Sequential Sampling Scheme Research Articles

Sensitivity-based adaptive sequential sampling for metamodel uncertainty reduction in multilevel systems

Decomposition-based technique is often used in the analysis and design of complex engineering systems for reducing the computational complexity by studying the subsystems decomposed from multilevel systems. Metamodels, as a replacement of original simulation models, can further alleviate the computational burden. However, discrepancy between the simulation models and metamodels, which is defined as metamodel uncertainty, may be introduced in the analysis process of multilevel systems owing to the lack of data. The metamodel uncertainties of sub-models will be further amplified because of the hierarchical uncertainty propagation and interaction between uncertainties, which will have a great impact on the system results. An adaptive sequential sampling strategy based on sensitivity is proposed in this paper so as to improve the prediction accuracy of system response. In this strategy, polynomial-chaos expansion is used to realize the forward propagation of metamodel uncertainty quantified by the Kriging model. The forward propagation is combined with optimization based on maximum variance criterion for searching the input locations that results in the largest variance of system response. Then, the indices of subsystems are obtained to make decisions about which subsystem needs extra samples by combining Karhunen-Loeve expansion and sensitivity analysis. The effectiveness of the proposed sequential sampling strategy method is verified by two mathematical examples and a multiscale composite material.

Coarse-Grained Force Field Calibration Based on Multiobjective Bayesian Optimization to Simulate Water Diffusion in Poly-ε-caprolactone.

Molecular dynamics at the atomistic scale is increasingly being used to predict material properties and speed up the material design and development process. However, the accuracy of molecular dynamics predictions is sensitively dependent on the force fields. In the traditional force field calibration process, a specific property, predicted by the model, is compared with the experimental observation and the force field parameters are adjusted to minimize the difference. This leads to the issue that the calibrated force fields are not generic and robust enough to predict different properties. Here, a new calibration method based on multiobjective Bayesian optimization is developed to speed up the development of molecular dynamics force fields that are capable of predicting multiple properties accurately. This is achieved by reducing the number of simulation runs to generate the Pareto front with an efficient sequential sampling strategy. The methodology is demonstrated by generating a new coarse-grained force field for polycaprolactone, where the force field can predict the mechanical properties and water diffusion in the polymer.

A new sequential space-filling sampling strategy for elementary effects-based screening method

To predict or control the response of a complicated numerical model which involves a large number of input variables but is mainly affected by only a part of variables, it is necessary to screening those active variables. This paper proposes a new space-filling sampling strategy, which is used to screening the parameters based on the Morris’ elementary effect method. The beginning points of sampling trajectories are selected by using the maximin principle of Latin Hypercube Sampling method. The remaining points of trajectories are determined by using the one-factor-at-a-time design. Being different from other sampling strategies to determine the sequence of factors randomly in one-factor-at-a-time design, the proposed method formulates the sequence of factors by a deterministic algorithm, which sequentially maximizes the Euclidean distance among sampling trajectories. A new efficient algorithm is proposed to transform the distance maximization problem to a coordinate sorting problem, which saves computational cost much. After the elementary effects are computed using the sampling points, a detailed criterion is presented to select the active factors. Two mathematic examples and an engineering problem are used to validate the proposed sampling method, which demonstrates the priority in computational efficiency, space-filling performance, and screening efficiency.

Sequential tests of multiple hypotheses controlling false discovery and nondiscovery rates

We propose a general and flexible procedure for testing multiple hypotheses about sequential (or streaming) data that simultaneously controls both the false discovery rate (FDR) and false nondiscovery rate (FNR) under minimal assumptions about the data streams, which may differ in distribution and dimension and be dependent. All that is needed is a test statistic for each data stream that controls its conventional type I and II error probabilities, and no information or assumptions are required about the joint distribution of the statistics or data streams. The procedure can be used with sequential, group sequential, truncated, or other sampling schemes. The procedure is a natural extension of Benjamini and Hochberg’s (1995) widely used fixed sample size procedure to the domain of sequential data, with the added benefit of simultaneous FDR and FNR control that sequential sampling affords. We prove the procedure’s error control and give some tips for implementation in commonly encountered testing situations.

An enhanced nonparametric EWMA sign control chart using sequential mechanism.

Control charts play a significant role to monitor the performance of a process. Nonparametric control charts are helpful when the probability model of the process output is not known. In such cases, the sampling mechanism becomes very important for picking a suitable sample for process monitoring. This study proposes a nonparametric arcsine exponentially weighted moving average sign chart by using an efficient scheme, namely, sequential sampling scheme. The proposal intends to enhance the detection ability of the arcsine exponentially weighted moving average sign chart, particularly for the detection of small shifts. The performance of the proposal is assessed, and compared with its counterparts, by using some popular run length properties including average, median and standard deviation run lengths. The proposed chart shows efficient shift detection ability as compared to the other charts, considered in this study. A real-life application based on the smartphone accelerometer data-set, for the implementation of the proposed scheme, is also presented.

AKM2D: An adaptive framework for online sensing and anomaly quantification

In point-based sensing systems such as coordinate measuring machines and laser ultrasonics where complete sensing is impractical due to the high sensing time and cost, adaptive sensing through a systematic exploration is vital for online inspection and anomaly quantification. Most of the existing sequential sampling methodologies focus on reducing the overall fitting error for the entire sampling space. However, in many anomaly quantification applications, the main goal is to estimate sparse anomalous regions at pixel-level accurately. In this article, we develop a novel framework named Adaptive Kernelized Maximum-Minimum Distance to speed up the inspection and anomaly detection process through an intelligent sequential sampling scheme integrated with fast estimation and detection. The proposed method balances the sampling efforts between the space-filling sampling (exploration) and focused sampling near the anomalous region (exploitation). The proposed methodology is validated by conducting simulations and a case study of anomaly detection in composite sheets using a guided wave test.

A model-independent adaptive sequential sampling technique based on response nonlinearity estimation

Sequential adaptive sampling strategies attempt to efficiently and accurately generate surrogate model (SM) training datasets by limiting the number of required function evaluations. Among these techniques, those that are model independent have attracted attention during the last decade because they do not use a global SM to supervise the sampling process, thereby relieving the user from the burden of selecting an appropriate SM formulation at the beginning of the sampling process. In this study, we propose a new model-independent sequential adaptive sampling technique called nearest neighbors adaptive sampling (NNAS). The NNAS formulation introduces a refinement metric based on local linear models that leads to a quasilinear dependency of the algorithm complexity with respect to the number of samples. Additionally, the exploration-refinement balance is achieved by a stochastic Pareto-ranking-based selection criterion that attempts to simultaneously maximize both the exploration and refinement. NNAS is tested on ten two-dimensional and one ten-dimensional analytic functions, a five-dimensional engineering test case based on the XRotor solver (Drela and Youngren 2014), and a two-response two-dimensional analytic problem. The results show that NNAS is more computationally efficient than comparable methods without causing a relevant increase in sample requirement.

Performance assessment of a cross-validation sampling strategy with active surrogate model selection

Surrogate Models (SM) are now regarded as powerful tools for engineering design applications; they approximate expensive responses obtained by either a computer simulation or a real experiment with more computationally efficient mathematical models. The goal of reducing the number of function evaluations required to create the training dataset led to the development of strategies capable of effectively sampling the design space. In particular, sequential adaptive techniques seem to be the most promising approaches for engineering design applications. Unfortunately, most of these techniques supervise the sampling phase with an SM created from the available training set, making their behavior dependent on the chosen SM formulation. This characteristic can cause sampling performance deterioration, in particular when an inaccurate SM formulation is used to supervise the sampling process. The solution proposed in this paper tries to mitigate this problem by coupling the model-dependent sequential adaptive technique with an active SM selection approach. This surrogate modeling architecture is tested on several example functions, and results indicate that it inherits the advantages of both constituent elements: an increased flexibility due to the active SM selection and a reduced total number of samples due to the sequential adaptive sampling strategy. Other parameters which may affect the sampling performance (such as the SM selection frequency and criterion) are also analyzed in an attempt to define general guidelines for the application of the method. The sampling technique considered in this study is based on cross-validation variance, and the surrogate modeling performance is assessed on nine two-dimensional and two five-dimensional test functions.

Density-invariant dispersion indices and fixed precision sequential sampling plans for the peach twig borer Anarsia lineatella (Lepidoptera: Gelechiidae)

Estimating the spatial dispersion of pest arthropods is crucial for the development of reliable sampling programs and one of the main components of integrated pest management. The natural spatial distribution of a population of a species may be random, uniform, or aggregated and can be so classified based on calculation of variance to mean relations and related dispersion indices. In this work some classical density-invariant dispersion indices and related regression models are used for the first time to quantify the spatial dispersion of an important peach pest Anarsia lineatella Zeller (Lepidoptera: Gelechiidae) and construct fixed precision sequential sampling schemes. Taylor's power law, Iwao's patchiness regression and Nachman's model were used to analyse the damage to peaches caused by A. lineatella. All three regression models fit the data well, although the results indicate that Iwao's patchiness model provides a better description of the relationship between variance and mean density. Taylor's b and Iwao's b regression indices were both significantly smaller than 1, indicating that the distribution of individuals was uniform rather than random or aggregated. According to Green's and Kuno's models, the minimum sample size at the precision level of 0.2 varies from 3 samples, when total population density is more than 3 larvae/sample, to 10 samples, when population density is between 1 and 2 larvae/sample. Kuno's fixed sampling plan indicates that a small number of samples (i.e., 3-10 branches with fruit) is sufficient to estimate the mean population density of A. lineatella larvae with a precision of 0.2. The Resampling for validation of sampling plans (RVSP) method confirmed that the average level of precision of the fixed sequential plans matched the desired precision in most cases. The sampling plan presented here provides a level understanding of A. lineatella spatial ecology suitable for pest management decisions.

Extending SORA method for reliability-based design optimization using probability and convex set mixed models

In many practical applications, probabilistic and bounded uncertainties often arise simultaneously, and these uncertainties can be described by using probability and convex set models. However, the computing cost becomes unacceptable when directly solving the reliability-based design optimization (RBDO) problem with these uncertainties involved. To address this issue, in this study, a sequential sampling strategy by extending classical sequential optimization and reliability assessment (SORA) method for RBDO is developed. The proposed strategy can successively select sample points to update the surrogate model at each step of the optimization process. New samples for reliability constraints are mainly chosen from the local region around the approximate minimum performance target point (MPTP) and worst-case point (WCP). Typical design examples, including one engineering application, are investigated to demonstrate the efficiency and accuracy of the proposed method.

Minimally sufficient numbers of measurements for validation of 24-hour blood pressure monitoring in chronic kidney disease

Ambulatory blood pressure monitoring (ABPM) remains a reference standard, but the minimal number of ABPM readings required to diagnose hypertension has not been empirically validated. Among 360 patients with chronic kidney disease and 38 healthy controls, 24-hour blood pressure was recorded 2 times per hour during the night and 3 times per hour during the day. All subjects had at least 90% of the expected readings recorded. From this full set of ABPM recordings, we selected variable numbers of measurements and compared the performance of the selected readings against that of the full sample under either random or sequential sampling schemes. With 8 randomly selected systolic blood pressure readings, we were able to make diagnostic decisions in concordance with that from the full ABPM sample 91.0% of the time (kappa 0.804). With 15 randomly selected diastolic blood pressure readings, we made concordant decisions 96.3% of the time (kappa 0.810). A serial selection scheme generally required a greater number of readings to achieve the same levels of concordance with the full ABPM data. With a random selection scheme, 26 readings provided 95% confidence that the sample mean will be within 5 mm Hg of the true systolic blood pressure mean, and within 3.5 mm Hg of the true diastolic blood pressure mean.

Sequential sampling strategy for extreme event statistics in nonlinear dynamical systems

We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems from a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the "next-best" data point (set of parameters) that when evaluated results in improved estimates of the probability density function (pdf) for a scalar quantity of interest. The approach uses Gaussian process regression to perform Bayesian inference on the parameter-to-observation map describing the quantity of interest. We then approximate the desired pdf along with uncertainty bounds using the posterior distribution of the inferred map. The next-best design point is sequentially determined through an optimization procedure that selects the point in parameter space that maximally reduces uncertainty between the estimated bounds of the pdf prediction. Since the optimization process uses only information from the inferred map, it has minimal computational cost. Moreover, the special form of the metric emphasizes the tails of the pdf. The method is practical for systems where the dimensionality of the parameter space is of moderate size and for problems where each sample is very expensive to obtain. We apply the method to estimate the extreme event statistics for a very high-dimensional system with millions of degrees of freedom: an offshore platform subjected to 3D irregular waves. It is demonstrated that the developed approach can accurately determine the extreme event statistics using a limited number of samples.

An Efficient Sampling Algorithm for Network Motif Detection

ABSTRACTWe propose a sequential importance sampling strategy to estimate subgraph frequencies and detect network motifs. The method is developed by sampling subgraphs sequentially node by node using a carefully chosen proposal distribution. Viewing the subgraphs as rooted trees, we propose a recursive formula that approximates the number of subgraphs containing a particular node or set of nodes. The proposal used to sample nodes is proportional to this estimated number of subgraphs. The method generates subgraphs from a distribution close to uniform, and performs better than competing methods. We apply the method to four real-world networks and demonstrate outstanding performance in practical examples. Supplemental materials for the article are available online.

A sparse polynomial surrogate model for phononic crystals with uncertain parameters

The traditional analysis and design of the phononic crystals (PhCs) are based on the deterministic physical models. However, uncertainties, unavoidably existing in the PhCs, seriously affect their physical properties. To quantify the influence of uncertainties on the band structures of the PhCs, three uncertain models, including an interval model, a random model and a hybrid uncertain model, are considered. In order to overcome the considerably computational cost of the evaluation of the band structures of the PhCs, a new high-order sparse Gegenbauer polynomial surrogate model (HOSGPSM) is proposed. In the HOSGPSM, a new spare sequential sampling scheme based on the maximin principle is employed in the sampling process, greatly reducing the potential samples. And then, the least square method is introduced to calculate the unknown coefficients of the HOSGPSM. According to the orthogonal property of the Gegenbauer polynomial, the expectation and variance of the HOSGPSM with respect to random variables can be directly yielded. The bounds of the HOSGPSM with respect to the interval model and the hybrid uncertain model can be obtained by the Monte Carlo method. The numerical results of three typical PhCs show that the HOSGPSM can accurately and efficiently evaluate the band structures of the PhCs under three uncertain models, providing a unified platform for the numerical analysis and the optimal design of various uncertain PhCs.

A new sequential sampling method for constructing the high-order polynomial surrogate models

PurposeThis paper aims to study the sampling methods (or design of experiments) which have a large influence on the performance of the surrogate model. To improve the adaptability of modelling, a new sequential sampling method termed as sequential Chebyshev sampling method (SCSM) is proposed in this study.Design/methodology/approachThe high-order polynomials are used to construct the global surrogated model, which retains the advantages of the traditional low-order polynomial models while overcoming their disadvantage in accuracy. First, the zeros of Chebyshev polynomials with the highest allowable order will be used as sampling candidates to improve the stability and accuracy of the high-order polynomial model. In the second step, some initial sampling points will be selected from the candidates by using a coordinate alternation algorithm, which keeps the initial sampling set uniformly distributed. Third, a fast sequential sampling scheme based on the space-filling principle is developed to collect more samples from the candidates, and the order of polynomial model is also updated in this procedure. The final surrogate model will be determined as the polynomial that has the largest adjusted R-square after the sequential sampling is terminated.FindingsThe SCSM has better performance in efficiency, accuracy and stability compared with several popular sequential sampling methods, e.g. LOLA-Voronoi algorithm and global Monte Carlo method from the SED toolbox, and the Halton sequence.Originality/valueThe SCSM has good performance in building the high-order surrogate model, including the high stability and accuracy, which may save a large amount of cost in solving complicated engineering design or optimisation problems.

Simulating flood risk under non-stationary climate and urban development conditions – Experimental setup for multiple hazards and a variety of scenarios

A framework for assessing economic flood damage for a large number of climate and urban development scenarios with limited computational effort is presented. Response surfaces are applied to characterize flood damage based on physical variables describing climate-driven hazards and changing vulnerability resulting from urban growth. The framework is embedded in an experimental setup where flood damage obtained from combined hydraulic-urban development simulations is approximated using kriging-metamodels. Space-filling, sequential and stratified sequential sampling strategies are tested. Reliable approximations of economic damage are obtained in a theoretical case study involving pluvial and coastal hazards, and the stratified sequential sampling strategy is most robust to irregular surface shapes. The setup is currently limited to considering only planned urban development patterns and flood adaptation options implemented over short time horizons. However, the number of simulations is reduced by up to one order of magnitude compared to scenario-based methods, highlighting the potential of the approach.

An innovative adaptive sparse response surface method for structural reliability analysis

In the scope of infrastructure risk assessment, structural reliability analysis leads to a challenging problem in order to deal with conflicting objectives: accurate estimation of failure probabilities and computational efficiency. Since the application of classical reliability methods is limited and often leads to a prohibitive computational cost, metamodeling techniques (e.g. polynomial chaos, kriging, response surface methods (RSM), etc.) have been widely used. Nevertheless, existing RSM present limitations handling with highly non-linear limit states, large-scale problems and approximation error. To overcome these problems, this paper describes a cutting-edge response surface algorithm covering the following issues: (i) dimensionality reduction by a variable screening procedure; (ii) definition of a promising search domain; (iii) initial experimental design based on an optimized space-filling scheme; (iv) model selection according to a stepwise regression procedure; (v) model validation by a cross-validation approach; (vi) model fitting using a double weighted regression technique; (vii) sequential sampling scheme by exploring a defined region of interest; (viii) confidence interval of reliability estimates based on a bootstrapping technique. With the aim of proving its efficiency, a wide collection of six illustration examples, concerning both analytical and FE-based problems, was selected. By benchmarking obtained results with literature findings, proposed method not only outperforms existing RSM, but also provides a powerful alternative to the use of other metamodeling techniques.

Sequential search leads to faster, more efficient fragment-based de novo protein structure prediction.

MotivationMost current de novo structure prediction methods randomly sample protein conformations and thus require large amounts of computational resource. Here, we consider a sequential sampling strategy, building on ideas from recent experimental work which shows that many proteins fold cotranslationally.ResultsWe have investigated whether a pseudo-greedy search approach, which begins sequentially from one of the termini, can improve the performance and accuracy of de novo protein structure prediction. We observed that our sequential approach converges when fewer than 20 000 decoys have been produced, fewer than commonly expected. Using our software, SAINT2, we also compared the run time and quality of models produced in a sequential fashion against a standard, non-sequential approach. Sequential prediction produces an individual decoy 1.5–2.5 times faster than non-sequential prediction. When considering the quality of the best model, sequential prediction led to a better model being produced for 31 out of 41 soluble protein validation cases and for 18 out of 24 transmembrane protein cases. Correct models (TM-Score > 0.5) were produced for 29 of these cases by the sequential mode and for only 22 by the non-sequential mode. Our comparison reveals that a sequential search strategy can be used to drastically reduce computational time of de novo protein structure prediction and improve accuracy.Availability and implementationData are available for download from: http://opig.stats.ox.ac.uk/resources. SAINT2 is available for download from: https://github.com/sauloho/SAINT2.Supplementary information Supplementary data are available at Bioinformatics online.

Metamodel-based design optimization employing a novel sequential sampling strategy

PurposeMetamodels are widely used to replace simulation models in engineering design optimization to reduce the computational cost. The purpose of this paper is to develop a novel sequential sampling strategy (weighted accumulative error sampling, WAES) to obtain accurate metamodels and apply it to improve the quality of global optimization.Design/methodology/approachA sequential single objective formulation is constructed to adaptively select new sample points. In this formulation, the optimization objective is to select a sample point with the maximum weighted accumulative predicted error obtained by analyzing data from previous iterations, and a space-filling criterion is introduced and treated as a constraint to avoid generating clustered sample points. Based on the proposed sequential sampling strategy, a two-step global optimization approach is developed.FindingsThe proposed WAES approach and the global optimization approach are tested in several cases. A comparison has been made between the proposed approach and other existing approaches. Results illustrate that WAES approach performs the best in improving metamodel accuracy and the two-step global optimization approach has a great ability to avoid local optimum.Originality/valueThe proposed WAES approach overcomes the shortcomings of some existing approaches. Besides, the two-step global optimization approach can be used for improving the optimization results.

An active learning radial basis function modeling method based on self-organization maps for simulation-based design problems

The radial basis function has been widely used in constructing metamodels as response surfaces. Yet, it often faces the challenge of accuracy if a sequential sampling strategy is used to insert samples sequentially and refine the models, especially under the constraint of computational resources. In this paper, a sensitive region pursuing based active learning radial basis function (SRP-ALRBF) metamodeling approach is proposed to sequentially exploit the already-acquired knowledge in the modeling process for obtaining a desirable estimation of the relationship between the input design variables and the output response. In this method, the leave-one-out (LOO) errors of each sample point are taken to identify the boundaries of sensitive regions. According to the obtained LOO information, the original design space is divided into some subspaces by adopting the self-organization maps (SOMs). The boundary of the most sensitive region, where the output response is multi-modal or non-smooth with abrupt changes, is determined by the topological graph generated by cluster analysis in SOMs. In the most sensitive region, infill sample point searching is performed based on an optimization formulation. Ten numerical examples are used to compare the proposed SRP-ALRBF with four existing active learning RBF metamodeling approaches. Results show the advantage of the proposed SRP-ALRBF approach in both prediction accuracy and robustness. It is also applied to three engineering cases to illustrate its ability to support complex engineering design.