A subset selection procedure under input parameter uncertainty

Dependencies occur naturally between input processes of many manufacturing and service applications. When the dependence parameters are known with certainty, the failure to factor the dependencies into decisions is well known to waste significant resources in system management. Our focus is on the case of unknown dependence parameters that must be estimated from finite amounts of historical input data. In this case, the estimates of the unknown dependence parameters are random variables and simulations are designed to account for the dependence parameter uncertainty to better support the data-driven decision making. The premise of our paper is that there are certain cases in which the assumption of an independent input process to minimize the expected cost of input parameter uncertainty becomes preferable to accounting for the dependence parameter uncertainty in the simulation. Therefore, a fundamental question to answer before capturing the dependence parameter uncertainty in a stochastic system simulation is whether there is sufficient statistical evidence to represent the dependence, despite the uncertainty around its estimate, in the presence of limited data. We seek an answer for this question within a data-driven inventory-management context by considering an intermittent demand process with correlated demand size and number of inter-demand periods. We propose two new finite-sample hypothesis tests to serve as the decision support tools determining when to ignore the correlation and when to account for the correlation together with the uncertainty around its estimate. We show that a statistical test accounting for the expected cost of correlation parameter uncertainty tends to reject the independence assumption less frequently than a statistical test which only considers the sampling distribution of the correlation-parameter estimator. The use of these tests is illustrated with examples and insights are provided into operational testing for dependence modeling.

Parameter uncertainty in hydrologic modeling is commonly evaluated, but assessing the impact of spatial input data uncertainty in spatially descriptive ‘distributed’ models is not common. This study compares the significance of uncertainty in spatial input data and model parameters on the output uncertainty of a distributed hydrology and sediment transport model, HYdrology Simulation using Time-ARea method (HYSTAR). The Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm was used to quantify parameter uncertainty of the model. Errors in elevation and land cover layers were simulated using the Sequential Gaussian/Indicator Simulation (SGS/SIS) techniques and then incorporated into the model to evaluate their impact on the outputs relative to those of the parameter uncertainty. This study demonstrated that parameter uncertainty had a greater impact on model output than did errors in the spatial input data. In addition, errors in elevation data had a greater impact on model output than did errors in land cover data. Thus, for the HYSTAR distributed hydrologic model, accuracy and reliability can be improved more effectively by refining parameters rather than further improving the accuracy of spatial input data and by emphasizing the topographic data over the land cover data.

ABSTRACTStochastic inventory system simulation is often the tool of choice by industry practitioners who struggle with the evaluation of the quality of proposed inventory targets using service levels. However, driving simulations with unknown input distribution parameters has its own challenges. In this paper, we focus on the newsvendor problem and quantify the amount of demand parameter uncertainty – the uncertainty around the unknown demand distribution parameters which are estimated from the limited historical demand data – in the confidence interval of the mean service level. We use this quantification to understand how the variance of the mean service level, due to the amount of the demand parameter uncertainty in the simulation output process, changes with the choice of Type-1 and Type-2 service-level criteria, the historical data length, the ratio of the unit shortage cost to the unit holding cost, and the distributional shape of the demand’s density function.

Natural and anthropogenic emissions of sulfur-bearing species significantly alter the sulfur and energy budgets of the Earth's atmosphere. Simulations of the atmospheric sulfur cycle, sulfate radiative forcing, and predictions of their future changes require a precise understanding of the SO2 oxidation rates that control the formation of secondary sulfate aerosols. Given the unique single source of radiosulfur (cosmogenic 35S radionuclide), combined measurements of atmospheric radiosulfur in both sulfur dioxide (35SO2) and sulfate (35SO4 2-) have been employed to constrain sulfur oxidation rates in the atmosphere. This approach employed box model calculations, incorporating several key assumed parameters, including sulfur deposition rates. However, previous calculations did not fully consider uncertainties in parametrizations, necessitating a re-examination of the estimated values. In this study, we applied a new approach to revisit existing combined measurements of 35SO2 and 35SO4 2- at coastal and inland sites. We estimated the temporospatial variability in SO2 oxidation rates by incorporating a comprehensive consideration of parametrization uncertainties. We adopted deposition data from nine models of the Atmospheric Chemistry and Climate Model Intercomparison Project. Uncertainties in deposition data and other key parameters, such as cosmogenic 35S production rates and 35SO2/35SO4 2- ratios in the free troposphere, were evaluated by using a Monte Carlo approach. Our new analysis reveals higher SO2 oxidation rates than previously estimated, consistent with recent multiphase kinetics studies. Additionally, the potential relationship between changes in SO2 oxidation rates and sulfate formation pathways was elucidated by comparing these results to sulfate oxygen-17 anomalies. Our approach and findings offer a stringent assessment of how various sulfate formation pathways contribute to the overall SO2 oxidation rate in the planetary boundary layer and are therefore useful for evaluating the impacts of the atmospheric sulfur cycle on environmental health, public health, and climate.

<strong class="journal-contentHeaderColor">Abstract.</strong> Due to the remote location of many volcanoes, there is substantial uncertainty about the timing, amount and vertical distribution of volcanic ash released when they erupt. One approach to determine these properties is to combine prior estimates with satellite retrievals and simulations from atmospheric dispersion models to create posterior emission estimates, constrained by both the observations and the prior estimates, using a technique known as source inversion. However, the results are dependent not only on the accuracy of the prior assumptions, the atmospheric dispersion model and the observations used, but also on the accuracy of the meteorological data used in the dispersion simulations. In this study, we advance the source inversion approach by using an ensemble of meteorological data from the Met Office Global and Regional Ensemble Prediction System to represent the uncertainty in the meteorological data and apply it to the 2019 eruption of Raikoke. Retrievals from the Himawari-8 satellite are combined with NAME dispersion model simulations to create posterior emission estimates. The use of ensemble meteorology provides confidence in the posterior emission estimates and associated dispersion simulations that are used to produce ash forecasts. Prior mean estimates of fine volcanic ash emissions for the Raikoke eruption based on plume height observations are more than 15 times higher than any of the mean posterior ensemble estimates. In addition, the posterior estimates have a different vertical distribution, with 27 %–44 % of ash being emitted into the stratosphere compared to 8 % in the mean prior estimate. This has consequences for the long-range transport of ash, as deposition to the surface from this region of the atmosphere happens over long timescales. The posterior ensemble spread represents uncertainty in the inversion estimate of the ash emissions. For the first 48 h following the eruption, the prior ash column loadings lie outside an estimate of the error associated with a set of independent satellite retrievals, whereas the posterior ensemble column loadings do not. Applying a risk-based methodology to an ensemble of dispersion simulations using the posterior emissions shows that the area deemed to be of the highest risk to aviation, based on the fraction of ensemble members exceeding predefined ash concentration thresholds, is reduced by 49 %. This is compared to estimates using an ensemble of dispersion simulations using the prior emissions with ensemble meteorology. If source inversion had been used following the eruption of Raikoke, it would have had the potential to significantly reduce disruptions to aviation operations. The posterior inversion emission estimates are also sensitive to uncertainty in other eruption source parameters and internal dispersion model parameters. Extending the ensemble inversion methodology to account for uncertainty in these parameters would give a more complete picture of the emission uncertainty, further increasing confidence in these estimates.

Input modeling is the selection of a probability distribution to capture the uncertainty in the input environment of a stochastic system. Example applications of input modeling include the representation of the randomness in the time to failure for a machining process, the time between arrivals of calls to a call center, and the demand received for a product of an inventory system. Building simulations of stochastic systems requires the development of input models that adequately represent the uncertainty in such random variables. Since there are an abundance of probability distributions that can be used for this purpose, a natural question to ask is how to identify the probability distribution that best represents the particular situation under study. For example, is the exponential distribution a reasonable choice to represent the time to failure for a machining process, or is it better to use an empirical distribution function obtained from the historical time-to-failure data? Recognizing the fact that there is no true input model waiting to be found, the goal of stochastic input modeling is to obtain an approximation that captures the key characteristics of the system inputs. The development of a good input model requires the collection of as much information as possible about the relevant randomness in the system as well as the historical data consisting of the past realizations of the random variables of interest. In the presence of a data set, the input model can be identified by fitting a probability distribution to the historical data. However, it may be difficult and/or costly to collect data for the stochastic system under study; it can also be impossible to properly collect any data at all such as when the proposed system does not exist. In the absence of historical data, any relevant information (e.g., expert opinion and the conventional bounds suggested by the underlying physical situation) can be used for input modeling. This article addresses the key issues that arise in stochastic input modeling both in the presence and in the absence of historical data. The first step in input modeling is to identify the sources of randomness in the input environment of the system under study. Many stochastic systems contain multiple sources of uncertainty, e.g., the completion time of an item on a particular machine, the potential breakdown of the machine, and the percentage of defective items produced by the machine might be among the sources of uncertainty in a manufacturing setting. Throughout, the random vector X = (X1, X2, …, X K )′ is used to represent the collection of K different inputs of a stochastic system, where X k is the random variable denoting the kth system input. The K components of this random vector might also be correlated with each other. Therefore, the stochastic properties of the random inputs X k , k = 1, 2, …, K, are captured in the joint probability

This interim report presents progress towards the development of meso-scale models of magnetic behavior that incorporate microstructural information. Modeling magnetic signatures in irradiated materials with complex microstructures (such as structural steels) is a significant challenge. The complexity is addressed incrementally, using the monocrystalline Fe (i.e., ferrite) film as model systems to develop and validate initial models, followed by polycrystalline Fe films, and by more complicated and representative alloys. In addition, the modeling incrementally addresses inclusion of other major phases (e.g., martensite, austenite), minor magnetic phases (e.g., carbides, FeCr precipitates), and minor nonmagnetic phases (e.g., Cu precipitates, voids). The focus of the magnetic modeling is on phase-field models. The models are based on the numerical solution to the Landau-Lifshitz-Gilbert equation. From the computational standpoint, phase-field modeling allows the simulation of large enough systems that relevant defect structures and their effects on functional properties like magnetism can be simulated. To date, two phase-field models have been generated in support of this work. First, a bulk iron model with periodic boundary conditions was generated as a proof-of-concept to investigate major loop effects of single versus polycrystalline bulk iron and effects of single non-magnetic defects. More recently, to support the experimental program herein using iron thin films, a new model was generated that uses finite boundary conditions representing surfaces and edges. This model has provided key insights into the domain structures observed in magnetic force microscopy (MFM) measurements. Simulation results for single crystal thin-film iron indicate the feasibility of the model for determining magnetic domain wall thickness and mobility in an externally applied field. Because the phase-field model dimensions are limited relative to the size of most specimens used in experiments, special experimental methods were devised to create similar boundary conditions in the iron films. Preliminary MFM studies conducted on single and polycrystalline iron films with small sub-areas created with focused ion beam have correlated quite well qualitatively with phase-field simulations. However, phase-field model dimensions are still small relative to experiments thus far. We are in the process of increasing the size of the models and decreasing specimen size so both have identical dimensions. Ongoing research is focused on validation of the phase-field model. Validation is being accomplished through comparison with experimentally obtained MFM images (in progress), and planned measurements of major hysteresis loops and first order reversal curves. Extrapolation of simulation sizes to represent a more stochastic bulk-like system will require sampling of various simulations (i.e., with single non-magnetic defect, single magnetic defect, single grain boundary, single dislocation, etc.) with distributions of input parameters. These outputs can then be compared to laboratory magnetic measurements and ultimately to simulate magnetic Barkhausen noise signals.

This paper mainly focuses on output feedback practical tracking controller design for stochastic nonlinear systems with polynomial function growth conditions. Mostly, there are some studies on output feedback tracking control problem for general nonlinear systems with parametric certainty in existing achievements. Moreover, we extend it to stochastic nonlinear systems with parametric uncertainty and system nonlinear terms are assumed to satisfy polynomial function growth conditions which are more relaxed than linear growth conditions or power growth conditions. Due to the presence of unknown parametric uncertainty, an output feedback practical tracking controller with dynamically updated gains is constructed explicitly so that all the states of the closed-loop systems are globally bounded and the tracking error belongs to arbitrarily small interval after some positive finite time. An example illustrates the efficiency of the theoretical results.

Uncertainty in structural dynamics: Experimental validation of a Wishart random matrix model

The concept of the time-optimal control algorithm [10] for linear discrete time systems with additional boundary constraints is extended to stochastic systems with parameter and state uncertainty. The Deterministic Time-Optimal Control problem has been solved by means of linear programming techniques. However, the optimal control strategy for stochastic systems yields control decisions which are cautious of the uncertainty in the system and which probe it for estimation purposes. Mathematical difficulties make it is hard to derive optimal (dual) control algorithms. Several suboptimal algorithms which have ignored the probing property are referred to as cautious control algorithms. In this paper a Cautious Time-Optimal Control algorithm will be derived.

A comparison is made between the convergence rates of two important algorithms in adaptation theory; one of them minimizes the empirical risk, while the other minimizes the Bayes a posteriori risk and is calculated according to the stipulated system of probability distributions which depend on a set of unknown parameters. The class of distributions is established for which the convergence rates of the indicated algorithms coincide. The relation between the conditions governing the indicated coincidence and the conditions governing the existence of efficient estimates of the unknown probability distribution parameters is investigated.

Understanding the impact of climate change and its variability on regional hydrology is predicated, to a large extent, on availability of long records of high quality climate data. Although recent advances in satellite technology have improved our observation capabilities, past records come from traditional in situ measurements that have large associated uncertainties. Further, the uncertainties in historical observations vary signicantly over space and in time. The information on uncertainty that is available with latest datasets is vastly ignored in the hydrologic literature. Since any relationship linking hydrologic and climatic variables is underpinned by historical data, ignoring this uncertainty information can be misleading. In this study, a methodology is developed to incorporate the observation uncertainty in climate data for hydrologic prediction by combining Bayesian learning theory and the concepts of robust optimization. A Bayesian variant of principal component analysis is used to propagate uncertainties in observations to derive a new representation of data with reduced dimensionality. Robust optimization is then used to obtain the parameters of the prediction model, a linear support vector machine in this case, by accounting for the uncertainty in data representation. The developed methodology is applied to make long-range prediction of Indian summer monsoon rainfall (ISMR) by capturing dynamic relationships between ISMR and sea surface temperature. The advantages of incorporating observation uncertainties for hydrologic predictions are discussed in the light of results obtained.

The reliability of buildings under winds is evaluated. The uncertainties in terms of the first and second statistical moments are included in the formulation. The dynamic response of the structure is obtained based on a random vibration analysis. In estimating the statistics of the wind load effects, uncertainties in the wind environment parameters and dynamic structural properties are considered. Risks of exceeding various safety and serviceability limit states are evaluated at critical sections of a 25 story steel building. Results indicate that uncertainties in the dynamic structural properties and wind environment parameters contribute significantly to the risk. The risk is also sensitive to the form of the extreme value distribution and errors in sampling and estimation of distribution parameters. The proposed method provides a tool for a comprehensive assessment of reliability of structures under wind loadings.

This chapter examines systems simulation as a solution in solving farm management problems. It is presented in four topics. The first and third cover the uses of simulation and general simulation methodology while the second contains a discussion on the simulation of stochastic systems. The remaining discussion covers a sample problem.

The Total Hazard Construction, Antithetic Variates and Simulation of Stochastic Systems.