Analyzing Stochastic Computer Models: A Review with Opportunities

Fault tree analysis (FTA) has been widely utilized as a reliability evaluation technique for complex systems, such as nuclear power plants and aerospace systems. However, it is hard to obtain the crisp failure probabilities of basic events, owning to the insufficient information about some complex engineering systems. Hence, fuzzy set theory and fuzzy arithmetic operation (FAO) have been used as effective methods to analyze system reliability. However, it is cumbersome to evaluate complex systems based on FAO. To improve the evaluation efficiency, stochastic computational models are proposed in this paper to perform reliability analysis of a fuzzy system. Due to the features of Gaussian distribution in stochastic computation, a basic event’s failure possibility given by a fuzzy number is transformed into the expected value of it. The standard deviation of stochastic computational results gives the spread of the fuzzy number. A fuzzy system is then converted into a deterministic system. The analysis of an illustrating example shows that the proposed stochastic approach can efficiently evaluate the failure probability of a system.

Computer models are widely used to simulate real processes. Within the computer model, there always exist some parameters which are unobservable in the real process but need to be specified in the computer model. The procedure to adjust these unknown parameters in order to fit the model to observed data and improve its predictive capability is known as calibration. In traditional calibration, once the optimal calibration parameter set is obtained, it is treated as known for future prediction. Calibration parameter uncertainty introduced from estimation is not accounted for. We will present a Bayesian calibration approach for stochastic computer models. We account for these additional uncertainties and derive the predictive distribution for the real process. Two numerical examples are used to illustrate the accuracy of the proposed method.

A finite state machine (FSM) is a classical abstract model for sequential circuits that are at the core of any digital system. Due to fabrication defects and transient faults, the reliable operation of sequential circuits is greatly desired. In this thesis, computational models are initially constructed using state transition matrices (STMs) and binary decision diagrams (BDDs) of an FSM; a phenomenon called error masking and the restoring properties of sequential circuits are then analyzed in detail. This analysis provides a basis for further devising efficient and robust implementation when designing FSMs. Arithmetic circuits play an important role in many digital systems and have fundamentally critical applications in signal processing. Addition is perhaps the most important and basic arithmetic operation for many applications. Recent research has focused on probabilistic and approximate adders that trade off accuracy for energy saving. Since there was a lack of appropriate metrics to evaluate the efficacy of these inexact designs, several new metrics are proposed in this work for evaluating the reliability as well as the power efficiency of an adder. These new metrics can be used in future designs for a better assessment of the power and precision tradeoff. Although current digital systems are based on complementary metal–oxide–semiconductor (CMOS) technology and employ binary values in the representation of signals, multiple valued logic (MVL) circuits using novel nano-devices have been investigated due to their advantages in information density and operating speed. In this thesis, pseudo-complementary MVL circuits are further proposed for implementations using carbon nanotube field effect transistors (CNTFETs). Because of the fabrication non-idealities, reliability evaluation of these MVL circuits becomes important. Subsequently, stochastic computational models (SCMs) are developed to analyze the reliability of CNT MVL circuits. Finally, the stochastic computational model is applied in the modeling of biological networks. Specifically, stochastic Boolean networks (SBNs) are proposed for an efficient modeling of genetic regulatory networks (GRNs). The proposed SBN can accurately and efficiently simulate a GRN without and with random gene perturbation, which will help to reveal biologically meaningful insights for a better understanding of the dynamics of GRNs.

Recent interest in near-road exposure to air pollutants and related health and environmental justice issues has highlighted the importance of improving the accuracy of intraurban ambient concentration estimates. Unfortunately, except in rare cases, no single source of information can accurately estimate the concentration at the desired spatial and temporal resolution over the full time period of epidemiological interest. However, it is possible to blend information from several sources so as to exploit the strengths and offset the weaknesses of each. Specifically, we are interested in combining data from ambient monitors with output from deterministic air pollution computer models. Monitor networks are sparse in both space and time, are costly to maintain, and are usually designed expressly to avoid detecting local-scale features. We use two types of computer models to compensate for these drawbacks. The first, a grid-based regional photochemical model, Community Multiscale Air Quality (CMAQ), covers large areas at high time resolution but cannot resolve features smaller than a grid cell, usually 4, 12, or 36 km across. The second, a plume dispersion model, AMS/EPA Regulatory Model (AERMOD), can resolve these features but cannot track long-distance transport or chemical reactions. We present a new Bayesian method that combines these three sources of information to resolve the intraurban pollution field. This method represents the true latent field using a two-dimensional wavelet basis, which allows direct, efficient incorporation of data at multiple levels of resolution. It furthermore allows a priori selection of the relative importance of each data source. We test its predictive accuracy and precision in a realistic urban-scale simulation. Finally, in the context of two air pollution health studies in Atlanta, Georgia, we use our model to estimate the daily mean concentrations of oxides of nitrogen (NOx), particulate matter with an aerodynamic diameter ≤2.5 μm (PM2.5), and carbon monoxide (CO) at a mixture of census block group and zip code centroids for the years 2001–2002. Implications: This paper describes a novel method of blending regional and local model results with observations to produce accurate air pollutant concentrations at the desired spatial and temporal resolution over urban areas to support environmental epidemiological studies.

The out-of-plane flexural bending capacity of masonry is a fundamental property for understanding the behavior of masonry structures. This study investigates the behavior of unreinforced masonry wallettes subjected to combined compression-flexural loading using the discrete element method (DEM), and provides a novel framework to estimate the masonry strength. A simplified micro-modeling strategy is utilized to analyze a masonry wallette, including the variation of the mechanical properties in masonry units and joints. Stochastic DEM analyses are performed to simulate brickwork assemblages, assuming a strong unit-weak joint material model typical of most masonry buildings, including historical ones. Once the proposed computational approach is validated against the experimental findings, the effect of spatial and non-spatial variation of mechanical properties is explored. Two failure types are identified: joint failure and brick failure. For each failure mechanism, the variability of the response and the effects of the modeling parameters on the load-carrying capacity is quantified. Afterward, Lasso regression is employed to determine predictive equations in terms of the material properties and vertical pressure on the wallette. The results show that the most important parameters changing the response are the joint tensile strength and the amount of vertical stress for joint failure, whereas the unit tensile strength dominates the response for brick failure. Overall, this research proposes a novel framework adopting validated advanced computational models that feed on simple test results to generate data that is further utilized for training response prediction models for complex structures.

Robust parameter design for 3D printing process using stochastic computer model

Computer models (CMs), which are called simulators, may be computationally expensive. Gaussian process regression models (GPRMs) are statistical models that have been used as a surrogate for expensive computer models. GPRMs are built based on assumptions similar to any statistical model. Thus, we must verify the validity of GPRMs before using them. In this paper, we use GPRMs for stochastic computer models (CMs). Then, we discussed how to verify the GPRMs for stochastic CMs by using the Cross-Validation method to predict the GPRMs. The stochastic GPRM was applied to a real CM represented by OTL Circuit function as an illustrative example. The accuracy of the GPRM was verified using stochastic measures, and it was verified that the GPRM is suitable as an alternative to the complex CM.

Extreme quantiles are important measures in reliability analysis. At the system design stage, quantiles are often estimated via stochastic simulations. This article aims to quantify quantile estimation uncertainties by constructing confidence intervals using importance sampling when quantiles are estimated via stochastic computer models. We validate the asymptotic normality for the importance sampling quantile estimator and construct a theoretically valid confidence interval in a closed form. A drawback of the theoretical confidence interval is that it needs to consistently estimate a variance parameter. To resolve the limitation of the theoretical confidence interval, we present batching-based approaches that are also built upon the asymptotic normality of the quantile estimator. We compare the estimation performance of studied methods and other alternative methods using numerical examples and wind turbine case study.

A stochastic computer model was developed that simulates the formation and binding properties of molecularly imprinted polymers (MIPs). This simulation allowed examination of possible mechanisms in the imprinting process. The simulation enabled the rapid study of each variable in the imprinting process, which is difficult to do experimentally because of the interdependence of the variables. In particular, the simulation allowed examination of influence of binding site heterogeneity on the imprinting effect and on the binding properties of MIPs. The simulation was based on a lattice model in which monomer, template, cross-linker, and solvent units occupy positions in a square grid. A stochastic algorithm was utilized to position the monomer and template units in the lattice matrix based on the monomer−template binding constant. The lattice model simulation provides a method to study the imprinting mechanism and also to rapidly optimize the imprinting process. The model was able to simulate the imprinting effect as evidenced by a higher population of high-affinity binding sites in polymers made with the presence of template units. The lattice model simulation was also able to accurately reproduce the structural and energetic binding site heterogeneity of MIPs. Next, the effects of changing the imprinting variables such as the monomer−template stoichiometry and association constant were examined. Again, the simulated MIPs displayed the same trends as experimental MIPs formed under similar imprinting conditions. Finally, the simulation was carried out with isomeric template units to examine the origins of selectivity in MIPs. A clear preference for the imprinted isomer was observed. The ability of this lattice model to accurately replicate the binding properties of MIPs gives credence to the importance of binding site heterogeneity in determining the binding properties of MIPs. The simulation gives support for the hypothesis that the diverse mixture of monomer−template complexes in the prepolymerization mixture is a major source of binding site heterogeneity in MIPs. The simulation suggests new mechanisms and strategies for improving the imprinting effect such as the careful optimization of the statistical ratios of monomer and template or the introduction of blocking groups to reduce the number of low-affinity background binding sites.

This paper explores the linkages between key features of the new product development (NPD) process and NPD performance and suggests ways of designing the process to improve performance. Using a stochastic computer model, we examine, under varying uncertainty conditions, how the key features of overlapping and functional interaction affect the performance measures of development time and effort (total person-days for a project). Findings indicate that, first and foremost, whether or not overlapping occurs, increasing functional interaction eventually leads to a trade-off between development time and effort. Second, an “early-start-in-the-dark” approach of increasing overlapping with no functional interaction is inferior even to an “over-the-wall” approach. Third, increasing overlapping when some functional interaction exists is beneficial in low uncertainty and harmful in high uncertainty. Fourth, concurrent engineering (CE) is appropriate under low uncertainty, while a type of sequential engineering (SE), different than the “over-the-wall” approach, should be used under high uncertainty, and last, dedicated teams are suitable under high, and not low, uncertainty. We developed the model with the aid of a company and validated it against a published account of five case studies.

Abstract: A stochastic computer model was used to examine the effects of varying degrees of habitat fragmentation on the dynamics of a hypothetical population of forest‐interior bid. The primary demographic parameter that influenced the population's dynamics was fecundity, which varied as a function of how far a birds territory was from an ecological edge. As our model landscape became more fragmented the proportion of forest habitat that was near edges increased geometrically, and the population's overall fecundity dropped as a result. The model demonstrates that impaired reproduction in a fragmented landscape is, by itself a sufficient disruption of the population's dynamics to generate population declines and shifts in distribution similar to those observed in the fragmented forests of southern Wisconsin. Without immigration of recruits from other regions where reproduction is better, habitat‐interior populations in a severely fragmented landscape can become locally extinct.

Many computer models of large complex systems are time consuming to experiment on. Even when surrogate models are developed to approximate the computer models, estimating an appropriate surrogate model can still be computationally challenging. In this article, we propose an Additive Global and Local Gaussian Process (AGLGP) model as a flexible surrogate for stochastic computer models. This model attempts to capture the overall global spatial trend and the local trends of the responses separately. The proposed additive structure reduces the computational complexity in model fitting, and allows for more efficient predictions with large data sets. We show that this metamodel form is effective in modelling various complicated stochastic model forms.

Computer experiments are used frequently for the study and improvement of a process under study. Optimizing such process based on a computer model is costly, so an approximation of the computer model, or metamodel, is used. Efficient global optimization (EGO) is a sequential optimization method for computer experiments based on a Gaussian process model approximation to the computer model response. A long‐standing problem in EGO is that it does not consider the uncertainty in the parameter estimates of the Gaussian process. Treating these estimates as if they are the true parameters leads to an improper assessment of the precision of the approximation, a precision that is crucial to assess not only in optimization but in metamodeling in general. One way to account for these uncertainties is to use bootstrapping, studied by previous authors. Alternatively, some other authors have mentioned how a Bayesian approach may be the best way to incorporate the parameter uncertainty in the optimization, but no fully Bayesian approach for EGO has been implemented in practice. In this paper, we present a fully Bayesian implementation of the EGO method. The proposed Bayesian EGO algorithm is validated through simulation of noisy nonlinear functions and compared with the standard EGO method and the bootstrapped EGO. We also apply the Bayesian EGO algorithm to the optimization of a stochastic computer model. It is shown how a Bayesian approach to EGO allows one to optimize any function of the posterior predictive density. Copyright © 2014 John Wiley & Sons, Ltd.

We look at the behavior of biological oscillators, specifically analyzing a genetic circuit that has oscillatory behavior. Implementing the system in deterministic and stochastic models, we compare the two models using various tests and analyze the effect of stochastic noise on these oscillations. We first investigate the effect of volume and find that at small system volumes, stochastic events cause the system to exhibit more sporadic oscillations and a longer period of oscillation. Next, we develop classification systems for discerning the boundary in the parameter space where the model begins to show oscillations. This is more challenging in the stochastic model, due to persistent fluctuations. We compare different methods of analysis of our deterministic and stochastic models and visualize the conditions which lead to oscillation in each model. We find that the parameter range of oscillation is larger in the stochastic model than in the deterministic model. Finally, we find an increased rate of mRNA production can create greater noise in a system and amplify the difference between a stochastic and deterministic system.

Unraveling pine wilt disease: Comparative study of stochastic and deterministic model using spectral method