Sequential Sampling Scheme Research Articles

A deep-learning-based surrogate modeling method with application to plasma processing

Rapid and accurate system evolution predictions are crucial in scientific and engineering research. However, the complexity of processing systems, involving multiple physical field couplings and slow convergence of iterative numerical algorithms, leads to low computational efficiency. Hence, this paper introduces a systematic deep-learning-based surrogate modeling methodology for multi-physics-coupled process systems with limited data and long-range time evolution, accurately predicting physics dynamics and considerably improving computational efficiency and generalization. The methodology comprises three main components: (1) generating datasets using a sequential sampling strategy, (2) modeling multi-physics spatio-temporal dynamics by designing a heterogeneous Convolutional Autoencoder and Recurrent Neural Network, and (3) training high-precision models with limited data and long-range time evolution via a dual-phase training strategy. A holistic evaluation using a 2D low-temperature plasma processing example demonstrates the methodology’s superior computational efficiency, accuracy, and generalization capabilities. It predicts plasma dynamics approximately 105 times faster than traditional numerical solvers, with a consistent 2% relative error across different generalization tasks. Furthermore, the potential for transferability across various geometries is explored, and the model’s transfer capability is demonstrated with two distinct geometric domain examples.

Applying sequential adaptive strategies for sampling animal populations: An empirical study

AbstractTraditional sampling methods may prove inadequate when dealing with spatially clustered populations or when studying rare events or traits that are not easily detectable across the target population. When both scenarios occur simultaneously, adaptive sampling strategies can represent a viable option to enhance the detectability of cases of interest. This paper delves into the application of a novel class of sequential adaptive sampling strategies to animal surveys. These strategies, originally proposed for human population tuberculosis prevalence surveys, allow oversampling of the rare interest variables while managing on‐field constraints. This ensures that the unfixed sample size, typical of adaptive sampling, does not compromise overall cost‐effectiveness. We explore a strategy within this class that integrates an adaptive component into a Poisson sequential selection. The aim is twofold: to intensify the detection of cases by exploiting the spatial clustering and to provide a flexible framework for managing logistics and budget constraints. To illustrate the strengths and weaknesses of this Poisson‐based sequential adaptive sampling strategy compared to traditional sampling methods, a simulation study was conducted on a blue‐winged teal population in Florida, USA. The results showcase the benefits of the proposed strategy and open avenues for future methodological and practical improvements.

Life-history of Palaeoloxodon antiquus reveals Middle Pleistocene glacial refugium in the Megalopolis basin, Greece

The Balkans are considered a major glacial refugium where flora and fauna survived glacial periods and repopulated the rest of Europe during interglacials. While it is also thought to have harboured Pleistocene human populations, evidence linking human activity, paleoenvironmental indicators and a secure temporal placement to glacial periods is scant. Here, we present the first intra-tooth multi-isotope analysis for the European straight-tusked elephant Palaeoloxodon antiquus, on an adult male individual excavated in association with lithic artefacts at the MIS 12 site Marathousa 1 (Megalopolis basin, Greece). The studied find also exhibits anthropogenic modifications, providing direct evidence of hominin presence. We employed strontium, carbon and oxygen isotope analysis on enamel bioapatite to investigate its foraging and mobility behaviour, using a sequential sampling strategy along the tooth growth axis of the third upper molar, to assess ecological changes during the last decade of life. We found a geographically restricted range, in a C3-dominated open woodland environment, and relatively stable conditions over the examined timeframe. Our results show that, despite the severity of the MIS 12 glacial, the Megalopolis basin sustained a mesic habitat, sufficient plant cover and limited seasonal fluctuations in resource availability, pointing to its role as a glacial refugium for both fauna and hominins.

Investigating adaptive sampling strategies for optimal building energy performance using artificial neural networks and kriging surrogate models

Recent studies highlight surrogate models as efficient alternatives to energy simulation tools, reducing computational burden. However, accurate metamodels often require extensive evaluations, leading to high computational costs. Adaptive sampling approaches offer a promising solution by constructing accurate surrogate models at a lower computational expense compared to static sampling. The selection of an appropriate adaptive sampling criterion is crucial in sequential sampling strategies, as it determines how new sample points are chosen based on previous iterations. However, concerns remain regarding the impact of the sampling infill criterion on surrogate model accuracy. Additionally, a lack of studies exists comparing artificial neural networks (ANN) and Kriging models in terms of potential computational improvements through sequential sampling. This study aims to explore the potential of adaptive sampling strategies to estimate optimal building energy consumption within a reasonable computational budget, thus reducing the number of energy simulation model runs required. Furthermore, a comprehensive comparison between sequential sampling techniques employing ANN-based and Kriging-based surrogate models is conducted. Four different sampling criteria are evaluated to understand the relationship between sampling strategies and accuracy. The findings contribute to a more efficient resolution of building optimization problems. The results indicate that the choice of a sampling strategy depends on the model's requirements and the specific problem. Each strategy has distinct strengths and weaknesses, necessitating careful consideration of the model's needs. Selecting the appropriate sampling strategy improves model accuracy and reduces training time. Adaptive sampling methods yield significant improvements, saving 25 %–68 % of simulation samples compared to static approaches.

Estimation of fixed-accuracy confidence interval of the stress–strength reliability for inverse Pareto distribution using two-stage sampling technique

In recent years, several probability distributions have been introduced in the literature to analyze the data exhibiting an upside-down bathtub–shaped failure rate; an inverse Pareto distribution (IPD) is an appropriate choice among them. For stress–strength reliability models, estimation of parameters is an interesting area of research. In this article, we estimate the stress–strength reliability parameter R = P ( X > Y ) (where X and Y are strength and stress variables, respectively) of the IPD, whereby we focus on the problem of fixed-accuracy confidence interval estimation of R. It is established that the proposed interval estimation problem cannot be solved with the help of any fixed sample technique. As a result, we propose a two-stage sequential sampling strategy (which reduces the sample size significantly) to solve the given estimation problem. We obtain the expressions of several exact operating characteristics associated with our two-stage sampling technique. We also establish that the proposed two-stage procedure enjoys interesting first-order asymptotic properties. The detailed simulation analyses support our theoretical findings, and two real data sets based on insurance claims reinforce the practical utility of the proposed technique.

Load-independent multi-objective sensor placement method for localization and reconstruction of external excitations under interval uncertainties

The direct measurement of external excitations under operation conditions remains challenging in many engineering applications. This study proposes a method of optimal sensor placement for the best localization and reconstruction of external excitations when considering multi-source uncertainties. The excitation inversion is achieved in the framework of minimizing the discrepancy between the forward and inversed modal loads. To accurately obtain the modal force in the time-domain excitation reconstruction algorithm, three combined indicators of the interested modal matrix are defined, which integrate measures of effectiveness, stability, orthogonality, and robustness of inverse modal transformation. The optimal sensor placement is determined by multi-objective particle swarm optimization and Pareto optimal solution. In addition, to alleviate the computational burden of loading localization, a surrogate model based on an interval kriging interpolation model and sequential sampling strategies is established for the forward modal forces. And a time-dependent interval error of modal forces inspired by the theory of second-order narrow bounds in system reliability is developed to guide the inversion process. Notably, the developed sensor selection and excitation inversion methods are independent of the type, location, and time evolution of external excitations. Eventually, two numerical examples and an experimental case are discussed to demonstrate the validity and feasibility of the developed approach.

A PC-kriging-HDMR Integrated with an Adaptive Sequential Sampling Strategy for High-Dimensional Approximate Modeling

A PC-kriging-HDMR Integrated with an Adaptive Sequential Sampling Strategy for High-Dimensional Approximate Modeling

An optimal sequential design in ethical allocation with an adaptive interim analysis

The present article provides a distribution-free test procedure for comparing the effectiveness of two competing treatments A and B, say, in a clinical trial. Here, the relative treatment effect is measured by the functional θ = P ( X < Y ) , where X and Y are respectively the response variables corresponding to two treatments, A and B. The treatment comparison is done through a testing of hypothesis regarding θ under a patient-benefit oriented two-stage response-adaptive design with an interim analysis in which an optimal sequential sampling scheme with equal randomisation is adopted in stage 1 and a response-adaptive randomisation is employed in stage 2 with the objective of allocating more patients to more promising treatment. The performance of the proposed procedure is compared with that of various other competitive procedures.

Sequential adaptive strategies for sampling rare clustered populations

A new class of sampling strategies is proposed that can be applied to population-based surveys targeting a rare trait that is unevenly spread over an area of interest. Our proposal is characterised by the ability to tailor the data collection to specific features and challenges of the survey at hand. It is based on integrating an adaptive component into a sequential selection, which aims both to intensify the detection of positive cases, upon exploiting the spatial clustering, and to provide a flexible framework to manage logistics and budget constraints. A class of estimators is also proposed to account for the selection bias, that are proved unbiased for the population mean (prevalence) as well as consistent and asymptotically Normal distributed. Unbiased variance estimation is also provided. A ready-to-implement weighting system is developed for estimation purposes. Two special strategies included in the proposed class are presented, that are based on the Poisson sampling and proved more efficient. The selection of primary sampling units is also illustrated for tuberculosis prevalence surveys, which are recommended in many countries and supported by the World Health Organisation as an emblematic example of the need for an improved sampling design. Simulation results are given in the tuberculosis application to illustrate the strengths and weaknesses of the proposed sequential adaptive sampling strategies with respect to traditional cross-sectional non-informative sampling as currently suggested by World Health Organisation guidelines.

A novel sparse polynomial chaos expansion technique with high adaptiveness for surrogate modelling

In this paper, a novel adaptive modelling framework for sparse polynomial chaos expansion is proposed, which can automatically determine adequate truncation degree and training sample set simultaneously. Moreover, the curse of dimensionality issue in polynomial chaos expansion, which generally arises in dealing with high input dimension or large truncation degree, can be alleviated to a large extent. In this framework, a new basis selection strategy, which leverages basis expansion, pruning and refinement, is pursued to adaptively select the polynomial terms of proper degree during the modelling process. Besides, an outstanding sequential sampling strategy is adopted to collect samples of high quality and in relatively small quantity for training polynomial chaos expansion model, and a sparse representation method, Bayesian compressive sensing, is employed for regression calculation. To reconcile the sequential sampling and adaptive basis selection in a consistent framework, a stability evaluation process which works in parallel with the sequential sampling process is performed. The performance of the proposed adaptive modelling framework is evaluated on two benchmark functions and a physical model through comparison with an existing adaptive polynomial chaos expansion modelling technique, a sequential sampling-only approach, and several basis adaptivity strategies. Results demonstrate that the proposed method has high adaptiveness in building surrogate models for various problems. It outperforms the existing adaptive polynomial chaos expansion modelling technique in terms of modelling precision and convergence rate, and it has similar performance with the sequential sampling-only method while lessening the burden in regression calculation and enabling adaptive determination of the truncation degree. Limitations of the proposed method are also summarized after comparing it with various basis adaptivity strategies.

Online Monitoring of Test‐Taking Behavior Based on Item Responses and Response Times

AbstractThe study presents multivariate sequential monitoring procedures for examining test‐taking behaviors online. The procedures monitor examinee's responses and response times and signal aberrancy as soon as significant change is identifieddetected in the test‐taking behavior. The study in particular proposes three schemes to track different indicators of a test‐taking mode—the observable manifest variables, latent trait variables, and measurement likelihood. For each procedure, sequential sampling strategies are presented to implement online monitoring. Numerical experimentation based on simulated data suggests that the proposed procedures demonstrate adequate performance. The procedures identified examinees with aberrant behaviors with high detection power and timeliness, while maintaining error rates reasonably small. Experimental application to real data also suggested that the procedures have practical relevance to real assessments. Based on the observations from the experiential analysis, the study discusses implications and guidelines for practical use.

AN ENHANCED FRAMEWORK FOR MORRIS BY COMBINING WITH A SEQUENTIAL SAMPLING STRATEGY

The Morris method is an effective sample-based sensitivity analysis technique that has been applied in various disciplines. To ensure a more proper coverage of the input space and better performance, an enhanced framework for Morris is proposed by considering the combination of a sequential sampling strategy and the traditional Morris method. The paper introduces utilizing progressive Latin hypercube sampling to generate starting points while progressively preserving Latin hypercube property. Then the calculations for Elementary Effects, which occupies the major computational cost of Morris, become sequential. An adaptive stop criterion is also constructed to end the algorithm when the convergence condition is satisfied. Therefore, the proposed procedure makes the cost of Morris more manageable and minimizes the computational burden by conducting only model runs that are necessary to achieve reliable results. Two numerical examples and two real-world cases are given to illustrate the effectiveness and robustness of the framework.

An Adaptive and Scalable Multi-Object Tracker Based on the Non-Homogeneous Poisson Process

This paper proposes a new adaptive framework for tracking multiple objects in the presence of data association uncertainty and heavy clutter, either with or without knowledge of the measurement rates and/or target shapes. Built upon an online Gibbs sequential Markov chain Monte Carlo sampling scheme, the adaptive tracker is Bayesian optimal and robust, requiring no additional approximations or measurement partition steps. With a non-homogeneous Poisson process measurement model, our tracker can tackle the data association task with linear computational complexity. Meanwhile, we study generalised inverse Gaussian and inverse Wishart distributions for modelling Poisson rates and object shapes, respectively; these prior models ensure closed-form full conditionals in our online Gibbs sampling steps, under which object states and shapes can be jointly estimated with associations and Poisson rates in a parallel fashion. Furthermore, a fast Rao-Blackwellisation scheme for linear Gaussian dynamics is designed and demonstrated to significantly improve both tracking efficiency and accuracy. We validate the efficacy of our method on real and simulated data.

Diagnostic Accuracy of Sonosalpingography for Assessing Tubal Patency in Women with Infertility Taking Laparoscopy as the Gold Standard

Objective: To evaluate the diagnostic validity of Sonosalphingography as a tubal patency test in infertile women using laparoscopy as gold standard. Methodology: This study was carried out at the Shifa International Hospital Islamabad, and the duration of this study was from January 2021 to June 2021. We used the WHO method for sample size by taking the prevalence of tuboperitoneal factors as 30%, sensitivity 72.9%, specificity 81.22%, margin of error 12%, and 95% confidence interval. It was a cross-sectional study that lasted for 6 months and assessed a total of 178 patients. Additionally, a non-probability, sequential sampling strategy was utilized to acquire the sample. Results: Our patients aged between 18-45 years, out of which 30% of the participants aged 18 to 25 years, 55% were between 26 and 35 years, and 15% were between 36 and 45 years. Standard deviation was 1.26, with a mean age of 27. The data collected from both the diagnostic tests was analyzed, diagnostic accuracy of Sonosalphingography was calculated as a sensitivity of 81%, specificity of 76%, positive predictive value of 90%, negative predictive value of 60%, and diagnostic accuracy of 79%. Conclusion: According to the results of our study, Sonosalphingography is a very helpful supplemental diagnostic tool for evaluating tubal disease in patients with infertility, though direct laparoscopic assessment is the gold standard. Sonosalphingography and laparoscopy can be used to evaluate patients with secondary infertility. This spares the patient from being exposed to radiations and the discomfort of contrast administration in HSG. Keywords: Diagnostic Accuracy, Sonosalphingography, Tubal Patency, Infertility, Laparoscopy

IE-AK: A novel adaptive sampling strategy based on information entropy for Kriging in metamodel-based reliability analysis

This article focuses on the adaptive Kriging metamodel-based reliability analysis for reducing a sequential number of calls of the complex original functions. To avoid the repetitive and tedious deterministic response analysis with stochastic simulation method (including Monte Carlo Simulation and its various improvement, such as importance sampling, subset simulation) in reliability analysis, herein a novel sequential sampling strategy related to Kriging metamodel is proposed, which is implemented based on information entropy theory. In addition, the generalized F-discrepancy method is simultaneously quoted to further optimize the candidate pool to improve the effectiveness of the training metamodel. Finally, a new structural reliability analysis method is proposed, which continuously reduces the number of deterministic analysis of structures without sacrificing accuracy. To highlight the applicability of the method and verify its accuracy and effectiveness, a series of typical examples are tested and compared, including highly nonlinear limit state functions, high-dimension performance function with analytic expressions and dynamic reliability analysis of nonlinear engineering structures subject to seismic excitation with implicit performance function. Numerical results show that significant computational savings and desired accuracy can be achieved when dealing with different reliability analysis cases.

Diagnostic Accuracy of Sonosalpingography for Assessing Tubal Patency in Women with Infertility Taking Laparoscopy as Gold Standard

Background: Infertility is defined as the failure to conceive after 1 year of unprotected sexual intercourse in women less than 35 years of age and 6 months in women older than 35 years [1, 2]. It affects 10 to 15 % of the couples [1]. Abnormalities of fallopian tubes account for 35 to 40 % of the cases of infertility [3]. Sonosalpingography is a non-invasive, safe and cost- effective diagnostic technique which provides reliable diagnosis of tubal patency [4]. Objective: To evaluate the diagnostic validity of Sonosalpingography as a tubal patency test in infertile women using laparoscopy as gold standard. Methodology: This study was carried out at the Radiology Departments of Khyber Teaching Hospital and Kuwait Teaching Hospital in Peshawar. We used the WHO method for sample size by taking the prevalence of tuboperitoneal factors as 30%, sensitivity 72.9%, specificity 81.22%, margin of error 12%, and 95% confidence interval. It was a cross-sectional study that lasted for 6 months and assessed a total of 178 patients. Additionally, a non-probability, sequential sampling strategy was utilized to acquire the sample. Results: Our patients aged between 18-45 years, out of which 30% of the participants aged 18 to 25years, 55% were between 26 and 35years, and 15% were between 36 and 45years. Standard deviation was 1.26, with a mean age of 27. The data collected from both the diagnostic tests was analyzed, diagnostic accuracy of Sonosalpingography was calculated as a sensitivity of 81%, specificity of 76%, positive predictive value of 90%, negative predictive value of 60%, and diagnostic accuracy of 79%. Conclusion: According to the results of our study, sonosalpingography is a very helpful supplemental diagnostic tool for evaluating tubal disease in patients with infertility, though direct laparoscopic assessment is the gold standard. Sonosalpingography and laparoscopy can be used to evaluate patients with secondary infertility. This spares the patient from being exposed to radiations and the discomfort of contrast administration in HSG. Keywords: Diagnostic Accuracy, Sonosalpingography, Tubal Patency, Infertility, Laparoscopy

A survey of sequential adaptive sampling strategy for transmission power loss measurement

Laboratory experiments for characterizing the power loss behavior in transmissions causes time and energy costs when performing the traditional factorial design strategy. This is because the space filling strategy may locate redundant samples with low information regarding the measurement targets. This article proposes a sequential adaptive sampling methodology for performing efficient and informative power loss measurements. The presented sampling methodology associates surrogate modeling based on a Gaussian Process approach with Subset Simulation. Gaussian Process Regression creates a statistical model with the estimation targets and the expression of uncertainty. Subset Simulation is applied to efficiently identify the regions where an objective function reaches a predefined critical threshold. The proposed adaptive sampling method is implemented for the real-time measurement of a 7-speed DCT on a drivetrain test bench. Compared to the traditional factorial design, the iterative adaption of the proposed method ensures an informative and effective measurement and an automatic termination with reduced time and energy cost.

A Sequential Sampling Approach for Multi-Fidelity Surrogate Modeling-Based Robust Design Optimization

Abstract Multi-fidelity surrogate modeling has been extensively used in engineering design to achieve a balance between computational efficiency and prediction accuracy. Sequential sampling strategies have been investigated to improve the computational efficiency of surrogate-assisted design optimization. The existing sequential sampling approaches, however, are dedicated to either deterministic multi-fidelity design optimization or robust design under uncertainty using single-fidelity models. This paper proposes a sequential sampling method for robust design optimization based on multi-fidelity modeling. The proposed method considers both design variable uncertainty and interpolation uncertainty during the sequential sampling. An extended upper confidence boundary (EUCB) function is developed to determine both the sampling locations and the fidelity levels of the sequential samples. In the EUCB function, the cost ratio between high- and low-fidelity models and the sampling density are considered. Moreover, the EUCB function is extended to handle constrained robust design optimization problems by combining the probability of feasibility. The performance of the proposed approach is verified using two analytical examples and an engineering case. Results show that the proposed sequential approach is more efficient than the one-shot sampling method for robust design optimization problems.

An Efficient Orthogonal Polynomial Method for Auxetic Structure Analysis with Epistemic Uncertainties

Traditional approaches used for analyzing the mechanical properties of auxetic structures are commonly based on deterministic techniques, where the effects of uncertainties are neglected. However, uncertainty is widely presented in auxetic structures, which may affect their mechanical properties greatly. The evidence theory has a strong ability to deal with uncertainties; thus, it is introduced for the modelling of epistemic uncertainties in auxetic structures. For the response analysis of a typical double-V negative Poisson’s ratio (NPR) structure with epistemic uncertainty, a new sequence-sampling-based arbitrary orthogonal polynomial (SS-AOP) expansion is proposed by introducing arbitrary orthogonal polynomial theory and the sequential sampling strategy. In SS-AOP, a sampling technique is developed to calculate the coefficient of AOP expansion. In particular, the candidate points for sampling are generated using the Gauss points associated with the optimal Gauss weight function for each evidence variable, and the sequential-sampling technique is introduced to select the sampling points from candidate points. By using the SS-AOP, the number of sampling points needed for establishing AOP expansion can be effectively reduced; thus, the efficiency of the AOP expansion method can be improved without sacrificing accuracy. The proposed SS-AOP is thoroughly investigated through comparison to the Gaussian quadrature-based AOP method, the Latin-hypercube-sampling-based AOP (LHS-AOP) method and the optimal Latin-hypercube-sampling-based AOP (OLHS-AOP) method.

Process Monitoring Using Kernel PCA and Kernel Density Estimation-Based SSGLR Method for Nonlinear Fault Detection

Fault monitoring is often employed for the secure functioning of industrial systems. To assess performance and enhance product quality, statistical process control (SPC) charts such as Shewhart, CUSUM, and EWMA statistics have historically been utilized. When implemented to multivariate procedures, unfortunately, such univariate control charts demonstrate low fault sensing ability. Due to some limitations of univariate charts, numerous process monitoring techniques dependent on multivariate statistical approaches such as principal component analysis (PCA) and partial least squares (PLS) have been designed. Yet, in some challenging scenarios in industrial chemical and biological processes with notably nonlinear properties, PCA works poorly, according to its presumption that the dataset generally be linear. However, Kernel Principal Component Analysis (KPCA) is a reliable and precise nonlinear process control methodology, but the interaction mainly through upper control limits (UCLs) dependent on the Gaussian distribution may weaken its output. This article introduces time-varying statistical error tracking through Kernel Principal Component Analysis (KPCA) based on Generalized Likelihood Ratio statistics (GLR) using a sequential sampling scheme named KPCA-SSGLR for nonlinear fault detection. The main issue of employing just T2 and Q statistic in KPCA is that they cannot correctly give practitioners the change point of the system fault, preventing practitioners from diagnosing the issue. Based on this perspective, this study attempts to incorporate KPCA with sequential sampling Generalized Likelihood Ratio (SSGLR) for monitoring the nonlinear fault in multivariate systems. The KPCA is utilized for dimension reduction, while the SSGLR is employed as a tracking statistic. The kernel density estimation (KDE) was employed to approximate UCLs for variational system operation relying on KPCA. The testing efficiency of the corresponding KPCA-KDE-SSGLR technique was then analyzed and competed with KPCA and kernel locality preserving projection (KLPP), the UCLs of which were focused on the Gaussian distribution. The purpose of this analysis is to enhance the development of KPCA-KDE-SSGLR to accomplish future enhancements and to advance the practical use of the established model by implementing the sequential sampling GLR approach. The fault monitoring efficiency is demonstrated through different simulation scenarios, one utilizing synthetic data, the other from the Tennessee Eastman technique, and lastly through a hot strip mill. The findings indicate the applicability of the KPCA-KDE-based SSGLR system over the KLPP and KPCA-KDE methods by its two T2 and Q charts to recognize the faults.