State-space Method Research Articles

Modulatory dynamics mark the transition between anesthetic states of unconsciousness

Unconsciousness maintained by GABAergic anesthetics, such as propofol and sevoflurane, is characterized by slow-delta oscillations (0.3 to 4 Hz) and alpha oscillations (8 to 14 Hz) that are readily visible in the electroencephalogram. At higher doses, these slow-delta-alpha (SDA) oscillations transition into burst suppression. This is a marker of a state of profound brain inactivation during which isoelectric (flatline) periods alternate with periods of the SDA patterns present at lower doses. While the SDA and burst suppression patterns have been analyzed separately, the transition from one to the other has not. Using state-space methods, we characterize the dynamic evolution of brain activity from SDA to burst suppression and back during unconsciousness maintained with propofol or sevoflurane in volunteer subjects and surgical patients. We uncover two dynamical processes that continuously modulate the SDA oscillations: alpha-wave amplitude and slow-wave frequency modulation. We present an alpha modulation index and a slow modulation index which characterize how these processes track the transition from SDA oscillations to burst suppression and back to SDA oscillations as a function of increasing and decreasing anesthetic doses, respectively. Our biophysical model reveals that these dynamics track the combined evolution of the neurophysiological and metabolic effects of a GABAergic anesthetic on brain circuits. Our characterization of the modulatory dynamics mediated by GABAergic anesthetics offers insights into the mechanisms of these agents and strategies for monitoring and precisely controlling the level of unconsciousness in patients under general anesthesia.

A Modular Modeling Method of Mistuned Blisk Based on State-Space Theory with Fitting Aerodynamic Excitation

In order to improve the solution efficiency of vibration characteristics for the mistuned blisk, a modular method combined with state-space method based on lumped-parametric model is developed for the first attempt, which provides a general modeling framework which can be employed to conveniently construct the lumped-parametric models of bladed disk systems with multiple mistuning and variable blade number. It is noteworthy that a pressure fit in the axial-span-pressure space is performed to obtain the continuous equations of aerodynamic forces according to the aerodynamic loads acting on the blade surface. The function of traveling wake excitation is established by considering the rotational velocity. Subsequently, 1N-degree-of-freedom (1N-DOF) and 2N-DOF lumped-parametirc models are respectively used to construct the mistuned blisk. A modular solution method of multiple mistuned lumped-parametirc model is derived from the controllable canonical form and minimum realisation, which reveals that the minimum dimension of the state space is two times of its DOF. The correctness of the present method is varified by several comparisions. Vibration localization is found in the transient response and steady-state response of the blisk. The effects of the mistuning on the blades and the disk are discussed, respectively.

Multi-type dynamic load identification algorithm in continuous system: A numerical and experimental study based on SSM-Newmark-β

Dynamic load identification based on structural responses is an important problem in the field of engineering and plays an important role in the condition assessment of mechanical structures. Current popular load identification methods such as the state-space method (SSM) and the Green's kernel function method (GKFM) are implemented on discrete systems with outstanding performance, but when dealing with complex continuous systems, there are some limitations such as low efficiency and inaccuracy. In this paper, a continuous system load identification algorithm based on SSM and Newmark-β is proposed for the first time. Using modal coordinate transformation and modal truncation methods, the number of infinite vibration differential equations of a continuous system in physical space are converted to a finite number of vibration differential equations in modal space, where the modal truncation order and the optimal layout of the sensors are combined by modal strain energy. The Newmark-β method in modal space is derived and thus combined with SSM to obtain a load identification model Y=HF called SSM-Newmark-β method, which reduces the size of the transfer matrix H. The solution time of the proposed algorithm is 0.38 s for continuous systems, which is rather shorter than that for discrete systems. Furthermore, the simulations show that it has better accuracy and noise immunity than SSM and GKFM in the identification of sinusoidal load, impact load, and random load. The effect of time step is also discussed which reveals that the larger time step has less effect on the proposed algorithm. An experimental study is carried out on a cantilever beam system. The result verifies that the SSM-Newmark-β algorithm has better accuracy in load identification for the continuous system. This research provides a new sight for the real-time identification of dynamic loads for complex structures.

Adaptive Optimization Operation of Electric Vehicle Energy Replenishment Stations Considering the Degradation of Energy Storage Batteries

As the construction of supporting infrastructure for electric vehicles (EV) becomes more and more perfect, an energy replenishment station (ERS) involving photovoltaics (PV) that can provide charging and battery swapping services for electric vehicle owners comes into the vision of humanity. The operation optimization of each device in the ERS is conducive to improving the service capacity of the ERS, extending the service life of the energy storage batteries (ESB), and enhancing the economic benefits of the ERS. However, traditional model-based optimization algorithms cannot fully consider the stochastic nature of EV owners’ charging and battery swapping demands, the uncertainty of PV output, and the complex operating characteristics of ESB. Therefore, we propose a deep reinforcement learning-based adaptive optimal operation method for ERS considering ESB’s losses. Firstly, a mathematical model of each device in the ERS is established, and a refined energy storage model is introduced to describe ESB’s capacity degradation and efficiency decay. Secondly, to solve the dimensional disaster problem, the state space and action space selection method, and the charging strategy of batteries in the battery swapping station (BSS) are proposed to apply to the ERS, thus modeling the ERS optimization operation problem as a Markov decision process. Then, the solution is performed using a neural network-based proximal policy optimization (PPO) algorithm, consisting of a recurrent neural network that extracts information about the PV outflow trend and a deep neural network used to generate a control policy. Finally, the effectiveness of the proposed method is verified by simulation calculations, which not only enable adaptive decision-making under different PV output scenarios, but also consider the availability of EV battery swapping services, energy storage losses, and the economic benefits of the ERS.

Inerter-assisted pendulum-tuned mass damper for across-wind response control of tall buildings

The present study proposes an inerter-assisted pendulum-tuned mass damper (IA-PTMD) to control across-wind response in tall buildings. An inerter is introduced between the pendulum’s mass and structure, thereby enhancing the structural control effectiveness of a classical one-story pendulum-tuned mass damper (PTMD). Across-wind response of a benchmark tall building with IA-PTMD is investigated in this study. The combined equations of motion were solved numerically using the state-space variable method. The design of the IA-PTMD was carried out using this numerical analysis, and optimum parameters were obtained. It is found that with a lower mass and inerter ratio, the structure does not require the addition of viscous dampers. With an identical structure mass ratio, IA-PTMD outperforms the PTMD and was found fairly robust against off-tuning due to uncertainties in building stiffness. From the results observed in this study, it can be concluded that an optimally designed IA-PTMD effectively controls across-wind response in tall buildings.

Wavelet Multiscale Granger Causality Analysis Based on State Space Models

Granger causality (GC) is a popular method in causal linkage recovery and has been applied to various fields, such as economics and neuroscience. While the conventional Granger causality model is capable of identifying symmetrical causal relationships among variables, it is the asymmetric Granger causality that provides a more comprehensive perspective of the short- and long-term interactions between variables, which is of greater value for empirical study. Traditional vector autoregressive models lack the ability to explore multiscale information flow and are affected by the moving average component. Therefore, by combining the wavelet-based approach and state space model, we propose a new Granger causality analysis method to overcome the inherent limitation of vector autoregressive models and extend to multiscale causality exploration. Two simulations were conducted to compare the proposed approach to an existing wavelet-based method, and five evaluation indicators were utilized. The results indicate that the proposed method efficiently identifies the accurate asymmetric causalities at varying scales, while improving accuracy and reducing bias as compared to the current wavelet-based method. In conclusion, the combination of the wavelet approach and state space method enhances the multiscale causality detecting capability and can potentially contribute to multiscale Granger causality research.

Near-to-Far Field RCS Calculation Using Correction Optimization Technique

Radar cross section (RCS) is a scattering measure of an object that scatters to the radar. However, existing methods for near-field (NF) measurement and data processing rarely extract amplitude characteristics, and there is a lack of effective verification of far-field (FF) data in the process of NF to FF transformation, which leads to inaccuracies in FF prediction accuracy. In this paper, we propose a method to establish the relationship between the NF and FF RCS using the state space method (SSM), which is based on accurate estimation of the NF amplitude in NF measurement, and then deriving the FF RCS from the NF scattering signal convolved with a near-to-far kernel. The proposed solution to address the uncertainty issue in reference FF data involves using the geometric theory of diffraction (GTD) scattering center model as the reference FF data and establishing a linear equation with the derived FF model. The negative gradient search (NGS) system identification concept is used to optimize the FF model in order to reduce the discrepancy between the reference and derived values. Finally, the corrected RCS error is provided as additional proof of the effectiveness of these techniques in enhancing near-to-far transformation accuracy by examining the outcomes of three experiments.

Multi-Tempo Forecasting of Soil Temperature Data; Application over Quebec, Canada

The profound impact of soil temperature (TS) on crucial environmental processes, including water infiltration, subsurface movement, plant growth, and its influence on land–atmosphere dynamics, cannot be undermined. While satellite and land surface model-based data are valuable in data-sparse areas, they necessitate innovative solutions to bridge gaps and overcome temporal delays arising from their dependence on atmospheric and hydro–meteorological factors. This research introduces a viable technique to address the lag in the Famine Early Warning Network Land Data Assimilation System (FLDAS). Notably, this approach exhibits versatility, proving highly effective in analyzing datasets characterized by significant seasonal trends, and its application holds immense value in watershed-scaled hydrological research. Leveraging the enhanced state-space (SS) method for forecasting in the FLDAS, this technique harnesses TS datasets collected over time at various depths (0–10 cm, 10–40 cm, and 40–100 cm), employing a multiplicative SS model for modeling purposes. By employing the 1-step, 6-step, and 12-step-ahead models at different depths and 2 locations in Quebec, Canada, the outcomes showcased a performance with an average coefficient of determination (R2) of 0.88 and root mean squared error (RMSE) of 2.073 °C for the dynamic model, R2 of 0.834 and RMSE of 2.979 °C for the 6-step-ahead model, and R2 of 0.921 and RMSE of 1.865 °C for the 12-step-ahead model. The results revealed that as the prediction horizon expands and the length of the input data increases, the accuracy of predictions progressively improves, indicating that this model becomes increasingly accurate over time.

Load effects on vessel-shaped fish cage steel structures, nets and connectors considering the effects of diffraction and radiation waves under irregular waves

Vessel-shaped fish cages are mainly composed of a large floating body, aquaculture nets and a number of steel frames. Due to the large scale of vessel-shaped fish cages, the velocity field induced by the diffraction waves and radiation waves cannot be ignored in the calculation of the loads on the net and steel frames. In turn, the loads can affect the wave-induced response of the floating body and hence the radiation waves as well as the sectional forces. In this paper, a novel method is proposed to consider the coupling effect. First, considering the irregular waves in short-term periods, the global response of the floating body is calculated in the time domain by the state-space method based on potential flow theory. Meanwhile, the velocity field considering the influence of the floating body is built according to the velocity transfer function. Then, the Morison formula is used to calculate the loads on the nets and the steel frames. Finally, the coupling achieved through numerical iterations is considered in the calculation of the twine tension, load effect of connector and the global cross-section under irregular waves. It is found that the diffraction and radiation waves make a significant difference in the twine tension and connector load effect.

Interlaminar mechanical performance of a multi-layered photovoltaic-thermoelectric hybrid device

A concentrated photovoltaic-thermoelectric hybrid device made up of a six-layer composite structure is considered. The hybrid device is composed of, from top to bottom, photovoltaic cell, ethylene vinyl acetate (EVA) layer, tedlar polyester tedlar (TPT) layer, ceramic layer, electrode, and thermoelectric legs. Under the service condition, the poor interlaminar mechanical performance of the hybrid device induced by the high interlaminar stresses level can give rise to very poor power generation performance. To understand this, an analytical model is built to study the influence of the thermal contact resistance and interfacial slip stiffness on the interlaminar stresses of the hybrid device. In particular, effects of the material parameters and geometric dimensions of the hybrid device are also studied by using the state space method. It is found that the thermal contact resistance mainly affects the interlaminar stresses of the photovoltaic module. The interlaminar stresses without considering the temperature-dependent material properties are greater than the actual stresses. The highest interlaminar shearing stress appears at the lower surface of the photovoltaic cell and the maximum peeling stress occurs at the interface between the EVA layer and TPT layer. A lower interfacial slip stiffness is conducive to reducing the interlaminar stresses. The interlaminar stresses decrease with decreasing elastic modulus and coefficient of thermal expansion of the EVA layer. In addition, a thinner thermoelectric layer contributes to lower the interlaminar stresses. The results offer helpful suggestions for the optimization of the interlaminar mechanical performance of the hybrid device.

Identification of the High-Order Rational Function of Bridge Decks by SDOF Forced Vibration Testing

The high-order rational function provides an accurate and effective model of self-excited forces for flutter analysis of bridges. This study proposes a direct identification method for the rational function of a bridge deck, which enables high-order modeling. In this method, the single degree of freedom (SDOF) forced vibration test is first carried out on the sectional model of the bridge deck. The tested results are then processed by a harmonic function-based filter, yielding force time histories with high signal-to-noise ratios. Formulas are derived to identify parameters of the high-order rational function from these time histories. To deal with the numerical difficulties of the formulas, two practical optimal nonlinear fitting procedures were proposed, which simplify the identification but at the same time maintain a reasonable accuracy. A thin flat plate and a streamlined box section under various wind angles of attack were used as examples to elucidate the effectiveness and feasibility of the proposed identification method. Results showed that the identified high-order rational function could accurately replicate the self-excited force. In contrast, a significant deviation was observed if the first-order rational function was utilized as an alternative. Finally, the high-order rational function model identified was applied in the flutter analysis by a state-space method. The yielded critical flutter wind speed matched satisfactorily with the free-vibration wind tunnel test results, confirming the advantage of the proposed model.

Impedance Modeling and Stability Analysis of Energy Controlled Modular Multilevel Converter

In recent years, the modular multilevel converter (MMC) has been widely used in high-voltage dc (HVDC) transmission, which, however, brings about various stability issues, such as sub- -synchronous oscillation (SSO). To deal with these stability issues, many active and passive damping methods have been proposed. In fact, the MMC itself has more control degrees of freedom compared to the two-level voltage-source converter (VSC), such as internal energy, circulating current, etc., which can be exploited to improve the system stability. Based on the idea, the internal energy of MMC is utilized to suppress the SSOs in this paper. The frequency-coupling impedance model of MMC with energy controller is first developed based on the harmonic state-space (HSS) method by considering the internal dynamics and all control links, which is verified by frequency scanning result in simulation. The stability analysis of the energy controlled MMC-HVDC for wind farm integration is conducted and a modified energy control structure of MMC is also proposed to further improve the stability of the interconnected system.

Systematic Evaluation of Deep Neural Network Based Dynamic Modeling Method for AC Power Electronic System

Since the high penetration of renewable energy complicates the dynamic characteristics of the AC power electronic system (ACPES), it is essential to establish an accurate dynamic model to obtain its dynamic behavior for ensure the safe and stable operation of the system. However, due to the no or limited internal control details, the state-space modeling method cannot be realized. It leads to the ACPES system becoming a black-box dynamic system. The dynamic modeling method based on deep neural network can simulate the dynamic behavior using port data without obtaining internal control details. However, deep neural network modeling methods are rarely systematically evaluated. In practice, the construction of neural network faces the selection of massive data and various network structure parameters. However, different sample distributions make the trained network performance quite different. Different network structure hyperparameters also mean different convergence time. Due to the lack of systematic evaluation and targeted suggestions, neural network modeling with high precision and high training speed cannot be realized quickly and conveniently in practical engineering applications. To fill this gap, this paper systematically evaluates the deep neural network from sample distribution and structural hyperparameter selection. The influence on modeling accuracy is analyzed in detail, then some modeling suggestions are presented. Simulation results under multiple operating points verify the effectiveness of the proposed method.

A High-Resolution Analytical Thermal Modeling Method of Capacitor Bank Considering Thermal Coupling and Different Cooling Modes

Thermal stress is of crucial importance to capacitor reliability. However, for a capacitor bank, on spatial scale, the complex heat transfer modes are not clearly illustrated; and on time scale, the ESR aging is neither fully discussed in current evaluation methods. These could lead to a glaring error in the prediction of temperature distribution and lifetime estimation. Therefore, this paper proposed an analytical thermal modeling method with high-resolution for the capacitor bank, considering the thermal coupling effect between individual capacitors, as well as different cooling conditions and the heat variation caused by ESR aging. Firstly, the improved thermal state-space modeling method is proposed to universally describe a multiple heat source system. Then, based on heat transfer and fluid mechanic theories, the characterization method of thermal coupling effect in different cooling modes is discussed. Furthermore, the ESR aging model is applied in the electro-thermal analysis of capacitor bank, aiming to improve the accuracy of thermal calculation in long time scale. Finally, to alleviate the uneven temperature distribution in an in-line designed capacitor bank, a staggered design method is proposed followed by a case study, where a nine-capacitor bank is presented to validate the corresponding modeling method and optimization.

Laplace and State-Space Methods for Calculating the Heat Losses in Case of Heavyweight Building Elements and Short Sampling Times

Reducing heat losses through the building envelope is one of the most important aspects to be met if the targets set by the European Union are to be achieved. In order to obtain a more realistic energy demand, dynamic heat transfer simulations are used to calculate the energy consumption of buildings, since steady-state calculations do not take into account the thermal mass in buildings. These dynamic simulations employ methods based on analytical models since numerical models are unsuitable for longer time periods. The analytical models used herein fall into the category of conduction transfer functions (CTFs). Two methods for computing CTFs that are addressed in this research are the Laplace method and the State-Space method. The objective of this paper is to verify the efficiency of the Laplace and State-Space methods for calculating the energy demand of a building in the case of heavyweight building elements and shorter sampling times, and to provide a means for improving the algorithms used by these methods. The Laplace and State-Space method algorithms were implemented in Mathematica, and the results were compared to EnergyPlus and TRNSYS, which use similar algorithms to calculate energy demand. It was shown in this paper that for the heavyweight wall element and a time step of 0.25 h, the difference between the total energy transferred through the inner surface was about 31% for EnergyPlus and 78% for TRNSYS compared to the reference solution. For the lightweight wall element, the results were stable for the time step of 0.25 h, but for the time step of 0.1 h, the differences were 45.64% and 303% between EnergyPlus, TRNSYS and the reference solution, respectively, compared to the State-Space and Laplace methods for which the maximum difference was 12.03% with a time step of 0.1 h. While dynamic heat transfer simulations are better than calculations based on steady-state boundary conditions, they also have their limitations and could lead to unsatisfactory results for short sampling times and if not applied properly.

Dynamic analysis of reinforced concrete plate resting on elastic foundation using state space method and refined plate theory

This paper studies the dynamic response of rectangular reinforced concrete plates on an elastic foundation by state space method. The system of differential equations of vibration of the plate is developed by using Hamilton's principle. With a single-link rectangular plate, the displacements are represented through a double trigonometric series. Use the state space method to find the plate vibrational responses. The calculation examples are performed to calculate the displacement and stress of the plate with different structural parameters, thereby evaluating the influence of these parameters.

실시간 상태-공간 식별 기반 제어기를 이용한 유한 국부공진 메타물질 평판의 적응형 진동 저감

To improve the internal sound quality of an electric vehicle, the noises (tire and road noises), vibration, and discomfort should be reduced effectively. Compared to the conventional damping materials, the locally resonant metamaterial is advantageous in terms of reducing the vibration in the low frequency band and reducing the weight through a stop band, where vibration is not transmitted. However, the locally resonant metamaterial installed in a finite structure fails to form an ideal stop band. Additionally, there is a problem of occurrence vibration mode at an arbitrary frequency. Accordingly, there is a need for an active vibration control method capable of learning and actively reducing the vibration modes occurring at arbitrary frequencies within the stop band in real-time. In this study, a real-time state-space identification-based active vibration control method was proposed to reduce the vibration modes occurring at arbitrary frequencies within the stationary band of local resonance metamaterials. The active vibration control method proposed in this study, combined with the existing passive vibration reduction method, can be utilized to effectively reduce the vibration for random disturbance of a fluctuating system.

Finite Element Model Updating of Steel Arch Bridge Based on First-Order Mode Test Data

In order to obtain an accurate finite element model of a steel arch bridge, a first-order modal finite element model updating method is proposed by using the measured first-order modal data of the bridge. Using the measured acceleration time history data under random excitation and the first-order mode updating method, the stiffness matrix of the finite element model is updated, and the first-order frequencies and first-order mode shapes before and after updating of the model are compared and analyzed. The state space method is used to compare and analyze the dynamic response and the reliability of the structure before and after the updating of the model. The results show that the difference of the first-order frequencies between the updated finite element model and the measured result is about 0.001, and the difference of the first-order mode shapes is less than 0.197, which meets the needs of engineering. Dynamic response values of the updated structural model are much larger than those of the structural model before updating. The theoretical model is different from the dynamic response of actual structure, so it is necessary to update the theoretical model. The finite element model updating method can provide a reliable analytical way for bridge structural health monitoring, state evaluation, and damage identification.

Thermo-mechanical coupled behavior of laminated beams with temperature-dependent viscoelastic interlayers

The present research proposes analytical solutions of simply-supported laminated beams bonded by viscoelastic interlayers under both non-uniform temperature field and mechanical loads, in order to study its time-varying thermo-mechanical coupled behavior. The temperature has two effect mechanisms to the laminated beams, including the thermal expansion difference and the temperature-dependent property of viscoelastic interlayer. In the analytical model, the non-uniform temperature field is solved first by the transfer matrix method, based on the heat transport theory. The standard linear solid model is utilized to simulate the time-varying characteristic of the interlayer, which renders the mechanical property of the laminated beam changes over time. Then, the temperature effects on the interlayer modulus degradation are determined according to the Time-Temperature-Superposition-Principle (TTSP). By virtue of the state space method and Fourier series expansion, the general solutions of stress and displacement components are solved with undetermined coefficients. The analytical solutions are solved by means of Laplace transform and Cramer rule. The analysis results indicate that the present solutions are in accordance with the finite element solution and have superior computational efficiency. The influences of temperature, geometric and material parameters on the long-term thermo-mechanical coupled behavior of the laminated beam are studied in detail.

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.