Accurate Parameter Estimates Research Articles

Application of Hierarchical Bayesian Models for Modeling Economic Costs in the Implementation of New Diagnostic Tests

The COVID-19 pandemic has highlighted the need for reliable and rapid diagnostic tests to control the spread of infection. The introduction of new rapid antigen tests often goes in tandem with the limited data availability, making it challenging to assess their performance at the initial phase of the pandemic. Sensitivity and specificity, the key performance characteristics provided by manufacturers, are typically derived under laboratory conditions and may not accurately reflect the tests' performance in field settings. We use the hierarchical Bayesian model to obtain their realistic estimates in real world conditions and show how it may be used in situations in which new tests with limited history are presented on the market. Proposed methodology allows for the efficient information pooling, thereby improving on the accuracy of parameter estimates for new tests. The results suggest that the application of hierarchical model on the Czech data led to a considerabile reduction in uncertainty associated with the parameter estimates as well as with potential economic cost implied by false positive test results. The model can thus assist in better informed decision-making and financial planning of both the government and corporations.

Rapid parameter estimation for merging massive black hole binaries using continuous normalizing flows

Abstract Detecting the coalescences of massive black hole binaries (MBHBs) is one of the primary targets for space-based gravitational wave observatories such as laser interferometer space antenna, Taiji, and Tianqin. The fast and accurate parameter estimation of merging MBHBs is of great significance for the global fitting of all resolvable sources, as well as the astrophysical interpretation of gravitational wave signals. However, such analyses usually entail significant computational costs. To address these challenges, inspired by the latest progress in generative models, we explore the application of continuous normalizing flows (CNFs) on the parameter estimation of MBHBs. Specifically, we employ linear interpolation and trig interpolation methods to construct transport paths for training CNFs. Additionally, we creatively introduce a parameter transformation method based on the symmetry in the detector’s response function. This transformation is integrated within CNFs, allowing us to train the model using a simplified dataset, and then perform parameter estimation on more general data, hence also acting as a crucial factor in improving the training speed. In conclusion, for the first time, within a comprehensive and reasonable parameter range, we have achieved a complete and unbiased 11-dimensional rapid inference for MBHBs in the presence of astrophysical confusion noise using CNFs. In the experiments based on simulated data, our model produces posterior distributions comparable to those obtained by nested sampling.

Enhanced TomoSAR imaging method with complex least squares for 3D building reconstruction

ABSTRACT Synthetic aperture radar tomography (TomoSAR) has emerged as an advanced technology for the rapid acquisition of three-dimensional information, with model solutions dependent on a specific complex least squares adjustment criterion. We design two TomoSAR imaging algorithms based on two adjustment criterions minimizing the square sum of the real and imaginary components of observation vector residual, and minimizing the square sum of the L2-norm of observation vector residual. Additionally, we propose a strong scatterer recognition method that combines amplitude thresholding and density-based spatial clustering of applications with noise to alleviate the low efficiency and excessive noise in real images. The simulated and practical experiments are conducted to evaluate the performance of algorithms. Results suggested that two algorithms perform similarly in parameter estimation accuracy and noise immunity for buildings with simple structures and single scatterer. However, for buildings with multiple scatterers, the algorithm derived by minimizing the square sum of the L2-norm from the observation vector residual exhibits more robustly than the other algorithm, accurately distinguishing multiple scatterers within pixels and reconstructing 3D scenes mirroring the actual ones. The results verify the effectiveness of the proposed strong scatterer recognition method and the importance of the adjustment criterion in TomoSAR imaging.

Full-field Modal Analysis of a Tensegrity Column Using a Three-dimensional Scanning Laser Doppler Vibrometer with a Mirror

Abstract Tensegrity structures become important components of various engineering structures due to their high stiffness, light weight, and deployable capability. Existing studies on their dynamic analyses mainly focus on responses of their nodal points while overlook deformations of their cable and strut members. This study proposes a non-contact approach for experimental modal analysis of a tensegrity structure to identify its three-dimensional (3D) natural frequencies and full-field mode shapes, which include modes with deformations of its cable and strut members. A 3D scanning laser Doppler vibrometer is used with a mirror for extending its field of view to measure full-field vibration of a novel three-strut metal tensegrity column with free boundaries. Tensions and axial stiffnesses of its cable members are determined using natural frequencies of their transverse and longitudinal modes, respectively, to build its theoretical model for dynamic analysis and model validation purposes. Modal assurance criterion (MAC) values between experimental and theoretical mode shapes are used to identify their paired modes. Modal parameters of the first 15 elastic modes of the tensegrity column identified from the experiment, including those of the overall structure and its cable members, can be classified into five mode groups depending on their types. Modes paired between experimental and theoretical results have MAC values larger than 78%. Differences between natural frequencies of paired modes of the tensegrity column are less than 15%. The proposed non-contact 3D vibration measurement approach allows accurate estimation of 3D full-field modal parameters of the tensegrity column.

A Neural-Metaheuristic Kalman Filter for Moving Microburst Wind Shear Identification

Microburst wind shears (MB) are powerful localized three dimensional (3D) columns of wind that occur when cooled air drops from the base of thunderstorms at high speeds. They eventually hit the ground and spread out in all directions. As such MBs are considered a major atmospheric hazard for aircrafts (ACs), especially in terminal flight phases. Though pilots train regularly to survive it, yet the most recommended practice within the aviation community is to avoid its encounter upon detection. Some modern aircrafts have predictive wind shear warning systems, but they have limited short range capability and do not provide quantitative data for engineering application. In this sense, accurate onboard detection and identification of MBs and its characteristics is of importance for flight safety, whose success can lead to design of automatic flight control systems (FCSs) that reduce the risk of aircraft crash landings and accidents. Even though there are some studies on FCS designs for MB encounter, research on MB identification is rare but ongoing. To this aim, the present study is among the firsts that focuses on online identification of multiple and moving MB parameters using onboard aircraft air data and inertial sensors. The identification task is initially performed using the aircraft six degrees of freedom (6DoF) equations of motion (EOM) integrated with a 3D MB model via the utility of nonlinear Kalman filtering (KF) algorithms. Subsequently, an enhanced neural metaheuristic Kalman filter (NMKF) is proposed that improves the estimation accuracy of the MB model parameters. The results demonstrate the efficacy of the proposed NMKF in comparison with previous studies.

Accurate Modeling and Parameters Estimation of Photovoltaic Models: Analytical and Artificial Intelligence Solutions

Accurate Modeling and Parameters Estimation of Photovoltaic Models: Analytical and Artificial Intelligence Solutions

Inverse Problem for the Moisture Transfer Equation: Development of a Method for Finding the Unknown Parameter and Proof of the Convergence of the Iterative Process

This study develops a mathematical model for soil moisture diffusion, addressing the inverse problem of determining both the diffusion coefficient and the variation coefficient in a nonlinear moisture transfer equation. The model incorporates specific boundary and initial conditions and utilizes experimentally measured moisture values at a boundary point as input data. An iterative method, based on an explicit gradient scheme, is introduced to estimate the soil parameters. The initial boundary value problem is discretized, leading to a difference analog and the formulation of a conjugate difference problem. Iterative formulas for calculating the unknown parameters are derived, with a priori estimates ensuring the convergence of the iterative process. Additionally, the research establishes the convergence of the numerical model itself, providing a rigorous foundation for the proposed approach. The study also emphasizes symmetry in moisture calculations, ensuring consistency regardless of the calculation direction (from right to left or left to right) and confirming that moisture distribution remains symmetric within specified intervals. This preservation of symmetry enhances the model’s robustness and accuracy in parameter estimation. The numerical simulations were successfully conducted over a 7-day period, demonstrating the model’s reliability. The discrepancy between the numerical predictions and experimental observations remained within the margin of measurement error, confirming the model’s accuracy.

Enhancing reliability in estimating modal parameters for automotive disk Brakes: A comprehensive approach using the Eigensystem Realization algorithm and additional criteria

This paper investigates the challenges in accurately identifying and assessing vibration characteristics in automotive disk brakes, which, due to their geometric symmetry, exhibit closely spaced vibration modes. Understanding the damping characteristics is crucial due to their significant impact on dynamic stability and the potential onset of brake squeal, as damping directly influences the stability threshold and its uneven distribution can destabilize the system. Therefore, this study primarily focuses on the identification of modal parameters with an emphasis on the damping of disk brakes. Traditional Experimental Modal Analysis (EMA) techniques, which rely heavily on Frequency Response Function (FRF) measurements, encounter challenges in distinguishing closely spaced modes, thereby affecting the reliability of parameter estimation, particularly damping. These algorithms are primarily based on FRF measurements and are of multi-input – single-output type (MISO). In comparison to Operational Modal Analyses (OMA) algorithms, which are widely used in civil engineering and are of the multi-input − multi-output type and contain statistical tools for assessing the uncertainty of the estimate, EMA provides limited possibilities to assess the quality of estimating parameters. The primary contribution of this work is demonstrating that the Eigensystem Realization Algorithm (ERA), supplemented with indicators such as Extended Modal Amplitude Coherence (EMAC), Modal Phase Collinearity (MPC), and the Consistent Mode Indicator (CMI), offers a robust tool for accurate damping estimation. Additionally, the application of ERA to data originally acquired for frequency-based methods, specifically the Rational Fraction Polynomial (RFP) method, allows for a direct comparison of these two EMA algorithms using the same dataset. The results demonstrate that the proposed identification process effectively distinguishes system modes from those influenced by noise, providing a pathway to optimize test data acquisition and improve the accuracy of modal parameter estimation, especially in systems with closely spaced modes. The method can also serve as a tool for optimizing the acquisition of test data to improve the estimation of modal parameters, by varying the positions of input (SIMO) or by transitioning to MIMO identification to enhance the observability and controllability of closely spaced modes of disk brake.

Bayesian finite element model inversion of offshore wind turbine structures for joint parameter-load estimation

Operating in harsh and unsteady marine environment, offshore wind turbine (OWT) structures are exposed to unpredictable wind and wave loads. Identifying the structural loads and their effects on the OWTs allow for predicting the remaining fatigue life of these structures and improving the structural design procedure. In this paper, a finite element (FE) model inversion method is presented to estimate the unknown loads and model parameters of OWTs using sparse measurement data. A realistic FE model of an OWT structure with jacket substructure is created in the open-source simulation platform, OpenSees. A Bayesian inference framework is presented to integrate the measured data with the FE model to estimate unknown wind loads and mass of rotor-nacelle assembly. To evaluate the performance of this data assimilation framework, the effect of sensor type, number of sensors, and modeling errors on the estimation accuracy of wind loads and model parameters are investigated through different case studies where synthetic data are used as measurements. The results of this study are important to guide instrumentation of new OWT structures, and to understand the potential limitations and sources of error in the real-world application of this data assimilation framework for joint model parameter and input load estimation.

Multivariate Cluster Point Process to Quantify and Explore Multi-Entity Configurations: Application to Biofilm Image Data.

Clusters of similar or dissimilar objects are encountered in many fields. Frequently used approaches treat each cluster's central object as latent. Yet, often objects of one or more types cluster around objects of another type. Such arrangements are common in biomedical images of cells, in which nearby cell types likely interact. Quantifying spatial relationships may elucidate biological mechanisms. Parent-offspring statistical frameworks can be usefully applied even when central objects ("parents") differ from peripheral ones ("offspring"). We propose the novel multivariate cluster point process (MCPP) to quantify multi-object (e.g., multi-cellular) arrangements. Unlike commonly used approaches, the MCPP exploits locations of the central parent object in clusters. It accounts for possibly multilayered, multivariate clustering. The model formulation requires specification of which object types function as cluster centers and which reside peripherally. If such information is unknown, the relative roles of object types may be explored by comparing fit of different models via the deviance information criterion (DIC). In simulated data, we compared a series of models' DIC; the MCPP correctly identified simulated relationships. It also produced more accurate and precise parameter estimates than the classical univariate Neyman-Scott process model. We also used the MCPP to quantify proposed configurations and explore new ones in human dental plaque biofilm image data. MCPP models quantified simultaneous clustering of Streptococcus and Porphyromonas around Corynebacterium and of Pasteurellaceae around Streptococcus and successfully captured hypothesized structures for all taxa. Further exploration suggested the presence of clustering between Fusobacterium and Leptotrichia, a previously unreported relationship.

Uniformization and bounded Taylor series in Newton-Raphsonmethod improves computational performance for a multistate transition model estimation and inference.

Multistate transition models (MSTMs) are valuable tools depicting disease progression. However, due to the complexity of MSTMs, larger sample size and longer follow-up time in real-world data, the computation of statistical estimation and inference for MSTMs becomes challenging. A bounded Taylor series in Newton-Raphson procedure is proposed which leverages the uniformization technique to derive maximum likelihood estimates and corresponding covariance matrix. The proposed method, namely uniformization Taylor-bounded Newton-Raphson, is validated in three simulation studies, which demonstrate the accuracy in parameter estimation, the efficiency in computation time and robustness in terms of different situations. This method is also illustrated using a large electronic medical record data related to statin-induced side effects and discontinuation.

Bayesian grouping-Gibbs sampling estimation of high-dimensional linear model with non-sparsity

In high-dimensional linear regression models, common assumptions typically entail sparsity of regression coefficients β∈Rp. However, these assumptions may not hold when the majority, if not all, of regression coefficients are non-zeros. Statistical methods designed for sparse models may lead to substantial bias in model estimation. Therefore, this article proposes a novel Bayesian Grouping-Gibbs Sampling (BGGS) method, which departs from the common sparse assumptions in high-dimensional problems. The BGGS method leverages a grouping strategy that partitions β into distinct groups, facilitating rapid sampling in high-dimensional space. The grouping number (k) can be determined using the ‘Elbow plot’, which operates efficiently and is robust against the initial value. Theoretical analysis, under some regular conditions, guarantees model selection and parameter estimation consistency, and bound for the prediction error. Furthermore, three finite simulations are conducted to assess the competitive advantages of the proposed method in terms of parameter estimation and prediction accuracy. Finally, the BGGS method is applied to a financial dataset to explore its practical utility.

Advanced parameter estimation for lithium-ion battery model using the information sharing group teaching optimization algorithm

Accurate battery modeling is crucial for optimizing the performance and safety of Lithium-ion batteries (LiBs), particularly in applications such as electric vehicles and smart grids. This paper introduces the Information Sharing Group Teaching Optimization Algorithm (ISGTOA), a novel human-based metaheuristic algorithm designed to estimate the 21 parameters of third-order Equivalent Circuit Model (ECM) for LiBs. Unlike existing methods, ISGTOA effectively manages the increased complexity of a model through advanced group teaching strategies and sophisticated information-sharing mechanisms inspired by classroom dynamics. We validated the effectiveness of ISGTOA using two distinct datasets—High Dynamic Profile (HDP) and Urban Dynamometer Driving Schedule (UDDS)—across various LiB chemistries (NCA and NMC) and temperature conditions (−5 °C, 25 °C and 45 °C). The results demonstrate that ISGTOA achieves superior parameter estimation accuracy and convergence speed compared to established and recent optimization methods such as TLBO, TLSBO, AISA, MTBO, and DTBO. Specifically, ISGTOA attained a minimum RMSE of 8.357 mV with rapid convergence and high stability in the HDP dataset and minimized RMSE to 10 mV within ten iterations at both 25 °C and 45 °C in the UDDS dataset. Additionally, ISGTOA exhibited high efficiency (up to 97.75 %) under varying thermal environments. This work not only introduces a novel algorithm for complex battery modeling but also sets the stage for future advancements in real-time battery management systems, emphasizing the importance of robust, versatile, and efficient parameter estimation techniques.

Inversion of biophysical parameters of potato based on an active learning pool-based sampling strategy

ABSTRACT Timely estimations of leaf chlorophyll content (LCC) and leaf area index (LAI) can provide critical information for potato field management. We employed a hybrid method that integrated machine learning with a radiative transfer model to estimate potato growth parameters. A look-up table was generated using the PROSAIL model, which was used as an unlabelled sample set. Measurements were taken from a potato field, and the data were labelled according to growth period and variety. Then, training samples for potato LCC, LAI, and canopy chlorophyll content (CCC) were selected from the simulated unlabelled sample set using the Euclidean distance-based diversity algorithm based on different labelled data sets. The training sample size required to accurately estimate the parameters varied considerably depending on the parameter, variety, and growth period, despite using the same labelled data set. Moreover, our results indicate that the growth period has a substantial impact on model accuracy and needs to be considered when constructing the labelled data set. The study results indicate that the hybrid method combined with the radiative transfer model and active learning can effectively select informative training samples from a data pool and improve the accuracy of potato parameter estimation, which provides a valid tool for accurately monitoring crop growth and growth health.

UltraStat: Ultrafast Spectroscopy beyond the Fourier Limit Using Bayesian Inference.

The discrete Fourier transform (dFT) plays a central role in many ultrafast experiments, allowing the recovery of spectroscopic observables from time-domain measurements. In resonant experiments when population relaxation and coherence components of the signal coexist, the dFT is usually preceded by multiexponential fitting to remove the large population term. However, this procedure results in errors in both the recovered decay rates and the line shapes of the coherence spectral components. While other methods such as linear prediction singular value decomposition fit both terms simultaneously, they are limited to specific models that may not represent the true signal. These methods do not allow for systematic noise analysis or error estimation and require a priori knowledge of the signal rank. Here, we describe a general approach to parameter estimation in ultrafast spectroscopy─UltraStat─grounded in Bayesian analysis without the limitations set by Fourier theory. Using simulated, but realistic data, we demonstrate in a statistical sense how UltraStat provides accurate parameter estimation in the presence of many experimental constraints: noise, signal truncation, limited photon budget, and nonuniform sampling. UltraStat provides superior resolution compared to the dFT, up to an order of magnitude in cases where the line shapes are well-approximated. In these cases, we establish that primarily noise, not sampling, limits spectral resolution. Moreover, we show that subsampling may reduce the number of acquired points by 90% compared to the Nyquist-Shannon criteria. UltraStat greatly improves parameter estimation by providing statistically bound spectral and dynamics analysis, pushing the limits of ultrafast science.

Adaptive fault estimation and accommodation for distributed parameter systems with coupled parabolic partial differential equations

This paper presents a novel model-based approach for fault detection, estimation and accommodation in linear distributed parameter systems (DPS) governed by parabolic partial differential equations (PDEs), prone to sensor and actuator faults. Unlike traditional methods, our approach utilises a filter-based observer directly employing the PDE representation and relies solely on boundary measurements, eliminating the need for extensive sensor arrays. By generating fault detection residuals from a comparison of measured and observer outputs, our method offers efficient fault detection. Innovative parameter update laws facilitate accurate estimation of fault parameters, enabling precise adjustment of the nominal controller to mitigate fault effects. Rigorous Lyapunov analysis ensures the robustness of our approach. Additionally, we derive a formula for estimating time-to-accommodation (TTA), providing valuable insights into fault resolution timelines. Simulations on a linearised diffusion process validate the effectiveness of our scheme, highlighting its superiority over existing approaches.

Response-Aided Score-Matching Representative Approaches for Big Data Analysis and Model Selection under Generalized Linear Models

In this paper, we propose an efficient method called the response-aided score-matching representative (RASMR) approach to facilitate massive data model selection and data analysis with generalized linear models (GLMs) and a predetermined data partition due to data localization. Similar to the original score-matching representative (SMR) approach, RASMR constructs an artificial data point, called the representative, for each data block. It then fits a GLM on the representative dataset, which provides not only an efficient approach for massive data analysis but also an ideal solution in response to privacy concerns by avoiding the transfer of sensitive data. By further splitting the data blocks according to the values of the response variables, RASMR can obtain more accurate parameter estimates than SMR. Furthermore, by theoretical justifications and simulation studies, we show that RASMR can be more efficiently utilized for model selection and variable selection for a massive dataset by approximating the Akaike information criterion (AIC) and the aggregated prediction errors for cross-validation, which are commonly used for choosing the most appropriate statistical model and drawing reliable conclusions. We also apply the proposed RASMR approach to the airline on-time performance data, which consists of 371 data files labeled by month, and show that RASMR can be successfully used for selecting the most appropriate model for real massive data analysis.

Wideband beam domain sparse Bayesian learning passive focusing localisation algorithm

AbstractTo address the challenges of large‐aperture sonar systems passive localisation, this paper proposes the application of sparse Bayesian learning (SBL) for passive target localisation in the wideband beam domain. The proposed algorithm aims to overcome the issues of massive computational requirements for two‐dimensional SBL scanning and increased localisation errors due to interference energy leakage. The wideband beam domain SBL focusing localisation algorithm is developed by constructing an azimuth‐range two‐dimensional transformation matrix to preprocess array data, which effectively reduces the computational load of SBL processing while suppressing strong interference energy leakage in passive sonar operating environments, thus improving the range resolution and parameter estimation accuracy of focusing localisation. Simulation and sea trial data analyses demonstrate the feasibility of the proposed algorithm, with results indicating its superior performance compared to existing algorithms.

Frequency and damping factor estimation of damped sinusoid by using DFT and DTFT

An algorithm for estimating the frequency and damping factor of damped complex sinusoidal signal is presented. After the rough estimation of frequency by discrete Fourier transform (DFT), the fine estimation of frequency and damping factor is achieved by utilizing the DFT bin with the maximum magnitude and two arbitrarily spaced discrete time Fourier transform (DTFT) spectral lines located on the same side of the maximum DFT spectrum bin. Then the theoretical mean square error (MSE) in additive white noise is analyzed. Simulation results show that the proposed algorithm tracks the Cramer-Rao lower bound (CRLB), and the parameters estimation accuracy is higher than the competing algorithms in most situations. The computational requirements are almost the same as several existing methods.

Assessing Transducer Parameters for Accurate Medium Sound Speed Estimation and Image Reconstruction.

The influence of the transducer lens on image reconstruction is often overlooked. Lenses usually exhibit a lower sound speed than soft biological tissues. In academic research, the exact lens sound speed and thickness are typically unknown. Here, we present a simple and nondestructive method to characterize the lens sound speed and thickness as well as the time to peak of the round-trip ultrasound waveform, another key parameter for optimal image reconstruction. We applied our method to three transducers with center frequencies of 2.5, 7.5, and 15 MHz. We estimated the three parameters with an element-by-element transmission sequence that records internal reflections within the lens. We validated the retrieved parameters using an autofocusing approach that estimates sound speed in water. We show that the combination of our parameters estimation method with two-layer ray tracing outperforms standard image reconstruction. For all transducers, we successfully improved the accuracy of medium sound speed estimation, spatial resolution, and contrast. The proposed method is simple and robust and provides an accurate estimation of the transducer lens parameters and the time to peak of the ultrasound waveform, which leads to improved ultrasound image quality.