Multi-Resolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multi-resolution functional ANOVA model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input non-linear regression problems. An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. New results on consistency and inference for the (potentially overlapping) group lasso in a high-dimensional setting are developed and applied to the proposed multi-resolution functional ANOVA model. Importantly, these results allow us to quantify the uncertainty in our predictions. Numerical examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, both in terms of sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy

Calibration of Computational Models with Categorical Parameters and Correlated Outputs via Bayesian Smoothing Spline ANOVA

It has become commonplace to use complex computer models to predict outcomes in regions where data does not exist. Typically these models need to be calibrated and validated using some experimental data, which often consists of multiple correlated outcomes. In addition, some of the model parameters may be categorical in nature, such as a pointer variable to alternate models (or submodels) for some of the physics of the system. Here we present a general approach for calibration in such situations where an emulator of the computationally demanding models and a discrepancy term from the model to reality are represented within a Bayesian Smoothing Spline (BSS) ANOVA framework. The BSS-ANOVA framework has several advantages over the traditional Gaussian Process, including ease of handling categorical inputs and correlated outputs, and improved computational efficiency. Finally this framework is then applied to the problem that motivated its design; a calibration of a computational fluid dynamics model of a bubbling fluidized which is used as an absorber in a CO2 capture system

Screening and metamodeling of computer experiments with functional outputs. Application to thermal-hydraulic computations

To perform uncertainty, sensitivity or optimization analysis on scalar variables calculated by a cpu time expensive computer code, a widely accepted methodology consists in first identifying the most influential uncertain inputs (by screening techniques), and then in replacing the cpu time expensive model by a cpu inexpensive mathematical function, called a metamodel. This paper extends this methodology to the functional output case, for instance when the model output variables are curves. The screening approach is based on the analysis of variance and principal component analysis of output curves. The functional metamodeling consists in a curve classification step, a dimension reduction step, then a classical metamodeling step. An industrial nuclear reactor application (dealing with uncertainties in the pressurized thermal shock analysis) illustrates all these steps

The wavelet-NARMAX representation : a hybrid model structure combining polynomial models with multiresolution wavelet decompositions

A new hybrid model structure combing polynomial models with multiresolution wavelet decompositions is introduced for nonlinear system identification. Polynomial models play an important role in approximation theory, and have been extensively used in linear and nonlinear system identification. Wavelet decompositions, in which the basis functions have the property of localization in both time and frequency, outperform many other approximation schemes and offer a flexible solution for approximating arbitrary functions. Although wavelet representations can approximate even severe nonlinearities in a given signal very well, the advantage of these representations can be lost when wavelets are used to capture linear or low-order nonlinear behaviour in a signal. In order to sufficiently utilise the global property of polynomials and the local property of wavelet representations simultaneously, in this study polynomial models and wavelet decompositions are combined together in a parallel structure to represent nonlinear input-output systems. As a special form of the NARMAX model, this hybrid model structure will be referred to as the WAvelet-NARMAX model, or simply WANARMAX. Generally, such a WANARMAX representation for an input-output system might involve a large number of basis functions and therefore a great number of model terms. Experience reveals that only a small number of these model terms are significant to the system output. A new fast orthogonal least squares algorithm, called the matching pursuit orthogonal least squares (MPOLS) algorithm, is also introduced in this study to determine which terms should be included in the final model

Input variable selection in time-critical knowledge integration applications: A review, analysis, and recommendation paper

This is the post-print version of the final paper published in Advanced Engineering Informatics. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2013 Elsevier B.V.The purpose of this research is twofold: first, to undertake a thorough appraisal of existing Input Variable Selection (IVS) methods within the context of time-critical and computation resource-limited dimensionality reduction problems; second, to demonstrate improvements to, and the application of, a recently proposed time-critical sensitivity analysis method called EventTracker to an environment science industrial use-case, i.e., sub-surface drilling. Producing time-critical accurate knowledge about the state of a system (effect) under computational and data acquisition (cause) constraints is a major challenge, especially if the knowledge required is critical to the system operation where the safety of operators or integrity of costly equipment is at stake. Understanding and interpreting, a chain of interrelated events, predicted or unpredicted, that may or may not result in a specific state of the system, is the core challenge of this research. The main objective is then to identify which set of input data signals has a significant impact on the set of system state information (i.e. output). Through a cause-effect analysis technique, the proposed technique supports the filtering of unsolicited data that can otherwise clog up the communication and computational capabilities of a standard supervisory control and data acquisition system. The paper analyzes the performance of input variable selection techniques from a series of perspectives. It then expands the categorization and assessment of sensitivity analysis methods in a structured framework that takes into account the relationship between inputs and outputs, the nature of their time series, and the computational effort required. The outcome of this analysis is that established methods have a limited suitability for use by time-critical variable selection applications. By way of a geological drilling monitoring scenario, the suitability of the proposed EventTracker Sensitivity Analysis method for use in high volume and time critical input variable selection problems is demonstrated.E

Ecological study of chalk streams. Lambourn project. Interim report October 1977 to April 1979

Few detailed studies have been made on the ecology of the chalk streams. A complex community of plants and animals is present and much more information is required to achieve an understanding of the requirements and interactions of all the species. It is important that the rivers affected by this scheme should be studied and kept under continued observation so that any effects produced by the scheme can be detected. The report gives a synopsis of work carried out between 1971 and 1979 focusing on the present phase 1978-1979. It assumes some familiarity with the investigations carried out on the River Lambourn during the preceding years. The aims of the present phase of the project may be divided into two broad aspects. The first involves collecting further information in the field and includes three objectives: a continuation of studies on the Lambourn sites at Bagnor; comparative studies on other chalk streams; and a comparative study on a limestone stream. The second involves detailed analyses of data previously collected to document the recovery of the Lambourn from operational pumping and to attempt to develop simple conceptual and predictive models applicable over a wide range of physical and geographical variables. (PDF contains 43 pages

Transient fault behavior in a microprocessor: A case study

An experimental analysis is described which studies the susceptibility of a microprocessor based jet engine controller to upsets caused by current and voltage transients. A design automation environment which allows the run time injection of transients and the tracing from their impact device to the pin level is described. The resulting error data are categorized by the charge levels of the injected transients by location and by their potential to cause logic upsets, latched errors, and pin errors. The results show a 3 picoCouloumb threshold, below which the transients have little impact. An Arithmetic and Logic Unit transient is most likely to result in logic upsets and pin errors (i.e., impact the external environment). The transients in the countdown unit are potentially serious since they can result in latched errors, thus causing latent faults. Suggestions to protect the processor against these errors, by incorporating internal error detection and transient suppression techniques, are also made

Measuring neuromuscular junction functionality

Neuromuscular junction (NMJ) functionality plays a pivotal role when studying diseases in which the communication between motor neuron and muscle is impaired, such as aging and amyotrophic lateral sclerosis (ALS). Here we describe an experimental protocol that can be used to measure NMJ functionality by combining two types of electrical stimulation: direct muscle membrane stimulation and the stimulation through the nerve. The comparison of the muscle response to these two different stimulations can help to define, at the functional level, potential alterations in the NMJ that lead to functional decline in muscle. Ex vivo preparations are suited to well-controlled studies. Here we describe an intensive protocol to measure several parameters of muscle and NMJ functionality for the soleus-sciatic nerve preparation and for the diaphragm-phrenic nerve preparation. The protocol lasts approximately 60 min and is conducted uninterruptedly by means of a custom-made software that measures the twitch kinetics properties, the force-frequency relationship for both muscle and nerve stimulations, and two parameters specific to NMJ functionality, i.e. neurotransmission failure and intratetanic fatigue. This methodology was used to detect damages in soleus and diaphragm muscle-nerve preparations by using SOD1G93A transgenic mouse, an experimental model of ALS that ubiquitously overexpresses the mutant antioxidant enzyme superoxide dismutase 1 (SOD1)