Capacity Uncertainty Research Articles

Density and isochoric heat capacity of {x trans-1,3,3,3-Tetrafluoropropene + (1-x) Propane} at temperatures from (285.45 to 349.71) K and pressures up to 10.384 MPa

The increasingly serious global warming problem has accelerated the elimination of traditional hydrofluorocarbon (HFC) refrigerants. R1234ze(E) + R290 binary mixture as a potential alternative refrigerant are expected to overcome the deficiencies of R1234ze(E) (low volumetric refrigeration capacity) and R290 (flammability and explosiveness). In this paper, the 38 density and 119 isochoric specific heat capacity data of R1234ze(E)+R290 mixtures were measured at temperatures from (285.45 to 349.71) K using an adiabatic batch calorimeter with intermittent heating. Uncertainties of temperature, pressure, density and isochoric heat capacity were estimated to be less than 12 mK, 5 kPa, 0.30% and 1.0%. The density data were correlated using the Tait equation, and good regression results were obtained, with the AARD of 0.19% and MARD of 0.83%. A comparison was conducted between the Tait equation and REFPROP 10 and Peng-Robinson equation of state (PR EoS), the Tait equation gives the best prediction performance. In addition, the isochoric specific heat capacity data were compared with the values calculated by four models (PR model, Zhong model, Sheng model and REFPROP 10). Among them, the three models, the Zhong model, Sheng model and REFPROP 10, give the same prediction performance, with AARD of 2.88%, 2.47% and 2.51%, respectively. But for the PR model, the density data has a significant impact on the result, especially for the low-temperature region. When the density data were calculated by the Tait equation, the PR model presents the best prediction performance for the heat capacity of R1234ze(E) + R290 mixtures with the AARD of 2.00%, nevertheless, when the density data were calculated from the PR EoS, the PR model showed a large deviation in the prediction of isochoric heat capacity with the AARD and MARD of 3.74% and 11.11%. An empirical equation was correlated to represent the experimental heat capacity data with the MARD of 3.07% and the AARD of 1.15%.

Seismic risk analysis based on imprecise distribution and failure probability function under multidimensional limit state

Traditional probabilistic seismic risk analysis (PSRA) often adopts accurate probabilistic model to measure the uncertainties of structural response and capacity, which cannot evaluate the effect of the number of seismic waves on structural failure probability. A novel PSRA method based on imprecise distribution and failure probability function is proposed to solve the above problems. Multidimensional limit state function is adopted to measure the structural limit state. Based on lognormal distribution assumption, the means and standard deviations of engineering demand parameters (EDPs) and thresholds are all regarded as uncertain parameters, and the traditional PSRA formula is extended to the field of imprecise probability distribution. Interval estimation is used to evaluate the confidence interval and measure the uncertainties of the means and standard deviations at the given confidence level. Bayes formula method is adopted to solve the failure probability function and obtain the upper and lower bounds of vulnerability curve and mean annual failure probability. The results show that: The proposed method can measure the uncertainty of failure probability caused by the number of seismic waves through the width of vulnerability curve, which is very helpful to judge the reliability of estimated parameters. The wider width means the greater discreteness of structure response and the lower reliability of failure probability based on accurate parameters. With the increase of damage degree, the influence of the number of seismic waves on structural failure probability increases gradually.

Facility and microgrid location-allocation for integrated supply chain and transactive energy operations

Supply chain network design usually focuses on the uncertainties in materials, capacity, yield, and demand. However, the challenges of prosumer energy integration are not adequately addressed. This paper proposes an integrated facility and microgrid location-allocation model for achieving low-carbon supply chain operations at the nexus of manufacturing, renewables, and climate. The model strategically locates the site for establishing factories, warehouses, and microgrids subject to product demand and energy supply uncertainty. The model further allocates production, inventory, transportation, generation, and energy transactions to lower the net supply chain cost. The study represents a first-of-its-kind in jointly siting and sizing industrial facilities and prosumer microgrids under a unified optimization framework. The proposed model is implemented in a three-tier production supply chain network over a one-year period, covering the US pacific region with broad climate conditions. Numerical experiments show that transactive energy, time-of-use tariff, and climate conditions play a critical role in locating factories, warehouses, wind turbines, solar photovoltaics, and energy storage systems. Since transactive energy market brings new revenue stream, locations with stronger renewables become competitive to establish facilities despite of higher fixed and logistics cost. Contrary to the intuition, energy storage systems, which balance the intermittent power and uncertain load, have limited benefits to the cost saving.

Analysis of Non-Destructive Indicating Properties for Predicting Compressive Strengths of Dendrocalamus sericeus Munro Bamboo Culms

Bamboo is a natural material with the potential for being used in sustainable construction. However, uncertainty in the bearing capacity of the bamboo results in nonstandard values for structural engineering design. This research studied the simple and multiple linear regression analyses for indicating properties to predict the axial compressive load capacity and strength of bamboo culms, which will be useful information for quality control during building construction and further structural grading. First, twelve basic physical properties were measured from 111 samples of Dendrocalamus sericeus Munro bamboo culms, and axial compressive load tests of the bamboo culms were performed. Then, the correlation significance of the physical properties to axial load capacity and strength (load per area) were analyzed by the Pearson correlation method. The results show that five parameters, i.e., linear mass, culm wall thickness, external diameter, moisture content, and density, were statistically significant with the responses (compressive load capacity and compressive strength) and then defined as "candidates for indicating properties". Next, simple linear and multiple linear regression were analyzed to formulate the relationship between the significant indicating properties and the responses. From the simple linear regression analysis, linear mass can be best used as an indicating property for predicting the maximum compressive load. The maximum compressive strength was well associated with density. The multiple linear regression analysis shows an improvement in the response predictions with respect to the simple linear regression analysis with the higher R2-values. Finally, structural grading of the bamboo is determined.

Flood Protection Reliability: The Impact of Uncertainty and Nonstationarity

AbstractRecent catastrophic flood events, increasing flood losses, and climate change challenge current reliability estimates defined by the probability that flood levels will not exceed protection measures over a planning horizon. These estimates depict an expected reliability that mask uncertainty in streamflow and the capacity of river channels and floodplains. We described reliability as a random variable whose distribution depends on uncertainty and nonstationarity in annual maximum flood (AMF) distributions and flow capacity uncertainty. Numerical experiments quantified the impacts of nonstationarity and variance in AMFs and flow capacity uncertainty on estimates of flood protection reliability, thereby providing the first examination of their interacting effects. The distribution of reliability along a regulatory floodplain boundary was quantified through a bootstrap scheme that accounts for nonstationarity and uncertainty in AMFs and flow capacity uncertainty. Results indicated that accounting for uncertainty in flow capacity substantially reduces reliability compared to estimates based solely on flood likelihood; the divergence is greater in the presence of nonstationary AMFs. The distribution of reliability along the regulatory floodplain boundary was spatially heterogeneous due to within‐reach variation in flow capacity uncertainty. Quantifying the distribution of reliability for flood protection measures enables transparent communication and selection of a desired confidence level that is commensurate with a contextually appropriate risk tolerance. Similarly, we show that a desired level of confidence in reliability can be specified to estimate a design flood protection level. These results reveal how the combined impacts of uncertainty and nonstationarity can impact reliability estimates and confidence in those estimates.

Departure time choices in the morning commute with a mixed distribution of capacity

Incidents and other random factors may create variations to the transportation system and thus result in stochastic road capacity during the travel period. The realized capacity on a given day (i.e., an average value over the travel period) changes from day to day. For instance, existing empirical studies indicate that incident capacity reduction can be approximated as a continuous random variable. This study examines the morning commute problem with a road bottleneck whose capacity is constant within a day but changes stochastically from day to day. This study extends existing stochastic bottleneck model studies by considering a more general distribution of the bottleneck capacity. In particular, the capacity of bottleneck is at the designed value under good external conditions and degrades into a smaller value within an interval (i.e., the capacity degradation range) under adverse external conditions (a “mixed” distribution). Commuters’ departure time choices follow the Wardrop’s first principle in terms of their mean individual travel cost. Given the considered distribution of capacity, additional equilibrium departure/arrival patterns not identified by the literature have been identified and examined. How the mean travel cost and the mean of total travel time may vary with the capacity degradation probability and the level of capacity degradation have been analyzed. The impacts of the width of degraded capacity range have also been investigated to quantify how the results are affected if the degraded capacity is assumed as the mean value (rather than a degraded capacity range). Our results indicate that with less severe capacity degradation, the mean travel cost always decreases and improving the capacity under the “worst condition” can be more effective than improving the capacity under the “best adverse condition”. However, it is not always the case for reducing the total travel time, and the mentioned measures may exacerbate the system’s congestion, especially when the capacity degradation rarely occurs. Under a given mean capacity, the mean travel cost would be underestimated if the capacity degradation range is ignored. We also compare system performance considering different capacity distributions. It is found that the “mixed” capacity distribution defined in this study outperforms the binary capacity distribution in terms of evaluating the departure/arrival pattern and the mean travel cost. This study enhances our understanding on the morning commute problem under capacity uncertainty.

Fire Fragility Curves for Industrial Steel Pipe-Racks Integrating Demand and Capacity Uncertainties

Fire Fragility Curves for Industrial Steel Pipe-Racks Integrating Demand and Capacity Uncertainties

On a Fair and Risk-averse Urban Air Mobility Resource Allocation Problem Under Demand and Capacity Uncertainties

On a Fair and Risk-averse Urban Air Mobility Resource Allocation Problem Under Demand and Capacity Uncertainties

Research on the Evolutionary Game Model of Railway Cold Chain Logistics between Cargo Owners and Transport Enterprises

The transportation mode of the railway cold chain has an essential impact on operational efficiency and cost. Under the uncertainty of demand and limited transportation capacity, an evolutionary game model of railway cold chain logistics is constructed to explain and analyze the dynamic decision‐making processes and mechanisms between cargo owners and railway transport enterprises. The results show that the evolutionary path and convergence speed of the model are influenced by the initial value and its allocation coefficient, cargo volume, additional benefit, and default cost. By using Matlab, numerical simulation is conducted to verify the theoretical assumptions and results. The conclusion provides a basis for studying and managing railway cold chain logistics.

Real-time forecast of hurricane-induced damage risk to envelope systems of engineered buildings through metamodeling

The growing intensity and frequency of extreme wind events, together with the continued economic and population growth of coastal areas, has created an urgent need for methodologies that can inform emergency responders and managers of the increasing risk to the infrastructure of these areas. To this end, this work outlines a real-time risk forecast framework for hurricane-induced damage to building envelope systems of engineered buildings. Damage is quantified through a recently introduced multi-demand and coupled progressive fragility model, with a full range of uncertainty in structural properties, capacities, and wind stochasticity. To enable real-time assessment, an efficient Kriging metamodel is introduced to capture the damage statistics conditioned on intensity measures. From official real-time hurricane advisories, site-specific intensity measures are forecast based on a parametric wind field model while considering the uncertainty in, among others, the hurricane track, pressure deficit, and filling model. Damage risk is predicted through propagating uncertainty by Monte Carlo simulation through the Kriging metamodels calibrated to forecast intensity measures. For illustration, the real time damage risk of the envelope system of a 45-story building located in Miami, Fl, was estimated for hurricanes Matthew (2016), Irma (2017), and Dorian (2019). The efficiency and accuracy of the proposed framework is demonstrated.

Robust goal programming approach for healthcare network management for perishable products under disruption

In this paper, a robust goal programming model for a healthcare network design problem under disruption is developed. The objective of the proposed multi-period, multi-echelon model is to simultaneously optimize the total deviation from the considered three goals, including minimizing network cost, maximizing network coverage, and maximizing network reliability. Distribution uncertainty of healthcare demand and facility capacity is captured. The perishability of healthcare products is regarded with limited shelf-life. Using an option contract ensures appropriate coordination with suppliers during pre and post-disaster periods. Via handling the tractable robust budget-based counterpart model, suitable strategies are proposed to present the designed network's efficiency and effectiveness. Risk mitigation strategies deal with disrupted demand and supply in the healthcare network with specific impacts on coverage, cost, and reliability of the services. The proposed cooperate coverage mechanism provides appropriate service coverage under disruption propagation. Finally, the option contract has achieved cost-efficient coordination under demand uncertainty. Furthermore, practical managerial insights are demonstrated by investigating a real-life case study and conducting extensive sensitivity analyses.

Seismic Fragility Analysis of Aqueduct Structural Systems Based on G-PCM Method

In order to accurately predict the seismic fragility of an aqueduct system, the General Product of Conditional Marginal (G-PCM) method was applied to the seismic fragility analysis of the aqueduct structural system, consisting of interrelated components such as the aqueduct body, pier, and support. First, a finite element dynamic analysis model of a three-span aqueduct with an equidistant simply-supported beam was established, based on the OpenSees platform. The uncertainties of structure, ground motion, and structural capacity were considered, and then the incremental dynamic analysis (IDA) method was used to calculate the seismic fragility of the three individual components, such as the aqueduct pier, the plate rubber bearing at the cap beam, and the PTFE sliding plate bearing at the aqueduct platform. Subsequently, seismic fragility curves of the aqueduct system were established using the G-PCM method and were compared with the traditional second-order bound method. The results showed that the two bearings of the aqueduct are more likely to be damaged than the pier; the failure probability of the aqueduct system is higher than that of any single component; and the seismic fragility curves of the aqueduct system acquired via the G-PCM method were all within the range of the failure probability obtained by the second-order bound method and had a better accuracy, which is suitable for the seismic fragility analysis of multi-failure mode aqueduct systems.

Metaheuristic algorithms for a sustainable agri-food supply chain considering marketing practices under uncertainty

In recent decades, the rapid growth of the global population has caused a significant increase in agricultural and food product demands. Thereby, the production of various items in the agricultural food supply chain network has increased to diminish food security concerns. On the other hand, the excessive production of products has led to various issues, such as greenhouse gas emissions and increased water consumption in farmlands, followed by supply chain-related challenges affecting the intermediaries in the next network levels. In this study, an agricultural food supply chain network under marketing practices is firstly probed by developing a stochastic multi-objective programming model to effectively improve three main pillars of sustainability. A convex robust optimization approach addresses the uncertainty of the farm production capacity and the saffron demands in the supply network. The effectiveness of the proposed mathematical model is certified by a case study on saffron business using the LP-metric method. A metaheuristic-oriented methodology comprising a modified Keshtel Algorithm is adapted to deal with the NP-hardness of the problems. The performance of the proposed solution methods is evaluated by two strategies, a statistical comparison and a supportive tool developed based on multi-criteria decision-making (MCDM) methods. The results validate the capability of the applied algorithms to solve the problem in different dimensions. Moreover, the MCDM method approves that MOKASEO outclassed in small, medium, and large-sized problems compared to other algorithms.

A socio-economic optimization model for blood supply chain network design during the COVID-19 pandemic: An interactive possibilistic programming approach for a real case study

In uncertain circumstances like the COVID-19 pandemic, designing an efficient Blood Supply Chain Network (BSCN) is crucial. This study tries to optimally configure a multi-echelon BSCN under uncertainty of demand, capacity, and blood disposal rates. The supply chain comprises blood donors, collection facilities, blood banks, regional hospitals, and consumption points. A novel bi-objective Mixed-Integer Linear Programming (MILP) model is suggested to formulate the problem which aims to minimize network costs and maximize job opportunities while considering the adverse effects of the pandemic. Interactive possibilistic programming is then utilized to optimally treat the problem with respect to the special conditions of the pandemic. In contrast to previous studies, we incorporated socio-economic factors and COVID-19 impact into the BSCN design. To validate the developed methodology, a real case study of a Blood Supply Chain (BSC) is analyzed, along with sensitivity analyses of the main parameters. According to the obtained results, the suggested approach can simultaneously handle the bi-objectiveness and uncertainty of the model while finding the optimal number of facilities to satisfy the uncertain demand, blood flow between supply chain echelons, network cost, and the number of jobs created.

A scenario-based stochastic programming model for multi-commodity distribution considering disruption in distribution network

As one of the core operations in disaster management, the relief distribution has been challenged by factors such as occurrence time, nature, the intensity of disasters impact, and the existence of secondary disasters (e.g., aftershock, landslides). The distribution of multi-commodity relief after disaster strikes becomes more significant when secondary disasters occur in the same or close areas. Secondary disasters may take place right after the primary disaster attack. Because of the diverse natures and the destruction of secondary disasters, the temporary relief distribution centers in operation for distributing commodities after the primary disaster can be disrupted. New temporary distribution centers should be constructed to cover the capacity of disrupted distribution centers. In addition, roads may be unavailable to transport the commodity, and the demand can vary significantly because of secondary disasters. To hedge against the disruption of temporary distribution canters and road unavailability, this paper proposes a mixed-integer stochastic programming model under demand and capacity uncertainty. The objective of this model is to minimize the unmet demand at relief collection centers. A computational study is performed to highlight the significance of this study, and the results show that the proposed approach is effective in secondary disasters perspective.

Dynamic Scheduling and Optimal Control of Coordination Supply Chain Based on Automatic Allocation of Orders for Multicycle Integrators

Selecting suppliers and allocating orders scientifically and rationally not only have important theoretical value but also have extremely important practical significance to enterprises. This study proposes an improved multicycle integration method that can effectively determine the optimal number of suppliers under the premise of considering the risk of supply interruption and transaction costs that may be caused by various uncertain factors. The supply interruption risk is divided into two categories: “common risk event” and “individual risk event.” On the basis of balancing the transaction cost of the company’s choice of suppliers and the financial loss of supply interruption, quantitative analysis methods are used to determine the optimal number of suppliers for the company. The problem is analyzed, the corresponding model is given, and the influence of each parameter on the optimal number of suppliers is analyzed. From the perspective of stochastic uncertainty in both customer demand and supplier supply capacity, this study analyzes the optimization problem of enterprise purchase quantity allocation under the volume discount environment. The relaxation factor is somewhat adaptive because the particle swarm is continuously updated. Aiming at ordering cost, transaction cost, transportation cost, order delay quantity, and product quality, considering random demand constraints, supplier supply capacity constraints, and multisupplier multiproduct situations, we establish supplier selection in an environment of uncertain demand and supply capacity and dynamic relaxation approximation algorithm for order allocation. The research results show that the dynamic relaxation approximation algorithm can not only determine the optimal supplier but also determine the optimal procurement allocation for each supplier.

Research on slot allocation for airport network in the presence of uncertainty

In this paper, a slot allocation model for airport network in the presence of uncertainty is proposed. The airport resource planning problem is modeled as a process from an aggregate level and an individual level for multiple days' slot scheduling in order to consider capacity uncertainty at airports characterized by meteorological scenarios. The aggregate level uses a two-stage model to minimize the sum of displacement cost and delay cost in the worst-case scenario using Benders’ Decomposition-based algorithm. At the individual level, an integer linear programming model is developed based on the results from the aggregate level to provide specific departure slot and arrival slot for each flight. An airport network composed of 15 coordinated airports in China is studied and shows that by experimental analysis the overall optimization method is capable of providing robust and efficient solutions for slot allocation and benefits from high computational efficiency. The outperformance of the two-stage optimization method from the aggregate level is also illustrated in comparison with the one-stage optimization method. Finally, recommendations for the slot allocation policy in practice are provided.

Development of an aqueous lignin mixture thermophysical model for hydrothermal liquefaction applications using uncertainty quantification tools

A thermophysical model is developed that can predict the properties of two lignin mixtures, black liquor and lignosulfonates, up to 50% mass fractions, at hydrothermal conditions. An uncertainty quantification framework linked with classic thermodynamical modelling was included to account for the extreme variability of the raw material. An idealised flow simulation verified the model, where hot compressed water mixes with a cold, aqueous lignin stream in a T-piece reactor configuration. The uncertainty quantification procedure determined that density and heat capacity uncertainty significantly influence residence time, and viscosity uncertainty mainly affects mixing. Micromixing time is fivefold and ten-fold higher for black liquor and lignosulfonates mixtures, respectively, compared to pure water mixing. The uncertainty in all simulated quantities of interest caused by the thermophysical model is reduced by increasing flow rates. This study predicted chemical reactor behaviour under varying thermophysical conditions and their final effect in terms of confidence intervals.

A Safety-Aware Real-Time Air Traffic Flow Management Model Under Demand and Capacity Uncertainties

Inherent uncertainties of the air transportation system (ATS) can induce unexpected anomalies in its operations such as deviations in flight schedules, sudden imbalances of demands and capacities, etc.. Current air traffic flow management (ATFM) models rarely consider both demand and capacity uncertainties in their algorithms, and generally focus on minimizing the flight delays under deterministic constraints. Thus, to bridge this gap, we propose a framework for en-route ATFM while scrutinizing uncertainties in en-route capacity and demand and their imbalance, via a chance constraint based probabilistic approach. The proposed framework plays a key role in ensuring the safety of the overall ATS in terms of maintaining the safety separation between flights and constraining the capacity of the sectors as well. Moreover, flight level assignments scheme is proposed based on the Base of Aircraft Data (BADA) of the European Organization for the Safety of Air Navigation (EUROCONTROL) with the objective of minimizing the fuel consumption. The model further minimizes the overall expected delay of the system using the control actions of ground holding, speed control, rerouting, and flight cancellations. At the implementation stage, two phases of ATFM as pre-tactical and tactical are considered, in which the former focuses on generating optimal trajectories and the latter focuses on real-time updates of flight plans. The computational complexity is reduced by shrinking the feasibility region and decomposing the problem into maximum weighted independent sets. The experimental results of realistic large-scale problems demonstrate the effectiveness and computational feasibility of our ATFM framework.

Backup Resource Allocation of Virtual Machines for Probabilistic Protection under Capacity Uncertainty

Backup Resource Allocation of Virtual Machines for Probabilistic Protection under Capacity Uncertainty