Approximate Estimation Research Articles

A preventive maintenance policy and a method to approximate the failure process for multi-component systems

Numerous maintenance policies have been proposed in the reliability mathematics and engineering literature. Nevertheless, little has been reported on their practical applications in industries. This gap is largely due to restrictive assumptions of the maintenance policies. Two of the main assumptions are that maintenance is conducted on typical components and that the reliability of an item under maintenance is known (where the item can be a component or a system composed of multiple components). These assumptions do not often hold in the real world: maintenance is often performed on a collection of components such as an integrated circuit plate and the reliability of each individual component may not be known. To reduce these gaps, this paper develops a new maintenance policy for a collection of components and an approximate method to estimate the reliability of this collection based on the failure data collected from the field. The maintenance policy considers that a system is composed of three subsystems with different levels of maintenance effectiveness (i.e, minimal, imperfect, and perfect). The approximate estimate of the reliability of each subsystem is derived based on the failure data that are time between failures of the system but not those of the components that cause the system to fail. An algorithm for simulating the superposition of generalised renewal processes is then proposed. Numerical examples are used to illustrate the proposed approximation method.

Behaviour Analysis of Modeling and Model Evaluating Methods in System Identification for a Multiprocess Station

Systems are designed to perform specific task by giving certain input which produces the required output in an orderly manner known as process. The input, output, and the state variables should be known that will help in interacting with the system. The relation between these variables can be brought out by building a model that resembles or expresses the original performance of the system. The parameters of the model are estimated using the least squares approximation, maximum likelihood, maximum log-likelihood, and Bayesian parameter estimation methods by utilizing the experimental data from the multiprocess station. The selected parameters are converted to nine different transfer function models that represent the given dynamic system. The models framed are analyzed by the criterion curve technique using seven criterion functions evaluating the fitness of the model. Order of the model is found from Hankel matrix representation methods such as singular value decomposition and determinant method. Response of the models is compared with the original response to choose the best fit model by calculating ISE standard. All the above methods are used to model the system without physical and theoretical laws which is known as system identification.

Adaptive event‐triggered control and observer design for discrete‐time nonlinear Markov jump systems with DoS attacks using policy iteration‐based adaptive dynamic programming

AbstractThis article addresses adaptive event‐triggered discrete‐time nonlinear Markov jump systems (MJs) with DoS attacks, where the introduced DoS attacks are considered as more general stochastic models with fixed trigger frequency and duration. To solve the optimal control problem, we use an adaptive dynamic programming (ADP) algorithm based on policy iteration (PI). The approximate process is as follows: the performance index function (PIF) is first updated by the iteration policy in advance, and the control policy is obtained from the PIF. Subsequently, an approximate estimation of the optimal PIF and the optimal control policy is made using the actor‐critic structure obtained through neural network techniques. In order to reduce the occupied communication resources required for control policy iteration, we introduce an adaptive event triggering mechanism with an adaptive triggering threshold, which reduces the conservatism of resource occupation by the PIF compared to the fixed‐threshold ETM. In addition, an observer identifying the unknown dynamics part of the system is designed. Finally, using the Lyapunov function, it is shown that the designed control policy ensures the stability and convergence of the MJS, and the designed observer is effective. Simulation examples are given to verify the feasibility of the controller and the observer.

Calibration Estimation of Population Total in Two-Stage Sampling Design under unavailability of Population Level Auxiliary Information for the selected PSUs

Calibration approach is a popular technique in sample surveys which incorporates auxiliary information in the estimation process assuming that population aggregates of auxiliary variable are available. Many often under two-stage sampling design, such population aggregates of auxiliary variable, i.e., population mean or total are unavailable and under such situations, estimation of population total has been limited to the use of two phase sampling. Therefore, in the present study, efficient estimator of population total is developed under two-stage sampling design when population aggregates of auxiliary variable are unavailable for the selected psu’s. The calibrated estimator is developed using the information on known population aggregates of additional auxiliary variable which is less linearly related to the study variable through two step calibration approach. The approximate variance and variance estimator of the proposed calibrated estimator has also been developed. Empirical evaluations using both real and simulated data shows the superior performance of the developed calibrated estimator in comparison to the existing estimators.

Gradient preserving Operator Inference: Data-driven reduced-order models for equations with gradient structure

Hamiltonian Operator Inference has been introduced in Sharma et al. (2022) to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. This approach constructs a low-dimensional model using only data and knowledge of the Hamiltonian function. Such ROMs can keep the intrinsic structure of the system, allowing them to capture the physics described by the governing equations. In this work, we extend this approach to more general systems that are either conservative or dissipative in energy, and which possess a gradient structure. We derive the optimization problems for inferring structure-preserving ROMs that preserve the gradient structure. We further derive an a priori error estimate for the reduced-order approximation. To test the algorithms, we consider semi-discretized partial differential equations with gradient structure, such as the parameterized wave and Korteweg–de-Vries equations, and equations of three-dimensional linear elasticity in the conservative case and the one- and two-dimensional Allen-Cahn equations in the dissipative case. The numerical results illustrate the accuracy, structure-preservation properties, and predictive capabilities of the gradient-preserving Operator Inference ROMs.

Optimal error estimates for non-conforming approximations of linear parabolic problems with minimal regularity

Optimal error estimates for non-conforming approximations of linear parabolic problems with minimal regularity

MAGNETIC CONTROL SYSTEM WITH TWO-COMPONENT VIBRATION-INDUCTION MAGNETIC FIELD TRANSDUCER

The features of identifying and evaluating the parameters of surface cracks by the amplitude and phase change of the spectral components of the signals of a magnetic control system with a two-component vibration-induction primary transducer (VIT) are considered. The structure of the magnetic control system and the device of a two-component VIT are given. Spectral diagnostic signs of the signal of measuring information on the normal and tangential control channels during the movement of the VIT over the crack are determined. Estimates of the threshold sensitivity to small cracks, the depth of occurrence of subsurface cracks, and the range of variation of the working gap are given. It is shown that it is possible to obtain approximate estimates of the depth and width of a rectangular surface crack by the lowering gradient method based on statistically constructed regression dependences of depth and width on the amplitude values of the main significant harmonics of the normal and tangential control channels.

Unsupervised Characterization of Prediction Error Markers in Unisensory and Multisensory Streams Reveal the Spatiotemporal Hierarchy of Cortical Information Processing.

Elicited upon violation of regularity in stimulus presentation, mismatch negativity (MMN) reflects the brain's ability to perform automatic comparisons between consecutive stimuli and provides an electrophysiological index of sensory error detection whereas P300 is associated with cognitive processes such as updating of the working memory. To date, there has been extensive research on the roles of MMN and P300 individually, because of their potential to be used as clinical markers of consciousness and attention, respectively. Here, we intend to explore with an unsupervised and rigorous source estimation approach, the underlying cortical generators of MMN and P300, in the context of prediction error propagation along the hierarchies of brain information processing in healthy human participants. The existing methods of characterizing the two ERPs involve only approximate estimations of their amplitudes and latencies based on specific sensors of interest. Our objective is twofold: first, we introduce a novel data-driven unsupervised approach to compute latencies and amplitude of ERP components accurately on an individual-subject basis and reconfirm earlier findings. Second, we demonstrate that in multisensory environments, MMN generators seem to reflect a significant overlap of "modality-specific" and "modality-independent" information processing while P300 generators mark a shift toward completely "modality-independent" processing. Advancing earlier understanding that multisensory contexts speed up early sensory processing, our study reveals that temporal facilitation extends to even the later components of prediction error processing, using EEG experiments. Such knowledge can be of value to clinical research for characterizing the key developmental stages of lifespan aging, schizophrenia, and depression.

A Comparative Analysis of Discrete Entropy Estimators for Large-Alphabet Problems.

This paper presents a comparative study of entropy estimation in a large-alphabet regime. A variety of entropy estimators have been proposed over the years, where each estimator is designed for a different setup with its own strengths and caveats. As a consequence, no estimator is known to be universally better than the others. This work addresses this gap by comparing twenty-one entropy estimators in the studied regime, starting with the simplest plug-in estimator and leading up to the most recent neural network-based and polynomial approximate estimators. Our findings show that the estimators' performance highly depends on the underlying distribution. Specifically, we distinguish between three types of distributions, ranging from uniform to degenerate distributions. For each class of distribution, we recommend the most suitable estimator. Further, we propose a sample-dependent approach, which again considers three classes of distribution, and report the top-performing estimators in each class. This approach provides a data-dependent framework for choosing the desired estimator in practical setups.

Enhanced Laplace approximation

The Laplace approximation has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators derived from the Laplace approximation are often biased for binary or temporally and/or spatially correlated data. Additionally, the corresponding Hessian matrix tends to underestimates the standard errors of these approximate maximum likelihood estimators. While higher-order approximations have been suggested, they are not applicable to complex models, such as correlated random effects models, and fail to provide consistent variance estimators. In this paper, we propose an enhanced Laplace approximation that provides the true maximum likelihood estimator and its consistent variance estimator. We study its relationship with the variational Bayes method. We also define a new restricted maximum likelihood estimator for estimating dispersion parameters and study their asymptotic properties. Enhanced Laplace approximation generally demonstrates how to obtain the true restricted maximum likelihood estimators and their variance estimators. Our numerical studies indicate that the enhanced Laplace approximation provides a satisfactory maximum likelihood estimator and restricted maximum likelihood estimator, as well as their variance estimators in the frequentist perspective. The maximum likelihood estimator and restricted maximum likelihood estimator can be also interpreted as the posterior mode and marginal posterior mode under flat priors, respectively. Furthermore, we present some comparisons with Bayesian procedures under different priors.

Russian Scientific Diaspora in Germany in 1990s-2010s: Formation Paths and Development Features

This article examines the process of formation and transformations of the Russian scientific diaspora in Germany in the 1990s-2010s. It raises questions about the reasons and paths of creating a large community of scientific workers and researchers who moved from Russia to Germany. An approximate estimate of the number of members of the group under study at the turn of the XX-XXI centuries is provided. Special attention is paid to the analysis of forms and types of association among Russian compatriot scientists in Germany. Sources include data from Russian and German state statistical agencies, documents from the German Academic Exchange Service, a transcript of the German government’s report to the Bundestag, and others. An overview of the tools used by the German authorities to attract scientific personnel from Russia in the 1990s-2010s is conducted. The policy of Russian authorities regarding interaction with the scientific diaspora during the period under review is analyzed. It is shown how Moscow increased contacts with the scientific diaspora in Germany in the early 2010s amid intensified competition for highly qualified personnel. It is noted that although these initiatives contributed to the development of new formats of cooperation between scientists of Russian origin in Germany and Russian scientific institutions, they were later suspended and did not lead to a systemic activation of interaction.

Generalized Yang Chizhong filtering and interpolation method without stationarity assumption

The stationarity assumption of geostatistical methods is difficult to satisfy in practice. To overcome this limitation, this study proposed a geometric and statistical coupling strategy for modeling spatial dependence structures and developed a generalized Yang Chizhong filtering and interpolation (GYangCZ) method without the assumption of stationarity. In this work, we theoretically prove the effectiveness of Yang Chizhong filtering in fitting spatial dependence structures from a geometric perspective, and develop an orientation-constrained Yang Chizhong filtering to fit the local and discontinuous spatial dependence structures. To measure nonstationary spatial dependence structure, we define a local statistical indicator (i.e., fundamental variation function) by comparing the variance of the original data and the fitted geometric surfaces obtained under different filtering radii. The fundamental variation function is used as the kernel function to obtain the approximate best linear unbiased estimators at unobserved locations. We theoretically demonstrate that when only a linear drift exists in local areas, GYangCZ does not require the stationarity assumption. GYangCZ was used to estimate the gold grade of the Xiadian gold deposit in China. The results show that GYangCZ outperformed ordinary kriging, moving window kriging, and kriging convolution networks. GYangCZ is easy to implement with wide applications in geoscience.

Iterative‐recursive estimation of parameters of regression models with resistance to outliers on practical examples

AbstractHere, identification of processes and systems in the sense of the least sum of absolute values is taken into consideration. The respective absolute value estimators are recognised as exceptionally insensitive to large measurement faults or other defects in the processed data, whereas the classical least squares procedure appears to be completely impractical for processing the data contaminated with such parasitic distortions. Since the absolute value quality index cannot be minimised analytically, an iterative solution is used to find optimal estimates of the parameters of the underlying regression model. In addition, an approximate recursive estimator is proposed and implemented for on‐line evaluation of system parameters. The convergence (basic property) of the iterative estimator is show to be proven and some aspects related to the absolute value criterion are explained. This allows for the formulation of practical conclusions and indication of directions for further research. In addition, the effectiveness of the described iterative‐recursive estimation procedures is practically verified by appropriate numerical experiments.

Exact selective inference with randomization

Summary We introduce a pivot for exact selective inference with randomization. Not only does our pivot lead to exact inference in Gaussian regression models, but it is also available in closed form. We reduce this problem to inference for a bivariate truncated Gaussian variable. By doing so, we give up some power that is achieved with approximate maximum likelihood estimation in Panigrahi & Taylor (2023). Yet our pivot always produces narrower confidence intervals than a closely related data-splitting procedure. We investigate the trade-off between power and exact selective inference on simulated datasets and an HIV drug resistance dataset.

An Estimate of Approximation of an Analytic Function of Two Matrices by a Polynomial

An Estimate of Approximation of an Analytic Function of Two Matrices by a Polynomial

Hybrid unadjusted Langevin methods for high-dimensional latent variable models

The exact estimation of latent variable models with big data is known to be challenging. The latents have to be integrated out numerically, and the dimension of the latent variables increases with the sample size. This paper develops a novel approximate Bayesian method based on the Langevin diffusion process. The method employs the Fisher identity to integrate out the latent variables, which makes it accurate and computationally feasible when applied to big data. In contrast to other approximate estimation methods, it does not require the choice of a parametric distribution for the unknowns, which often leads to inaccuracies. In an empirical discrete choice example with a million observations, the proposed method accurately estimates the posterior choice probabilities using only 2% of the computation time of exact MCMC.

THE INFLUENCE OF DIGITAL MARKETING AND PRODUCT ATTRIBUTES ON BRAND IMAGE AND THEIR IMPACT ON THE PURCHASE DECISION OF MOTOR VEHICLE INSURANCE PRODUCTS IN SERANG CITY

Consumer purchasing decisions become an important factor in determining the existence of a company. Departing from the increase in numbers, and with various risks of accidents that will make the competition of insurance companies even higher. The purpose of this study is to analyze the factors that influence purchasing decisions for motor vehicle insurance products. The method used in this study uses the SEM (Structural Equation Modeling) method. The data analysis technique uses variance-based structural equation modeling (VB-SEM) through Smart PLS 3 (Partial Least Square) programs and activities. The sampling technique used was purposive sampling. The number of samples can be determined by approximate estimates according to Haire's opinion, so that based on the calculation of the number of samples to be taken as many as 140 people who have motorized vehicles in Serang City. The data sources in this study used primary data in the form of surveys with questionnaire instruments and secondary data sources in the form of documentation studies with observation sheet instruments. The results of the outer model test show that all indicators used are valid because they have a loading factor value > 0.70. The conclusion from the results of hypothesis testing is that 4 hypotheses are accepted and 3 hypotheses are rejected.

Evaluation of the thermal regime of the cathode operation of a high-voltage glow discharge electron gun, which forms a ribbon electron beam

The article discusses the various methods of estimating the surface cathode temperature of the high-voltage glow discharge electron gun, which forms a ribbon electron beam with a linear focus. Numerical estimations have been made to design the cathode assembly of an industrial gun. It is shown that the most effective way to make approximate estimates of the temperature of the cathode surface in high-voltage glow discharge electron guns for various technological purposes is to use arithmetic-logical ratios for modeling the geometry of the cathode assembly and locus functions for estimating the temperature distribution. The accuracy of such estimates, made using the heat balance equation, was 5–10%, sufficient at the initial stage of designing an electron gun. It is shown that using the SolidWorks CAD software complex for designing high-voltage glow discharge electron guns is effective only for solving the complex engineering design tasks and preparing the corresponding technical documentation. The results of the theoretical research published in the article are of interest to a wide range of specialists engaged in developing electron beam equipment and its implementation in industrial production.

On the Use of Inverse Exponentiation to Improve the Efficiency of Calibration Estimators in Stratified Double Sampling

This study introduces the concept of inverse exponentiation in formulating calibration weights in stratified double sampling and proposes a more improved calibration estimator based on Koyuncu and Kadilar (2014) calibration estimator. The variance of the proposed logarithmic calibration estimator has been derived under large sample approximation. Calibration asymptotic optimum estimator and its approximate variance estimator are derived for the proposed logarithmic calibration estimator. Results of empirical study showed that the proposed logarithmic calibration estimator performs better than the Koyuncu and Kadilar (2014) calibration estimator with appreciable gains in efficiency. Also, simulation study for the comparison of the proposed logarithmic estimator with a Global estimator [Generalized Regression (GREG) estimator ] proved the robustness of the proposed logarithmic calibration estimator and by extension the efficacy of inverse exponentiation in calibration weightings. Analysis and evaluation are presented. International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 91-102

Error estimates for finite element approximations of viscoelastic dynamics: The generalized Maxwell model

We prove error estimates for a finite element approximation of viscoelastic dynamics based on continuous Galerkin in space and time, both in energy norm and in L2 norm. The proof is based on an error representation formula using a discrete dual problem and a stability estimate involving the kinetic, elastic, and viscoelastic energies. To set up the dual error analysis and to prove the basic stability estimates, it is natural to formulate the problem as a first-order-in-time system involving evolution equations for the viscoelastic stress, the displacements, and the velocities. The equations for the viscoelastic stress can, however, be solved analytically in terms of the deviatoric strain velocity, and therefore, the viscoelastic stress can be eliminated from the system, resulting in a system for displacements and velocities.