State Estimation Theory Research Articles

Robust fractional control based on high gain observers design (RNFC) for a Spirulina maxima culture interfaced with an advanced oxidation process

Abstract In this article, the theory of fractional control and state estimation applied to biological science is studied, particularly in hybrid wastewater treatment. For nonlinear systems with stable and known states, an interconnected fractional robust control design with high gain state estimation is proposed to generate a control insensitive to nutritional perturbations originated by an advanced oxidation process in a microalgae culture. An online study is proposed for the mineralization of glyphosate and its feedback in a microalgae cultivation process where through the designed control the light dynamics is manipulated to robustly and automatically regulate the biomass signal provided by an analog sensor and nutrient estimation via state observers. In the literature, there are few results developed with real-time results. This work is a multidisciplinary study with online results where the performance and improvement of the proposed complex process are concluded.

디지털변전소 중앙집중식 보호시스템에서의 불량데이터 검출에 관한 연구

In this paper, a weighted least square (WLS)-based state estimation algorithm is proposed to improve the reliability of measurement data used in centralized protection systems for substation automation research. In this paper, the theory of state estimation based on WLS is explained, and the SW development process based on algorithm is explained. The IEC-61850-based centralized protection system was developed using the MMS-Ease Lite library tool and uses a database for storing measured data. In addition, Python-based state estimation and bad data detection programs were designed to verify the suitability of WLS-based state estimation algorithms in centralized protection systems after linking three environments. The verification simulation system uses Real Time Digital Simulator to generate voltage and current data.

Robust observer design and Nash-game-driven fuzzy optimization for uncertain dynamical systems

The estimation of system state is pivotal especially when system state can't be directly measured. In this paper, an optimal robust observer is proposed for uncertain dynamical systems. The fuzzy set theory is utilized to interpret the uncertainty bound. Unlike fuzzy-logic based observer, the proposed observer is not IF-THEN fuzzy rules-based. The uniform boundedness and ultimate uniform boundedness of estimation error are guaranteed. Then, the optimal design problem of the two tunable parameters is formulated under the framework of a two-player Nash game. The fuzzy-set theoretic cost functions of the two players are associated with the observer performance. We prove that the Nash equilibria does exist, and provide procedures in solving this optimal problem. Numerical simulations are conducted on an inverted pendulum using MATLAB/Simulink. The theory is illustrated by the observer design for an inverted pendulum subject to the earthquake excitation. The novelty of this work is an integrated framework for optimal robust observer design, which creatively blends the state estimation theory, the fuzzy set theory and the Nash game theory.

Towards vendor-agnostic real-time optical network design with extended Kalman state estimation and recurrent neural network machine learning [Invited

The network operator’s call for open, disaggregated optical networks to accelerate innovation and reduce cost, make progress in the standardization of interfaces, and raise telemetry capabilities in optical network systems has created an opportunity to adopt a new paradigm for optical network design. This new paradigm is driven by direct measurement and continuous learning from the actual optical hardware deployed in the field. We report an approach towards practical, vendor-agnostic, real-time optical network design and network management using a combination of two learning models. We generalize our physics-based optical model parameter estimation algorithm using the extended Kalman state estimation theory and, for the first time, to the best of our knowledge, present results using real optical network field data. An observed 0.3 dB standard deviation of the difference between typical predicted and measured signal quality appears mostly attributable to transponder performance variance. We further propose using the physics-based optical model parameter values as inputs to a second learning model with a recurrent neural network such as a gated recurrent unit (GRU) to allocate the appropriate required optical margin relative to the typical signal quality predicted by the physics-based optical model. A proof of concept shows that for a dataset of 3000 optical connections with a wide variety of amplified spontaneous emission noise and nonlinear noise limited conditions, a 10-hidden-unit 2-layer GRU was sufficient to realize a margin prediction error standard deviation below 0.2 dB. This approach of measurement data-driven automated network design will simplify deployment and enable efficient operation of open optical networks.

Dynamic wake tracking and characteristics estimation using a cost-effective LiDAR

Recent developments in Light Detection And Ranging (LiDAR) systems provide the possibility of remote measurement of the upcoming wind speed. Despite significant advances in remote sensing, extracting useful inflow characteristics from a limited number of line-of-sight measurements still requires assumptions of the inflow. Typically, the wind direction is derived based on the assumption of horizontal homogeneous inflow that is well satisfied in flat terrain and over sufficiently large time averages. However, such an assumption is violated if the wake from a neighbouring turbine impinges the inflow, and the velocity deficit in the wake causes a bias on the wind direction, misinterpreting as yaw misalignment by the downstream turbine. The actual yaw misalignment can be recovered by isolating the effect of the wake velocity deficit from the ambient inflow. A scanning LiDAR can easily track and characterise the wake; however, it is non-trivial for a cost-effective LiDAR with only a few fixed laser beams. Therefore, this paper presents a dynamic wake tracking and characteristics estimation algorithm for a cost-effective LiDAR. The proposed algorithm provides estimates of the wake centre location and other wake characteristics by exploiting the nature of wake meandering dynamics and state estimation theory. Assuming neutral stratification of the atmospheric boundary layer, the simulation results show that the wake position and its characteristics estimation is achievable in full and partial wake situations, thus presenting an estimation framework for potential applications, including yaw misalignment control and wake steering control.

State estimation for dynamic weighing using Kalman filter

Dynamic weighing has become an essential requirement in a diverse range of industries. In dynamic weighing, loadcell based weighing mechanisms are employed in determining the weight of the products while they are in motion. This paper proposes a method of weight ascertainment based on state estimation theory. A simplified time domain response of the weighing system is modelled as an output error model and the 1-D Kalman filter is used in two stages to determine the weight of the fruit. The dependency of the weight with the change of speed is taken into account in the calibration stage. The validity of the method is tested using the data provided by Compac sorting equipment, Auckland, New Zealand.

Robust Observer Design and Fuzzy Optimization for Uncertain Dynamic Systems

To achieve the state estimation of uncertain nonlinear systems, this paper proposes a novel optimal robust observer via the fuzzy bound information of the uncertainty. A robust observer scheme is first proposed to guarantee the uniform boundedness and uniform ultimate boundedness of the state estimation system regardless of the actual value of the uncertainty. To optimize the observer gain, a fuzzy set-theoretic-based optimal approach is then proposed by utilizing the fuzzy information of the uncertainty bound. The optimization problem is completely solved in analytic form. The resulting observer is able to guarantee the robustness of the state estimation system to the uncertainty, while minimizing an optimization index related to the state estimation performance and the observer cost. The novelty of this research is a creative optimal robust observer design by blending state estimation theory, fuzzy set theory, and optimization theory into an integrated framework.

Dynamic Liquid Nitrogen Level Detection of Cryostats Onboard the HTS Maglev Vehicle

For the safe operation of high-temperature superconducting (HTS) Maglev vehicles, the liquid nitrogen (LN2) level in the onboard cryostat should be monitored in real-time during the whole running process. The previous method of LN2 level detection was proposed by using resistance sensors or liquid volume meters as the testing equipment to estimate the liquid level. However, the fluctuation of LN2 level causes great disturbance for the liquid level detection, which leads to unsteady detection and loss of valid data. In this paper, an effective method for LN2 level detection under dynamic conditions is proposed. First, the static evaporation of LN2 in rectangular and circular containers are measured by PT100 platinum resistances. And then, a self-developed simple hardware is designed for onboard cryostats, further improving the HTS maglev vehicle performance. Furthermore, the state estimation theory, which uses particle filter algorithm, is employed to eliminate the interference caused by fluctuation of the LN2 level. The real-time measurement results illustrate that the proposed dynamic liquid nitrogen level detection is able to meet the requirements of the LN2 level detection with high precision.

Data assimilation in the geosciences: An overview of methods, issues, and perspectives

We commonly refer to state estimation theory in geosciences as data assimilation (DA). This term encompasses the entire sequence of operations that, starting from the observations of a system, and from additional statistical and dynamical information (such as a dynamical evolution model), provides an estimate of its state. DA is standard practice in numerical weather prediction, but its application is becoming widespread in many other areas of climate, atmosphere, ocean, and environment modeling; in all circumstances where one intends to estimate the state of a large dynamical system based on limited information. While the complexity of DA, and of the methods thereof, stands on its interdisciplinary nature across statistics, dynamical systems, and numerical optimization, when applied to geosciences, an additional difficulty arises by the continually increasing sophistication of the environmental models. Thus, in spite of DA being nowadays ubiquitous in geosciences, it has so far remained a topic mostly reserved to experts. We aim this overview article at geoscientists with a background in mathematical and physical modeling, who are interested in the rapid development of DA and its growing domains of application in environmental science, but so far have not delved into its conceptual and methodological complexities.This article is categorized under: Climate Models and Modeling > Knowledge Generation with Models

Three-Stage Distributed State Estimation for AC-DC Hybrid Distribution Network Under Mixed Measurement Environment

The ac–dc hybrid distribution network is a credible path for the future evolution of distribution network. State estimation is a paramount foundation for the safe and stable operation of the complex distribution network. The application of the centralized state estimation method in an ac–dc distribution network has some obstacles, such as low computational efficiency, large communication capacity, and privacy protection problem. Based on the three-stage state estimation theory, this paper established a three-stage state estimation model for the ac–dc hybrid distribution network integrating supervisory control and data acquisition system and phasor measurement unit. The proposed three-stage estimation model achieves linearization of the nonlinear state estimation for the ac–dc hybrid distribution network. That is, the first and third stages simply solve the linear state estimation problem, and the second stage is a one-step nonlinear transform. Moreover, the alternating direction method of multipliers (ADMM) is applied to solving the distributed problem. Thus, an accurate and efficient three-stage distributed state estimation method for the ac–dc hybrid distribution network is proposed. In this method, ac subsystems and dc subsystems execute state estimation tasks based on local information and eventually achieve the overall consistency of the system state estimation through the transfer iteration of the boundary information, respectively. The combination of bilinear theory and ADMM ensures the convergence of distributed state estimation while improving computational efficiency. The simulation results verified the advantage of the proposal over the existing methods in many aspects.

Testing equations method for electrical energy measurements systematic errors detection and measurements results adjustment

State estimation theory is widely used for telemetry verification. Similar approaches can successfully be applied to electric energy measurements. Testing equations method was proposed in the frameworks of the state estimation theory and adopted for bad energy measurements detection. It is proposed to employ the modified testing equations method for detecting the systematic measurements errors of automatic electrical energy meter reading complexes. It is shown and confirmed that provided the statistical sample it is possible to detect and evaluate the systematic error, which, in turn, allows taking this error into account and adjusting the measurements results.

Research on the method of information system risk state estimation based on clustering particle filter

AbstractWith the purpose of reinforcing correlation analysis of risk assessment threat factors, a dynamic assessment method of safety risks based on particle filtering is proposed, which takes threat analysis as the core. Based on the risk assessment standards, the method selects threat indicates, applies a particle filtering algorithm to calculate influencing weight of threat indications, and confirms information system risk levels by combining with state estimation theory. In order to improve the calculating efficiency of the particle filtering algorithm, the k-means cluster algorithm is introduced to the particle filtering algorithm. By clustering all particles, the author regards centroid as the representative to operate, so as to reduce calculated amount. The empirical experience indicates that the method can embody the relation of mutual dependence and influence in risk elements reasonably. Under the circumstance of limited information, it provides the scientific basis on fabricating a risk management control strategy.

Observer design for a nonlinear diffusion system based on the Kirchhoff transformation

This paper deals with the state estimation for a nonlinear diffusion system. An observer that reconstructs the whole state, from the available measurements, is proposed based on an equivalent linear diffusion model obtained using the Kirchhoff tangent transformation. This bijective mapping allows to apply the available and powerful state estimation theory of linear distributed parameter systems and simplifies the observer design. Hence, an observer can be designed for the obtained equivalent linear diffusion system and by using the Kirchhoff transformation, the whole state of the original nonlinear diffusion system is recovered. The observability analysis of the nonlinear diffusion system and the convergence of the proposed observer are also investigated based on the equivalent linear diffusion system. The effectiveness of the proposed observer is shown, through numerical simulation runs, in the case of a heated steel rod by considering both an uniformly distributed and a punctual boundary sensing.

Optimizing qubit phase estimation

The theory of quantum state estimation is exploited here to investigate the most efficient strategies for this task, especially targeting a complete picture identifying optimal conditions in terms of Fisher information, quantum measurement, and associated estimator. The approach is specified to estimation of the phase of a qubit in a rotation around an arbitrary given axis, equivalent to estimating the phase of an arbitrary single-qubit quantum gate, both in noise-free and then in noisy conditions. In noise-free conditions, we establish the possibility of defining an optimal quantum probe, optimal quantum measurement, and optimal estimator together capable of achieving the ultimate best performance uniformly for any unknown phase. With arbitrary quantum noise, we show that in general the optimal solutions are phase dependent and require adaptive techniques for practical implementation. However, for the important case of the depolarizing noise, we again establish the possibility of a quantum probe, quantum measurement, and estimator uniformly optimal for any unknown phase. In this way, for qubit phase estimation, without and then with quantum noise, we characterize the phase-independent optimal solutions when they generally exist, and also identify the complementary conditions where the optimal solutions are phase dependent and only adaptively implementable.

A state estimation approach for fault location in transmission lines considering data acquisition errors and non-synchronized records

Abstract The performance of algorithms for fault location is directly related to the accuracy of its input data. Thus, factors such as errors in the line parameters, failures in synchronization of oscillographic records and errors in measurements of voltage and current can significantly influence the accuracy of algorithms that use bad data to indicate the faults location. This paper presents a methodology for fault location based on the theory of state estimation in order to determine the location of faults more accurately by considering realistic systematic errors that may be present in measurements of voltage and current. The methodology developed is innovative because, besides calculating the most likely fault distance obtained from measurement errors, the variance associated with the distance found is also determined, using the errors theory. The obtained results are relevant to show that the proposed estimation approach works even adopting realistic variances. Moreover, the fault location brings performance gains compared to a traditional algorithm, available in the literature.

Bayesian supervised learning and state estimation in a model of the cerebellum

The last decade has seen an explosion of research on the topic of Bayesian inference in neural systems. The cerebral cortex is now widely believed to form predictive internals models of the environment. But what does this mean for the cerebellum, which has historically been attributed just this function? And what might Bayesian inference mean in the cerebellar context? I present a cerebellar model unifying the Bayesian framework with classical cerebellar theories of supervised learning, state estimation, and control theory. This model builds on the dominant supervised learning theory of cerebellar function, which traces to the pioneering work of Marr. This model is extended to account for Bayesian optimal updating of the uncertainties inherent in probabilistic inference. Further, the model is capable of learning about states with little to no supervised input. It also provides theoretical explanation for a wide range of phenomenology observed of the circuit -- most importantly unsupervised synaptic plasticity upstream of cerebellar Purkinje cells. The connectionist architecture of this model is closely based on that of the cerebellum. In the input stage, unsupervised learning in the cerebellar granular layer is seen as essential for subsequent supervised learning in the Purkinje layer. Based on Golgi cell feedback, the granular layer learns to encode supervised learning covariances in a manner akin to the kernel learning of Gaussian processes. This circuit then predicts and filters mossy fiber input, conveying only select signals downstream for supervised learning. This granular representation is further influenced by a global serotonergic signal conveyed by Lugaro cells. In the cerebellar molecular layer, inhibitory interneurons then provide higher-order corrections to these estimates. Finally, learning in the cerebellar nuclei is seen as a parallel, simpler, regression model, allowing for faster, courser adjustments, corrected in time by the cerebellar cortical circuit.

A mathematical method for verifying the validity of measured information about the flows of energy resources based on the state estimation theory

Efforts aimed at improving energy efficiency in all branches of the fuel and energy complex shall be commenced with setting up a high-tech automated system for monitoring and accounting energy resources. Malfunctions and failures in the measurement and information parts of this system may distort commercial measurements of energy resources and lead to financial risks for power supplying organizations. In addition, measurement errors may be connected with intentional distortion of measurements for reducing payment for using energy resources on the consumer’s side, which leads to commercial loss of energy resource. The article presents a universal mathematical method for verifying the validity of measurement information in networks for transporting energy resources, such as electricity and heat, petroleum, gas, etc., based on the state estimation theory. The energy resource transportation network is represented by a graph the nodes of which correspond to producers and consumers, and its branches stand for transportation mains (power lines, pipelines, and heat network elements). The main idea of state estimation is connected with obtaining the calculated analogs of energy resources for all available measurements. Unlike “raw” measurements, which contain inaccuracies, the calculated flows of energy resources, called estimates, will fully satisfy the suitability condition for all state equations describing the energy resource transportation network. The state equations written in terms of calculated estimates will be already free from residuals. The difference between a measurement and its calculated analog (estimate) is called in the estimation theory an estimation remainder. The obtained large values of estimation remainders are an indicator of high errors of particular energy resource measurements. By using the presented method it is possible to improve the validity of energy resource measurements, to estimate the transportation network observability, to eliminate the energy resource flows measurement imbalances, and to filter invalid measurements at the data acquisition and processing stage in performing monitoring of an automated energy resource monitoring and accounting system.

Optimal continuous-time state estimation for linear finite and infinite-dimensional chemical process systems with state constraints

This work addresses optimal constrained state estimation problem for finite and infinite-dimensional chemical process systems. We consider cases when the prior information, in addition to the model parameters and the measurements, is available in the form of an inequality constraint with respect to the system's state. In the latest developments of the optimal state estimation theory, considerations of the state constraints have been often neglected since constraints do not fit easily in the structure of the optimal state estimator. Therefore, the issue of the state constraints being present needs to be addressed adequately, in particular, nonnegativity of concentration. Motivated by this, we developed a sequential, algorithmic optimal constrained state estimator for both finite and infinite-dimensional process systems commonly found in chemical process engineering (CSTR, tubular reactor). In this paper, we also designed an optimal constrained state estimator for a large class of dissipative infinite-dimensional systems which involve boundary actuation and point observation. Finally, illustrative examples of chemical process systems and proposed optimal state constrained estimation are presented.

Improving of Energy Measurements Reliability Using Weighted and Normalized Residual Analysis

The article considers the possibility of a posteriori methods implementation for energy measurements verification. Posteriori methods are developed in the framework of state estimation theory. The new approach to calculate the parameters of electric conditions using electrical energy measurements is discussed. Test scheme with different measurements sets is considered. Results demonstrate the implementation of a posteriori analysis.

Optimal State Estimation for Linear Systems with State Constraints

This paper considers the optimal strategies for constrained linear state estimation. Prior information for estimating state variables is often available in the form of inequality constraints on states. In the latest developments of optimal state estimation theory consideration of state constraints has been often neglected since constraints do not fit easily in the structure of the optimal filter, for example, the issue of state constraints being present has to be addressed adequately, for example nonnegativity of concentration. In order to address this issue and to extend previous developments on the accuracy of state estimation, this work develops the constrained optimal state estimation for finite-dimensional systems. Finally, a numerical example illustrating the proposed method is presented.