Multiple Surrogates Research Articles

Surrogate model‐based strategy for cryogenic cavitation model validation and sensitivity evaluation

AbstractThe study of cavitation dynamics in cryogenic environment has critical implications for the performance and safety of liquid rocket engines, but there is no established method to estimate cavitation‐induced loads. To help develop such a computational capability, we employ a multiple‐surrogate model‐based approach to aid in the model validation and calibration process of a transport‐based, homogeneous cryogenic cavitation model. We assess the role of empirical parameters in the cavitation model and uncertainties in material properties via global sensitivity analysis coupled with multiple surrogates including polynomial response surface, radial basis neural network, kriging, and a predicted residual sum of squares‐based weighted average surrogate model. The global sensitivity analysis results indicate that the performance of cavitation model is more sensitive to the changes in model parameters than to uncertainties in material properties. Although the impact of uncertainty in temperature‐dependent vapor pressure on the predictions seems significant, uncertainty in latent heat influences only temperature field. The influence of wall heat transfer on pressure load is insignificant. We find that slower onset of vapor condensation leads to deviation of the predictions from the experiments. The recalibrated model parameters rectify the importance of evaporation source terms, resulting in significant improvements in pressure predictions. The model parameters need to be adjusted for different fluids, but for a given fluid, they help capture the essential fluid physics with different geometry and operating conditions. Copyright © 2008 John Wiley & Sons, Ltd.

Multiple Surrogate Modeling for Axial Compressor Blade Shape Optimization

A major issue in surrogate model-based design optimization is the modeling fidelity. An effective approach is to employ multiple surrogates based on the same training data to offer approximations from alternative modeling viewpoints. This approach is employed in a compressor blade shape optimization using the NASA rotor 37 as the case study. The surrogate models considered include polynomial response surface approximation, Kriging, and radial basis neural network. In addition, a weighted average model based on global error measures is constructed. Sequential quadratic programming is used to search the optimal point based on these alternative surrogates. Three design variables characterizing the blade regarding sweep, lean, and skew are selected along with the three-level full factorial approach for design of experiment. The optimization is guided by three objectives aimed at maximizing the adiabatic efficiency, as well as the total pressure and total temperature ratios. The optimized compressor blades yield lower losses by moving the separation line toward the downstream direction. The optima for total pressure and total temperature ratios are similar, but the optimum for adiabatic efficiency is located far from them. It is found that the most accurate surrogate did not always lead to the best design. This demonstrated that using multiple surrogates can improve the robustness of the optimization at a minimal computational cost.

Designing protected areas to conserve riverine biodiversity: Lessons from a hypothetical redesign of the Kruger National Park

The process of designing protected areas to represent all ecosystems in an area adequately is becoming increasingly sophisticated. To date freshwater aquatic ecosystems have seldom been considered in this process. How much of a difference does it make when they are considered as well? This study examined the conservation of riverine biodiversity within 17 assessment units contained by the catchment areas of five perennial rivers flowing through Kruger National Park and two seasonal rivers that are largely contained within this park. Physical river types, fish species and invertebrate families or genera were used as surrogates of riverine biodiversity. Conservation planning software was used to select an optimal set of planning units to represent and maintain riverine biodiversity. The current spatial configuration of Kruger National Park, largely an accident of history, is particularly poor when assessed against the objective of conserving riverine biodiversity. Several alternative layouts are examined. These options are theoretical since there is little current opportunity to reassign land uses in the region. This study shows that substantially improved layouts for both riverine and terrestrial biodiversity are possible, under the constraint of the same total area under protection. The study also shows that even these optimal layouts are only partially successful in efforts to conserve fully representative samples of riverine biodiversity. Because of the longitudinal connectivity of rivers, conservation strategies that extend beyond protected areas are essential. Explicit conservation visions, targets and strategies need to be included in integrated water resource management plans. Based on the results of this study, nine recommendations are provided for increasing the effectiveness of current and future protected areas in conserving riverine biodiversity. These are to use systematic conservation planning to make biodiversity benefits explicit; mend the disconnect between terrestrial and freshwater conservation; use multiple surrogates wherever possible; be strategic about the collection and management of primary data; strive for maximum hydrologic connectivity; resist development pressure; foster good relationships across park fences; where relevant, pursue multi-national cooperation at the basin scale; and engage the value debate and resolve awareness and capacity constraints.

Global sensitivity analysis of Alkali–Surfactant–Polymer enhanced oil recovery processes

After conventional waterflooding processes the residual oil in the reservoir remains as a discontinuous phase in the form of oil drops trapped by capillary forces and is likely to be around 70% of the original oil in place (OOIP). The EOR method so-called Alkaline–Surfactant–Polymer (ASP) flooding has been proved to be effective in reducing the oil residual saturation in laboratory experiments and field projects through reduction of interfacial tension and mobility ratio between oil and water phases. A critical step for the optimal design and control of ASP recovery processes is to find the relative contributions of design variables such as, slug size and chemical concentrations, in the variability of given performance measures (e.g., net present value, cumulative oil recovery), considering a heterogeneous and multiphase petroleum reservoir (sensitivity analysis). Previously reported works using reservoir numerical simulation have been limited to local sensitivity analyses because a global sensitivity analysis may require hundreds or even thousands of computationally expensive evaluations (field scale numerical simulations). To overcome this issue, a surrogate-based approach is suggested. Surrogate-based analysis/optimization makes reference to the idea of constructing an alternative fast model (surrogate) from numerical simulation data and using it for analysis/optimization purposes. This paper presents an efficient global sensitivity approach based on Sobol's method and multiple surrogates (i.e., Polynomial Regression, Kriging, Radial Base Functions and a Weighed Adaptive Model), with the multiple surrogates used to address the uncertainty in the analysis derived from plausible alternative surrogate-modeling schemes. The proposed approach was evaluated in the context of the global sensitivity analysis of a field scale Alkali–Surfactant–Polymer flooding process. The design variables and the performance measure in the ASP process were selected as slug size/concentration of chemical agents, and cumulative oil recovery, respectively. The results show the effectiveness and efficiency of the proposed approach since it allows establishing the relative contribution of the design variables (main factors and interactions) to the performance measure variability using a limited number of computationally expensive reservoir simulations.

Regression calibration for logistic regression with multiple surrogates for one exposure

Methods have been developed by several authors to address the problem of bias in regression coefficients due to errors in exposure measurement. These approaches typically assume that there is one surrogate for each exposure. Occupational exposures are quite complex and are often described by characteristics of the workplace and the amount of time that one has worked in a particular area. In this setting, there are several surrogates which are used to define an individual's exposure. To analyze this type of data, regression calibration methodology is extended to adjust the estimates of exposure-response associations for the bias and additional uncertainty due to exposure measurement error from multiple surrogates. The health outcome is assumed to be binary and related to the quantitative measure of exposure by a logistic link function. The model for the conditional mean of the quantitative exposure measurement in relation to job characteristics is assumed to be linear. This approach is applied to a cross-sectional epidemiologic study of lung function in relation to metal working fluid exposure and the corresponding exposure assessment study with quantitative measurements from personal monitors. A simulation study investigates the performance of the proposed estimator for various values of the baseline prevalence of disease, exposure effect and measurement error variance. The efficiency of the proposed estimator relative to the one proposed by Carroll et al. [1995. Measurement Error in Nonlinear Models. Chapman & Hall, New York] is evaluated numerically for the motivating example. User-friendly and fully documented Splus and SAS routines implementing these methods are available ( http://www.hsph.harvard.edu/faculty/spiegelman/multsurr.html ).

Association of indoor nitrogen dioxide with respiratory symptoms in children: Application of measurement error correction techniques to utilize data from multiple surrogates

In 1991, Neas et al. reported that indoor nitrogen dioxide (NO(2)), a byproduct of high-temperature combustion, was significantly associated with lower respiratory symptoms among a cohort of 1,159 white children aged 7-11 years in six US cities studied from 1983 to 1988. For each 15 p.p.b. increment of NO(2), the multivariate adjusted odds ratio (OR) was 1.4 (95% confidence interval (CI)=[1.1, 1.7]). Although indoor NO(2) concentration in the ambient air was assessed only in a subset of the children, the prevalence of lower respiratory symptoms and surrogate exposure variables were available in all of the children at the time of the indoor monitoring program. This paper evaluates the effect of indoor NO(2) exposure on the annual risk of lower respiratory symptoms by applying a regression calibration method to the 2,891 children in the overall study with complete covariate and outcome data, 1,137 of whom had NO(2) directly measured and 1,754 of whom only surrogate exposure data were available. An estimate of the indoor annual NO(2) exposure effect (p.p.b.) is obtained, which is adjusted for measurement error induced by the use of surrogate NO(2) sources among the 1,754. These sources include the presence of a gas stove with or without a pilot light, the presence of a kerosene space heater, the presence of a wood stove, and the usage of a stove for heating, and residential characteristics, including fan usage for kitchen ventilation and the total number of rooms in the home. After adjusting for age, gender, city, parental history of respiratory diseases, and smoking inside the children's home (packs/day), a 15-p.p.b. increment in NO(2) exposure was found to be associated with a significant 50% increased annual risk of lower respiratory symptoms (OR=1.5, 95% CI=[1.2, 1.8]). Simulation results indicated that, under conditions similar to those observed in these data, the estimator is unbiased and has a coverage probability close to the nominal value. Using the methodology illustrated in this paper, it became possible to utilize all data available and obtain a 34% more precise estimate of the NO(2) exposure effect on lower respiratory symptoms, which was adjusted for measurement error due to using NO(2) surrogates instead of directly measured NO(2).

Riverbank Filtration for IESWTR Compliance

The Central Wyoming Regional Water System operates 29 groundwater collection devices in an alluvial aquifer adjacent to the North Platte River. These collection devices were previously designated “groundwater under the direct influence of surface water.” In lieu of constructing a conventional surface water treatment plant, the utility opted to perform a two‐year study to demonstrate that riverbank filtration (i.e., natural filtration) provided the 2.0‐log reduction of Cryptosporidium required under the Interim Enhanced Surface Water Treatment Rule (e.g., riverbank filtration is the primary filtration process). Using multiple surrogates of various sizes encompassing those of Giardia and Cryptosporidium, the utility demonstrated 2.0‐log reductions in more than 90% of matched data pairs. No Giardia cysts or Cryptosporidium oocysts were found in any of the 170 groundwater samples. This level of removal was achieved during the summer months when infiltration rates are high because of increased river stage and well‐field production.

An optimization methodology of alkaline–surfactant–polymer flooding processes using field scale numerical simulation and multiple surrogates

After conventional waterflood processes the residual oil in the reservoir remains as a discontinuous phase in the form of oil drops trapped by capillary forces and is likely to be around 70% of the original oil in place (OOIP). The EOR method so-called alkaline–surfactant–polymer (ASP) flooding has proved to be effective in reducing the oil residual saturation in laboratory experiments and field projects through the reduction of interfacial tension and mobility ratio between oil and water phases. A critical step to make ASP floodings more effective is to find the optimal values of design variables that will maximize a given performance measure (e.g., net present value, cumulative oil recovery) considering a heterogeneous and multiphase petroleum reservoir. Previously reported works using reservoir numerical simulation have been limited to sensitivity analyses at core and field scale levels because the formal optimization problem includes computationally expensive objective function evaluations (field scale numerical simulations). This work presents a surrogate-based optimization methodology to overcome this shortcoming. The proposed approach estimates the optimal values for a set of design variables (e.g., slug size and concentration of the chemical agents) to maximize the cumulative oil recovery from a heterogeneous and multiphase petroleum reservoir subject to an ASP flooding. The surrogate-based optimization approach has been shown to be useful in the optimization of computationally expensive simulation-based models in the aerospace, automotive, and oil industries. In this work, we improve upon this approach along two directions: (i) using multiple surrogates for optimization, and (ii) incorporating an adaptive weighted average model of the individual surrogates. The cited approach involves the coupled execution of a global optimization algorithm and fast surrogates (i.e., based on Polynomial Regression, Kriging, Radial Basis Functions and a Weighted Average Model) constructed from field scale numerical simulation data. The global optimization program implements the DIRECT algorithm and the reservoir numerical simulations are conducted using the UTCHEM program from the University of Texas at Austin. The effectiveness and efficiency of the proposed methodology is demonstrated using a field scale case study.

Bayesian latent variable models for median regression on multiple outcomes.

Often a response of interest cannot be measured directly and it is necessary to rely on multiple surrogates, which can be assumed to be conditionally independent given the latent response and observed covariates. Latent response models typically assume that residual densities are Gaussian. This article proposes a Bayesian median regression modeling approach, which avoids parametric assumptions about residual densities by relying on an approximation based on quantiles. To accommodate within-subject dependency, the quantile response categories of the surrogate outcomes are related to underlying normal variables, which depend on a latent normal response. This underlying Gaussian covariance structure simplifies interpretation and model fitting, without restricting the marginal densities of the surrogate outcomes. A Markov chain Monte Carlo algorithm is proposed for posterior computation, and the methods are applied to single-cell electrophoresis (comet assay) data from a genetic toxicology study.

Bayesian modeling of incidence and progression of disease from cross-sectional data.

In the absence of longitudinal data, the current presence and severity of disease can be measured for a sample of individuals to investigate factors related to disease incidence and progression. In this article, Bayesian discrete-time stochastic models are developed for inference from cross-sectional data consisting of the age at first diagnosis, the current presence of disease, and one or more surrogates of disease severity. Semiparametric models are used for the age-specific hazards of onset and diagnosis, and a normal underlying variable approach is proposed for modeling of changes with latency time in disease severity. The model accommodates multiple surrogates of disease severity having different measurement scales and heterogeneity among individuals in disease progression. A Markov chain Monte Carlo algorithm is described for posterior computation, and the methods are applied to data from a study of uterine leiomyoma.

The Evaluation of Multiple Surrogate Endpoints

Surrogate endpoints are desirable because they typically result in smaller, faster efficacy studies compared with the ones using the clinical endpoints. Research on surrogate endpoints has received substantial attention lately, but most investigations have focused on the validity of using a single biomarker as a surrogate. Our paper studies whether the use of multiple markers can improve inferences about a treatment's effects on a clinical endpoint. We propose a joint model for a time to clinical event and for repeated measures over time on multiple biomarkers that are potential surrogates. This model extends the formulation of Xu and Zeger (2001, in press) and Fawcett and Thomas (1996, Statistics in Medicine 15, 1663-1685). We propose two complementary measures of the relative benefit of multiple surrogates as opposed to a single one. Markov chain Monte Carlo is implemented to estimate model parameters. The methodology is illustrated with an analysis of data from a schizophrenia clinical trial.

From Static to Dynamic Surrogates

This paper explores how resource discovery in the networked (or digital) environment presents new opportunities for the use of surrogates. Our argument has several elements. We show that resource discovery is a complex process that includes multiple phases, is iterative, and highly dynamic. In agreement with others, we argue that resource discovery involves the manipulation of object surrogates, which are vital because of their order-making role. Resource discovery in the physical realm -- for example searches in the traditional library -- has been constrained by the use of static surrogates. In the traditional library these are the card catalog and its digital analog, the OPAC. These static surrogates have been quite successful as resource discovery aids, albeit frequently with the mediation of trained reference librarians. We argue that significant improvements to resource discovery in the networked realm can be made using techniques that match surrogate semantics to the instance-specific requirements of the resource discovery process. This can be accomplished most easily through architectures, such as the Warwick Framework, that allow the association of multiple surrogates with objects, or more ambitiously through methods that construct derived, or dynamic surrogates that respond to current resource discovery needs. The Complexity of the Resource Discovery Process With or without the computer and the Internet, the resource discovery process is complex and often oversimplified. To begin with, what is the goal of resource discovery? It is easy to assume that what is sought is the to some information need, or query. Yet, depending on the situation, person, costs, and other factors this answer may have quite different characteristics. In some cases, what one is seeking is the best possible response to a query (we ignore the vagaries of what characterizes best). In other cases, because of constraints such as time, cost, patience, and the like, the information seeker may be satisfied with less response specificity in the response. In some cases, the goal of the discovery process may change as the seeker is sidetracked by intervening needs or newly discovered information. Finally, the process may begin without even a clearly defined information goal, and the satisfactory might be some information that is of value simply as a result of the serendipity of the process itself. Our focus here is the character of the process as it proceeds from initiation to realization of goal. By understanding this process we will be better equipped to formulate architectures to facilitate networked resource discovery. For a broader perspective on networked resource discovery and retrieval (NIDR), we refer readers to the draft of a White Paper on Networked Information and Discovery and Retrieval [CNI], being prepared for the Coalition for Networked Information (CNI). This white paper, while unfinished, is the clearest exploration to date on many of the issues relevant to discovery and retrieval in a networked environment.

Adjustment for non‐differential misclassification error in the generalized linear model

It is well known that estimates of association between an outcome variable and a set of categorical covariates, some of which are measured with misclassification, tend to be biased upon application of the usual methods of estimation that ignore the classification error. We propose a method to adjust for misclassification in covariates when one applies the generalized linear model. In the case where one can observe some true covariates only through surrogates, we combine a latent class analysis with the approach to incorporate multiple surrogates into the model. We include discussion on the efficacy of repeated measurements which one can view as a special case of multiple surrogates with identical distribution. We provide two examples to demonstrate the applicability of the method and the efficacy of multiple replicates for a covariate subject to misclassification in a regression framework.