Parameter Estimation Algorithm Research Articles

A New Mixture Model With Cure Rate Applied to Breast Cancer Data.

We introduce a new modelling for long-term survival models, assuming that the number of competing causes follows a mixture of Poisson and the Birnbaum-Saunders distribution. In this context, we present some statistical properties of our model and demonstrate that the promotion time model emerges as a limiting case. We delve into detailed discussions of specific models within this class. Notably, we examine the expected number of competing causes, which depends on covariates. This allows for direct modeling of the cure rate as a function of covariates. We present an Expectation-Maximization (EM) algorithm for parameter estimation, to discuss the estimation via maximum likelihood (ML) and provide insights into parameter inference for this model. Additionally, we outline sufficient conditions for ensuring the consistency and asymptotic normal distribution of ML estimators. To evaluate the performance of our estimation method, we conduct a Monte Carlo simulation to provide asymptotic properties and a power study of LR test by contrasting our methodology against the promotion time model. To demonstrate the practical applicability of our model, we apply it to a real medical dataset from a population-based study of incidence of breast cancer in São Paulo, Brazil. Our results illustrate that the proposed model can outperform traditional approaches in terms of model fitting, highlighting its potential utility in real-world scenarios.

Damage identification of reinforced concrete slabs using experimental modal testing and finite element model updating

Condition assessment and health monitoring of reinforced concrete structures is an essential part of their effective maintenance throughout their service life. Vibration-based damage detection and health monitoring is one of the most popular global approaches where experimentally measured modal parameters, such as frequencies, mode shapes, etc. are compared to their corresponding finite element counterparts to estimate possible stiffness loss. The present investigation implements a vibration-based parameter estimation algorithm for updating a finite-element (FE) model for damage assessment of reinforced concrete slabs using measured frequency response functions (FRF) data through a mixed numerical-experimental technique. An inverse eigen-sensitivity algorithm has been implemented to minimize the error function realized as the weighted differences in the mode shapes and frequencies of the FE model and the modal test data. Three reinforced concrete slabs were subjected to real physical damage conditions to verify the efficacy of the proposed methodology. The technique is found to be resilient in the presence of modal and coordinate sparsity. In general, damage can be assessed even if the portions of the structure are inaccessible to the users, thereby extending the possibility of its application to most of the practical configurations of reinforced concrete slabs.

Two datasheet-based approaches for double-diode PV modeling with an efficient trade-off between accuracy and simplicity

A reliable photovoltaic (PV) model with logical trade-off between accuracy and simplicity can be utilized for optimal design, monitoring, fault detection and prediction of operational power. In this research work, two novel datasheet-based approaches are developed for PV module identification through double-diode model (DDM). In both methods the four unknown parameters are derived as functions of series resistance (Rs). It is shown that each parameter estimation algorithm has its own unique solution. Effective numerical methods are applied for fast convergence and with absolute certainty to the corresponding unique solution. The established methods are both reasonably simple and accurate while one is simpler (faster) and the other is more accurate. The performances of the proposed algorithms are evaluated by real experimental data and through a comparison with other similar datasheet-based algorithms. The results reveal that the developed methods have superb performance in comparison with other techniques.

Estimation of ultrasonic flight time based on SHADE algorithm and extended kalman filtering

Abstract Traditional methods of using ultrasound to measure oxygen concentration have the issue of inaccuracy and susceptibility to noise interference when measuring the time of flight (TOF) of ultrasonic echo signals. A proposed algorithm for ultrasonic parameter estimation, utilizing an asymmetric Gaussian model, aims to enhance the precision and reliability of TOF estimation, aiming to reduce the influence of noise interference. The algorithm combines an improved Self-Adaptive Differential Evolution (SHADE) algorithm based on successful historical records with an Extended Kalman Filter (EKF). The improved SHADE algorithm controls the degree of mutation strategy greediness during the mutation operation based on the number of iterations, thereby enhancing the algorithm’s iteration speed. Then, the obtained solution is used as the initial value for the EKF to estimate the model parameters, thus addressing the issue of EKF’s dependency on accurate initial values to obtain precise outputs. Through simulation and experimental measurements of ultrasonic oxygen concentration, several commonly used parameter estimation algorithms are compared with the proposed SHADE-EKF algorithm. Results demonstrate that the SHADE-EKF algorithm exhibits superior performance in estimating the TOF of ultrasonic waves.

Calibrating the Discrete Boundary Conditions of a Dynamic Simulation: A Combinatorial Approximate Bayesian Computation Sequential Monte Carlo (ABC-SMC) Approach.

This paper presents a novel adaptation of the conventional approximate Bayesian computation sequential Monte Carlo (ABC-SMC) sampling algorithm for parameter estimation in the presence of uncertainties, coined combinatorial ABC-SMC. Inference of this type is used in situations where there does not exist a closed form of the associated likelihood function, which is replaced by a simulating model capable of producing artificial data. In the literature, conventional ABC-SMC is utilised to perform inference on continuous parameters. The novel scheme presented here has been developed to perform inference on parameters that are high-dimensional binary, rather than continuous. By altering the form of the proposal distribution from which to sample candidates in subsequent iterations (referred to as waves), high-dimensional binary variables may be targeted and inferred by the scheme. The efficacy of the proposed scheme is demonstrated through application to vibration data obtained in a structural dynamics experiment on a fibre-optic sensor simulated as a finite plate with uncertain boundary conditions at its edges. Results indicate that the method provides sound inference on the plate boundary conditions, which is validated through subsequent application of the method to multiple vibration datasets. Comparisons between appropriate forms of the metric function used in the scheme are also developed to highlight the effect of this element in the schemes convergence.

Bayesian peak identification method for low count rate gamma spectrum under short-time measurement based on physical priors

A Bayesian peak identification method based on physical model had been proposed in this study to perform qualitative analysis for the low count rate gamma spectrum under short-time measurement. Based on the prior knowledge about gamma detection, the distribution of energy deposited in the detector near the region of interest of a target peak through photoelectric effect, Compton scattering and multiple scattering had been analyzed and approximated using three elementary components, then, the distribution of each component after convolution had been studied, and at last, a probabilistic mixture model had been proposed to directly describe the distribution of measured energy within region of interest. When the data measurement has been completed, a Gibbs sampler was used to estimate the posterior distribution of model parameters to discriminate the existence of target peaks. The numerical and physical experiments were performed to verify the effectiveness of the parameter estimation algorithm and the performance of the proposed identification method. The numerical experiments showed the identification precision is proportional to counts and peak-to-total ratio, when the peak-to-total ratio is greater than 0.5, the proposed method could identify the peak with a probability greater than 50% given 50 observations. The physical experiment used a NaI(Tl) detector to measure 137Cs, 60Co and 152Eu sources in a laboratory environment at different equivalent distances, the peak identification precision had been tested for the proposed method, and the experiments proved that the probabilistic model is a good approximation to the physical process, and the proposed identification method outperformed the conventional method under short-time measurement conditions.

A new class of zero-truncated counting models and its application

Count data is a type of data derived from the number of times an event occurs per unit of time, and zero-truncated count data refers to count data without zero, which often appears in various fields. In this paper, a new zero-truncated Bell (ZTBell) distribution is proposed on the basis of Bell distribution. We studied its statistical properties, exploring methods such as maximum likelihood estimation (MLE), expectation–maximization (EM) algorithm, and minimization–maximization (MM) algorithm for parameter estimation, as well as conducting likelihood ratio tests. In addition, we used the Bootstrap method to calculate the standard errors and confidence intervals of the parameters. The simulation results found that all of the MLE, MM algorithm and EM algorithm are effective. And, as the sample size increases, the estimates of the parameters are closer to the true values and the root mean square error is smaller. Finally, applying the model to a set of factory accident data, we found that the ZTBell distribution fits better than the other models and is close to the fitting results of the zero-truncated generalized Poisson distribution. But ZTBell distribution has only one parameter, so it’s even simpler compared to the latter. Therefore, the ZTBell distribution can be a good alternative to other zero-truncated distributions, which provides more options available for statistical analysis in this domain.

Adaptive management of borehole heat exchanger fields under transient groundwater flow conditions

Uncontrolled heat extraction by multiple interacting borehole heat exchangers (BHEs) in high-density energy-use districts can lead to undesirable thermal conditions in the subsurface which can affect both system performance and regulatory compliance. The difficulty in controlling heat extraction arises in particular from predictive uncertainties, such as when forecasting trends in energy demand or groundwater flow. In this study, a combined simulation-calibration-optimization framework is introduced to consider BHE fields with the presence of a transient groundwater flow regime. In the first part, a semi-analytical modeling technique is proposed based on temporal superpositioning of variable flow conditions. Two synthetic case studies verify its accuracy under different groundwater fluctuation patterns. The mean absolute error of the proposed model in comparison to numerical calculation does not exceed 0.18 K over ten years of operation. In the second part, the model is augmented by a parameter estimation algorithm that is employed for continuous model updating. The benefit of resolving transient flow conditions is demonstrated by using this approach for monthly optimization of individual BHE heat extraction. The result of dynamic optimization compared to a synthetic case without calibration shows a 10 % lower imposed temperature change in the subsurface.

A framework for co-existence of radar and communication with joint design

The integration of both sensing and communication functions is a crucial feature for future communication systems. This paper considers a novel scenario where a radar covers multiple small-cell base stations which operate in different spectra. Due to the limited spectra resource, the radar needs to reuse the spectra of one BS for tracking. To suppress interference and improve performance, we propose a framework including two stages and the corresponding communication and sensing algorithms. Specifically, at the detection stage, we aim to minimize the system transmit power while maintaining the performance of both radar and communication. At the tracking stage, our goal is to maximize the radar sensing performance under a given power budget, while ensuring communication quality. Due to the complexity of the original problem, we address it by introducing auxiliary variables and proposing a penalty dual decomposition-based algorithm, enabling us to solve a more tractable form of the problem. In the inner loop, we propose a concave–convex procedure-based algorithm to handle the optimization problem, while adopting the block coordinate descent algorithm to iteratively update the variables. In the outer loop, we update the penalty term or Lagrange multipliers. Furthermore, we propose a radar target parameter estimation algorithm based on successive interference cancellation, which aims to mitigate communication interference. Finally, numerical simulations demonstrate the effectiveness of the proposed system, and the superior performance of our proposed algorithms over benchmark algorithms.

A Semi-Explicit Algorithm for Parameters Estimation in a Time-Fractional Dual-Phase-Lag Heat Conduction Model

This paper presents a new semi-explicit algorithm for parameters estimation in a time-fractional generalization of a dual-phase-lag heat conduction model with Caputo fractional derivatives. It is shown that this model can be derived from a general linear constitutive relation for the heat transfer by conduction when the heat conduction relaxation kernel contains the Mittag–Leffler function. The model can be used to describe heat conduction phenomena in a material with power-law memory. The proposed algorithm of parameters estimation is based on the time integral characteristics method. The explicit representations of the thermal diffusivity and the fractional analogues of the thermal relaxation time and the thermal retardation are obtained via a Laplace transform of the temperature field and utilized in the algorithm. An implicit relation is derived for the order of fractional differentiation. In the algorithm, this relation is resolved numerically. An example illustrates the proposed technique.

Evaluation of Sampling Algorithms Used for Bayesian Uncertainty Quantification of Molecular Dynamics Force Fields.

New Bayesian parameter estimation methods have the capability to enable more physically realistic and reliable molecular dynamics (MD) simulations by providing accurate estimates of uncertainties of force-field (FF) parameters and associated properties. However, the choice of which Bayesian parameter estimation algorithm to use has not been widely investigated, despite its impact on the effective exploration of parameter space. Here, using a case example of the Embedded Atom Method (EAM) FF parameters, we investigated the ramifications of several of the algorithm choices. We found that Ensemble Slice Sampling (ESS) and Affine-Invariant Ensemble Sampling (AIES) demonstrate a new level of superior performance, culminating in more accurate parameter and property estimations with tighter uncertainty bounds, compared to traditional methods such as Metropolis-Hastings (MH), Gradient Search (GS), and Uniform Random Sampler (URS). We demonstrate that Bayesian Uncertainty Quantification with ESS and AIES leads to significantly more accurate and reliable predictions of the FF parameters and properties. The results suggest that ESS and AIES should be used to obtain more accurate parameter and uncertainty estimations while providing deeper physical insights.

Waveform Design for the Integrated Sensing, Communication, and Simultaneous Wireless Information and Power Transfer System.

Next-generation communication systems demand the integration of sensing, communication, and power transfer (PT) capabilities, requiring high spectral efficiency, energy efficiency, and low cost while also necessitating robustness in high-speed scenarios. Integrated sensing and communication systems (ISACSs) exhibit the ability to simultaneously perform communication and sensing tasks using a single RF signal, while simultaneous wireless information and power transfer (SWIPT) systems can handle simultaneous information and energy transmission, and orthogonal time frequency space (OTFS) signals are adept at handling high Doppler scenarios. Combining the advantages of these three technologies, a novel cyclic prefix (CP) OTFS-based integrated simultaneous wireless sensing, communication, and power transfer system (ISWSCPTS) framework is proposed in this work. Within the ISWSCPTS, the CP-OTFS matched filter (MF)-based target detection and parameter estimation (MF-TDaPE) algorithm is proposed to endow the system with sensing capabilities. To enhance the system's sensing capability, a waveform design algorithm based on CP-OTFS ambiguity function shaping (AFS) is proposed, which is solved by an iterative method. Furthermore, to maximize the system's sensing performance under communication and PT quality of service (QoS) constraints, a semidefinite relaxation (SDR) beamforming design (SDR-BD) algorithm is proposed, which is solved using through the SDR technique. The simulation results demonstrate that the ISWSCPTS exhibits stronger parameter estimation performance in high-speed scenarios compared to orthogonal frequency division multiplexing (OFDM), the waveform designed by CP-OTFS AFS demonstrates superior interference resilience, and the beamforming designed by SDR-BD strikes a balance in the overall performance of the ISWSCPTS.

GBTM: Community detection and network reconstruction for noisy and time-evolving data

Community detection and network reconstruction are two major concerns in network analysis. However, these two tasks are extremely challenging since most of the existing methods are not suitable for noisy and red time-evolving data, which are common in real world situations. To cope with this, we propose a novel method called the group-based binary time-evolving mixture (GBTM) model to detect communities and recover network structures jointly. This is the first to study address the challenges of community detection and network reconstruction in scenarios where data are dynamic and cannot be directly observed. In this work, the hidden Markov method is employed to capture the temporal evolution of node connections. In addition, we develop the grouped Baum-Welch algorithm for parameter estimation using a forward-backward procedure. Our GBTM model shows that conducting community detection and network reconstruction simultaneously can yield synergistic benefits. Furthermore, we introduce an innovative Bayesian information criterion (BIC) for determining the number of communities. The results of various simulations under different settings and two real-world networks show that the proposed GBTM model outperforms the existing community detection or network reconstruction methods and has great potential for solving time-evolving and noisy network problems.

Joint dereverberation and blind source separation using a hybrid autoregressive and convolutive transfer function-based model

Most frequency-domain blind source separation (BSS) methods are based on the multiplicative narrowband assumption, which is not valid in long reverberation environments. In contrast, convolutive transfer function (CTF)-based BSS methods do not rely on the narrowband assumption, and the separation performance is significantly improved compared to the traditional algorithms in long reverberation environments. However, the CTF-based BSS methods and their variants, e.g., autoregressive (AR) BSS methods, introduce modeling errors to some extent, due to the truncation or approximation during the optimization process. To address this problem, we propose a frequency-domain BSS method employing a hybrid AR and CTF model, which can provide more precise representations of the early reflections and late reverberations. Furthermore, we utilize the Gaussian noise model to deal with the BSS problem in noisy reverberant environments. We formulate the objective function using the maximum log-likelihood criterion, and derive an efficient iterative algorithm for parameter estimation with the block coordinate descent (BCD) method. Experimental results show that the proposed method has a better separation performance than the existing methods in long reverberation environments.

Research on Quantile Regression Method for Longitudinal Interval-Censored Data Based on Bayesian Double Penalty

The increasing prominence of the problem of censored data in various fields has made studying how to perform parameter estimation and variable selection in censored mixed-effects models one of the hotspots of current research. In this paper, considering the situation that the response variable is restricted by the bilateral limit, a double-penalty Bayesian Tobit quantile regression model was constructed to carry out parameter estimation and variable selection in the interval-censored mixed-effects model, and at the same time, the fixed-effects and random effects coefficients are compressed in Tobit’s mixed-effects model, so as to reduce the estimation error of the model at the same time as the variable selection of the model is carried out. The posterior distribution of each unknown parameter was derived using the conditional Laplace prior and the mixed truncated normal distribution of interval-censored data, and then the Gibbs sampling algorithm for unknown parameter estimation was constructed. Through Monte Carlo simulation, it was found that the new method is more advantageous than the classical method in terms of variable selection and parameter estimation accuracy in various situations, such as different model sparsity, different data censoring ratios and different random error distributions, and the model is able to realize automatic variable selection. Finally, the new method is used to analyze the correlation between the crime rate and various economic indicators in China.

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