Effect Of Input Uncertainties Research Articles

Reproductive Performance and Partial Budget Analysis of a Prostaglandin or a Modified Ovsynch Protocol in Autumn Calving Dairy Herds.

Simple SummaryIn autumn calving dairy herds cattle must conceive within a restricted timeframe to maintain the seasonality of calving. Cattle not observed in estrus prior to the mating start date are frequently treated with a single prostaglandin injection even though its relative effectiveness is unknown. The perceived cost of other treatments, such as a modified Ovsynch protocol, may be a reason why they are less favored. This study compares the reproductive and economic outcomes associated with treating cows not observed in estrus prior to breeding with a modified Ovsynch protocol, in comparison to a single prostaglandin injection. The main inputs influencing profitability are identified, and differences in dry-off strategy are considered. From the analyses, cows treated with a modified Ovsynch protocol had a greater likelihood of conception at the beginning of, and throughout, the breeding season. Differences in barren rate and the amount of milk produced were the main variables affecting profitability, the latter strongly influenced by drying-off policy. Farmers and advisors should consider the relative performance of their breeding strategies as well as their own management policies to optimize reproductive and economic performance.In autumn calving dairy herds, treatment of cattle not observed in estrus prior to the breeding season is common. Routinely, a single prostaglandin or a modified Ovsynch (MOFT) protocol are used—without evidence of their relative effectiveness. This study compares the effects on conception, associated timing, and profitability of administering cows with prostaglandin or MOFT treatment. A hundred and ninety-two Holstein-Friesian cows from three herds without an observed estrus within 28-days before mating start date were randomly treated with d-cloprostenol (PGOD) or an 8-day MOFT protocol. The association of treatment and calving-breeding start-date interval (CBSI) on the risk of conception were investigated. Partial budget, sensitivity analysis, and Monte Carlo simulation was used to assess economic performance, identify critical input variables, and explore the effects of input uncertainties on model output. There was a significant association between MOFT treatment and conception during 21 and 84 days after mating start date, compared to PGOD. MOFT treatment was associated with a mean net benefit of £58.21 (sd £19.42) and £27.29 (sd £17.75) per cow for herds with a fixed or variable dry-off date, respectively. The relative profitability of an MOFT protocol is dependent on its effects on barren rate and herd dry-off strategy.

Uncertainty Propagation Through a Simulation of Industrial High Pressure Die Casting

Abstract While numerical models are often used in industry to evaluate the transport phenomena in solidification processes, the uncertainty in the results propagated from uncertain input parameters is rarely considered. In this work, in order to investigate the effects of input uncertainty on the outputs of high pressure die casting (HPDC) simulations, the Center for Prediction of Reliability, Integrity, and Survivability of Microsystems (PRISM) uncertainty quantification (PUQ) framework was applied. Three uncertainty propagation trials investigate the impact of uncertainty in metal material properties, thermal boundary conditions, and a modeling parameter on outputs of interest, such as fraction liquid at different times in the process cycle and shrinkage porosity volume, in an industrial A380 aluminum alloy HPDC process. This quantification of the output uncertainty establishes the reliability of the simulation results and can inform process design choices, such as the determination of the part ejection time. The results are most sensitive to the uncertainty in the interfacial heat transfer (for both outputs of interest) and the feeding effectivity (FE) (a model parameter controlling porosity formation determination), while the other heat transfer boundary conditions, model parameters, and all the properties play a secondary role in output uncertainty.

What is needed to make cardiovascular models suitable for clinical decision support? A viewpoint paper

The potential impact of hemodynamic and vascular wall models on the diagnosis, treatment, and well-being of thousands of patients suffering from cardiovascular diseases, is tremendous. Despite the potential impact, it is not straightforward to use these models for individualized diagnosis and intervention planning (model predictive decision support). Major challenges are the adaptation of the models to patient-specific conditions and the necessary uncertainty assessment of the simulated outcome measures.In this manuscript, we will present our view on what is needed to make cardiovascular models suitable for clinical decision support. Hereto, we will first describe how an engineer might support clinical decisions. Secondly, we will give a description of the challenges faced by the engineers. Finally we will introduce an innovative approach in which model personalization is guided by sensitivity analysis, and in which the effect of input uncertainties and model assumptions (acknowledged model errors) on model predictions are considered during model corroboration. The approach is illustrated by two different vascular cases.Hopefully our view will be useful in bringing models from the pre-clinical phase to the clinical phase where they will actually be used for model predictive decision support.

Quantification of Epistemic Uncertainty in Grain Attachment Models for Equiaxed Solidification

Recent work has investigated various schemes for the attachment of free-floating grains in models of equiaxed solidification in multicomponent alloys. However, these models are deterministic in nature, and simply investigating their differences for a limited number of results would not constitute an adequate comparison of their predictions. Instead, the models are compared in the context of the uncertainty in the most important input parameters. This approach is especially important in light of the effort required to implement a new model. If the predictions are essentially the same, then either model will suffice, or one may be selected for ease of implementation, numerical robustness, or computational efficiency. If, however, the models are significantly different, then the most accurate should be selected. In order to investigate the effects of input uncertainty on the output of grain attachment models, the PRISM Uncertainty Quantification framework was employed. The three models investigated were a constant packing fraction (CPF) scheme, an average solid velocity method (AVM), and a continuum attachment approach. Comparisons were made between the CPF and AVM models to estimate the importance of the local velocity field and between the CPF and continuum models to determine the sensitivity of the macrosegregation to new parameters unique to the continuum model.

Probability density distribution in the prediction of reaction equilibria

Reaction equilibria play an important role in chemical engineering. They can be calculated from substance properties of the compounds involved in the reaction. Since these substance properties usually come from measurements there is always an uncertainty with them. This uncertainty in the input data causes an uncertainty of the simulation results, even if the model itself is perfect. The effect of input uncertainty on uncertainty in equilibrium calculations has been studied. Monte Carlo sampling has been applied for accessing uncertainty and probability density distribution. Uncertainty in equilibrium conversion can be very high. However, the shape of the curve of equilibrium conversion over temperature can be predicted very precisely. As a consequence, simulations of reaction equilibria can still be useful, because temperatures required for achieving a certain conversion can be determined with comparatively high accuracy. The probability density distributions of the obtained equilibria can strongly deviate from those of the input data and in some cases can even become bimodal.

Sensitivity analysis of Repast computational ecology models with R/Repast

Computational ecology is an emerging interdisciplinary discipline founded mainly on modeling and simulation methods for studying ecological systems. Among the existing modeling formalisms, the individual‐based modeling is particularly well suited for capturing the complex temporal and spatial dynamics as well as the nonlinearities arising in ecosystems, communities, or populations due to individual variability. In addition, being a bottom‐up approach, it is useful for providing new insights on the local mechanisms which are generating some observed global dynamics. Of course, no conclusions about model results could be taken seriously if they are based on a single model execution and they are not analyzed carefully. Therefore, a sound methodology should always be used for underpinning the interpretation of model results. The sensitivity analysis is a methodology for quantitatively assessing the effect of input uncertainty in the simulation output which should be incorporated compulsorily to every work based on in‐silico experimental setup. In this article, we present R/Repast a GNU R package for running and analyzing Repast Simphony models accompanied by two worked examples on how to perform global sensitivity analysis and how to interpret the results.

Uncertainty propagation in computationally expensive models: A survey of sampling methods and application to scatterometry

Abstract Partial differential equations with uncertain input parameters are used in many applications in metrology, physics and engineering. The effect of input uncertainties on the solutions can be determined by the law of propagation of uncertainties. According to the guide to the expression of uncertainties in measurements (GUM) and its supplements, Monte Carlo sampling is recommended for nonlinear problems. In practice, large sampling sizes have to be chosen to ensure accuracy and precision. For computationally expensive problems only small sampling sizes are accessible. In this article we study and compare the propagation of uncertainties using three different sampling methods. The sampling methods chosen are Monte Carlo sampling, Latin hypercube sampling and a Sobol sequence based quasi Monte Carlo sampling. The methods are applied to the inverse problem of scatterometry with several simplifying assumptions in the measurement model. The solution of the inverse problem of scatterometry involves finite element solutions of a two dimensional Helmholtz equation. We found that among methods chosen Latin hypercube provides the most accurate and reliable results with respect to estimates of the geometry parameters, uncertainties and to repeatability.

A variance decomposition approach to uncertainty quantification and sensitivity analysis of the Johnson and Ettinger model

The Johnson and Ettinger (J&E) model is the most widely used vapor intrusion model in the United States. It is routinely used as part of hazardous waste site assessments to evaluate the potential for vapor intrusion exposure risks. This study incorporates mathematical approaches that allow sensitivity and uncertainty of the J&E model to be evaluated. In addition to performing Monte Carlo simulations to examine the uncertainty in the J&E model output, a powerful global sensitivity analysis technique based on Sobol indices is used to evaluate J&E model sensitivity to variations in the input parameters. The results suggest that the J&E model is most sensitive to the building air exchange rate, regardless of soil type and source depth. Building air exchange rate is not routinely measured during vapor intrusion investigations, but clearly improved estimates and/or measurements of the air exchange rate would lead to improved model predictions. It is also found that the J&E model is more sensitive to effective diffusivity than to effective permeability. Field measurements of effective diffusivity are not commonly collected during vapor intrusion investigations; however, consideration of this parameter warrants additional attention. Finally, the effects of input uncertainties on model predictions for different scenarios (e.g., sandy soil as compared to clayey soil, and “shallow” sources as compared to “deep” sources) are evaluated. Our results not only identify the range of variability to be expected depending on the scenario at hand, but also mark the important cases where special care is needed when estimating the input parameters to which the J&E model is most sensitive.Implications: The research described herein uses stochastic approaches to investigate the effect of individual input parameters on the J&E model. The results suggest that the J&E model is most sensitive to the building air exchange rate, regardless of soil type and source depth. Additional analysis reveals that chemical transport is more sensitive to effective diffusivity of the soil, rather than effective permeability of the soil. Accordingly, effective diffusivity and air exchange rates warrant additional attention when assessing vapor intrusion exposure risks at hazardous waste sites.

Effects of input uncertainty and variability on the modelled environmental fate of organic pollutants under global climate change scenarios

Global climate change (GCC) is expected to influence the fate, exposure and risks of organic pollutants to wildlife and humans. Multimedia chemical fate models have been previously applied to estimate how GCC affects pollutant concentrations in the environment and biota, but previous studies have not addressed how uncertainty and variability of model inputs affect model predictions. Here, we assess the influence of climate variability and chemical property uncertainty on future projections of environmental fate of six polychlorinated biphenyl congeners under different GCC scenarios using a spreadsheet version of the ChemCAN model and the Crystal Ball® software. Regardless of emission mode, results demonstrate: (i) uncertainty in degradation half-lives dominates the variance of modelled absolute levels of PCB congeners under GCC scenarios; (ii) when the ratios of predictions under GCC to predictions under present day climate are modelled, climate variability dominates the variance of modelled ratios; and (iii) the ratios also indicate a maximum of about a factor of 2 change in the long-term average environmental concentrations due to GCC that is forecasted between present conditions and the period between 2080 and 2099. We conclude that chemical property uncertainty does not preclude assessing relative changes in a GCC scenario compared to a present-day scenario if variance in model outputs due to chemical properties and degradation half-lives can be assumed to cancel out in the two scenarios.

The trajectory importance measure of the shaping machine under stochastic excitation

Two trajectory importance measures, the trajectory importance measure based on variance and the moment-independent trajectory importance measure, are proposed to represent the time-variant effects of input uncertainty on the output uncertainty of the shaping machine under stochastic excitation in its work stroke, respectively. At the same time, the trajectory importance measure based on the failure probability is proposed to reflect the contribution of the input uncertainty on the dynamic reliability of the mechanism. These three trajectory importance measures provide different references to improve the performance and reliability of the mechanism from the time-variant perspective. As the probability density evolution method (PDEM) is employed to solve the proposed trajectory importance measures, it can improve the computational efficiency largely without losing precision. Results of the shaping mechanism illustrate the feasibility of the proposed trajectory importance measures and the veracity of the PDEM in solving the lathe mechanism.

Streamflow prediction with uncertainty analysis, Weida catchment, Germany

This study investigated the effects of rainfall input uncertainty on parameter estimation and predictions of stream flow in Weida catchment, Germany. Based on rainfall systematic and non-systematic errors, the uncertainty in the rainfall input data was implemented using the rainfall data of five gauging stations. 100 rainfall time series were generated based on precipitations for each gauging station. These randomly generated rainfall time series were employed with a type of Probability Distribution Model (PDM). Using the Monte Carlo method, the posterior distributions of the model parameters were computed, and the effects of the input uncertainty were assessed. This was done by following the concept of the extended GLUE. The hydrographs were simulated using all combinations of feasible rainfall data (i.e., 100 series) and model parameters (i.e., behavioural model parameter sets), the aim of which was to include the uncertainty sources of input data and model parameter. The 90% confidence interval of these hydrographs covers 31% of observed flows. Although the results in this study provide no clear evidence of the effects of rainfall uncertainty on parameter estimation, it does indicate that the suggested method in this study has the potential to cover major uncertainty in input data and model parameter.

Integrated multi-objective robust optimization and sensitivity analysis with irreducible and reducible interval uncertainty

Uncertainty considered in robust optimization is usually treated as irreducible since it is not reduced during an optimization procedure. In contrast, uncertainty considered in sensitivity analysis is treated as partially or fully reducible in order to quantify the effect of input uncertainty on the outputs of the system. Considering this, and the usual existence of both reducible and irreducible uncertainty, an approach that can perform robust optimization and sensitivity analysis simultaneously is of much interest. This article presents such an integrated optimization model that can be used for both robust optimization and sensitivity analysis for problems that have irreducible and reducible interval uncertainty, multiple objective functions and mixed continuous-discrete design variables. The proposed model is demonstrated by two engineering examples with differing complexity to demonstrate its applicability.

Addressing equifinality and uncertainty in eutrophication models

Large simulation models of eutrophication processes are commonly used to aid scientific understanding and to guide management decisions. Confidence in models for these purposes depends on uncertainty in model equations (structural uncertainty) and on effects of input uncertainties (model parameters, initial conditions, and forcing functions) on model outputs. Our objective herein is to illustrate two strategies, a generalized likelihood uncertainty estimation (GLUE) approach combined with a simple Monte Carlo sampling scheme and a Bayesian methodological framework along with Markov Chain Monte Carlo (MCMC) simulations, for elucidating the propagation of uncertainty in the high‐dimensional parameter spaces of mechanistic eutrophication models. We examine the ability of the two approaches to offer insights into the degree of information about model inputs that the data contain, to quantify the correlation structure among parameter estimates, and to obtain predictions along with uncertainty bounds for modeled output variables. Our analysis is based on a four‐state‐variable (phosphate‐detritus‐phytoplankton‐zooplankton) model and the mesotrophic Lake Washington (Washington State, United States) as a case study. Scientific knowledge, expert judgment, and observational data were used to formulate prior probability distributions and characterize the uncertainty pertaining to 14 model parameters. Despite the conceptual differences for addressing model equifinality, that is, wide ranges of parameter values subject to complex multivariate relationships that result in plausible observed behaviors and produce equivalently accurate predictions, we found that the two strategies provided fairly consistent estimates of the posterior parameter correlation structure and output uncertainty. Nonetheless, our analysis also shows that MCMC can more efficiently quantify the joint probability distribution of model parameters and make inference about this distribution. The latter finding can be explained by the basic idea underlying the MCMC methodology, that is, the configuration of a Markov process whose stationary distribution approximates the joint posterior distribution of all the stochastic model nodes; as a result, Monte Carlo samples are not drawn from the prior parameter space, and problems of wide or highly correlated prior distributions can be overcome. Finally, our study stresses the lack of perfect simulators of natural system dynamics and introduces two statistical formulations that can explicitly account for the discrepancy between mathematical models and environmental systems.

Confidence of simulation results: put a sensitivity analysis module in your MODEL: The IEA-ECBCS Annex 23 experience of model evaluation

The goal of performing sensitivity analysis of a simulation model is to determine the effect of input variation and the effect of input uncertainty on the output data. Sensitivity analysis is an unavoidable step in model validation, and it is also generally useful in performing simulations. The user must know the influence of the accuracy of the data that is input to the program. This paper presents a methodology for performing sensitivity analysis as well as the tools that implement this methodology, MISA and LiSA, that were developed within the IEA-ECBCS Annex 23 `Multizone air flow modeling'. The basic concepts of sensitivity analysis as well as the main characteristics of the developed tool are presented. More detailed information are available in the final report of the sub-task 3 `Evaluation of COMIS' of the Annex 23 [J.-M. Fürbringer, C.-A. Roulet, R. Borchiellini, Evaluation of COMIS, final report IEA.ECB&CS Annex 23 Multizone Air flow Modelling, LESO-PB, EPFL, 1015 Lausanne, Switzerland, 1996.].

On Monte Carlo simulations of dynamic systems

The Monte Carlo method provides both design and research engineers with a useful tool for evaluating the effect of input uncertainty on system performance. This paper addresses the basics and the utility of the Monte Carlo approach. Two practical applications of the method help to demonstrate why Monte Carlo simulation is becoming a contemporary trend in system analysis.