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Debnath, Sarupa, Soumya Ranjan Sahoo, Bernard Twum Agyeman, and Jinfeng Liu. "Input-Output Selection for LSTM-Based Reduced-Order State Estimator Design." Mathematics 11, no. 2 (January 12, 2023): 400. http://dx.doi.org/10.3390/math11020400.
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In this work, we propose a sensitivity-based approach to construct reduced-order state estimators based on recurrent neural networks (RNN). It is assumed that a mechanistic model is available but is too computationally complex for estimator design and that only some target outputs are of interest and should be estimated. A reduced-order estimator that can estimate the target outputs is sufficient to address such a problem. We introduce an approach based on sensitivity analysis to determine how to select the appropriate inputs and outputs for data collection and data-driven model development to estimate the desired outputs accurately. Specifically, we consider the long short-term memory (LSTM) neural network, a type of RNN, as the tool to train the data-driven model. Based on it, an extended Kalman filter, a state estimator, is designed to estimate the target outputs. Simulations are carried out to illustrate the effectiveness and applicability of the proposed approach.
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Debnath, Sarupa, Soumya R. Sahoo, Bernard T. Agyeman, and Jinfeng Liu. "Input-output selection for LSTM-based reduced-order state estimator design." IFAC-PapersOnLine 56, no. 2 (2023): 6940–45. http://dx.doi.org/10.1016/j.ifacol.2023.10.512.
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Singalandapuram Mahadevan, Boopathi, John H. Johnson, and Mahdi Shahbakhti. "Development of a Kalman filter estimator for simulation and control of particulate matter distribution of a diesel catalyzed particulate filter." International Journal of Engine Research 21, no. 5 (July 17, 2018): 866–84. http://dx.doi.org/10.1177/1468087418785855.
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The knowledge of the temperature and particulate matter mass distribution is essential for monitoring the performance and durability of a catalyzed particulate filter. A catalyzed particulate filter model was developed, and it showed capability to accurately predict temperature and particulate matter mass distribution and pressure drop across the catalyzed particulate filter. However, the high-fidelity model is computationally demanding. Therefore, a reduced order multi-zone particulate filter model was developed to reduce computational complexity with an acceptable level of accuracy. In order to develop a reduced order model, a parametric study was carried out to determine the number of zones necessary for aftertreatment control applications. The catalyzed particulate filter model was further reduced by carrying out a sensitivity study of the selected model assumptions. The reduced order multi-zone particulate filter model with 5 × 5 zones was selected to develop a catalyzed particulate filter state estimator considering its computational time and accuracy. Next, a Kalman filter–based catalyzed particulate filter estimator was developed to estimate unknown states of the catalyzed particulate filter such as temperature and particulate matter mass distribution and pressure drop (Δ P) using the sensor inputs to the engine electronic control unit and the reduced order multi-zone particulate filter model. A diesel oxidation catalyst estimator was also integrated with the catalyzed particulate filter estimator in order to provide estimates of diesel oxidation catalyst outlet concentrations of NO2 and hydrocarbons and inlet temperature for the catalyzed particulate filter estimator. The combined diesel oxidation catalyst–catalyzed particulate filter estimator was validated for an active regeneration experiment. The validation results for catalyzed particulate filter temperature distribution showed that the root mean square temperature error by using the diesel oxidation catalyst–catalyzed particulate filter estimator is within 3.2 °C compared to the experimental data. Similarly, the Δ P estimator closely simulated the measured total Δ P and the estimated cake pressure drop error is within 0.2 kPa compared to the high-fidelity catalyzed particulate filter model.
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Li, Yunji, Wenzhuo Zhou, and Yajun Wu. "Event-Triggered Fault Estimation and Fault Tolerance for Cyber-Physical Systems with False Data Injection Attacks." Actuators 12, no. 5 (May 10, 2023): 197. http://dx.doi.org/10.3390/act12050197.
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This paper investigates an event-triggered framework for addressing fault estimation and fault tolerance issues in discrete-time cyber-physical systems (CPSs) with partial state saturations and random false data injection attacks (FDIAs). A stochastic variable is introduced to characterize the random FDIAs and to establish the corresponding model. A reduced-order fault estimator and an event condition are co-derived to reconstruct system states and actuator faults. The proposed event-triggered transmission scheme helps reduce network utilization in the sensor-to-estimator channel. A sufficient condition for the proposed event-triggered estimator is derived, which minimizes state and fault estimation errors even when the controlled plants are subject to exogenous disturbances, fault signals, and random attacks. Furthermore, a fault-tolerant compensation controller is proposed using the estimated states and faults, ensuring that the considered systems achieve mean-squared stability. Finally, a DC motor platform is developed to further demonstrate the effectiveness of the designed estimator-based fault-tolerant controller.
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Nguyen Van, Chi, and Thuy Nguyen Vinh. "Soc Estimation of the Lithium-Ion Battery Pack using a Sigma Point Kalman Filter Based on a Cell’s Second Order Dynamic Model." Applied Sciences 10, no. 5 (March 10, 2020): 1896. http://dx.doi.org/10.3390/app10051896.
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This paper deals with the state of charge (SoC) estimation of a lithium-ion battery pack (LiBP) connected by some cells in series and parallel. The voltage noise, noise and current bias of current through the LiBP are taken into account in the SoC estimation problem. In order to describe the cell dynamic more accurately, especially for practical applications with charge and discharge amplitude varying suddenly, in this paper we use the second dynamic order model of the cell to estimate the SoC of the LiBP. By applying the sigma point Kalman filter (SPKF), the average SoC of the pack and bias current of current measurement are estimated by first estimator; the second estimator estimates the SoC differences of the cell modules from average SoC of the pack. The SoC of the cell modules are the sum of average SoCs of the pack and the SoC differences. By only using two estimators, the calculation complexity for SoC estimation is more reduced; this is very useful for the LiBP, which has the number of cells connected in a large series. This method was applied for the pack of SAMSUNG ICR18650-22P connected by seven cell modules; the cell modules were connected by nine cells in parallel; the LiBP was charged and discharged with amplitude varying suddenly. The estimated SoC of seven cell modules is smaller than 2% for a temperature operating range typically −5 °C to 45 °C. The comparison of the accuracy of SoC estimation based on the first and the second order dynamic models is made; the result shows that the SoC estimation used the second order dynamic model is more exact.
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Pécute;Rez-Lozano, Rigoberto, and Rogelio Soto. "From Pole Placement Feedback to Estimator Design Using Analog Computers." International Journal of Electrical Engineering & Education 30, no. 4 (October 1993): 317–28. http://dx.doi.org/10.1177/002072099303000405.
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From pole placement feedback to estimator design using analog computers This paper describes analog-based control lab. simulations. Simulations deal with pole placement feedback and asymptotic observers. For asymptotic state observers, the transfer function approach is just outlined. All simulations are implemented using the state variable approach. Simulations are extended to analyze heuristic pole-placement selection and to evaluate reduced-order estimators.
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AHUJA, S., and C. W. ROWLEY. "Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators." Journal of Fluid Mechanics 645 (February 22, 2010): 447–78. http://dx.doi.org/10.1017/s0022112009992655.
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We present an estimator-based control design procedure for flow control, using reduced-order models of the governing equations linearized about a possibly unstable steady state. The reduced-order models are obtained using an approximate balanced truncation method that retains the most controllable and observable modes of the system. The original method is valid only for stable linear systems, and in this paper, we present an extension to unstable linear systems. The dynamics on the unstable subspace are represented by projecting the original equations onto the global unstable eigenmodes, assumed to be small in number. A snapshot-based algorithm is developed, using approximate balanced truncation, for obtaining a reduced-order model of the dynamics on the stable subspace.The proposed algorithm is used to study feedback control of two-dimensional flow over a flat plate at a low Reynolds number and at large angles of attack, where the natural flow is vortex shedding, though there also exists an unstable steady state. For control design, we derive reduced-order models valid in the neighbourhood of this unstable steady state. The actuation is modelled as a localized body force near the trailing edge of the flat plate, and the sensors are two velocity measurements in the near wake of the plate. A reduced-order Kalman filter is developed based on these models and is shown to accurately reconstruct the flow field from the sensor measurements, and the resulting estimator-based control is shown to stabilize the unstable steady state. For small perturbations of the steady state, the model accurately predicts the response of the full simulation. Furthermore, the resulting controller is even able to suppress the stable periodic vortex shedding, where the nonlinear effects are strong, thus implying a large domain of attraction of the stabilized steady state.
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Zaini, Zaini, Dwi Mutiara Harfina, and Agung P. Iswar. "Real-Time SoC Estimation for Li-Ion Batteries using Kalman Filter based on SBC Raspberry-Pi." Andalas Journal of Electrical and Electronic Engineering Technology 1, no. 2 (December 10, 2021): 48–57. http://dx.doi.org/10.25077/ajeeet.v1i2.12.
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Measurement of electric charge on the battery in real-time cannot be separated from external noise and disturbances such as temperature and interference. An optimal State of Charge (SoC) estimator model is needed to make the estimation more accurate. To obtain the model, the battery was tested under room temperature conditions and at a temperature of 40oC to obtain a second-order RC model for the Li-Ion battery used. Based on the test data obtained, the data will be tested first using the Kalman Filter method to get an estimate of the State of Charge (SoC). Tests were carried out using MATLAB software. After the method was tested, the online SoC Estimator design began using the Raspberry Pi Single Board Computer (SBC). After that, the estimator will be tested first using data from offline measurements and then used in real-time (online) SoC estimation measurements. The Voc before the battery discharge test was 13.16 V and after the test, the measured Voc was 11.58 V. During the discharge the Voc was reduced by 1.58 V. While the discharge data from the battery manufacturer showed the reduced Voc during the discharge was 1.2V.
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Zaini, Zaini, Dwi Mutiara Harfina, and Agung P. Iswar. "Real-Time SoC Estimation for Li-Ion Batteries using Kalman Filter based on SBC Raspberry-Pi." Andalas Journal of Electrical and Electronic Engineering Technology 1, no. 02 (December 10, 2021): 48–57. http://dx.doi.org/10.25077/ajeeet.v1i02.12.
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Measurement of electric charge on the battery in real-time cannot be separated from external noise and disturbances such as temperature and interference. An optimal State of Charge (SoC) estimator model is needed to make the estimation more accurate. To obtain the model, the battery was tested under room temperature conditions and at a temperature of 40oC to obtain a second-order RC model for the Li-Ion battery used. Based on the test data obtained, the data will be tested first using the Kalman Filter method to get an estimate of the State of Charge (SoC). Tests were carried out using MATLAB software. After the method was tested, the online SoC Estimator design began using the Raspberry Pi Single Board Computer (SBC). After that, the estimator will be tested first using data from offline measurements and then used in real-time (online) SoC estimation measurements. The Voc before the battery discharge test was 13.16 V and after the test, the measured Voc was 11.58 V. During the discharge the Voc was reduced by 1.58 V. While the discharge data from the battery manufacturer showed the reduced Voc during the discharge was 1.2V.
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Suppan, Thomas, Markus Neumayer, Thomas Bretterklieber, and Stefan Puttinger. "Prior design for tomographic volume fraction estimation in pneumatic conveying systems from capacitive data." Transactions of the Institute of Measurement and Control 42, no. 4 (November 18, 2019): 716–28. http://dx.doi.org/10.1177/0142331219884808.
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Pneumatic conveying systems have become a standard technique for the transport of bulk materials such as powdery or granulates. The spatial dependence of the material density and the stream velocity in such transport systems require a volumetric measurement principle for flow measurement. In this paper we analyse the capability to estimate the volume fraction from capacitive sensing data using electrical capacitance tomography (ECT). In particular, we investigate the capability of back-projection type imaging algorithms. The ill-posed nature of the imaging problem of ECT require the incorporation of prior knowledge in the design of the estimator. We analyse the different flow profiles in pneumatic conveying in order to generate specific sample-based prior information to improve the estimation performance and robustness. We discuss the construction of different linear image reconstruction algorithms and present a framework, which allows a detailed statistical analysis of the estimator performance. Simulation studies show the estimation behaviour of different algorithms with respect to the incorporated prior information. We demonstrate, that the incorporation of specific prior knowledge leads to an improved estimator behaviour; for example, reduced variance and unbiased estimates. We implemented laboratory experiments in order to analyse the presented approach for the application in real pneumatic conveying processes. We demonstrate the improved robust estimation behaviour by means of comparative reconstruction results obtained with different algorithms and priors. Furthermore, the uncertainty of the estimated volume fraction is analysed in steady state conveying processes. Hereby, it is demonstrated, that appropriate prior information improves the estimation performance also for measurements coming from real pneumatic conveying processes, making ECT a suitable tool for the volume fraction estimation in such transport systems.
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Yu, Fei, Qian Sun, Chongyang Lv, Yueyang Ben, and Yanwei Fu. "A SLAM Algorithm Based on Adaptive Cubature Kalman Filter." Mathematical Problems in Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/171958.
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We need to predict mathematical model of the system and a priori knowledge of the noise statistics when traditional simultaneous localization and mapping (SLAM) solutions are used. However, in many practical applications, prior statistics of the noise are unknown or time-varying, which will lead to large estimation errors or even cause divergence. In order to solve the above problem, an innovative cubature Kalman filter-based SLAM (CKF-SLAM) algorithm based on an adaptive cubature Kalman filter (ACKF) was established in this paper. The novel algorithm estimates the statistical parameters of the unknown system noise by introducing the Sage-Husa noise statistic estimator. Combining the advantages of the CKF-SLAM and the adaptive estimator, the new ACKF-SLAM algorithm can reduce the state estimated error significantly and improve the navigation accuracy of the SLAM system effectively. The performance of this new algorithm has been examined through numerical simulations in different scenarios. The results have shown that the position error can be effectively reduced with the new adaptive CKF-SLAM algorithm. Compared with other traditional SLAM methods, the accuracy of the nonlinear SLAM system is significantly improved. It verifies that the proposed ACKF-SLAM algorithm is valid and feasible.
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Borzacchiello, Domenico, Jose Vicente Aguado, and Francisco Chinesta. "Reduced order modelling for efficient numerical optimisation of a hot-wall chemical vapour deposition reactor." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 7 (July 3, 2017): 1602–22. http://dx.doi.org/10.1108/hff-04-2016-0153.
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Purpose The purpose of this paper is to present a reduced order computational strategy for a multi-physics simulation involving a fluid flow, electromagnetism and heat transfer in a hot-wall chemical vapour deposition reactor. The main goal is to produce a multi-parametric solution for fast exploration of the design space to perform numerical prototyping and process optimisation. Design/methodology/approach Different reduced order techniques are applied. In particular, proper generalized decomposition is used to solve the parameterised heat transfer equation in a five-dimensional space. Findings The solution of the state problem is provided in a compact separated-variable format allowing a fast evaluation of the process-specific quantities of interest that are involved in the optimisation algorithm. This is completely decoupled from the solution of the underlying state problem. Therefore, once the whole parameterised solution is known, the evaluation of the objective function is done on-the-fly. Originality/value Reduced order modelling is applied to solve a multi-parametric multi-physics problem and generate a fast estimator needed for preliminary process optimisation. Different order reduction techniques are combined to treat the flow, heat transfer and electromagnetism problems in the framework of separated-variable representations.
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Han, Kezhen, Jian Feng, Yueyang Li, and Shi Li. "Reduced-order simultaneous state and fault estimator based fault tolerant preview control for discrete-time linear time-invariant systems." IET Control Theory & Applications 12, no. 11 (July 24, 2018): 1601–10. http://dx.doi.org/10.1049/iet-cta.2017.1280.
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Zhu, Fengzeng, Xu Liu, Jiwei Wen, Linbo Xie, and Li Peng. "Distributed Robust Filtering for Wireless Sensor Networks with Markov Switching Topologies and Deception Attacks." Sensors 20, no. 7 (March 31, 2020): 1948. http://dx.doi.org/10.3390/s20071948.
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This paper is concerned with the distributed full- and reduced-order l 2 - l ∞ state estimation issue for a class of discrete time-invariant systems subjected to both randomly occurring switching topologies and deception attacks over wireless sensor networks. Firstly, a switching topology model is proposed which uses homogeneous Markov chain to reflect the change of filtering networks communication modes. Then, the sector-bound deception attacks among the communication channels are taken into consideration, which could better characterize the filtering network communication security. Additionally, a random variable obeying the Bernoulli distribution is used to describe the phenomenon of the randomly occurring deception attacks. Furthermore, through an adjustable parameter E, we can obtain full- and reduced-order l 2 - l ∞ state estimator over sensor networks, respectively. Sufficient conditions are established for the solvability of the addressed switching topology-dependent distributed filtering design in terms of certain convex optimization problem. The purpose of solving the problem is to design a distributed full- and reduced-order filter such that, in the presence of deception attacks, stochastic external interference and switching topologies, the resulting filtering dynamic system is exponentially mean-square stable with prescribed l 2 - l ∞ performance index. Finally, a simulation example is provided to show the effectiveness and flexibility of the designed approach.
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Evans, Tyler A. P., Tyrone Vincent, and Robert J. Kee. "The Use of Model-Predicted Internal States from Locally Linear, Gain-Scheduled, Reduced-Order Physics-Based Models in Model-Predictive Control Strategies." ECS Meeting Abstracts MA2023-01, no. 25 (August 28, 2023): 1686. http://dx.doi.org/10.1149/ma2023-01251686mtgabs.
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The objective of the research is to develop reduced-order state-space models that can predict internal states that are not directly observable with existing sensors. In doing so, battery management systems (BMS) can make real-time control decisions based upon sensor inferences. For example, estimating local electrode Li and electrolyte Li-ion concentrations or local electrostatic potential differences between electrode and electrolyte phases offer valuable knowledge in predicting behaviors such as Li plating, dendrite growth, or electrode fracture. Such indirect predictive capabilities, for example, can enable fast-charging protocols that avoid damage mechanisms. This talk explores the mathematical feasibility of estimating local Li concentrations and electrostatic potentials using observed current-voltage sequences. The approach for determining internal battery states begins with an estimator that uses observed input-output data from a physics-based reduced-order state-space model. If the model satisfies the property of observability, a sufficiently long window of input-output data can predict unique internal-state trajectories that are compatible with the observable data. The research considers understanding the effects of sampling time and state of charge on internal-state observability. Efficient estimation algorithms must incorporate battery physics and chemistry yet be sufficiently simple as to run in real-time on a battery management system (BMS). The present research first develops a physics-based pseudo-two-dimensional (P2D) model, which describes battery thermodynamics, transport, and kinetics, results in a system of nonlinear, coupled, differential-algebraic equations that can be solved computationally, but too slow for real-time implementation. The P2D model is then reduced to a gain-scheduled, locally linear, state-space model that can be run in real-time. Both models are implemented within the MATLAB/Simulink framework that facilitates development and evaluation of control strategies.
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Chen, Aoran, Wenbo Chen, and Heng Wan. "PMSM Sensorless Control Based on Moving Horizon Estimation and Parameter Self-Adaptation." Electronics 13, no. 13 (June 21, 2024): 2444. http://dx.doi.org/10.3390/electronics13132444.
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The field of sensorless control of permanent magnet synchronous motor (PMSM) systems has been the subject of extensive research. The accuracy of sensorless controllers depends on the precise estimation of PMSM state quantities, including rotational speed and rotor position. In order to enhance state estimation accuracy, this paper proposes a moving horizon estimator that can be utilized in the sensorless control system of PMSM. Considering the parameter variations observed in PMSM, a nonlinear mathematical model of PMSM is established. A model reference adaptive system (MRAS) is employed to identify parameters such as resistance, inductance, and magnetic chain in real time. This approach can mitigate the impact of parameter fluctuations. Moving horizon estimation (MHE) is an estimation method based on optimization that can directly handle nonlinear system models. In order to eliminate the influence of external interference and improve the robustness of state estimation, a method based on MHE has been designed for PMSM, and a sensorless observer has been established. Considering the traditional MHE with large computation and high memory occupation, the calculation of MHE is optimized by utilizing a Hessian matrix and gradient vector. The speed and position of the PMSM are estimated within constraints during a single-step iteration. The results of the simulation demonstrate that in comparison to the traditional control structure, the estimation error of rotational speed and rotor position can be reduced by utilizing the proposed method. A more accurate estimation can be achieved with good adaptability and computational speed, which can enhance the robustness of the control system of PMSM.
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Kwon, Baek-soon, Young-jin Hyun, and Kyongsu Yi. "Mode control of electro-mechanical suspension systems for vehicle height, levelling and ride comfort." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 234, no. 2-3 (June 6, 2019): 792–809. http://dx.doi.org/10.1177/0954407019851028.
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This paper proposes a mode control algorithm of electro-mechanical suspension for vehicle height, attitude control and improvement of ride quality. The proposed control algorithm consists of mode selector, upper-level and lower-level controllers, and suspension state estimator. The mode selector determines the present driving mode using vehicle signals, such as longitudinal speed, steering wheel angle, accelerator pedal position, brake pedal position and vertical acceleration of wheels. The upper-level controller determines the desired suspension state using the present driving mode. The lower-level controller derives the desired stroke speed of the actuator in each suspension by linear quadratic control theory. The suspension state estimator has been designed using accessible sensor measurement by discrete-time Kalman filter theory. The control and estimation algorithms have been developed based on a novel reduced-order vehicle model that includes only the vehicle body dynamics. The model enables the observer to completely remove the effect of unknown road disturbance on the estimation error. The performance of the proposed control algorithm has been evaluated via computer simulation study. The simulation results show that the proposed control algorithm is effective at controlling the electro-mechanical suspension systems. The paper also shows that the considered actuator is suited for vehicle height and levelling control, but not for improvement of ride comfort, due to voltage input constraints.
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Rocha, Ednardo, Max Pimentel Filho, Melinda Cruz, Marcos Almeida, and Manoel Medeiros Júnior. "A New Linear State Estimator for Fault Location in Distribution Systems Based on Backward-Forward Currents Sweep." Energies 13, no. 11 (May 27, 2020): 2692. http://dx.doi.org/10.3390/en13112692.
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This paper presents a new linear state estimation model based on a current summation load flow method for three-phase distribution systems. The developed estimator may be applied to both the supervision of distribution systems under normal operating conditions and the fault location in cases of low and high impedance faults. Our studies were conducted using a real distribution feeder. For fault location analysis, the system was modeled using the ATP (alternative transient program) in order to emulate measurements of voltages and currents at the substation, and voltage magnitudes registered by other meters during the fault. We used the MATLAB™ software to process the algorithms. The main contributions that arose after integrating the current method into system supervision in case of network failures under normal operating conditions and the fault location are as follows: (i) estimation of system losses; (ii) modeling of loads in real time to consider their contributions in the fault location process; and (iii) low influence of fault resistance in the location algorithm. The results show that the proposed method has good precision, low computational processing time, and is promising for distribution system supervision with a reduced number of meters.
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Midenyo, Kevin, David Angwenyi, and Duncan Oganga. "Second Order Extended Ensemble Filter for Non-linear Filtering." African Journal of Empirical Research 5, no. 4 (October 25, 2024): 302–16. http://dx.doi.org/10.51867/ajernet.mathematics.5.4.25.
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Whenever the state of a system must be estimated from noisy information, a state estimator is employed to fuse the data with the model to produce an accurate estimate of the state. When the system dynamics and observation models are linear, the Kalman Filter which is optimal, is used. However, in most applications of interest the system dynamics and observations equations are not- linear and suitable extensions of the Kalman Filter have been developed; for example, the Extended Kalman Filter(EKF). The Extended Kalman Filter is based on linearization by the Taylor series expansion about the mean of the state. This filtering process is however computationally expensive especially in high dimensional data. The cause for this is the high cost of integrating the equation of evolution of covariances. Due to this complexity in integration, new methods were sought known as the particle filters. It replaces linearization of non-linearities with Monte Carlo methods. The particle filter formed a basis for Ensemble Kalman Filter (EnKF) an extension of Kalman filter to non-linear filtering. The EnKF reduced the computational cost but its innovation process does not capture information sufficiently hence there is need to improve its performance. This study has developed a new filter, Second order Extended Ensemble Filter (SoEEF).We derived it from stochastic state models by expansion of expected values to the second order by use of Taylor series together with Monte Carlo method and Matlab. We used Lorenz 63 system of ordinary equations and differential Matlab to test the performance of the new filter. Then we compared its performance with four other filters like Bootstrap Particle Filter (BPF), First order Kalman Bucy Filter (FoEKBF),Second order Kalman Bucy Filter (SoKBF) and First order Extended Ensemble Filter (FoEEF). SoEEKF performs much better than the other four filters.
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Yang, Long, Yu Zhang, Gang Zheng, Qian Zheng, Pengfei Li, Jianhang Huang, and Gang Pan. "Policy Optimization with Stochastic Mirror Descent." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 8 (June 28, 2022): 8823–31. http://dx.doi.org/10.1609/aaai.v36i8.20863.
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Improving sample efficiency has been a longstanding goal in reinforcement learning. This paper proposes VRMPO algorithm: a sample efficient policy gradient method with stochastic mirror descent. In VRMPO, a novel variance-reduced policy gradient estimator is presented to improve sample efficiency. We prove that the proposed VRMPO needs only O(ε−3) sample trajectories to achieve an ε-approximate first-order stationary point, which matches the best sample complexity for policy optimization. Extensive empirical results demonstrate that VRMP outperforms the state-of-the-art policy gradient methods in various settings.
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Coluccia, Angelo, and Alessio Fascista. "Hybrid TOA/RSS Range-Based Localization with Self-Calibration in Asynchronous Wireless Networks." Journal of Sensor and Actuator Networks 8, no. 2 (May 24, 2019): 31. http://dx.doi.org/10.3390/jsan8020031.
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The paper addresses the problem of localization based on hybrid received signal strength (RSS) and time of arrival (TOA) measurements, in the presence of synchronization errors among all the nodes in a wireless network, and assuming all parameters are unknown. In most existing schemes, in fact, knowledge of the model parameters is postulated to reduce the high dimensionality of the cost functions involved in the position estimation process. However, such parameters depend on the operational wireless context, and change over time due to the presence of dynamic obstacles and other modification of the environment. Therefore, they should be adaptively estimated “on the field”, with a procedure that must be as simple as possible in order to suit multiple real-time re-calibrations, even in low-cost applications, without requiring human intervention. Unfortunately, the joint maximum likelihood (ML) position estimator for this problem does not admit a closed-form solution, and numerical optimization is practically unfeasible due to the large number of nuisance parameters. To circumvent such issues, a novel two-step algorithm with reduced complexity is proposed: A first calibration phase exploits nodes in known positions to estimate the unknown RSS and TOA model parameters; then, in a second localization step, an hybrid TOA/RSS range estimator is combined with an iterative least-squares procedure to finally estimate the unknown target position. The results show that the proposed hybrid TOA/RSS localization approach outperformed state-of-the-art competitors and, remarkably, achieved almost the same accuracy of the joint ML benchmark but with a significantly lower computational cost.
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Zhang, Chao, Xing Wang, Zhengfeng Ming, and Zhuang Cai. "Enhanced Nonlinear Robust Control for TCSC in Power System." Mathematical Problems in Engineering 2018 (2018): 1–11. http://dx.doi.org/10.1155/2018/1416059.
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This paper proposes an enhanced robust control method, which is for thyristor controlled series compensator (TCSC) in presences of time-delay nonlinearity, uncertain parameter, and external disturbances. Unlike conventional adaptive control methods, the uncertain parameter is estimated by using system immersion and manifold invariant (I&I) adaptive control. Thus, the oscillation of states caused by the coupling between parameter estimator and system states can be avoided. In addition, in order to overcome the influences of time-delay nonlinearity and external disturbances, backstepping sliding mode control is adopted to design control law recursively. Furthermore, robustness of TCSC control subsystem is achievable provided that dissipation inequality is satisfied in each step. Effectiveness and efficiencies of the proposed control method are verified by simulations. Compared with adaptive backstepping sliding mode control and adaptive backstepping control, the time of reaching steady state is shortened by at least 11% and the oscillation amplitudes of transient responses are reduced by at most 50%.
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Hu, Yonggang, Wei Wang, Zehong Gu, Tianpeng Mao, Xuchen Zhu, and Jiabao Jin. "Closed-form multiple source direction-of-arrival estimator under reverberant environments." Journal of the Acoustical Society of America 154, no. 4 (October 1, 2023): 2349–64. http://dx.doi.org/10.1121/10.0021873.
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Accurate direction-of-arrival (DOA) estimation of multiple sources, simultaneously active in a reverberant environment, remains a challenge, as the multi-path acoustic reflections and overlapped periods dramatically distort the direct-path wave propagation. This article proposes a prominent solution localizing multiple sources in a reverberant environment using closed-form estimates, circumventing any exhaustive search over the two-dimensional directional space. Apart from a low complexity cost, the algorithm has robustness to reverberant, inactive, and overlapped periods and an ease of operation in practice, achieving sufficient accuracy compared to state-of-the-art approaches. Specifically, this algorithm localizes an unknown number of sources through four steps: (i) decomposing the frequency domain signals on a spherical array to the spherical harmonics domain; (ii) extracting the first-order relative harmonic coefficients as the input features; (iii) achieving direct-path dominance detection and localization using closed-form estimation; and (iv) estimating the number of sources and their DOAs based on those pass the direct-path detection. Experimental results, using extensive simulated and real-life recordings, confirm the algorithm with a significantly reduced computational complexity, while preserving competitive localization accuracy as compared to the baseline approaches. Additional tests confirm this low-complexity algorithm even with a potential capacity for online DOA tracking of multiple moving sources.
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Canete, Luis, Sunao Kimura, and Takayuki Takahashi. "Control of Pushing and Pulling Motion of a Wheeled Inverted Pendulum Based on a Reduced Order Observer." Advanced Engineering Forum 2-3 (December 2011): 74–79. http://dx.doi.org/10.4028/www.scientific.net/aef.2-3.74.
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In this paper the control of the I-PENTAR, a wheeled inverted pendulum type robot being developed by the authors, for pushing and pulling a cart is examined. To control the movement of the object is being pushed or pulled, information regarding several external parameters, eg. Mass of the object and friction components, must be considered. In most cases these parameters are not known before hand or may change. One method of compensating for these unknown or changing external parameters is to represent them as an equivalent reaction force from the object. Our first subject of this research is to design a disturbance observer to estimate and compensate the equivalent force. Another situation is of pushing and pulling a cart with the inverted pendulum type robot traversing an inclined plane. As an initial step to solving this problem in this paper, a force application method using whole body motion of the inverted pendulum type robot is proposed. The whole body motion means changing the balance of the robot to attain a certain desired force. During application of this force the robot must remain in its stabilized or balanced state. For an inverted pendulum type robot, this instantly poses a major problem. To solve the problem, a reduced order disturbance observer is used in this paper to estimate the force applied by the robot. On the other hand, I-PENTAR is targeted for environments where it can interact with humans and so safety is a major concern. For example, in the event that an obstacle bumps the robot as it is pushing the cart, a large and sudden force estimator based on the disturbance observer is also built into the controller. Simulation and experiments using the reduced order disturbance observer and evaluation of the whole body motion force control are presented.
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Rajendran, Saravanakumar, and Debashisha Jena. "Load Mitigation and Optimal Power Capture for Variable Speed Wind Turbine in Region 2." Journal of Renewable Energy 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/978216.
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This paper proposes the two nonlinear controllers for variable speed wind turbine (VSWT) operating at below rated wind speed. The objective of the controller is to maximize the energy capture from the wind with reduced oscillation on the drive train. The conventional controllers such as aerodynamic torque feedforward (ATF) and indirect speed control (ISC) are adapted initially, which introduce more power loss, and the dynamic aspects of WT are not considered. In order to overcome the above drawbacks, modified nonlinear static state with feedback estimator (MNSSFE) and terminal sliding mode controller (TSMC) based on Modified Newton Raphson (MNR) wind speed estimator are proposed. The proposed controllers are simulated with nonlinear FAST (fatigue, aerodynamics, structures, and turbulence) WT dynamic simulation for different mean wind speeds at below rated wind speed. The frequency analysis of the drive train torque is done by taking the power spectral density (PSD) of low speed shaft torque. From the result, it is found that a trade-off is to be maintained between the transient load on the drive train and maximum power capture.
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Tsai, Jason Sheng-Hong, Yang-Fang Chen, Te-Jen Su, Chia-Yuan Chang, Shu-Mei Guo, Leang-San Shieh, and Jose I. Canelon. "A Modified Functional Observer-Based EID Estimator for Unknown Continuous-Time Singular Systems." Applied Sciences 10, no. 7 (March 28, 2020): 2316. http://dx.doi.org/10.3390/app10072316.
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This paper presents the design of a linear quadratic analog tracker (LQAT) based on the observer–Kalman-filter identification (OKID) method and the design of a modified functional observer-based equivalent input disturbance (EID) estimator for unknown square–non-square singular analog systems with unknown input and output disturbances. First, an equivalent mathematical model of the singular analog system is presented to simulate the time response of continuous-time linear singular analog systems to arbitrary inputs via the model conversion method. Then, for the unknown singular analog system, it constructs a linear quadratic analog tracker with state feedback and feed-forward gains based on the off-line OKID method. Furthermore, it extends the design methodology of the EID estimator for strictly proper regular systems with unknown matched–mismatched input and output disturbances to proper regular systems. It is important to mention that the newly developed modified functional observer for proper systems is used to estimate the unknown EID of singular analog systems and that the constraints on the dimensions of unknown disturbances can be eliminated by using the newly proposed EID estimation method. The contributions of this paper can be listed as follows: (1) based on both the OKID method and the discrete-to-continuous model conversion, the simulation of the time responses of the continuous-time linear singular models (which are not feasible using existing MATLAB toolboxes) become feasible; (2) for effective control of the unknown singular analog system, an off-line OKID method is proposed to design an LQAT with state feedback and feed-forward gains; and (3) based on the newly developed modified functional observer for the reduced-order proper regular system, the original EID estimator in the literature is newly extended to estimate the EID from the unknown strictly proper singular analog system, without the original dimensional constraints of the disturbances. It is important to mention that the disturbances of interest can be unknown matched–mismatched input and output disturbances.
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Grubišić, Luka, Marko Hajba, and Domagoj Lacmanović. "Deep Neural Network Model for Approximating Eigenmodes Localized by a Confining Potential." Entropy 23, no. 1 (January 11, 2021): 95. http://dx.doi.org/10.3390/e23010095.
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We study eigenmode localization for a class of elliptic reaction-diffusion operators. As the prototype model problem we use a family of Schrödinger Hamiltonians parametrized by random potentials and study the associated effective confining potential. This problem is posed in the finite domain and we compute localized bounded states at the lower end of the spectrum. We present several deep network architectures that predict the localization of bounded states from a sample of a potential. For tackling higher dimensional problems, we consider a class of physics-informed deep dense networks. In particular, we focus on the interpretability of the proposed approaches. Deep network is used as a general reduced order model that describes the nonlinear connection between the potential and the ground state. The performance of the surrogate reduced model is controlled by an error estimator and the model is updated if necessary. Finally, we present a host of experiments to measure the accuracy and performance of the proposed algorithm.
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Grubišić, Luka, Marko Hajba, and Domagoj Lacmanović. "Deep Neural Network Model for Approximating Eigenmodes Localized by a Confining Potential." Entropy 23, no. 1 (January 11, 2021): 95. http://dx.doi.org/10.3390/e23010095.
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We study eigenmode localization for a class of elliptic reaction-diffusion operators. As the prototype model problem we use a family of Schrödinger Hamiltonians parametrized by random potentials and study the associated effective confining potential. This problem is posed in the finite domain and we compute localized bounded states at the lower end of the spectrum. We present several deep network architectures that predict the localization of bounded states from a sample of a potential. For tackling higher dimensional problems, we consider a class of physics-informed deep dense networks. In particular, we focus on the interpretability of the proposed approaches. Deep network is used as a general reduced order model that describes the nonlinear connection between the potential and the ground state. The performance of the surrogate reduced model is controlled by an error estimator and the model is updated if necessary. Finally, we present a host of experiments to measure the accuracy and performance of the proposed algorithm.
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Nguyen Van, Phuoc, and Trang Nguyen-Cong. "Chattering-Free Second Order Robustness Sliding Mode Controller for Complex Interconnected Systems: A Moore-Penrose Inverse Technique." Journal of Advanced Engineering and Computation 7, no. 4 (December 30, 2023): 210. http://dx.doi.org/10.55579/jaec.202374.429.
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In this paper, a novel second order sliding mode control approach is extended toa class of complex interconnected systems with mismatched interconnections and unknown perturbations. The key contribution of this paper is to cancel two common restrictions clogging the application of the variable structure control to complex interconnected systems: 1) all of state variables must be accessible; 2) the control input is affected by chattering problems. First, a novel reduced-order sliding mode estimator (ROSME) is proposed to estimate the unmeasurable variables. Second, based on Moore-Penrose inverse technique and ROSME tool, a new decentralized chattering-free second order robustness sliding mode controller (CSORSMC) is developed to force the system states to stay in a sliding surface from the initial period instance and attenuate the chattering phenomenon in the control signal. Besides, a novel appropriate linear matrix inequality (LMI) requirement is proved such that the plant in sliding mode is asymptotically stable. Lastly, a mathematical model including two subsystems is simulated which confirms the usefulness and advantages of proposed technique.
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Fasbender, Dominique, Blanka Vajsová, Csaba Wirnhardt, and Slavko Lemajic. "A Simple Similarity Index for the Comparison of Remotely Sensed Time Series with Scarce Simultaneous Acquisitions." Remote Sensing 11, no. 13 (June 27, 2019): 1527. http://dx.doi.org/10.3390/rs11131527.
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Emergence of new state-of-the-art technologies has enabled an unprecedented amount of high spatial resolution satellite data having great potential for exploitation of extracted time series for a vast range of applications. Despite the high temporal resolution of time series, the number of real observations of optical data that can be utilized is reduced due to meteorological conditions (such as cloud or haze) prevailing at the time of acquisition. This fact has an effect on the density of the retrieved time series and subsequently on a number of coincidental observations when comparing the similarity of time series from two different data sources for which the simultaneous acquisition date is already scarce. Classical tools for assessing the similarity of such time series can prove to be difficult or even impossible because of a lack of simultaneous observations. In this paper, we propose a simple method in order to circumvent this scarcity issue. In the first step, we rely on an interpolation in order to produce artificial time series on the union of the original acquisition dates. Then, we extend the theory of the correlation coefficient (CC) estimator to these interpolated time series. After validation on synthetic data, this simple approach proved to be extremely efficient on a real case study where Sentinel-2 and PlanetScope NDVI time series on parcels in The Netherlands are compared. Indeed, compared to other methods, it reduced the number of undecided cases while also improving the power of the statistical test on the similarity between both types of time series and the precision of the estimated CC.
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Kumar, Kundan, Shovan Bhaumik, and Sanjeev Arulampalam. "Tracking an Underwater Object with Unknown Sensor Noise Covariance Using Orthogonal Polynomial Filters." Sensors 22, no. 13 (June 30, 2022): 4970. http://dx.doi.org/10.3390/s22134970.
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In this manuscript, an underwater target tracking problem with passive sensors is considered. The measurements used to track the target trajectories are (i) only bearing angles, and (ii) Doppler-shifted frequencies and bearing angles. Measurement noise is assumed to follow a zero mean Gaussian probability density function with unknown noise covariance. A method is developed which can estimate the position and velocity of the target along with the unknown measurement noise covariance at each time step. The proposed estimator linearises the nonlinear measurement using an orthogonal polynomial of first order, and the coefficients of the polynomial are evaluated using numerical integration. The unknown sensor noise covariance is estimated online from residual measurements. Compared to available adaptive sigma point filters, it is free from the Cholesky decomposition error. The developed method is applied to two underwater tracking scenarios which consider a nearly constant velocity target. The filter’s efficacy is evaluated using (i) root mean square error (RMSE), (ii) percentage of track loss, (iii) normalised (state) estimation error squared (NEES), (iv) bias norm, and (v) floating point operations (flops) count. From the simulation results, it is observed that the proposed method tracks the target in both scenarios, even for the unknown and time-varying measurement noise covariance case. Furthermore, the tracking accuracy increases with the incorporation of Doppler frequency measurements. The performance of the proposed method is comparable to the adaptive deterministic support point filters, with the advantage of a considerably reduced flops requirement.
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Vlahakis, Eleftherios, and George Halikias. "Temperature and concentration control of exothermic chemical processes in continuous stirred tank reactors." Transactions of the Institute of Measurement and Control 41, no. 15 (July 3, 2019): 4274–84. http://dx.doi.org/10.1177/0142331219855591.
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Exothermic chemical reaction taking place in continuous stirred tank reactor is considered. Heat release from the chemical reaction, non-linear dynamic behavior of the process and uncertainty in parameters are the main factors motivating the use of robust control design. Viewing temperature and molar concentration as variables both accessible in real time, PI and optimal state-feedback controllers driven by temperature and concentration error signals are proposed to regulate the system over reactor’s steady-state working points by counteracting undesired disturbances. Since access to concentration value has proved beneficial for the reactor’s performance, estimation techniques are examined to compensate for the problematic nature of the concentration’s measurement. A linear reduced-order observer is first proposed to estimate the concentration value using temperature measurements. In addition, assuming concentration measurement is available with a relatively short delay via sample analysis, a linear and non-linear discrete-time predictor is constructed to estimate the concentration’s real-time value. A linear combination of the two estimation schemes (observer, predictor) is proposed resulting in a combined estimator, in which the emphasis between the two individual schemes can be controlled via a scalar parameter. The work presented in this paper was supported by the GLOW project – New weather-stable low gloss powder coatings based on bifunctional acrylic solid resins and nanoadditives – as part of the development of novel and efficient processing technologies regarding the production of new families of powder coatings, responding to industrial requirements for quality improvement at lower cost and shorter development cycles.
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Nguyen, Cong-Trang, Thanh Long Duong, Minh Quan Duong, and Duc Tung Le. "Chattering-Free Single-Phase Robustness Sliding Mode Controller for Mismatched Uncertain Interconnected Systems with Unknown Time-Varying Delays." Energies 13, no. 1 (January 6, 2020): 282. http://dx.doi.org/10.3390/en13010282.
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Variable structure control with sliding mode can provide good control performance and excellent robustness. Unfortunately, the chattering phenomenon investigated due to discontinuous switching gain restricting their applications. In this paper, a chattering free improved variable structure control (IVSC) for a class of mismatched uncertain interconnected systems with an unknown time-varying delay is proposed. A sliding function is first established to eliminate the reaching phase in traditional variable structure control (TVSC). Next, a new reduced-order sliding mode estimator (ROSME) without time-varying delay is constructed to estimate all unmeasurable state variables of plants. Then, based on the Moore-Penrose inverse approach, a decentralized single-phase robustness sliding mode controller (DSPRSMC) is synthesized, which is independent of time delays. A DSPRSMC solves a complex interconnection problem with an unknown time-varying delay term and drives the system’s trajectories onto a switching surface from the initial time instance. Particularly, by applying the well-known Barbalat’s lemma, the chattering phenomenon in control input is alleviated. Moreover, a sufficient condition is established by using an appropriate Lyapunov theory and linear matrix inequality (LMI) method such that a sliding mode dynamics is asymptotically stable from the beginning time. Finally, a developed method is validated by numerical example with computer simulations.
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BERNSTEIN, DENNIS S., and WASSIM M. HADDAD. "Optimal reduced-order state estimation for unstable plants." International Journal of Control 50, no. 4 (October 1989): 1259–66. http://dx.doi.org/10.1080/00207178908953431.
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Farrell, Brian F., and Petros J. Ioannou. "State Estimation Using a Reduced-Order Kalman Filter." Journal of the Atmospheric Sciences 58, no. 23 (December 2001): 3666–80. http://dx.doi.org/10.1175/1520-0469(2001)058<3666:seuaro>2.0.co;2.
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Bernstein, D., and D. Hyland. "The optimal projection equations for reduced-order state estimation." IEEE Transactions on Automatic Control 30, no. 6 (June 1985): 583–85. http://dx.doi.org/10.1109/tac.1985.1104001.
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Huang, He, Tingwen Huang, and Xiaoping Chen. "Reduced-order state estimation of delayed recurrent neural networks." Neural Networks 98 (February 2018): 59–64. http://dx.doi.org/10.1016/j.neunet.2017.11.002.
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Kim, In Sung, Bruno O. S. Teixeira, Jaganath Chandrasekar, and Dennis S. Bernstein. "Reduced-order state estimation for linear time-varying systems." Asian Journal of Control 11, no. 6 (November 2009): 595–609. http://dx.doi.org/10.1002/asjc.141.
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Lungu, Mihai, and Romulus Lungu. "Reduced-Order Multiple Observer for Aircraft State Estimation during Landing." Applied Mechanics and Materials 841 (June 2016): 253–59. http://dx.doi.org/10.4028/www.scientific.net/amm.841.253.
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The paper presents a new reduced-order multiple observer which can achieve the finite-time reconstruction of the system’s state associated to a multiple-model. This observer is a combination of a reduced-order observer and a full-order multiple observer. The design of the new observer involves the usage of the Lyapunov theory, the solving of a linear matriceal inequality, and a variables’ change. The steps of the design procedure have been software implemented in order to validate the new reduced-order multiple observer for the case of an aircraft motion during landing.
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Karunathilake, Dulmini, Mahinda Vilathgamuwa, Yateendra Mishra, Paul Corry, Troy Farrell, and San Shing Choi. "Degradation-Conscious Multiobjective Optimal Control of Reconfigurable Li-Ion Battery Energy Storage Systems." Batteries 9, no. 4 (April 4, 2023): 217. http://dx.doi.org/10.3390/batteries9040217.
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Lithium-ion battery energy storage systems are made from sets of battery packs that are connected in series and parallel combinations depending on the application’s needs for power. To achieve optimal control, advanced battery management systems (ABMSs) with health-conscious optimal control are required for highly dynamic applications where safe operation, extended battery life, and maximum performance are critical requirements. The majority of earlier research assumed that the battery cells in these energy storage systems were identical and would vary uniformly over time in terms of cell characteristics. However, in real-world situations, the battery cells might behave differently for a number of reasons. Overcharging and over-discharging are caused by an electrical imbalance that results from the cells’ differences in properties and capacity. Therefore in this study, a stratified real-time control scheme was developed for the dual purposes of minimizing the capacity fade and the energy losses of a battery pack. Each of the cells in the pack is represented by a degradation-conscious physics-based reduced-order equivalent circuit model. In view of the inconsistencies between cells, the proposed control scheme uses a state estimator such that the parametric values of the circuit elements in the cell model are determined and updated in a decentralized manner. The minimization of the capacity fade and energy losses is then formulated as a multiobjective optimization problem, from which the resulting optimal control strategy is realized through the switching actions of a modular multilevel series-parallel converter which interconnects the battery pack to an external AC system. A centralized controller ensures optimal switching sequence of the converter leading to the maximum utilization of the capacity of the battery pack. Both simulation and experimental results are used to verify the proposed methodologies which aim at minimizing the battery degradation by reconfiguring the battery cells dynamically in accordance with the state of health (SOH) of the pack.
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Palomba, Ilaria, Dario Richiedei, and Alberto Trevisani. "Reduced-Order Observers for Nonlinear State Estimation in Flexible Multibody Systems." Shock and Vibration 2018 (November 1, 2018): 1–12. http://dx.doi.org/10.1155/2018/6538737.
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Modern control schemes adopted in multibody systems take advantage of the knowledge of a large set of measurements of the most important state variables to improve system performances. In the case of flexible-link multibody systems, however, the direct measurement of these state variables is not usually possible or convenient. Hence, it is necessary to estimate them through accurate models and a reduced set of measurements ensuring observability. In order to cope with the large dimension of models adopted for flexible multibody systems, this paper exploits model reduction for synthesizing reduced-order nonlinear state observers. Model reduction is done through a modified Craig-Bampton strategy that handles effectively nonlinearities due to large displacements of the mechanism and through a wise selection of the most important coordinates to be retained in the model. Starting from such a reduced nonlinear model, a nonlinear state observer is developed through the extended Kalman filter (EKF). The method is applied to the numerical test case of a six-bar planar mechanism. The smaller size of the model, compared with the original one, preserves accuracy of the estimates while reducing the computational effort.
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Parkinson, J., and R. Wynne. "Reduced-order modeling and state estimation applied to gas distribution systems." IEEE Transactions on Automatic Control 31, no. 8 (August 1986): 701–9. http://dx.doi.org/10.1109/tac.1986.1104376.
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Panossian, Hagop V. "Reduced-order observers applied to state and parameter estimation ofhydromechanical servoactuators." Journal of Guidance, Control, and Dynamics 9, no. 2 (March 1986): 249–51. http://dx.doi.org/10.2514/3.20098.
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Loiseau, Jean-Christophe, Bernd R. Noack, and Steven L. Brunton. "Sparse reduced-order modelling: sensor-based dynamics to full-state estimation." Journal of Fluid Mechanics 844 (April 6, 2018): 459–90. http://dx.doi.org/10.1017/jfm.2018.147.
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We propose a general dynamic reduced-order modelling framework for typical experimental data: time-resolved sensor data and optional non-time-resolved particle image velocimetry (PIV) snapshots. This framework can be decomposed into four building blocks. First, the sensor signals are lifted to a dynamic feature space without false neighbours. Second, we identify a sparse human-interpretable nonlinear dynamical system for the feature state based on the sparse identification of nonlinear dynamics (SINDy). Third, if PIV snapshots are available, a local linear mapping from the feature state to the velocity field is performed to reconstruct the full state of the system. Fourth, a generalized feature-based modal decomposition identifies coherent structures that are most dynamically correlated with the linear and nonlinear interaction terms in the sparse model, adding interpretability. Steps 1 and 2 define a black-box model. Optional steps 3 and 4 lift the black-box dynamics to a grey-box model in terms of the identified coherent structures, if non-time-resolved full-state data are available. This grey-box modelling strategy is successfully applied to the transient and post-transient laminar cylinder wake, and compares favourably with a proper orthogonal decomposition model. We foresee numerous applications of this highly flexible modelling strategy, including estimation, prediction and control. Moreover, the feature space may be based on intrinsic coordinates, which are unaffected by a key challenge of modal expansion: the slow change of low-dimensional coherent structures with changing geometry and varying parameters.
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Yin, Xunyuan, and Jinfeng Liu. "State estimation of wastewater treatment plants based on reduced-order model." IFAC-PapersOnLine 51, no. 18 (2018): 572–77. http://dx.doi.org/10.1016/j.ifacol.2018.09.363.
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NGUYEN, CHARLES C. "Design of reduced-order state estimators for linear time-varying multivariable systems." International Journal of Control 46, no. 6 (December 1987): 2113–26. http://dx.doi.org/10.1080/00207178708934038.
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TELFORD, ANDREW J., and JOHN B. MOORE. "Doubly coprime factorizations, reduced-order observers, and dynamic state estimate feedback." International Journal of Control 50, no. 6 (December 1989): 2583–97. http://dx.doi.org/10.1080/00207178908953516.
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Li, Yuanyuan, and Dietmar Bauer. "Modeling I(2) Processes Using Vector Autoregressions Where the Lag Length Increases with the Sample Size." Econometrics 8, no. 3 (September 17, 2020): 38. http://dx.doi.org/10.3390/econometrics8030038.
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In this paper the theory on the estimation of vector autoregressive (VAR) models for I(2) processes is extended to the case of long VAR approximation of more general processes. Hereby the order of the autoregression is allowed to tend to infinity at a certain rate depending on the sample size. We deal with unrestricted OLS estimators (in the model formulated in levels as well as in vector error correction form) as well as with two stage estimation (2SI2) in the vector error correction model (VECM) formulation. Our main results are analogous to the I(1) case: We show that the long VAR approximation leads to consistent estimates of the long and short run dynamics. Furthermore, tests on the autoregressive coefficients follow standard asymptotics. The pseudo likelihood ratio tests on the cointegrating ranks (using the Gaussian likelihood) used in the 2SI2 algorithm show under the null hypothesis the same distributions as in the case of data generating processes following finite order VARs. The same holds true for the asymptotic distribution of the long run dynamics both in the unrestricted VECM estimation and the reduced rank regression in the 2SI2 algorithm. Building on these results we show that if the data is generated by an invertible VARMA process, the VAR approximation can be used in order to derive a consistent initial estimator for subsequent pseudo likelihood optimization in the VARMA model.
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Sibille, L., T. S. Nord, B. Siedziako, and A. Fenerci. "Impact force identification on a ferry dock bridge." Journal of Physics: Conference Series 2647, no. 18 (June 1, 2024): 182012. http://dx.doi.org/10.1088/1742-6596/2647/18/182012.
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Abstract There is a scarcity of literature on the monitoring of operational loads and structural health of coastal infrastructure assets. In this paper we show the very first estimates of the impact force acting on a ferry quay bridge during ferry berthing based on vibration measurements. The input and state of the structure are estimated by means of a joint input-state estimation algorithm in conjunction with a modally reduced-order finite element model. The estimated and measured accelerations are compared, and a strong agreement is found, even when only a limited number of sensors was used, paving the way for an efficient full-scale monitoring of the structure in the long term.
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Estuningsih, Nenik, and Fatmawati Fatmawati. "Groundwater Pollution Concentration Estimation with Modified Kalman Filter Method." CAUCHY: Jurnal Matematika Murni dan Aplikasi 9, no. 2 (November 1, 2024): 237–46. http://dx.doi.org/10.18860/ca.v9i2.28467.
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Groundwater quality is very important for human health. Estimation of groundwater pollution concentration to determine groundwater quality is necessary. The concentration of groundwater pollution is estimated using the modified Kalman filter method. The modified Kalman filter method is a method that collaborates the Kalman filter estimation algorithm with the model order reduction method. The model order reduction method used in this research is the LMI (Linear Matrix Inequality) method because the model reduction error using the LMI method is the smallest error compared to the reduction error using the Balanced Truncation method or the Singular Pertrubation Approximation method. The modified Kalman filter method is used in order to obtain accurate estimation results with a short computation time. It is found that the implementation of the Kalman filter algorithm in the original system as well as the implementation of the modified Kalman filter method of the reduced system with the LMI method produces very good estimates, close to the real state variable. The estimation of the original system takes longer time than the reduced system.