Uncertainties In Other Parameters Research Articles

Stochastic Dual Dynamic Programming for Multiechelon Lot Sizing with Component Substitution

This work investigates lot sizing with component substitution under demand uncertainty. The integration of component substitution with lot sizing in an uncertain demand context is important because the consolidation of the demand for components naturally allows risk-pooling and reduces operating costs. The considered problem is relevant not only in a production context, but also in the context of distribution planning. We propose a stochastic programming formulation for the static–dynamic type of uncertainty, in which the setup decisions are frozen but the production and consumption quantities are decided dynamically. To tackle the scalability issues commonly encountered in multistage stochastic optimization, this paper investigates the use of stochastic dual dynamic programming (SDDP). In addition, we consider various improvements of SDDP, including the use of strong cuts, the fast generation of cuts by solving the linear relaxation of the problem, and retaining the average demand scenarios. Finally, we propose two heuristics, namely, a hybrid of progressive hedging with SDDP and a heuristic version of SDDP. Computational experiments conducted on well-known instances from the literature show that the heuristic version of SDDP outperforms other methods. The proposed method can plan with up to 10 decision stages and 20 scenarios per stage, which results in 2010 scenario paths in total. Moreover, as the heuristic version of SDDP can replan to account for new information in less than a second, it is convenient in a dynamic context. Summary of Contribution: We believe our paper is suitable for the mission and scope of IJOC because we design efficient algorithms to solve an operations research problem. More precisely, we investigate the use of stochastic dual dynamic programming (SDDP) for lot sizing with component substitution under demand uncertainty. In this work, we consider the static–dynamic decision framework, and a good approximation of the expected costs in this context requires us to solve the problem with a large number of scenarios of future demand. As solving the considered problem is computationally intensive, we investigate the use of SDDP, which decomposes the problem per decision stage. We study several enhancements of SDDP, such as the use of strong cuts, the incorporation of a lower bound computed with the average demand scenario, the multicut version of SDDP, and scenario sampling with randomized quasi–Monte Carlo. Despite these improvements, the convergence of SDDP remains slow. Consequently, we propose a heuristic version of SDDP and a hybrid of progressive hedging and SDDP. We present the results of an extensive computational study performed on well-known instances from the literature. The results show that the heuristic SDDP outperforms the hybrid of progressive hedging with SDDP and state-of-the-art methods from the literature. Besides, our analysis shows that component substitution can pool the risk, and it allows maintaining the same service level with less inventory. The presented methodology can be used by practitioners to size their production lots, and subsequent researchers can build upon our results to consider uncertainty in other parameters, such as lead times, yields, and production capacities. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This work was supported by Mitacs and the Institut de Valorisation des Données (IVADO). Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2022.1215 .

Effect of magnetic screening mass on the diffusion of heavy quarks

The drag and diffusion coefficients of heavy quarks propagating through quark–gluon plasma (QGP) have been estimated by shielding the infra-red divergences using electric and magnetic screening masses. The electric-type screening in perturbative quantum chromodynamics (pQCD) has been widely studied and used in evaluating the diffusion coefficient of heavy quarks (HQs). The impact of magnetic screening on diffusion coefficients of HQs is not studied before to the best of our knowledge. We explore the effect of magnetic screening mass on the drag and diffusion coefficients of HQs and found it to be non-negligible. Therefore, the effect of magnetic screening should be taken into consideration to characterize hot and dense matter formed in the collisions of nuclei at ultra-relativistic energies. We estimate the suppression of heavy flavored mesons in heavy ion collisions compared to proton+proton collisions at high transverse momenta and found that the suppression is less with the inclusion of magnetic screening. The value of the magnetic screening mass is not known exactly because of its nonperturbative nature. Moreover, it may not be possible to single out the effect of magnetic mass because of the uncertainties in other parameters involved in the diffusion process of HQs. Still it is important to include the effects of magnetic screening because of its physical origin in QCD.

Blanding's Turtle Demography and Population Viability

AbstractIn anticipation of U.S. federal status classification (warranted, warranted but precluded, not warranted), scheduled for 2023, we provide population viability analysis of the Blanding's turtle Emydoidea blandingii, a long-lived, late-maturing, semi-aquatic species of conservation concern throughout its range. We present demographic data from long-term study of a population in northeastern Illinois and use these data as the basis for viability and sensitivity analyses focused on parameter uncertainty and geographic parameter variation. We use population viability analysis to identify population sizes necessary to provide population resiliency to stochastic disturbance events and catastrophes, and demonstrate how alternative definitions of ‘foreseeable future' might affect status decisions. Demographic parameters within our focal population resulted in optimistic population projections (probability of extinction = 0% over 100 y) but results were less optimistic when catastrophes or uncertainty in parameter estimates were incorporated (probability of extinction = 3% and 16%, respectively). Uncertainty in estimates of age-specific mortality had the biggest impact on population viability analysis outcomes but uncertainty in other parameters (age of first reproduction, environmental variation in age-specific mortality, percent of females reproducing, clutch size) also contributed. Blanding's turtle demography varies geographically and incorporating this variation resulted in both mortality- and fecundity-related parameters affecting population viability analysis outcomes. Possibly, compensatory variation among demographic parameters allows for persistence across a wide range of parameter values. We found that extinction risk decreased and retention of genetic diversity increased rapidly with increasing initial population size. In the absence of catastrophes, demographic conservation goals could be met with a smaller initial population size than could genetic conservation goals; ≥20–50 adults were necessary for extinction risk <5%, whereas ≥50–110 adults were necessary to retain >95% of existing genetic diversity over 100 y. These thresholds shifted upward when catastrophes were included; ≥50–200 adults were necessary for extinction risk <5% and ≥110 to >200 adults were necessary to retain >95% of existing genetic diversity over 100 y. Impediments to Blanding's turtle conservation include an incomplete understanding of geographic covariation among demographic parameters, the large amount of effort necessary to estimate and monitor abundance, and uncertainty regarding the impacts of increasingly frequent extreme weather events.

Service life prediction of corrosion-affected reinforced concrete columns based on time-dependent reliability analysis

Reinforced concrete columns in chloride-laden environments are prone to steel reinforcement corrosion, which reduces their capacity to resist applied loads. The current study modeled the time-dependent effect of corrosion as a non-stationary Gaussian process while accounting for the uncertainties of other parameters using random variables. The down-crossing rate of the residual capacity of these structures under combined axial loads and bending moments from the safe domain has been calculated using a recently derived closed-form equation, and the corresponding first passage probability has been estimated over the service life of the column. It was found that corrosion significantly affected the remaining service life of the columns due to the loss of reinforcement, especially in the tensile region of the column interaction curve. This indicates that the probability of failure due to lateral loads and bending moments in corrosion-affected columns can be significantly high; therefore, the load and resistance factors in design codes and standards should be calibrated accordingly. It is also found that if the effects of confinement loss of core concrete of column and spalling of concrete cover due to corrosion of transverse reinforcement are modeled as well the reliability index profiles in tensile and compressive regions of the interaction curve would match more closely. This is a research domain which needs further investigations.

Uncertainty analysis of correlated parameters in automated reaction mechanism generation

AbstractUncertainty analysis is a useful tool for inspecting and improving detailed kinetic mechanisms because it can identify the greatest sources of model output error. Owing to the very nonlinear relationship between kinetic and thermodynamic parameters and computed concentrations, model predictions can be extremely sensitive to uncertainties in some parameters while uncertainties in other parameters can be irrelevant. Error propagation becomes even more convoluted in automatically generated kinetic models, where input uncertainties are correlated through kinetic rate rules and thermodynamic group values.Local and global uncertainty analyses were implemented and used to analyze error propagation in Reaction Mechanism Generator (RMG), an open‐source software for generating kinetic models. A framework for automatically assigning parameter uncertainties to estimated thermodynamics and kinetics was created, enabling tracking of correlated uncertainties. Local first‐order uncertainty propagation was implemented using sensitivities computed natively within RMG. Global uncertainty analysis was implemented using adaptive Smolyak pseudospectral approximations as implemented in the MIT Uncertainty Quantification Library to efficiently compute and construct polynomial chaos expansions to approximate the dependence of outputs on a subset of uncertain inputs. Cantera was used as a backend for simulating the reactor system in the global analysis. Analyses were performed for a phenyldodecane pyrolysis model. Local and global methods demonstrated similar trends; however, many uncertainties were significantly overestimated by the local analysis. Both local and global analyses show that correlated uncertainties based on kinetic rate rules and thermochemical groups drastically reduce a model's degrees of freedom and have a large impact on the determination of the most influential input parameters. These results highlight the necessity of incorporating uncertainty analysis in the mechanism generation workflow.

Time-dependent reliability analysis of the motor hanger for EMU based on stochastic process

Purpose Most of the previous work on reliability analysis was based on the traditional reliability theory. The calculated results can only reflect the reliability of components at a specific time, which neglects the uncertainty of load and resistance over time. The purpose of this paper is to develop a time-dependent reliability analysis approach based on stochastic process to deal with the problem and apply it to the structural design of railway vehicle components. Design/methodology/approach First, the parametric model of motor hanger for electric multiple unit (EMU) is established by ANSYS parametric design language, and its structural stress is analyzed according to relevant standards. The Latin hypercube method is used to analyze the sensitivity of the structure, and the uncertainty parameters (sizes and loads) which have great influence on the structural strength are determined. The D-optimal experimental design is carried out to establish the polynomial response surface function, which characterizes the relationship between uncertainty parameters and structural stress. Second, the Poisson stochastic process is adopted to describe the number of loads acting, and the Monte Carlo method is used to obtain the load acting history according to its probability distribution characteristics. The load history is introduced into the response surface function and the uncertainty of other parameters is considered at the same time, and the stress history of the motor hanger is obtained. Finally, the degradation process of structural resistance is described by a Gamma stochastic process, and the time-dependent reliability of the motor hanger is calculated based on the reliability theory. Findings Time and the uncertainties of parameters have great impact on reliability. The results of reliability decrease with time fluctuation are more reasonable, stable and credible than traditional methods. Practical implications In this paper, the proposed method is applied to the structural design of the motor hanger for EMU, which has a good guiding significance for accurately evaluating whether if the design meets the reliability requirements. Originality/value The value of this paper is that the method takes both the randomness of load over time and the uncertainty of structural parameters in the design and manufactures process into consideration, and describes the monotonous degradation characteristics of structural resistance. At the same time, the time-dependent reliability of mechanical components is calculated by a response surface method. It not only improves the accuracy of reliability analysis, but also improves the analysis efficiency and solves the problem that the traditional reliability analysis method can only reflect the static reliability of components.

Erratum

Erratum

Characterizing the effects of policy instruments on the future costs of carbon capture for coal power plants

We develop a methodology with which to assess the effects of policy instruments on the long-term abatement and costs of carbon capture and storage (CCS) technologies for coal power plants. Using an expert elicitation, historical data on the determinants of technological change in energy, values from the engineering literature, and demand estimates from an integrated assessment model, we simulate ranges of outcomes between 2025 and 2095. We introduce probability distributions of all important parameters and propagate them through the model to generate probability distributions of electricity costs, abatement costs, and CO2 avoided over time. Carbon pricing has larger effects than R&D and subsidies. But much of the range of outcomes is driven by uncertainty in other parameters, such as capital costs and returns to scale. Availability of other low carbon technologies, particularly bioenergy with CCS affects outcomes. Subsidies have the biggest impacts when they coincide with expanding manufacturing scale of CCS components. Our results point to 4 parameters for which better information is needed for future work informing technology policy to address climate change: capital costs, demonstration plants, growth constraints, and knowledge spillovers among technologies.

Effect of uncertainties in wind speed and direction on the fatigue damage of long-span bridges

In order to estimate wind-induced fatigue damage, most methods use the probability density functions of wind speed and direction. Conventional approaches assume that these functions are error-free and provide a single estimated damage value. However, the estimated damage may contain significant errors because the probability density functions are generally inexact, and the parameters for the functions rely on limited measured data. We propose a Bayesian approach to determine the fatigue damage while considering the uncertainties in the probability model and the parameter. The proposed approach provides a distribution of damage values, which enables more comprehensive analysis of fatigue damage using bounds and exceedance probability. The approach is applied to the estimation of fatigue damage of long-span bridges. We also illustrate an additional feature of the Bayesian approach, which is to systematically update the damage index as more measurements become available over time. Effect of data size is investigated to quantify the error due to the limited measured data. The influence of uncertainties in other parameters and effects of long term wind speed variability is also included in this study.

A Data Reconciliation Based Approach to Accuracy Enhancement of Operational Data in Power Plants

Accuracy of operational data of a power plant is essential for power plant performance monitoring and fault diagnosis. However, due to inevitable occurrence of systematic and measurement errors in the course of obtaining operational data, these errors can only be reduced to a certain level but never be eliminated. In this work, we propose a data reconciliation based approach to reduce the errors of operational data thus enhance the accuracy of the data. The reconciled data can then be used in performance monitoring and fault diagnosis systems to improve their performances. The proposed method is based on more efficient use of redundant data and a first-principle mathematical model of a power plant. Then an optimization process is performed where the weighted least square form of aggregated differences between measured data and their estimated values are minimized. To illustrate the capability of the proposed method, we provide a case study of data reconciliation for feedwater heater heat balance analysis in a 660 MW coal- fired power plant in China. Results show that uncertainty of four key parameters, namely feed water mass flow rate, condensate mass flow rate, deaerator pressure and outlet temperature, can be reduced by 24 %, 30 %, 5 % and 65 %, whilst the uncertainty of other parameters are also reduced to various extent. Moreover, the results also indicate that the proposed approach is effective over a wide range of measured data quality, where quality of some data could be much worse than others and the estimated measurement uncertainties of operational data may not be accurate.

Simulation of 3D Gaussian surface topography

Abstract Gaussian isotropic and anisotropic surfaces of desired areal autocorrelation function were modeled using procedures found in technical literature. Next measured 3D surfaces of normal ordinate distribution were tested. The special procedure was developed for simulating 3D surfaces after one-step honing. The similarities between the modeled and real areal autocorrelation functions were analysed. Measured and modeled surface topography parameters were also compared. It was found that surface topography modeling ensured good matching accuracy of statistical height parameters and slope. The uncertainty of other parameters was greater.

Using postglacial sea level, crustal velocities and gravity-rate-of-change to constrain the influence of thermal effects on mantle lateral heterogeneities

Lateral heterogeneities in the mantle can be caused by thermal, chemical and non-isotropic pre-stress effects. Here, we investigate the possibility of using observations of the glacial isostatic adjustment (GIA) process to constrain the thermal contribution to lateral variations in mantle viscosity. In particular, global historic relative sea level, GPS in Laurentide and Fennoscandia, altimetry together with tide-gauge data in the Great Lakes area, and GRACE data in Laurentide are used. The lateral viscosity perturbations are inferred from the seismic tomography model S20A by inserting the scaling factor β to determine the contribution of thermal effects versus compositional heterogeneity and non-isotropic pre-stress effects on lateral heterogeneity in mantle viscosity. When β = 1, lateral velocity variations are caused by thermal effects alone. With β < 1, the contribution of thermal effect decreases, so that for β = 0, there is no lateral viscosity variation and the Earth is laterally homogeneous. These lateral viscosity variations are superposed on four different reference models which differ significantly in the lower mantle viscosity. The Coupled Laplace Finite Element method is used to predict the GIA response on a spherical, self-gravitating, compressible, viscoelastic Earth with self-gravitating oceans, induced by the ICE-4G deglaciation model. Results show that the effect of β on uplift rates and gravity rate-of-change is not simple and involves the trade-off between the contribution of lateral viscosity variations in the transition zone and in the lower mantle. Models with small viscosity contrast in the lower mantle cannot explain the observed uplift rates in Laurentide and Fennoscandia. However, the RF3S20 model with a reference viscosity profile simplified from Peltier's VM2 with the value of β around 0.2–0.4 is found to explain most of the global RSL data, the uplift rates in Laurentide and Fennoscandia and the BIFROST horizontal velocity data. In addition, the changes in GIA signals caused by changes in the value of β are large enough to be detected by the data, although uncertainty in other parameters in the GIA models still exists. This may encourage us to further utilize GIA observations to constrain the thermal effect on mantle lateral heterogeneity as geodetic and satellite gravity measurements are improved.

Effect of leptonic CP phase in νμ→ νμoscillations

In the case of large 1-3 mixing angle as sin^2(2theta13 > 0.03, we investigate the possibility for measuring the leptonic CP phase by using only nu_mu --> nu_mu oscillations independently of nu_mu --> nu_e oscillations. As the result, we find that the CP phase can be measured best around the energy E=0.43 GeV and the baseline length L=5000km without strongly depending on the uncertainties of other parameters. In this region, the CP phase effect remains even after averaging over neutrino energy. We also find that there is the CP sensitivity even in the short baseline length L < 1000 km if Delta m_{31}^2 is determined with the uncertainty of about 0.1 . In the T2KK experiment, we explore the possibility for determining Delta m_{31}^2 by using one baseline from Tokai to Korea and then measuring the CP phase by using the baseline to Kamioka. As the result, we find that some information of the CP phase can be obtained from both measurements.

Simultaneous uncertainty quantification of fracture mechanics based life prediction model parameters

A Bayesian technique is developed for simultaneous estimation of the equivalent initial flaw size (EIFS) and crack growth rate distributions in fracture mechanics based life prediction models from inspection data. The inference method separately quantifies the different sources of variability to obtain a data set independent EIFS distribution without the requirement for prior knowledge of the uncertainties in other parameters. The ability to simultaneously and accurately predict the EIFS distribution and crack growth rate noise from a small, highly-scattered data set is demonstrated in a numerical example.

Systematic effects in lens inversions - Aleph(1) exact models for 0957 + 561

Due to the careful study of its VLBI structures, the gravitational lens 0957 + 561 is the most accurately characterized of the lens candidates. Nonetheless, the observational data supplies only five firm constraints, compared to a minimum of nine free parameters in simple models for the lens using an elliptical galaxy and an elliptical cluster both with fixed radial structure. This paper examines the systematic variations between models for the lens potential that satisfy the constraints exactly. This is done using both the 4 degrees of freedom left when the radial structure of the galaxy is fixed, as well as variations due to changes in the radial structure. The systematic variations between the models allow for a range of time delays from approximately 0.1h^-1^ to 1.0h^-1^ yr for a fixed Einstein-de Sitter cosmology if the galaxy and the cluster satisfy the velocity dispersion constraints of 240 &lt;~σ_g_&lt;~ 320 km s^-1^, and 500&lt;~σ_c_&lt;~ 1500 km s^-1^, and the center of the cluster lies within 30" of the galaxy. Given the formal value for the velocity dispersion (303 +/- 50 km s^-1^) and the measured time delay (1.3 +/- 0.1 yr), I find that h &lt;~ 0.6 +/- 0.2 considering only the observational errors in the velocity dispersion. However, there are large uncertainties in the relationship between the observed velocity dispersion and the mass distribution. For example, the presence of a dark matter halo which raises the velocity dispersion which characterizes the mass by a factor of (3/2)^1/2^ relative to the observed velocity dispersion, formally increases the value of the Hubble constant to h &lt;~ 0.9 +/- 0.3, although the + 0.3 error bar is probably an exaggeration. Even with a known velocity dispersion, uncertainties in other parameters of the system, such as the principal axis of the mass distribution in the galaxy, can also introduce large uncertainties into the time delay. Because the images in 0957 + 561 only weakly constrain the mass distribution of the lens, the 0957 + 561 system can be used to measure the Hubble constant only to the accuracy with which observational parameters such as central velocity dispersion, ellipticities, and orientations can be translated into information on the mass distribution in the system. This systematic problem is the ultimate limitation on the measurement, and the statement that the 0957 + 561 system can measure H_0_ to a given level of accuracy is equivalent to the claim that the mass distribution in the lens galaxy or cluster is understood to the same level of accuracy.