Parameter Coupling

With the increasing integration of new energy generation into the power system and the massive withdrawal of traditional fossil fuel generation, the power system is faced with a large number of stability problems. The phenomenon of low-frequency oscillation caused by lack of damping and moment of inertia is worth studying. In recent years, virtual synchronous generator (VSG) technique has been developed rapidly because it can provide considerable damping and moment of inertia. While improving the stability of the system, it also inevitably causes the problem of active power oscillation, especially the low mutual damping between the VSG and the power grid will make the oscillation more severe. The traditional time-domain state-space method cannot reflect the interaction among state variables and study the interaction between different nodes and branches of the power grid. In this paper, a frequency-domain method for analyzing low-frequency oscillations considering VSG parameter coupling is proposed. First, based on the rotor motion equation of the synchronous generator (SG), a second-order VSG model and linearized power-frequency control loop model are established. Then, the differences and connections between the coupling of key VSG parameters and low-frequency oscillation characteristics are studied through frequency domain analysis. The path and influence mechanism of a VSG during low-frequency power grid oscillations are illustrated. Finally, the correctness of the theoretical analysis model is verified by simulation.

Three-Dimensional Thermoelasticity Analysis of Viscoelastic FGM Plate Embedded in Piezoelectric Layers under Thermal Load

Due to the high importance of viscoelastic materials in modern industrial applications, besides the intensive popularity of piezoelectric smart structures, analyzing their thermoelastic response in extreme temperature conditions inevitably becomes very important. Accordingly, this research explores the thermoviscoelastic response of sandwich plates made of a functionally-graded Boltzmann viscoelastic core and two surrounding piezoelectric face-layers subjected to electrothermal load in the platform of three-dimensional elasticity theory. The relaxation modulus of the FG viscoelastic layer across the thickness follows the power law model. the plate’s governing equations are expressed in the Laplace domain to handle mathematical complications corresponding to the sandwich plate with a viscoelastic core. Then, the state-space method, combined with Fourier expansion, is utilized to extract the plate response precisely. Finally, the obtained solution is converted to the time domain using the inverse Laplace technique. Verification of the present formulation is compared with those reported in the published papers. Finally, the influences of plate dimension, temperature gradient, and relaxation time constant on the bending response of the above-mentioned sandwich plate are examined. As an interesting finding, it is revealed that increasing the length-to-thickness ratio leads to a decrease in deflections and an increase in stresses.

Seismic Response of Two-way Asymmetric building with Semi-Active Stiffness Damper Under Bi-Directional Excitations

This article presents a seismic response of a two-way asymmetric building installed with a semi-active stiffness damper (SASD). The seismic response analysis of asymmetric structure is studied in terms of peak responses subjected to bi-directional excitations. The responses are obtained by numerically solving the governing equation of motion using state-space method. The effect of stiffness ratio and lyapunov constant on peak response which includes lateral, torsional displacement, and acceleration. The responses of asymmetric controlled and uncontrolled systems are simulated through MATLAB. To study the effectiveness of dampers, the controlled response of the asymmetric system is compared with the corresponding uncontrolled response. The parametric study indicated that the semi-active stiffness damper is quite effective in reducing various responses. Furthermore, on the optimum value of stiffness ratio, effectiveness of semi-active stiffness damper is reduced for lateral and torsional acceleration.

Exceptional Points Induced by Time-Varying Mass to Enhance the Sensitivity of Defect Detection

The exceptional point (EP), a non-Hermitian degeneracy at which eigenvalues and eigenvectors coalesce simultaneously, is investigated in mechanical oscillators involving a time-varying mass. A dynamic modulation mechanism is employed to create the time-varying mass, which can potentially develop an EP by acting as an energy source and drain. To fully demonstrate the existence of EPs, the eigenvalue problem for the modulated system is theoretically formulated through two different schemes, based on the state-space and harmonic balance methods. A second-order EP is confirmed by both methods and exists as a result of the coalescence of fundamental and harmonic eigenmodes. As a salient property of this second-order EP, the square-root behavior of the eigenfrequency subject to small perturbations of the system parameters is theoretically demonstrated, and utilized to devise a proof-of-concept model for mechanical sensors with high sensitivity to void defects in elastic solids. The EP behavior induced by a time-varying mass may find potential applications in damage assessment and health monitoring of engineering structures.

Static solution of two-dimensional decagonal piezoelectric quasicrystal laminates with mixed boundary conditions

Piezoelectric quasicrystals have attracted the tremendous attention of researchers for their unique properties. In this paper, the semi-analysis solutions of the functionally graded multilayered two-dimensional decagonal piezoelectric quasicrystal plates are investigated for mixed boundary-value problems. Based on the quasicrystal linear elastic theory, the state-space method is employed to derive the state equations composed of partial differential along the thickness direction. The differential quadrature method is utilized to discretize state variables to satisfy the mixed boundary conditions in the horizontal plane. Different from the conventional propagator matrix, a new propagator relationship is proposed to study numerical instability caused by extensive discrete points. Comprehensive numerical results are shown for the sandwich quasicrystal plate with four different stacking sequences. The numerical results reveal the effect of the functional gradient index factors, and boundary conditions on the electric potential, electric displacements, stresses, and displacements under the mechanical/electric loadings.

Fault-tolerant tracking control for nonlinear observer-extended high-order fully-actuated systems

In the paper, a fault-tolerant tracking control strategy is proposed for a class of nonlinear high-order fully-actuated systems (HOFASs) with multiplicative and additive actuator faults. Different from general state space methods, HOFAS approaches can achieve global stability through specific nonlinear control laws, and maintain the fully-actuated and uncoupled characteristics of most physical objects. Starting from the HOFAS tracking error dynamics, a tracking differentiator is designed to solve the reference signal and its derivatives numerically. Furthermore, a specific extended state observer is firstly embedded into the HOFAS, which expands the application scenarios of the HOFAS theory. Based on Lyapunov stability theory, a fully-actuated fault-tolerant control technique is presented to ensure the uniformly ultimately bounded stability of the tracking error. A numerical comparative experiment fully illustrates the effectiveness of the proposed strategy.

Analytical Solution Using the State-Space Method for Free Vibration Analysis of Rotating Functionally Graded Nanotubes

Analytical Solution Using the State-Space Method for Free Vibration Analysis of Rotating Functionally Graded Nanotubes