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The details of a method to reduce the computational burden experienced while estimating the optimal model parameters for a Kriging model are presented. A Kriging model is a type of surrogate model that can be used to create a response surface based a set of observations of a computationally expensive system design analysis. This Kriging model can then be used as a computation-ally efficient surrogate to the original model, providing the opportunity for the rapid exploration of the resulting tradespace. The Kriging model can provide a more complex response surface than the more traditional linear regression response surface through the introduction of a few terms to quantify the spatial correlation of the observations. Implementation details and enhancements to gradient-based methods to estimate the model parameters are presented. It concludes with a comparison of these enhancements to using maximum likelihood estimation to estimate Kriging model parameters and their potential reduction in computational burden. These enhancements include the development of the analytic gradient and Hessian for the log-likelihood equation of a Kriging model that uses a Gaussian spatial correlation function. The suggested algorithm is similar to the SCORING algorithm traditionally used in statistics. [DOI: 10.1115/1.3151807]

The small-scale digesters treating agricultural wastewater and producing energy are analyzed in order to explore different ways for increasing the efficiency of the systems. The analysis has shown that the small-scale digesters can provide methane and electricity to meet household needs resulting in increase in household income and decrease in water pollution and deforestation.

Current design decisions must be made while considering uncertainty in both models of the design and inputs to the design. In most cases, high fidelity models are used with the assumption that the resulting model uncertainties are insignificant to the decision making process. This paper presents a methodology for managing uncertainty during system-level conceptual design of complex multidisciplinary systems. This methodology is based upon quantifying the information available in a set of observations of computationally expensive subsystem models with more computationally efficient kriging models. By using kriging models, the computational expense of a Monte Carlo simulation to assess the impact of the sources of uncertainty on system-level performance parameters becomes tractable. The use of a kriging model as an approximation to an original computer model introduces model uncertainty, which is included as part of the methodology. The methodology is demonstrated as a decision-making tool for the design of a satellite system. [DOI: 10.1115/1.2204975]

Large woody debris (LWD) has been used repeatedly to create aquatic habitats. This study attempts to quantify and predict geomorphological changes induced by LWD. Six cylindrical bundles of LWD were anchored in a stream in central Ohio, and bed elevations were monitored for up to seven months. A model was developed to predict deposition downstream of the LWD. Sediments accumulated immediately downstream of the LWD structures. The average accumulation depth 0.25 m downstream of the LWD was 0.10 m. At 1.25 m downstream, accumulation depth averaged 0.07 m. The model to predict the sediment deposition had [R.sup.2] values of 0.87-0.77, respectively, at the two downstream locations. The most important terms in the model were the Froude number and bankfull depth. An advantage of this model was the use of easily measurable variables including average bankfull velocities, depth, and cross-sectional area. This fact will facilitate the use of the model in field settings. Suggestions for future improvements to the model include calibration/ validation in different streams, inclusion of a temporal variable, and sediment characterization. DOI: 10.1061/(ASCE)0733-9429(2005)131:11(1011) CE Database subject headings: Aquatic habitats; Bridges; Drag; Energy dissipation; Energy methods; Froude number; Debris; Wood.

The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread use of kriging models appears to be hampered by 1) computationally efficient algorithms for accurately estimating the model's parameters, 2) an effective method to assess the resulting model's quality, and 3) the lack of guidance in selecting the appropriate form of the kriging model. We attempt to 'address these issues by comparing 1) maximum likelihood estimation and cross validation parameter estimation methods for selecting a kriging model's parameters given its form and 21 an [R.sup.2] of prediction and the corrected Akaike information criterion assessment methods for quantifying the quality of the created kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models.