Presence Of Measurement Noise Research Articles

[formula omitted]-space physics-informed neural network (k-PINN) for compressed spectral mapping and efficient inversion of vibrations in thin composite laminates

The vibrational response of structural components carries valuable information about their underlying mechanical properties, health status and operational conditions. This underscores the need for the development of efficient physics-based inversion algorithms which, given a limited set of sensing data points and in the presence of measurement noise, can reconstruct the response at locations where measurement data is not available and/or identify the unknown mechanical properties. Addressing this challenge, Physics-Informed Neural Networks (PINNs) have emerged as a promising approach. PINNs seamlessly integrate governing equations into their architecture and have gained significant interest in solving inversion problems. In the context of learning and inversion of multimodal, multiscale vibrational responses, this paper introduces a novel spectral extension of PINNs, utilizing Fourier basis functions in the wavenumber domain, commonly known as k-space. The proposed method, referred to as k-space PINN (k-PINN), offers a robust framework for adjusting complexity and wavenumber composition of the response. Notably, the spectral formulation of k-PINN, coupled with the generally sparse representation of vibrations in k-space, facilitate efficient reconstruction and learning of broadband vibrations and alleviate the spectral bias associated with standard PINN. Additionally, the spectral solution space introduced by k-PINN substantially reduces the computational cost associated with computing physics-informed loss terms. We evaluate the effectiveness of the proposed methodology on reconstructing the bending vibrational mode shapes of a thin composite laminate and identifying its effective bending stiffness coefficients. Mode shapes are initially obtained from finite element simulation, and virtual test data with added noise are generated for evaluation purposes. It is shown that the proposed k-PINN methodology outperforms the standard PINN in terms of both learning and computational efficiency. The performance of k-PINN is further demonstrated by show casing its capability in learning different selections of symmetric, anti-symmetric and asymmetric mode shapes.

Enhanced grid integration through advanced predictive control of a permanent magnet synchronous generator - Superconducting magnetic energy storage wind energy system

In this study, the use of an Unscented Kalman Filter as an indicator in predictive current control (PCC) for a wind energy conversion system (WECS) that employs a permanent magnetic synchronous generator (PMSG) and a superconducting magnetic energy storage (SMES) system connected to the main power grid is presented. The suggested UKF indication in the hybrid WECS-SMES arrangement is in charge of estimating vital metrics such as stator currents, electromagnetic torque, rotor angle, and rotor angular speed. To optimize control strategies, PCCs use these projected properties rather than direct observations. To control the unpredictable wind energy's nature, SMES must be regulated to minimize fluctuations in the DC-link voltage and power output to the main grid. Fractional order-PI (FOPI) controllers are used in a novel control structure for the SMES system to regulate the output power and DC-link voltage. An artificial bee colony optimization approach is employed to optimize the FOPI controllers. Three commonly utilized indicators, including sliding-mode, EKF, and Luenberger, were evaluated using “MATLAB" to evaluate the performance of the UKF estimate. Assessment criteria such as mean absolute percentage error and root mean squared error were used to gauge the accuracy of the estimates. Simulation findings showed the efficiency of fractional order-PI controllers for SMES and the proposed UKF indication for predictive current control, especially in the presence of measurement noise and over a variety of wind speeds. An improvement in estimation accuracy of up to 99.9 % was demonstrated by the UKF indicator. Moreover, the stability of the suggested UKF-based PCC control for the hybrid WECS-SMES combination was confirmed using Lyapunov stability criteria."

Robust inverse parameter fitting of thermal properties from the laser-based Ångstrom method in the presence of measurement noise using physics-informed neural networks (PINNs)

The two-dimensional laser-based Ångstrom method measures the in-plane thermal properties for anisotropic film-like materials. It involves periodic laser heating at the center of a suspended film sample and records its transient thermal response by infrared imaging. These spatiotemporal temperature data must be analyzed to extract the unknown thermal conductivity values in the orthotropic directions, an inverse parameter fitting problem. Previous demonstration of the metrology technique used a least-squares fitting method that relies on numerical differentiation to evaluate the second-order partial derivatives in the differential equation describing transient conduction in the physical system. This fitting approach is susceptible to measurement noise, introducing high uncertainty in the extracted properties when working with noisy data. For example, when noise of a signal-to-noise ratio of 10 is added to simulated amplitude and phase data, the error in the extracted thermal conductivity can exceed 80%. In this work, we introduce a new alternative inverse parameter fitting approach using physics-informed neural networks (PINNs) to increase the robustness of the measurement technique for noisy temperature data. We demonstrate the effectiveness of this approach even for scenarios with extreme levels of noise in the data. Specifically, the PINN-approach accurately extracts the properties to within 5% of the true values even for high noise levels (a signal-to-noise ratio of 1). This offers a promising avenue for improving the robustness and accuracy of advanced thermal metrology tools that rely on inverse parameter fitting of temperature data to extract thermal properties.

Enhancing rational approximation of wideband resonant MIMO systems with frequency-domain data

Vector Fitting (VF) is a successful methodology for both time and frequency domain estimation of dynamic systems. These algorithms have gained popularity as a system identification tool due to their ability to provide a practical procedure for accurately approximating the measured frequency response behavior of complex and highly resonant dynamic systems using rational models. Instrumental Variable (IV) techniques can also be added to the VF algorithm to enhance the optimality of the solutions in the presence of measurement noise. In this context, this paper presents a multiple-input multiple-output (MIMO) generalization of instrumental variable (IV-)VF. The proposed algorithm can be applied to accurately estimating models formed by either continuous- or discrete-time rational basis functions (RBFs). We show that such a generalization preserves the main implementation features observed in Standard VF, but with improved optimality property for its solutions. Additionally, in order to alleviate convergence problems that may arise from the fixed high-frequency normalization, we also present in this paper how to incorporate in the proposed IV-VF method the relaxed formulation found in standard VF for both the continuous and discrete-time cases. The resulting MIMO IV-VF algorithm can be easily understood by VF users, and its applicability is discussed by using an estimation case study with two power system pieces of equipment (an 88 kV Transformer and a 550 kV Instrument Transformer) for which actual frequency domain measurements were collected in the field. It is shown that the proposed algorithm significantly improves the modeling accuracy when compared to standard VF algorithms.

Sampled-data observer design for Linear Kuramoto–Sivashinsky systems with non-local output

The aim of this paper is to provide a novel systematic methodology for the design of sampled-data observers for Linear Kuramoto–Sivashinsky systems (LKS) with non-local outputs. More precisely, we extend the systematic sampled-data observer design approach which is based on the use of an Inter-Sample output predictor to the class of LKS systems. By using a small-gain methodology we provide sufficient conditions ensuring the Input-to-Output Stability property of the estimation errors in the presence of measurement noise. Our Inter-Sample output predictor contains a tuning term which can enlarge significantly the Maximum Allowable Sampling Period.

Control system of the radio-reflective surface shape of a large-size space reflector using its current-conducting structural parts

A comprehensive approach to creating a control system for the shape of the radio-reflecting surface of a large-size space reflector is considered. Large-aperture space antennas are used for satellite communications and space exploration. The design of these structures is one of the most promising areas. Ensuring the specified characteristics of the reflector is directly related to maintaining the specified shape of the radio-reflective netting. Developing a control system for the shape of the active antenna surface is an urgent task. Optimizing this process makes it possible to accomplish the mission during the operational period effectively. The paper evaluates the effects of perturbations on a large-scale structure operating in outer space. A method for adjusting the geometry of the frontal network is proposed. This allows for improved communication between spacecraft and ground stations, which is very important for the safety of space flights. The conductive parts of the reflector are considered to transmit energy and control signals to the actuators. The application results of various control algorithms of the executive device making it possible to correct the netting considering the minimization of energy costs and oscillations of the structure are shown. According to the simulation results, the optimal algorithm of the target criteria hierarchy showed greater stability in terms of convergence in the presence of measurement noise and disturbances, which allows it to be applied in real time. This algorithm is supposed to be used in the future when creating a prototype of the system for controlling the shape of the radio-reflective surface of a large-size space reflector using its current-conducting structural parts.

Multi-frequency probabilistic imaging fusion for impact localization on aircraft composite structures

Since the internal barely visible damage of aircraft composite structures caused by the impact is a critical problem, impact monitoring is essential for the integrity and reliability of aircraft composite structures. This paper presents a multi-frequency probabilistic imaging fusion method for localizing impacts on aircraft composite structures. To capture the impact signals, a network of distributed sensors is mounted on the structure. The impact signals are then processed using the continuous wavelet transform (CWT) to extract the multi-frequency narrowband Lamb wave signals. The time difference of arrival (TDOA), a key feature of the impact source, is measured using averaging techniques employed in the normalized variance sequence. Subsequently, a probabilistic imaging function is established, and the TDOA of narrowband Lamb wave signals at each frequency is used as the feature input to generate the multi-frequency probabilistic imaging results. To determine the performance of the imaging results at each frequency, an efficiency index is introduced, allowing for the retention or abandonment of the imaging results. By utilizing the retained multi-frequency probabilistic imaging results, the proposed method achieves impact localization through imaging fusion. Experimental verification is conducted on a stiffened aircraft composite panel, and a comparison is made with two existing methods: the hyperbolic locus imaging method and the virtual time reversal imaging method. The results show that the proposed method can significantly improve localization accuracy compared to the existing methods, and is effective even in the presence of measurement noise.

Recursive integral terminal sliding mode control with combined extended state observer and adaptive Kalman filter for MEMS gyroscopes

AbstractThe recursive integral terminal sliding mode control with combined extended state observer (ESO) and adaptive Kalman filter (AKF) is proposed in this article for micromechanical system gyroscopes. To accurately estimate the unmeasured system states in the presence of measurement noises, external disturbances and system uncertainties, the special combination of ESO and AKF is proposed. The AKF is employed to deal with measurement noises and prepare necessary signals for the ESO, while the ESO constantly provides the updated estimate of the lumped disturbance for the AKF. Furthermore, a robust control scheme is designed by using the recursive integral terminal sliding mode variable. Simulation results verify that more accurate unmeasured state estimation and higher tracking accuracy are achieved under the proposed method.

Using Constrained Convex Optimization in Parameter Estimation of Process Dynamics with Dead Time

Abstract This paper proposes the usage of constrained convex optimization in improving the quality of the parameter estimates of a typical process plant with dead time from its time response data by incorporating system-specific constraints that are not considered in standard estimation methods. As the majority of the process plants are identified as second-order plus dead time (SOPDT) systems, the proposed method uses the same for establishing the optimization process. Traditional methods for parameter estimation in SOPDT systems have often relied on heuristic approaches or simplified assumptions, leading to suboptimal results. The proposed methodology augments the accuracy of the estimated values by leveraging the power of constrained convex optimization techniques, using Newton's Quadratic Model and Sequential Quadratic Programming, which provide a rigorous mathematical framework for parameter estimation. By incorporating system constraints, such as bounds on the parameters or stability requirements, it is ensured that the obtained parameter estimates adhere to physical and practical limitations. The proposed approach is demonstrated using simulations and on a real-time system, and the results show that it is effective not only in accurately estimating the parameters of the underdamped SOPDT systems but also works efficiently for parameter estimation of SOPDT systems in the presence of measurement noise. The efficacy of the proposed algorithm is verified by comparing it with similar published methods.

Sampled-Data Observer Design for Linear Kuramoto-Sivashinsky Systems with Non-Local Output

The aim of this paper is to provide a novel systematic methodology for the design of sampled-data observers for Linear Kuramoto-Sivashinsky systems (LKS) with non-local outputs. More precisely, we extend the systematic sampled-data observer design approach which is based on the use of an Inter-Sample output predictor to the class of LKS systems. By using a small-gain methodology we provide sufficient conditions ensuring the Input-to-Output Stability property of the estimation errors in the presence of measurement noise. Our Inter-Sample output predictor contains a tuning term which can enlarge significantly the Maximum Allowable Sampling Period.

Fractional adaptive observer for variable structure high cell density fed-batch cultures

This paper presents the design and application of a fractional order asymptotic adaptive observer coupled to an adaptive controller for the robust operation of high-cell density cultures in fed-batch mode. The control goal is to maximize biomass productivity by controlling the culture’s estimated specific growth rate. Since the specific growth rate cannot be measured, a fractional order asymptotic adaptive observer is proposed, based on the equivalent integer order asymptotic observer proposed before. Simulations are performed to validate the observer and controller, under the assumption that the system is in the oxidative regime under aerobic conditions. Obtained results show that, in close loop operation, the fractional adaptive observer behaves better than the integer order observer in the presence of measurement noise. For fractional orders of the observer in the range α G [0.6,0.8], it was observed a 51.71% increase in biomass concentration, compared to the biomass obtained with the classic integer-order observer. Furthermore, the controlled system reaches very low ethanol concentrations (< 1 grams per liter), which is desirable in this process.

Weak Monotonicity With Trend Analysis for Unsupervised Feature Evaluation.

Performance in an engineering system tends to degrade over time due to a variety of wearing or ageing processes. In supervisory controlled processes there are typically many signals being monitored that may help to characterize performance degradation. It is preferred to select the least amount of information to obtain high quality of predictive analysis from a large amount of collected data, in which labeling the data is not always feasible. To this end a novel unsupervised feature selection method, robust with respect to significant measurement disturbances, is proposed using the notion of ``weak monotonicity'' (WM). The robustness of this notion makes it very attractive to identify the common trend in the presence of measurement noises and population variation from the collected data. Based on WM, a novel suitability indicator is proposed to evaluate the performance of each feature. This new indicator is then used to select the key features that contribute to the WM of a family of processes when noises and variations among processes exist. In order to evaluate the performance of the proposed framework of the WM and suitability, a comparative study with other nine state-of-the-arts unsupervised feature evaluation and selection methods is carried out on well-known benchmark datasets. The results show a promising performance of the proposed framework on unsupervised feature evaluation in the presence of measurement noises and population variations.

Petrophysical interpretation of logging-while-drilling borehole measurements in the presence of electrical anisotropy, mud-filtrate invasion, noise, and well deviation effects

Petrophysical interpretation of logging-while-drilling (LWD) borehole measurements in the presence of electrical anisotropy, mud-filtrate invasion, noise, and well deviation effects remains a challenge in formation evaluation. In high-angle and horizontal (HAHZ) wells penetrating electrically anisotropic sandstones, phase and attenuation apparent resistivity logs often exhibit values larger than resistivity parallel to bedding planes. Consequently, traditional interpretation methods often fail to accurately estimate hydrocarbon saturation when using only the long-spacing phase apparent resistivity log (P40H) in petrophysical calculations. We implement two approaches (analytical and Bayesian) to estimate horizontal and vertical resistivities from apparent resistivity measurements. The first analytical approach is based on the numerical simulation of LWD resistivity measurements using synthetic models under various conditions of electrical anisotropy and well inclination to derive analytical models. The relative error of analytical approximations is less than 6%. In the presence of measurement noise and shoulder-bed effects, we implement a Bayesian method for well-log inversion and uncertainty quantification. The relative error of Bayesian inversion is less than 2%. Estimates of horizontal and vertical resistivities then can be used for petrophysical analysis. A challenging set of synthetic and field examples of HAHZ wells penetrating electrically anisotropic formations is selected for examination and verification of the new methods. For radial lengths of invasion less than 20 cm (8 in), sensitivity analysis indicates that the effects of conductive mud-filtrate invasion on long-spacing resistivity logs are negligible. The long-spacing phase (P40H) and attenuation (A40H) apparent resistivities are used to estimate horizontal and vertical resistivities. In the field examples under study, electrical anisotropy is caused by intercalated laminations of coarse- and fine-grained sandstones; the volumetric concentration of shale is negligible. Considering that Archie’s parameters are direction dependent, sensitivity analysis indicates that the effective value of the saturation exponent parallel to bedding planes is less sensitive to the volumetric concentration of fine-grained sandstone layers compared with the saturation exponent perpendicular to bedding planes. Thus, water saturation of grain-laminated sandstones in HAHZ wells can be estimated using horizontal resistivity with Archie’s parameters that are consistent with petrophysical interpretations performed in vertical wells. Estimates of water saturation in the field examples using horizontal resistivity agree with saturation-height models. Compared with conventional interpretation methods that use P40H as the formation resistivity, the new approach improved the estimation of hydrocarbon saturation by 10%.

Comparative study of a newly proposed machine learning classification to detect damage occurrence in structures

Over the past two decades, an increasing number of large-scale structures have been built around the world. Constructing these structures has been a time consuming and highly expensive process. Thus, providing a structural health monitoring system to guarantee their proper functionality is important. In recent years, the advancement of technology and artificial intelligence methods based on signal processing and machine learning has attracted the attention of researchers. The challenges currently exist in the field of structural health monitoring to identify and classify damages to achieve high accuracy in a health-monitoring program. The presence of noise in measurement, various exciting load types, and varying environmental conditions cause difficulty in the practical identification and classification of damage in structures. Recent studies have employed finite element modeling to test the effectiveness of proposed methods for identifying damages in structures. However, detecting damage in real-world structures as mentioned above, presents unique difficulties, and the effectiveness of the proposed methods for damage detection in real-world structures remains uncertain. In order to improve the performance of damage detection methods and increase the accuracy of these methods as much as possible, the most important action is to identify damage sensitive data in the structure. The next challenge is to choose a high performance algorithm for damage identification and classification. One of the advanced algorithms, which has a very high ability to extract the desired features from the measured data, is the XGBoost algorithm. This algorithm has recently attracted the attention of researchers and has been used in different fields. So far, the ability of this algorithm has not been examined in the field of damage detection in order to extract desirable features. This article deals with the identification, classification, and severity of damages in the SMC benchmark bridge, which is an existing megastructure in the real world, as well as the IASC-ASCE benchmark structure, whose responses were taken under applied loads in the laboratory environment. First, using the XGBoost algorithm, the importance of the features extracted from the sensors' data is evaluated, and then the features, which are effective in the damage detection process, are selected. The results of this algorithm indicate that only by selecting 6 features from a large volume of data, the best performance can be achieved and selecting more does not help increase efficiency. In the next step, the Stacking method, which is a hybrid machine learning algorithm for damage classification, is evaluated and compared with some conventional machine learning algorithms that have been used in previous studies. The Stacking method stands out as the top performer with an average accuracy rate of 93.1%, leading to the conclusion that it is the most effective approach. Finally, by applying the presented algorithm to the two mentioned structures, its validation is appraised.

A novel class of adaptive observers for dynamic nonlinear uncertain systems

AbstractNumerous techniques have been proposed in the literature to improve the performance of high‐gain observers with noisy measurements. One such technique is the linear extended state observer, which is used to estimate the system's states and to account for the impact of internal uncertainties, undesirable nonlinearities, and external disturbances. This observer's primary purpose is to eliminate these disturbances from the input channel in real‐time. This enables the observer to precisely track the system states while compensating for the various sources of uncertainty that can influence the system's behaviour. So, in this paper, a novel nonlinear higher‐order extended state observer (NHOESO) is introduced to enhance the performance of high‐gain observers under noisy measurement conditions. The NHOESO is designed to observe the system states and total disturbance while eliminating the latter in real time from the input channel. It is capable of handling disturbances of higher‐order derivatives, including internal uncertainties, undesirable nonlinearities, and external disturbances. The paper also presents two innovative schemes for parametrizing the NHOESO parameters in the presence of measurement noise. These schemes are named time‐varying bandwidth NHOESO (TVB‐NHOESO) and online adaptive rule update NHOESO (OARU‐NHOESO). Numerical simulations are conducted to validate the effectiveness of the proposed schemes, using a nonlinear uncertain system as a test case. The results demonstrate that the OARU technique outperforms the TVB technique in terms of its ability to sense the presence of noise components in the output and respond accordingly. However, it is noted that the OARU technique is slower than the TVB technique and requires more complex parameter tuning to adaptively account for the measurement noise.

Multi-source-data state estimation for integrated electricity–heat-building networks

Building heating systems (BHS) play a major role in integrated electricity and heat systems (IEHS). To capture the real-time dynamic operating state of IEHS based on multi-source measurement data, this paper develops a comprehensive state estimation (SE) framework for IEHS with BHS fleets. First, a thermo-electrical SE model integrating BHS, electric power grid (EPG), and district heating network (DHN) is developed. Then, to jointly estimate the state variables of IEHS with different time scales of dynamics, a holistic SE algorithm is proposed based on the partial equivalence between the Weighted Least Squares (WLS) estimation problem and the correction stage of the Iterative Extended-Kalman Filter (IEKF). It also includes a data anomaly processing algorithm to combat data corruptions from sensing and communication processes. Simulation results show that the proposed framework can accurately track the thermo-electrical states of the system both in the presence of measurement noise and anomalies during various dynamics in IEHS.

Rendezvous and Proximity Operations in Cislunar Space Using Linearized Dynamics for Estimation

As interest in Moon exploration grows, and efforts to establish an orbiting outpost intensify, accurate modeling of spacecraft dynamics in cislunar space is becoming increasingly important. Contrary to satellites in Low Earth Orbit (LEO), where it takes around 5 ms to communicate back and forth with a ground station, it can take up to 2.4 s to communicate with satellites near the Moon. This delay in communication can make the difference between a successful docking and a catastrophic collision for a remotely controlled satellite. Moreover, due to the unstable nature of trajectories in cislunar space, it is necessary to design spacecraft that can autonomously make frequent maneuvers to stay on track with a reference orbit. The communication delay and unstable trajectories are exactly why autonomous navigation is critical for proximity operations and rendezvous and docking missions in cislunar space. Because spacecraft computational hardware is limited, reducing the computational complexity of navigational algorithms is both desirable and often necessary. By the introduction of a linear system approach to the deputy spacecraft motion, this research avoids the computational burden of integrating the deputy relative equations of motion. In this research, the relative CR3BP equations of motion are derived and linearized using a matrix exponential approximation. This research continues the development of the matrix exponential linearized relative circular restricted three-body problem (CR3BP) equations by applying the dynamics model to estimation and control applications. A simulation is performed to compare state estimation results obtained from using the linearized equations of motion utilizing a Kalman filter and for state estimation utilizing an unscented Kalman filter with the full nonlinear equations of motion. The linearized exponential model is shown to be sufficient for state estimation in the presence of noisy measurements for an example scenario. Additionally, a linear quadratic regulator (LQR) controller was added to optimally control a deputy spacecraft to rendezvous with a chief spacecraft in cislunar space. The contribution of this work is twofold: to provide a proof of concept that the matrix exponential solution for the linearized relative CR3BP equations can be used as the dynamics model for state estimation, as well as to simulate an optimal rendezvous maneuver in the presence of measurement noise.

Deep Neural Networks for Predicting Single-Cell Responses and Probability Landscapes.

Engineering biology relies on the accurate prediction of cell responses. However, making these predictions is challenging for a variety of reasons, including the stochasticity of biochemical reactions, variability between cells, and incomplete information about underlying biological processes. Machine learning methods, which can model diverse input-output relationships without requiring a priori mechanistic knowledge, are an ideal tool for this task. For example, such approaches can be used to predict gene expression dynamics given time-series data of past expression history. To explore this application, we computationally simulated single-cell responses, incorporating different sources of noise and alternative genetic circuit designs. We showed that deep neural networks trained on these simulated data were able to correctly infer the underlying dynamics of a cell response even in the presence of measurement noise and stochasticity in the biochemical reactions. The training set size and the amount of past data provided as inputs both affected prediction quality, with cascaded genetic circuits that introduce delays requiring more past data. We also tested prediction performance on a bistable auto-activation circuit, finding that our initial method for predicting a single trajectory was fundamentally ill-suited for multimodal dynamics. To address this, we updated the network architecture to predict the entire distribution of future states, showing it could accurately predict bimodal expression distributions. Overall, these methods can be readily applied to the diverse prediction tasks necessary to predict and control a variety of biological circuits, a key aspect of many synthetic biology applications.

Material Data Identification in an Induction Hardening Test Rig with Physics-Informed Neural Networks.

Physics-Informed neural networks (PINNs) have demonstrated remarkable performance in solving partial differential equations (PDEs) by incorporating the governing PDEs into the network's loss function during optimization. PINNs have been successfully applied to diverse inverse and forward problems. This study investigates the feasibility of using PINNs for material data identification in an induction hardening test rig. By utilizing temperature sensor data and imposing the heat equation with initial and boundary conditions, thermo-physical material properties, such as specific heat, thermal conductivity, and the heat convection coefficient, were estimated. To validate the effectiveness of the PINNs in material data estimation, benchmark data generated by a finite element model (FEM) of an air-cooled cylindrical sample were used. The accurate identification of the material data using only a limited number of virtual temperature sensor data points was demonstrated. The influence of the sensor positions and measurement noise on the uncertainty of the estimated parameters was examined. The study confirms the robustness and accuracy of this approach in the presence of measurement noise, albeit with lower efficiency, thereby requiring more time to converge. Lastly, the applicability of the presented approach to real measurement data obtained from an air-cooled cylindrical sample heated in an induction heating test rig was discussed. This research contributes to the accurate offline estimation of material data and has implications for optimizing induction heat treatments.

Synthesis of Adaptive Observer of State Variables for a Linear Stationary Object in the Presence of Measurement Noise

The paper is devoted to the problem of state variables observers synthesis for linear stationary system operating under condition of noise or disturbances in the measurement channel. The paper considers a completely observable linear stationary system with known parameters. It is assumed that the state variables are not measured, and the measured output variable contains a small amplitude (in general, modulo less than one) additive noise or disturbance. It is also assumed that there is no a priori information about the disturbance or noise in the measurement channel (for example, frequency spectrum, covariance, etc.). It is well known that many observer synthesis methods have been obtained for this type of systems, including the Kalman filter, which has proven itself in practice. Under the condition of complete observability and the presence of some a priori information about a random process (which is typical for the case when a disturbance in the measurement channel can be represented as white noise), approaches based on Kalman filtering demonstrate the highest quality estimates of state variables convergence to true values. Without disputing the numerous results obtained using the application of the Kalman filter, an alternative idea of the state variables observer constructing is considered in this paper. The alternative of the new approach is primarily due to the fact that there is no need to use the usual approaches based on the Luenberger observer. The paper proposes an approach based on the estimation of unknown parameters (in this case, an unknown vector of initial conditions of the plant state variables) of a linear regression model. Within the framework of the proposed method, after a simple transformation, a transition is made from a dynamic system to a linear regression model with unknown constant parameters containing noise or disturbing effects. After that, a new nonlinear parametrization of the original regression model and an algorithm for identifying unknown constant parameters using the procedure of dynamic expansion of the regressor and mixing are proposed which ensure reduction the influence of noise. The article presents the results of computer simulations verifying the stated theoretical results.