Estimation Of State Variables Research Articles

Feature-informed data assimilation

We introduce a mathematical formulation of feature-informed data assimilation (FIDA). In FIDA, the information about feature events, such as shock waves, level curves, wavefronts and peak value, in dynamical systems are used for the estimation of state variables and unknown parameters. The observation operator in FIDA is a set-valued functional that involves a search process over a function of state variables, which is fundamentally different from the observation operators in conventional data assimilation. We present three numerical experiments, in which shocks and expanding waves are observed features. These examples serve to demonstrate FIDA's ability to estimate model parameters from such noisy observations.

A Novel Bipartite Consensus Tracking Control for Multiagent Systems Under Sensor Deception Attacks.

This article presents a novel adaptive bipartite consensus tracking strategy for multiagent systems (MASs) under sensor deception attacks. The fundamental design philosophy is to develop a hierarchical algorithm based on shortest route technology that recasts the bipartite consensus tracking problem for MASs into the tracking problem for a single agent and eliminates the need for any global information of the Laplacian matrix. As the sensors suffer from malicious deception attacks, the states cannot be measured accurately, we thus construct a novel dynamic estimator to estimate the actual states, which, together with a new coordinate transformation involving the attacked and estimated state variables, allows a distributed security control scheme to be developed, in which the singularity of the adaptive iterative process involved in existing works is completely avoided. Furthermore, the Nussbaum functions are included in the controller to account for the influence of the unknown control gains caused by sensor deception attacks. It is shown that the distributed consensus tracking errors converge to a small neighborhood of the origin, and all the signals in the closed-loop system remain bounded. Simulation on a forced damped pendulums (FDPs) is conducted to demonstrate and verify the effectiveness of the proposed strategy.

Recurrent neural network based sensor fault detection and isolation for nonlinear systems: Application in PWR

Real-time monitoring of sensors is crucial in attaining consistent process performance with strict safety and eco-friendly measures. This article presents a fault detection and isolation (FDI) technique that diagnoses sensor faults regardless of the utilized model structure. A Recurrent Neural Network (RNN) is utilized to estimate state variables with the inputs and outputs of the process. RNNs build predictive models of the process. Then, a bank of residuals of state variables is obtained such that each residual is responsive to a subsection of faults and unresponsive to others. Consequently, an exclusive fault signature is attained for each fault case. One of the merits of the proposed procedure is that it does not necessitate the fault history of the process or first principle models contrasting to other existing outcomes in the literature. The efficacy of the proposed FDI methodology is studied on a highly nonlinear pressurized water nuclear reactor model.

A Predictive Control Method for LCC HVDC Participated Black Start With Commutation Failure Prevention

Line-commutated converter (LCC) based HVDC systems can significantly speed up the restoration of infeed power systems in blackout states. But they are fragile to commutation failure (CF) under the adverse black-start conditions. To improve the adaptability of LCC HVDC systems in such situations, a predictive control method is proposed in this paper. It includes the linear discrete time predictive model, receding horizon regulator, state estimator, and CF prevention (CFPREV) module. The model is based on the quasi-dynamic and transient-state analysis of load disturbances, where the black-start state is forecasted according to voltage sags caused by inrush currents. The regulator operates in real-time to optimize reference inputs for the HVDC controller. In the estimator, process error and measurement noise are modeled and the optimal system state is estimated with a Kalman filter. Moreover, the dc current setting for CFPREV is calculated using the predicted and estimated state variables. The CFPREV module and regulator work in coordination for secure and fast dc power recovery under abnormal conditions. Small-signal stability analysis and EMT simulations are implemented on the CIGRE benchmark model based black start test grid. The results show that the proposed method i) improves dc power response to black start load startups and ii) presents better recovery performance after the fault.

Deep Diffusion Kalman Filter Combining Large-Scale Neuronal Networks Simulation with Multimodal Neuroimaging Data

Using computers to numerically simulate large-scale neuronal networks has become a common method for studying the mechanism of the human brain, and neuroimaging has brought forth multimodal brain data. Determining how to fully consider these multimodal data in the process of brain modeling has become a crucial issue. Data assimilation is an efficient method for combining the dynamic system with the observation data, and many related algorithms have been developed. In this paper, we utilize data assimilation to perform brain state variables estimation, put forward a general form of a diffusion Kalman filter named the deep diffusion Kalman filter, and provide a specific algorithm that is combined with data assimilation. Then, we theoretically demonstrate the deep diffusion Kalman filter’s effectiveness and further validate it by using an experiment in the toy model. Finally, according to the resting state functional magnetic resonance imaging signals, we assimilate a cortex networks model with the resting state brain, where the correlation is as high as 98.42%.

Neural Network Applications in Electrical Drives—Trends in Control, Estimation, Diagnostics, and Construction

Currently, applications of the algorithms based on artificial intelligence (AI) principles can be observed in various fields. This can be also noticed in the wide area of electrical drives. Consideration has been limited to neural networks; however, the tasks for the models can be defined as follows: control, state variable estimation, and diagnostics. In the subsequent sections of this paper, electrical machines, as well as power electronic devices, are assumed as the main objects. This paper describes the basics, issues, and possibilities related to the used tools and explains the growing popularity of neural network applications in automatic systems with electrical drives. The paper begins with the overall considerations; following that, the content proceeds with the details, and two specific examples are shown. The first example deals with a neural network-based speed controller tested in a structure with a synchronous reluctance motor. Then, the implementation of recurrent neural networks as state variable estimators is analyzed. The achieved results present a precise estimation of the load speed and the shaft torque signals from a two-mass system. All descriptions in the article are considered in the context of the trends and perspectives in modern algorithm applications for electrical drives.

Joint assimilation of satellite soil moisture and streamflow data for the hydrological application of a two-dimensional shallow water model

Data assimilation (DA) in physically-based hydrodynamic models is conditioned by the difference in temporal and spatial scales of the observed data and the resolution of the model itself. In order to use remote sensing data in small-scale hydrodynamic modelling, it is necessary to explore innovative DA methods that can lead to a more plausible representation of the spatial variability of the parameters and processes involved. In the present study, satellite-derived soil moisture and in situ-observed streamflow data were jointly assimilated into a high-resolution hydrological-hydrodynamic model based on the Iber software, using the Tempered Particle Filter (TPF) for the dual estimation of model state variables and parameters. Twelve storm events occurring in a 199 km2 catchment located in NW Spain were used for testing the proposed approach. A 3-step procedure was followed: (1) sensitivity analysis of the model parameters; (2) joint assimilation of soil moisture and discharge data to estimate correlations between observations and model parameters; (3) joint assimilation of soil moisture and discharge data using an initial set of particles and parameter standard deviations derived from prior information. The numerical model correctly reproduces the observed data, with an average Nash-Sutcliffe efficiency (NSE) value of 0.74 over the 12 events when the prior information is used. The approach described is shown to be most efficient with storm events that produce isolated peak discharges.

Interval observers design for systems with ostensible Metzler system matrices

This paper attempts to resolve the problem concerning the interval observers design for linear systems with ostensible Metzler system matrices. Because system dynamics matrices are partially different from strictly Metzler structures, a solution is achieved by constructing a composed system matrix representation, which combines pre-compensated interval matrix structures fixed with a prescribed region of D-stability and the reconstructed strictly Metzler matrix structure, related to the original interval system matrix parameter definition. A novel design procedure is presented, which results in a strictly positive observer gain matrix and guarantees that the lower estimates of the positive state variables are non-negative when considering the given system structure and the non-negative system state initial values. The design is computationally simple since it is reduced to the feasibility of the set of linear matrix inequalities.

Which filter for data assimilation in water quality models? Focus on oxygen reaeration and heterotrophic bacteria activity

With the development of sophisticated water quality models and the advances in computational power, data assimilation (DA) techniques, especially ensemble-based methods (the ensemble Kalman filter and particle filter), are attracting considerable attention in water quality modeling for improving the estimation of state variables and parameters in water quality models. The ensemble Kalman filter (EnKF) has become the most popular DA method while the particle filter (PF), which does not rely on Gaussian or quasi-linearity assumptions, is seldom applied in water quality modeling. Here, we present a comparison between the PF and EnKF for the update of model parameters related to river metabolism. The two filters are implemented in ProSe-PA, a hydro-biogeochemical software, and their performance is assessed on two synthetic case studies. The results indicate that PF and EnKF can estimate dissolved oxygen concentrations and the posterior probability distribution function of the associated parameters, either precisely for both filters in the case of a slightly nonlinear system (reaeration at the air–water interface) or more precisely for the PF in the case of a strongly nonlinear system (organic matter degradation) dominated by heterotrophic bacterial activities. Since the PF is more accurate, its usage is recommended for water quality modeling and guidelines are provided for its set-up.

Design of a High-Order Kalman Filter for State and Measurement of A Class of Nonlinear Systems Based on Kronecker Product Augmented Dimension

A high-order Kalman filter for full-dimensional variables is proposed for a class of dynamic systems whose state model and measurement model are both nonlinear. The filter requires Taylor expansion of the system equations, and then performs Kronecker product operation on the linear part in the Taylor expansion. Finally, a linear dynamic model is achieved based on the full-dimensional vector formed by the state variables and the high-order dimension expansion variables. After designing the filter, the Kalman filter for the original state variables estimation was selected through the projection operator. The excellent performance of the novel filter is analyzed from the aspects of the information utilization of the state estimation value and the size of the state estimation error covariance matrix. The numerical verification is carried out by computer simulation.

Adaptive Fuzzy Output-Feedback Consensus Tracking Control of Nonlinear Multiagent Systems in Prescribed Performance.

This article addresses the finite-time consensus tracking control problem for nonlinear multiagent systems (MASs), in which state variables are unmeasured and nonlinear functions are totally unknown. An observer is designed to estimate state variables and fuzzy-logic systems are employed to approximate nonlinearities. Then, an observer-based adaptive fuzzy consensus tracking controller is developed by using the backstepping technique and constructing a novel barrier Lyapunov function with the consideration of the characteristics of MASs. The proposed control protocol can guarantee that: 1) all signals in the closed-loop system keep bounded and 2) the consensus tracking error converges to a prespecified region of the origin in the prescribed finite time. Compared with the existing observer-based finite/fixed-time control protocols, the settling time and the convergence region in our work can be both preassigned by the designer and not affected by the unknown positive constant, which lies in the Lyapunov derivative inequality. Finally, two comparison simulation examples, including a numerical example and a practical example, check the availability of the designed control scheme.

Robust particle filter for state estimation in presence of bounded but uncertain parameters based on ellipsoidal set membership approach

Accurate estimation of state variables plays an important role in control, monitoring and optimization. Considering that the uncertainty of parameter may back-propagate to the particle and then influence the state estimation, this paper proposes a robust particle filtering method in the presence of bounded uncertain parameters based on the ellipsoidal set membership filtering (ESMF) approach. This proposed method employs ellipsoidal sets to enclose the parameter uncertainty, and each prior particle and posterior particle are determined according to the ellipsoidal calculation based on the ESMF algorithm: The prior particle is characterized by an ellipsoid derived by the ellipsoidal summation of linear transformation ellipsoid, linearization error ellipsoid and system noise ellipsoid; Each posterior particle is obtained by updating the prior particle through the ellipsoidal intersection of the prior particle ellipsoid and the measurement ellipsoid. As a result, the uncertainty of parameter may be incorporated into the state estimation, and the advantages of both ESMF and particle filter are taken by the proposed method. The efficacy of the proposed method is shown by three simulation examples.

State estimation accuracy analysis of an induction electric drive by the algorithms of Luenberger and Kalman

In complex electromechanical objects containing electric drives with induction motors, it is often difficult or impossible to install sensors of output variables. In this case, to determine the output coordinates of the motor, it is necessary to introduce state observers into the control system of the electric drive. The main problems of creating observers are the presence of noise and interference in the measuring circuits of the control system which affect the accuracy of the estimation of immeasurable state variables. The paper presents a comparison of the accuracy of estimates obtained as a result of the work of the observer algorithms based on the Kalman filter and the observer of the Luenberger in the induction electric drive system, with vector control at the noise level of the current measurement channels in the stator windings of the induction motor. To synthesize algorithms for state observers, methods of identification theory and quasi-linearization of nonlinear models of the control object under consideration were used. The simulation model of an induction motor is based on a classical vector field-oriented control system where an estimate of the angular speed of the motor shaft is used as a feedback signal. The model implements the following blocks: a mathematical model of an induction motor in a two-phase fixed coordinate system α–β; the structure of the observer algorithm; the procedure for converting the basis of the current vector and the control voltage from stationary to rotating and vice versa; proportional-integral regulators of current, flux linkage and angular speed. The S-shaped intensity setter forms a speed setting curve. The input signals for observers are the stator voltages and currents of the reference model of an induction motor. The adaptation coefficients for the Luenberger observer were selected experimentally from the condition of obtaining the average minimum value of the difference modulus of the estimated values. The covariance matrices for the observer based on the Kalman filter are configured on the basis of the experiment, ensuring a minimum of the average value of the absolute error. The time dependences of the transients of the angular speed of the shaft, the modulus of the flux linkage vectors of the rotor and stator currents are obtained. The dependencies were evaluated when starting an induction motor with nominal values and values of frequency and voltage amounting to 10 % of the nominal values. The work of estimation algorithms in the presence of a noise component, as well as when changing the parameters of the induction motor replacement circuit by ± 10 %, is investigated. The results of modeling the operation of the electric drive in starting modes with a mechanical load equal to the nominal value at a supply voltage frequency of 50 Hz and at 10 % of the nominal value for a voltage of 1 Hz are obtained. It is shown that the greatest relative estimation errors occur in the starting mode of the electric drive, and the maximum accuracy is achieved in the case of using a nonlinear Kalman filter. The results of the work can be used in the development of automatic control systems for sensorless electric drives and frequency-controlled electric drive of centrifugal pumping units for oil production.

System Identification in Distribution Grid Without Phase Angle using Expectation Maximization

There has been a large increase in distributed energy resources (DERs) on the distribution grid (DG) and it is expected to continue. To support this increase active grid management and optimisation is required, for which accurate information of system state variables is required. This study presents a method for simultaneously estimating the line parameters and system state variables; active and reactive power at nodes. In addition, the study estimates the voltage magnitude accurately and requires no information about phase angle. The proposed approach uses a novel combination of Linearized Distflow and expectation maximisation (EM). The proposed approach is demonstrated on the IEEE 37 node test feeder and achieves accurate estimates of line parameters and state variables. Furthermore, the results show that the estimated line parameters give better voltage estimates using Linearised Distflow than the true parameters from the AC model which we argue is due to the estimated parameters making up for the approximation error.

Robust State Estimation Model for Low Voltage Distribution Networks in the Presence of Multiple Gross Errors

One of the primary challenges in solving the State Estimation (SE) problem in low voltage networks is the presence of Gross Errors (GE). If the SE model fails to accurately estimate state variables in the presence of GE, the system operator may receive a distorted image of the power network, potentially leading to unforeseen disruptions, blackouts, and significant economic losses. The classical weighted least squares method, which is commonly used in such problems, exhibits low accuracy when simultaneous GE occurs. This paper provides a comprehensive analysis comparing robust M-estimators designed to handle GE, such as Hachtel and the largest normalized residual test, and presents a novel SE method called the Adaptive Maximum Correntropy Criterion (AMCC). The AMCC employs the maximum correntropy criterion for the loss function and an interior point methodology. Additionally, an adaptive scheme is employed to automatically adjust a high parameter associated with the shape of the related gamma function. We show that, in a real low voltage network, the AMCC exhibits superior accuracy with smaller root-mean-square errors compared to the other estimators studied.

РАЗРАБОТКА НАБЛЮДАТЕЛЯ ЛЮЕНБЕРГЕРА ПОЛНОГО ПОРЯДКА ВЕКТОРА ПЕРЕМЕННЫХ СОСТОЯНИЯ УЧАСТКА КАБЕЛЬНОЙ ЛИНИИ С ПОВЫШЕННОЙ ПАРАМЕТРИЧЕСКОЙ РОБАСТНОСТЬЮ

In addition, in the Russian Federation, 75 % of oil-producing wells in operation at old fields are low- to medium-flow rate wells. One way to increase the profitability of oil production from low- to medium-flow rate wells using ESPs is to reduce the power consumption of the Submersible Electric Motor (SEM) by switching the ESP from a scalar open-loop control system to a sensorless vector control system. To implement the vector control system for ESPs, it is necessary to develop a methodology for identifying the parameters of the electrical equipment in the power channel of the ESP, as well as to implement a full-order observer of the SEM vector state variables to create a feedback channel for angular speed. One of the electrical components in the ESP power channel that affects the accuracy of the SEM vector state variable estimation is the power cable, which can reach up to 5 km in length. Such a long cable length results in the output voltage at the cable end being significantly different in amplitude and frequency from the measured input voltage, and the cable parameters themselves change as the temperature of the well varies depending on the depth. Failure to estimate the output voltage of the cable will result in incorrect estimation of the torque and angular speed of the SEM, which, in turn, may cause the angular speed of the SEM to oscillate and the ESP to trip at the bottom of the well. Due to the above factor, the development of a full-order observer for the vector state variables of the cable line with increased parametric robustness is a relevant and timely task

Population dynamics and the effect of drought in the threatened Nubian ibex

AbstractEstimating key state variables such as abundance, survival, and recruitment of wild populations, and their interaction with local conditions such as precipitation, is essential for state‐dependent decision making and management. Estimation of state variables remains challenging, especially in species such as mountain ungulates inhabiting rugged and remote terrains. Camera traps present a technological advance that can mitigate some of the challenges in state estimation and can be used to enhance existing methods. Here, we combined camera traps, individual markings, and GPS tracking to estimate abundance and survival for the threatened Nubian ibex (Capra nubiana) population of the Judean Desert, Israel. Since precipitation is a key determinant for recruitment in desert ungulates, we complemented our estimates with kid‐female ratios and regional precipitation records. Between 2016 and 2019, we individually marked 48 ibex of which 38 were also fitted with GPS collars within the Judean Desert. We performed 6 days of camera‐trap surveys each year to estimate abundance for the north Judean Desert population using mark‐resight in a robust‐design framework. Weight‐averaged abundance estimates for 2017–2019, respectively, were as follows: = 267 (95% CI = 117–418, SE = 51.27), 201 (95% CI = 115–288, SE = 36.85), and 226 (95% CI = 154–299, SE = 36.94) for females, and = 291 (95% CI = 154–299, SE = 36.94), 160 (95% CI = 108–212, SE = 25.19), and 283 (95% CI = 181–384, SE = 29.76) for males. By augmenting data from telemetry with camera traps, we estimated survival via known fates for the entire Judean Desert (north, mid, and south populations). Weight‐averaged survival estimates for 2016–2019, respectively, were: = 0.99 (95% CI = 0.97–1.00, SE = 0.012), 0.90 (95% CI = 0.24–0.99, SE = 0.153), 0.87 (95% CI = 0.62–0.97, SE = 0.081), and 0.88 (95% CI = 0.69–0.96, SE = 0.062) for females, and = 0.77 (95% CI = 0.26–0.97, SE = 0.203), 0.64 (95% CI = 0.33–0.86, SE = 0.151), 0.85 (95% CI = 0.60–0.96, SE = 0.087), and 0.88 (95% CI = 0.69–0.96, SE = 0.062) for males. The interannual trends of abundance and survival estimates corresponded with observed kid‐female ratios and the regional precipitation records, reflecting a population decline following 2017's drought and an increase following the increased precipitation in 2018. Our findings substantiate the efficacy of using camera traps to estimate Nubian ibex's key state variables, as well as detecting population trends driven by environmental conditions. Despite being costly, the capacity of statistically‐robust methods to estimate key state variables is indispensable, and camera traps make similar methods increasingly more feasible in remote and inaccessible populations.

Модальный синтез оценивателя неизмеряемых переменных состояния для системы стабилизации курса судна

The purpose of the study is to apply automation technologies and digitalization in estimating the unmeasurable variables of the ship course stabilization system to control the high-tech software and hardware and, thus, to intensify the use of ships at a qualitatively new level, as well as to improve the reliability and efficiency of their operation. It has been stated that estimating the vector of state variables in real time requires to use methods and computational algorithms 
 of stochastic and, in particular, binomial filtering. It is emphasized that for improving the reliability and accuracy of estimating the parameters of the system under perturbations of the roll angle, angular rotation speed or measurement noise there are required compromise solutions that take into account the required values of the system's speed and stability. It is shown that digitalization of mathematical and physical ship models, producing the adequate decisions, taking into account a wide range of environmental influences and navigation conditions allow to synthesize ship control complexes in the class of digital predictive systems with a transition to the control of unmanned objects. There has been considered the modal method of synthesis of the vector estimator of the state of full dimension (Kalman observer) which can obtain estimates of unmeasured state variables of the course stabilization system with measured output and input of the system by developing a model of the state of the extended system ‘object–observer’, which ensures stability of the ship on the course. A model and an algorithm for estimating unmeasured state variables by using binomial filtering algorithms, matrix laboratory tools and computer modeling technologies in the MATLAB environment are proposed. The proposed algorithm for the synthesis of a vector evaluator of unmeasured state variables is implemented in the form of a program compiled in MATLAB codes and demonstrated in calculating a two-dimensional dynamic observer for an unstable object of control. The obtained estimates of unmeasured variables, as well as the results of modeling the dynamic reactions of the course stabilization system correspond to the specified speed and stability transient processes of the ship object when transferring it into the steady state under the new initial conditions.

Uncertainty-bounded estimates of ash cloud properties using the ORAC algorithm: application to the 2019 Raikoke eruption

Abstract. Uncertainty-bounded satellite retrievals of volcanic ash cloud properties such as ash cloud-top height, effective radius, optical depth and mass loading are needed for the robust quantitative assessment required to warn aviation of potential hazards. Moreover, there is an imperative to improve quantitative ash cloud estimation due to the planned move towards quantitative ash concentration forecasts by the Volcanic Ash Advisory Centers. Here we apply the Optimal Retrieval of Aerosol and Cloud (ORAC) algorithm to Advanced Himawari Imager (AHI) measurements of the ash clouds produced by the June 2019 Raikoke (Russia) eruption. The ORAC algorithm uses an optimal estimation technique to consolidate a priori information, satellite measurements and associated uncertainties into uncertainty-bounded estimates of the desired state variables. Using ORAC, we demonstrate several improvements in thermal infrared volcanic ash retrievals applied to broadband imagers. These include an improved treatment of measurement noise, accounting for multi-layer cloud scenarios, distinguishing between heights in the troposphere and stratosphere, and the retrieval of a wider range of effective radii sizes than existing techniques by exploiting information from the 10.4 µm channel. Our results indicate that 0.73 ± 0.40 Tg of very fine ash (radius ≤ 15 µm) was injected into the atmosphere during the main eruptive period from 21 June 18:00 UTC to 22 June 10:00 UTC. The total mass of very fine ash decreased from 0.73 to 0.10 Tg over ∼ 48 h, with an e-folding time of 20 h. We estimate a distal fine ash mass fraction of 0.73 % ± 0.62 % based on the total mass of very fine ash retrieved and the ORAC-derived height–time series. Several distinct ash layers were revealed by the ORAC height retrievals. Generally, ash in the troposphere was composed of larger particles than ash present in the stratosphere. We also find that median ash cloud concentrations fall below peak ash concentration safety limits (< 4 mg m−3) 11–16 h after the eruption begins, if typical ash cloud geometric thicknesses are assumed. The ORAC height retrievals for the near-source plume showed good agreement with GOES-17 side-view height data (R=0.84; bias = −0.75 km); however, a larger negative bias was found when comparing ORAC height retrievals for distal ash clouds against Cloud-Aerosol Lidar with Orthogonal Polarisation (CALIOP) measurements (R=0.67; bias = −2.67 km). The dataset generated here provides uncertainties at the pixel level for all retrieved variables and could potentially be used for dispersion model validation or be implemented in data assimilation schemes. Future work should focus on improving ash detection, improving height estimation in the stratosphere and exploring the added benefit of visible channels for retrieving effective radius and optical depth in opaque regions of nascent ash plumes.

Robust Observer to estimate states and parameters of Nonlinear Quorum Sensing Dynamics with Time Delay

Quorum sensing (QS) is a self organization process in bacteria colonies where certain collective action is performed blue when a population density threshold is reached. Some medically relevant behaviors of bacteria are known to be described by QS dynamics such as virulence or antibiotics resistance. Estimation of states and parameters in QS model is important to address such medical issues but difficult in scenarios where measurements are limited and internal activation delay times are considered. In this paper an exteded Kalman filter is applied to estimate two unknown states and a nonlinear parameter of a time delay QS (TDQS) system. To the author's knowledge this is the first extended Kalman filter applied to estimate state variables of QS in its delayed version. In this work it is shown how, by measuring only one of the states of the TDQS, the rest of the variables can be estimated, as well one nonlinear parameter.