Parameter Estimation Algorithm Research Articles

A Bayesian Spatiotemporal Modeling Approach to the Inverse Heat Conduction Problem

Abstract This study introduces a Bayesian spatiotemporal modeling approach to solve inverse heat conduction problems (IHCPs), employing penalized splines within a spatiotemporal forward model. The complexity and ill-posed nature of IHCPs, characterized by potential nonexistence, nonuniqueness, or instability of solutions, pose significant challenges for traditional methods. Addressing this, our study presents a spatiotemporal forward model that incorporates spatial, temporal, and interaction terms, accurately capturing the intricate dynamics inherent in IHCPs and using this information as a leverage to solve the inverse problem. We adopted a Bayesian inference framework for the subsequent parameter estimation problem and developed a Gibbs sampling algorithm to sample from the posterior distribution of the model's parameters, enhancing the estimation process. Through case studies on a one-dimensional (1D) heat simulation and a pool boiling experiment using multisensor thermocouple data for heat flux reconstruction, we demonstrate the model's superiority over traditional methods. The inclusion of the spatiotemporal interaction term significantly enhances model performance, indicating its potential for broader application in solving IHCPs. The application of this method in both simulated and real-world scenarios highlights its effectiveness in capturing the spatiotemporal complexities of IHCPs. This work contributes to the field by offering a robust methodology for addressing the spatial and temporal complexities inherent in IHCPs, supported by a comprehensive Bayesian inference framework and the use of a Gibbs sampling algorithm for parameter estimation.

Congruential Summation-Triggered Identification of FIR Systems under Binary Observations and Uncertain Communications

With the advancement of network technology, there has been an increase in the volume of data being transmitted across networks. Due to the bandwidth limitation of communication channels, data often need to be quantized or event-triggered mechanisms are introduced to conserve communication resources. On the other hand, network uncertainty can lead to data loss and destroy data integrity. This paper investigates the identification of finite impulse response (FIR) systems under the framework of stochastic noise and the combined effects of the event-triggered mechanism and uncertain communications. The study provides a reference for the application of remote system identification under transmission-constrained and packet loss scenarios. First, a congruential summation-triggered communication scheme (CSTCS) is introduced to lower the communication rate. Then, parameter estimation algorithms are designed for scenarios with known and unknown packet loss probabilities, respectively, and their strong convergence is proved. Furthermore, an approximate expression for the convergence rate is obtained by data fitting under the condition of uncertain packet loss probability, treating the trade-off between convergence performance and communication resource usage as a constrained optimization problem. Finally, the rationality and correctness of the algorithm are verified by numerical simulations.

Matrix Decomposition Approach for Structural Equation Modeling as an Alternative to Covariance Structure Analysis and Its Theoretical Properties

Matrix decomposition structural equation modeling (MDSEM) is introduced as a novel approach in structural equation modeling, contrasting with traditional structural equation modeling (SEM). MDSEM approximates the data matrix using a model generated by the hypothetical model and addresses limitations faced by conventional SEM procedures by emphasizing factor analysis with L 2 penalization. Key advantages of MDSEM include preventing improper solutions, the ability to compute observation-wise residuals without post-hoc factor score estimation and ease in identifying equivalent models. These benefits are attributed to its matrix decomposition techniques, allowing for direct model fitting to the data matrix, unlike the covariance structure fitting in CS-SEM. An iterative algorithm for parameter estimation is proposed, guaranteeing a monotonically decreasing function value. Theoretical properties of MDSEM are examined, revealing its shared characteristics with existing factor analysis and SEM. Numerical simulations and real data examples validate that MDSEM produces results comparable to existing methods when adequately calibrated.

An Estimation Method of High-Order LC Circuits in Power Electronic Converters

This paper proposes a parameter estimation method for high-order LC circuits conducted during the power-OFF of power electronic converters. It is based on a battery-powered compact signal injection unit and a circuit modeling method to estimate the LC circuit parameters. The proposed method aims for LC component condition monitoring in applications with routine-based maintenance or frequent ON/OFF operation (e.g., wind power, photovoltaic, traction systems). Compared to LCR meters and impedance analyzers, the proposed method has a significantly lower implementation cost and does not require disassembly of components. Moreover, it is a converter-level method in which the signal injection unit only needs to connect the converter inputs or outputs. Compared to power-ON LC parameter estimation methods, the proposed one is non-invasive without adding any hardware or software algorithm that may introduce new risks to converter operation. This method can handle the converters with high-order LC structures (e.g., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2^{nd}$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$4^{th}$</tex-math></inline-formula> -order) in converter power-OFF state, which has not been achieved by existing power-OFF solutions. Therefore, the proposed method is promising for the specific applications of interest mentioned above. The parameter estimation algorithm and signal injection unit design are presented. The experimental results indicate that the estimation errors of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2^{nd}$</tex-math></inline-formula> -order equivalent circuit, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$3^{rd}$</tex-math></inline-formula> -order equivalent circuit, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$4^{th}$</tex-math></inline-formula> -order equivalent circuit are lower than 1.6%, 2.5%, and 3%, respectively. The estimated LC parameters can be further used as inputs for operation optimization or condition monitoring of the converters.

A Partial Maximum Likelihood Method to Estimate Cox Model for Competing Risk Data with Application

Many Research and clinical studies have addressed the occurrence of failure (death). As a result of other (external) factors, which may introduce additional risks that compete with the event under study. The resulting data refers to the complete data on Competing risks, which are affected by time differences. The exact times of occurrence of these risks are known, meaning the times of failure are observed for all observations with certainty. The impact of these risks on the hazard function is estimated based on the Cox proportional hazards model, which is estimated using the partial maximum likelihood method and numerical algorithms for parameter estimation. This includes the effect of variables on the Cox hazard function and the nonparametric part, estimated by assessing the effect of time on the hazard function using the Kaplan-Meier formula and calculating competing risks through the cumulative hazard function. These methods were applied to experimental data through large-scale simulations of different sizes and parameters and for several arithmetic means and standard deviations models. Moreover, applied to real data from a sample of 80 individuals with breast cancer. Analyzing the simulation results and real data revealed that the Downhill algorithm outperforms the Newton-Raphson algorithm in terms of estimation accuracy and efficiency, based on the statistical criterion for comparison, the root mean square error. In addition, competitive risks explained the effect of common variables in increasing competitive risks beyond the hazard function of the Cox model of the Newton-Raphson estimator. While it is converging to the hazard function of the Cox model for the Downhill estimator . Paper type: Research paper

CNN-LSTM based incremental attention mechanism enabled phase-space reconstruction for chaotic time series prediction

To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network, we propose a convolutional neural network (CNN)-long short-term memory (LSTM) prediction model based on the incremental attention mechanism. Firstly, a traversal search is conducted through the traversal layer for finite parameters in the phase space. Then, an incremental attention layer is utilized for parameter judgment based on the dimension weight criteria (DWC). The phase space parameters that best meet DWC are selected and fed into the input layer. Finally, the constructed CNN-LSTM network extracts spatiotemporal features and provides the final prediction results. The model is verified using Logistic, Lorenz, and sunspot chaotic time series, and the performance is compared from the two dimensions of prediction accuracy and network phase space structure. Additionally, the CNN-LSTM network based on incremental attention is compared with LSTM, CNN, recurrent neural network (RNN), and support vector regression (SVR) for prediction accuracy. The experiment results indicate that the proposed composite network model possesses enhanced capability in extracting temporal features and achieves higher prediction accuracy. Also, the algorithm to estimate the phase space parameter is compared with the traditional CAO, false nearest neighbor, and C–C, three typical methods for determining the chaotic phase space parameters. The experiments reveal that the phase space parameter estimation algorithm based on the incremental attention mechanism is superior in prediction accuracy compared with the traditional phase space reconstruction method in five networks, including CNN-LSTM, LSTM, CNN, RNN, and SVR.

Distributed adaptive parameter estimation over weakly connected digraphs using a relaxed excitation condition

SummaryIn this article, a novel distributed adaptive parameter estimation (DAPE) algorithm is proposed for an multi‐agent system over weakly connected digraph networks, where parameter convergence is ensured under a newly coined relaxed excitation condition, called generalized cooperative initial excitation (gC‐IE). This is in contrast to the past literature, where such DAPE algorithms demand cooperative persistent of excitation (C‐PE) and generalized cooperative persistent of excitation (gC‐PE) for strongly connected digraph, and weakly connected digraph networks, respectively, for parameter convergence. The gC‐PE and C‐PE conditions are restrictive in the sense that they require the richness/excitation of information over the entire time‐span of the signal/data, unlike gC‐IE condition where excitation is needed only in the initial time‐span. The newly coined gC‐IE condition is an extension of cooperative initial excitation (C‐IE) condition. While the C‐IE condition is applicable to a strongly connected digraph, the newly proposed gC‐IE condition extends the concept to weakly connected digraph. The proposed algorithm utilizes a novel set of weighted integrator dynamics, which omits the requirement of computationally involved multiples switching mechanisms in past literature, while still ensuring parameter convergence. The proposed algorithm provides global exponential stability of origin of the parameter estimation error dynamics under gC‐IE condition. Furthermore, robustness to unmodeled disturbance is also established in the form of input‐to‐state stability. Simulation results validate the efficacy of the proposed algorithm in contrast to the gC‐PE based algorithm.

Adaptive control of A class of nonlinear systems with guaranteed parameter estimation: A concurrent learning based approach

AbstractRecent advances in concurrent learning based adaptive controllers have relaxed the persistency of excitation condition required to achieve exponential tracking and parameter estimation error convergence. This was made possible via the use of additional concurrent learning stacks in the parameter estimation algorithm. However, the proposed concurrent learning components, that is, the history stacks, needed to be filled with “selected” values dependent on the actual system states. Therefore, the previously proposed concurrent learning adaptive controllers required the system to be stable initially for a finite time so that the corresponding history stacks can be filled (finite excitation condition). In this work, motivated to remove the finite excitation condition, a novel desired system state based concurrent learning adaptive controller is proposed. In order to remove the system state dependencies in the controller and estimation algorithms, a filtered version of the dynamics and a novel prediction error formulation have been designed. The overall exponential stability, parameter error convergence and boundedness of the system states during closed loop operations are ensured via Lyapunov based arguments. The main advantages of the proposed method are its dependence on the desired system states and the overall stability results that paved the way in removing the need for finite excitation condition. Numerical studies performed on a two link robotic device are also presented to illustrate the feasibility of the proposed method.

Least squares parameter estimation for uncertain fractional differential equations and application to stock model

In recent years, uncertain fractional differential equations was proposed for the description of complex uncertain dynamic systems with historical characteristics. For wider applications of uncertain fractional differential equations, researches on parameter estimation for uncertain fractional differential equations are of great importance. In this paper, based on the thought of least squares estimation and uncertain hypothesis test, an algorithm of parameter estimation for uncertain fractional differential equations is discussed. Finally, we consider the application of uncertain fractional differential equations based model to predict the forecasting stock price of three major indexes of U.S. stocks and make a comparison between uncertain fractional differential equations, uncertain differential equations and stochastic differential equations.

Electromagnetic telemetry signal denoising: An interference elimination via parameter estimation

Electromagnetic telemetry has emerged as a promising technique for the real-time acquisition of downhole data. However, the transmission of electromagnetic waves through the formation encounters attenuation, leading to a weakened received signal at the surface, typically registering at the microvolt level. The growing presence of surface electrical equipment in well-site environments has engendered heightened electromagnetic interference, thus deteriorating the signal-to-noise ratio (SNR) of received signals. The conventional linear filtering method can effectively eliminate the electromagnetic interference at the wellsite, but it has no effect on the low frequency interference close to the carrier frequency, especially the common low-frequency pulse interference (LPI) and power line interference (PLI). To mitigate the adverse effects of surface noise, we propose a nonlinear processing method based on parameter estimation algorithms. Generally, the proposed method entails reconstructing the interference by accurate parameter estimation and subtracting it from the received signal, aiming to enhance the SNR of the received signal. Simulation data and real noise data collected in the field are processed to verify the effectiveness of the proposed method. The results demonstrate the superiority of this approach over traditional filtering techniques in effectively eradicating surface interference.

An Integrated Deep Learning-Based Data Fusion and Degradation Modeling Method for Improving Prognostics

Accurate prognostics are crucially important to prevent unexpected failures in industrial and service systems. This process aims to monitor the degradation status of units and predict their remaining useful lifetime (RUL) by analyzing the data collected from multiple sensors. Existing studies for prognostics either focus on health index (HI)-based statistical fusion methods that are limited by restrictive assumptions or machine learning methods that model the HI and degradation status in two separate steps. However, the restrictive assumptions are often invalid in practice, and the intrinsic connection between the HI and degradation status is missing if the two parts are modeled separately, leading to poor prognostic results. This paper proposes an integrated deep learning-based data fusion and degradation modeling method by integrating a deep neural network (DNN) and a long short-term memory (LSTM) to characterize the nonlinear relationship between the HI and multiple sensor signals and to describe the underlying degradation status of units. In particular, our innovative idea is to develop an integrated backpropagation parameter estimation algorithm to solve the fusion procedure and the degradation modeling in an integrated manner by considering the properties of HI construction in the loss functions. Thus, the constructed HI is expected to better characterize the underlying degradation process and lead to a superior prognostic result. In the case study on the degradation of aircraft gas turbine engines, the proposed method achieves promising performance compared with the existing benchmarks of statistical models and other deep learning models. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper develops an integrated deep learning-based data fusion and degradation modeling method for improving prognostics when multiple sensors are available to monitor the degradation status of a unit. There are four steps for implementing this method in practice: 1) collecting multiple sensor signals of historical units; 2) constructing the HI and modeling the degradation status of units by combining a DNN model and an LSTM model; 3) solving the fusion procedure and the degradation modeling in an integrated manner by developing an integrated backpropagation parameter estimation algorithm; and 4) making prognostics for in-service units. The novelty of the proposed method is that it conducts prognostics by combining a DNN fusion model and an LSTM degradation model, and seamlessly integrates the fusion procedure with the degradation modeling to construct the HI for better characterizing the status of a unit. As a result, the proposed method has two main advantages: (i) capable of characterizing various degradation processes of different engineering systems; and (ii) superior prognostic results by constructing more suitable HI for the degradation process.

MT Method for Anomaly Detection and Classification using EM-λ Algorithm

Purpose: In this paper, we propose a method to classify and detect normal, known anomalies, and unknown anomalies by combining the expectation–maximisation (EM-λ) algorithm and the Mahalanobis–Taguchi (MT) method. Methodology/Approach: The proposed method learns normal data that are expected to be homogeneous and known abnormal data and performs classification and detection by parameter estimation using the EM-λ algorithm. Conventional methods perform analysis based on parameter estimation using the EM algorithm. However, the EM algorithm can degrade classification accuracy if it does not assume that the data fits the model's generative process. Findings: We verify the performance of the proposed method using artificially generated data and real-world bean data for classification as data that do not satisfy this assumption. The validation results show up to 6% improvement over the conventional method in classification accuracy and unknown anomaly discrimination accuracy. Research Limitation/implication: We try various patterns for the parameter of the proposed method in the verification. However, this way is computationally expensive. Originality/Value of paper: Conventional methods perform analysis based on parameter estimation using the EM algorithm. Our proposal method seeks to improve accuracy by using the EM-λ algorithm for parameter estimation, which is expected to improve classification accuracy when the data do not conform to the generative assumptions of the EM algorithm's model.

Near-field beamforming method based on motion model analysis for UAVs communication

This study presents a near-field beamforming method for the moving swarm composed of unmanned aerial vehicles (UAVs) to address the challenges of position errors that hinder effective beamforming. Firstly, a model with positional errors in moving UAVs was developed. The sources and characteristics of UAVs’ position errors were analyzed and classified into low-frequency motion errors and high-frequency vibration errors, and their effects on UAVs array beamforming were analyzed using coordinate transformation and decomposition. Secondly, a parameter estimation algorithm was proposed based on the Fast Fourier Transformation (FFT) and the Least Square (LS) method to estimate the unknown parameters of the UAV's low-frequency motion errors. Lastly, a near-field beamforming algorithm for UAVs was proposed based on the Interpolation Kalman filter (IKF). The effectiveness of the proposed model and algorithms was verified through simulations, which provided a theoretical basis for the near-field beamforming under the existence of the UAVs position errors.

Multi-Strategy Boosted Fick's Law Algorithm for Engineering Optimization Problems and Parameter Estimation.

To address the shortcomings of the recently proposed Fick's Law Algorithm, which is prone to local convergence and poor convergence efficiency, we propose a multi-strategy improved Fick's Law Algorithm (FLAS). The method combines multiple effective strategies, including differential mutation strategy, Gaussian local mutation strategy, interweaving-based comprehensive learning strategy, and seagull update strategy. First, the differential variation strategy is added in the search phase to increase the randomness and expand the search degree of space. Second, by introducing the Gaussian local variation, the search diversity is increased, and the exploration capability and convergence efficiency are further improved. Further, a comprehensive learning strategy that simultaneously updates multiple individual parameters is introduced to improve search diversity and shorten the running time. Finally, the stability of the update is improved by adding a global search mechanism to balance the distribution of molecules on both sides during seagull updates. To test the competitiveness of the algorithms, the exploration and exploitation capability of the proposed FLAS is validated on 23 benchmark functions, and CEC2020 tests. FLAS is compared with other algorithms in seven engineering optimizations such as a reducer, three-bar truss, gear transmission system, piston rod optimization, gas transmission compressor, pressure vessel, and stepped cone pulley. The experimental results verify that FLAS can effectively optimize conventional engineering optimization problems. Finally, the engineering applicability of the FLAS algorithm is further highlighted by analyzing the results of parameter estimation for the solar PV model.

Multiple Leap Maneuver Trajectory Design and Tracking Method Based on Prescribed Performance Control during the Gliding Phase of Vehicles

A novel standard trajectory design and tracking guidance used in the multiple active leap maneuver mode for hypersonic glide vehicles (HGVs) is proposed in this paper. First, the dynamic equation and multiconstraint model are first established in the flight path coordinate system. Second, the reference drag acceleration-normalized energy (D-e) profile of the multiple active leap maneuver mode is quickly determined by the Newton iterative algorithm with a single design parameter. The range to go error is corrected by the drag acceleration profile update algorithm, and the drag acceleration error of the gliding terminal is corrected by the aerodynamic parameter estimation algorithm. Then, the reference drag acceleration tracking guidance law is designed based on the prescribed performance control method. Finally, the CAV-L vehicle model is used for numerical simulation. The results show that the proposed method can satisfy the design requirements of drag acceleration under multiple active leap maneuver modes, and the reference drag acceleration can be tracked precisely. The adaptability and robustness of the proposed method are verified by the Monte Carlo simulations under various combined deviation conditions.

A Random Consideration Set Model for Demand Estimation, Assortment Optimization, and Pricing

Random Consideration Set Model We operationalize a microfounded consumer choice model—the random consideration set (RCS) choice model of Manzini and Mariotti [Manzini P, Mariotti M (2014) Stochastic choice and consideration sets. Econometrica 82(3):1153–1176]—that captures the limited attention of consumers, assuming that purchases are based on fixed preference orderings with consideration sets formed from independent attentions. We provide a condition for uniquely identifying model parameters and design an efficient algorithm for model parameters estimation. We offer a greedy-like algorithm for assortment optimization, adaptable for optimal assortment subject to cardinality constraint or discovering efficient sets. We extend the model to consider random product preferences, with a 1/2 performance-guaranteed approximation algorithm. Using data from a major U.S. airline, we find that the RCS model outperforms the mixed multinomial logit model in approximately half of the markets, particularly with smaller, less varied data sets.

Global optimization of multilayer dielectric coatings for precision measurements.

We describe the design of optimized multilayer dielectric coatings for precision laser interferometry. By setting up an appropriate cost function and then using a global optimizer to find a minimum in the parameter space, we were able to realize coating designs that meet the design requirements for spectral reflectivity, thermal noise, absorption, and tolerances to coating fabrication errors. We also present application of a Markov-Chain Monte Carlo (MCMC) based parameter estimation algorithm that can infer thicknesses of dielectric layers in a coating, given a measurement of the spectral reflectivity. This technique can be a powerful diagnostic tool for both commercial coating manufacturers, and the community using dielectric mirrors for precision metrology experiments.

Novel parameter estimation method for the systems with colored noises by using the filtering identification idea

Compared with the systems with white noise disturbances, the parameter identification of the systems with colored noises (i.e., correlated noises) is more difficult. In this letter, we use the model transformation to study the identification problem for the systems with colored noises by using the filtering identification idea. The basic idea is to transform a system with colored noise into two identification models with white noises and then to propose a novel parameter estimation algorithms, which can generate more accurate parameter estimates than some related existing identification algorithm. The proposed method can be applied to other linear or nonlinear stochastic systems with different structures and colored disturbance noises. The provided simulation example tests the proposed algorithm.

Parameter estimation of ground moving targets in synthetic aperture radar systems based on vortex echo data

Ground Moving Target Indication is a critical field within synthetic aperture radar (SAR) research, as traditional SAR images are defocused and displaced due to the target’s trajectory-direction velocity and radial velocity, respectively. Therefore, an accurate estimation of the target’s motion parameters is required. This study introduces a two-dimensional method for estimating target motion parameters using vortex SAR. It utilises the Bessel magnitude and spatial phase term from vortex echo data to calculate the pitch and azimuth angle, from which the motion parameters of ground slow-motion targets are derived. The proposed algorithm operates faster and has a lower computational cost than the traditional parameter estimation algorithm. Its efficacy was confirmed through simulation experiments and mean square error analysis of the estimated parameters.

Experimental and simulation investigation of stereo-DIC via a deep learning algorithm based on initial speckle positioning technology.

For the deep-learning-based stereo-digital image correlation technique, the initial speckle position is crucial as it influences the accuracy of the generated dataset and deformation fields. To ensure measurement accuracy, an optimized extrinsic parameter estimation algorithm is proposed in this study to determine the rotation and translation matrix of the plane in which the speckle is located between the world coordinate system and the left camera coordinate system. First, the accuracy of different extrinsic parameter estimation algorithms was studied by simulations. Subsequently, the dataset of stereo speckle images was generated using the optimized extrinsic parameters. Finally, the improved dual-branch CNN deconvolution architecture was proposed to output displacements and strains simultaneously. Simulation results indicate that DAS-Net exhibits enhanced expressive capabilities, as evidenced by a reduction in displacement errors compared to previous research. The experimental results reveal that the mean absolute percentage error between the stereo-DIC results and the generated dataset is less than 2%, suggesting that the initial speckle positioning technology effectively minimizes the discrepancy between the images in the dataset and those obtained experimentally. Furthermore, the DAS-Net algorithm accurately measures the displacement and strain fields as well as their morphological characteristics.