Capacity Uncertainty Research Articles

Robust optimization bidding strategy for user-side resource-side participation in the market distribution of electrical energy and peaking ancillary services considering risk expectations and opportunity constraints

Compared to traditional resources, user-side resources are of various types and have more significant uncertainty about their regulatory capacity, leading to difficulties in coordinating decisions about their simultaneous participation in the electric energy and peaking ancillary services markets. This paper proposes a joint bidding decision-making method for the day-ahead electricity energy and peak shaving auxiliary service market based on distributed robust opportunity constraints, which addresses the problem of difficulty in using an accurate probability density distribution to represent the uncertainty process of user-side resources. Firstly, a data-driven method for characterizing the uncertainty of load regulation capacity is investigated, and fuzzy sets are constructed without assuming specific probability distributions of random variables. Then, to minimize the risk expectation of the joint bidding cost on the customer side, a bidding strategy that considers the uncertainty is proposed. Finally, an example simulation verifies the reasonableness and effectiveness of the proposed joint bidding method, and the results show that the constructed model overcomes the problem of over-conservatism of the robust model, and the computational adaptability is better than that of the stochastic model, which achieves a better balance between robustness and economy.

Heat Capacity of Fish Oil at High Temperatures and Pressures

This paper reports new results from studies of the isobaric heat capacities of OMEGA-3 “950” fish oil provided by SOLGAR INC (USA) at high temperatures and high pressures. The measurements were carried out on a differential scanning calorimeter (ITs-400) with an automatic data acquisition system in the temperature range from 298.15 to 473.15 K and at pressures from 0.098 to 39.2 MPa. The coverage factor for the 95% confidence level for a two-way coverage interval is assumed to be 2. The expanded measurement uncertainty of heat capacity is estimated to be 2.4%, pressure is estimated to be 0.05% and temperature is estimated to be 15 mK. Experimental data on the fish oil isobaric heat capacity as a function of temperature and pressure are approximated by the correlation equation proposed in the work. At atmospheric pressure, the deviations between those calculated by the correlation equation and the current measured data on isobaric heat capacity are within the range of average absolute deviations (AAD) = 0.22% (standard deviation St. Dev = 0.28% and maximum deviation Max. Dev = 0.39%). Additionally, a comparison was made of the state parameters obtained during the experiment and the literature data at the studied parameters.

Analysis of hydraulic breakdown and seepage of tail sealing system in shield tunnel machines

The use of shield method in tunnel construction is limited by the engineering conditions of highwater pressure. This is mainly due to the uncertainty of the pressure-bearing capacity of the sealing chambers of the shield tail under different grades and conditions when subjected to different external water pressures. Therefore, it is crucial to determine the pressure-bearing capacity of the sealing chambers. However, there is a lack of studies on the calculating method of the pressure-bearing capacity, which requires more theoretical investigation. To explore the common patterns of multi-grade sealing-related parameters and quantify the pressure-bearing capacity of the sealing chambers, a breakdown and leakage model of the shield tail is proposed, targeting the basic sealing unit of the system. Based on non-Newtonian fluid dynamics and fractal theory of porous media, the model is used to calculate the breakdown pressure and grease seepage rate corresponding to tunneling and shutdown states. In addition, a hydraulic breakdown device of the sealing unit of the static shield tail is built to investigate the relationship between the shield tail clearance and the shield tail brush porous media area, which helps to verify the theoretical model. Finally, the analysis of sealing chamber geometry parameters, grease rheological parameters, and an environmental parameter using the proposed theoretical model shows that the pressure-bearing capacity of the shield tail can be improved by increasing the shield tail clearance and grease yield stress. It also shows that the length of the sealing chamber and the plastic viscosity of the grease do not have a significant effect on the breakdown pressure of the shield tail. The model proposed in this paper will provide ideas for the calculation of the pressure-bearing capacity of multi-grade sealing chambers in the future.

Uncertainty analysis of FLiNaK thermophysical properties on convective heat transfer characteristics in circular tube

Molten salts have attracted a spate of quantity of interests in energy and chemistry fields due to their large volumetric capacity, and thermodynamic stability at elevated temperature. However, there are significant uncertainties in the physical properties of molten salts, such as density, specific heat capacity, dynamic viscosity, and thermal conductivity, due to inexperienced measurement techniques and technology. These uncertainties could have certain impact on the evaluation of molten salts heat transfer characteristics. Therefore, an uncertainty analysis is performed regarding FLiNaK thermophysical properties on convective heat transfer characteristics in circular tube. Then, a polynomial chaos expansion (PCE) method is performed to study the uncertainty affecting the heat transfer characteristic. In the process of uncertainty analysis, tensor product quadrature nodes are used to calculate representative sample points and reduce computational costs. Three primary physical properties of molten salt are taken into account as the input parameters. The Sobol composition method is also used to analyze the contributions of each parameter to heat transfer. The results of the uncertainty analysis suggest that the uncertainties in dynamic viscosity, thermal conductivity, and specific heat capacity have a significant impact on the heat transfer of molten salt, contributing to 80 %, 14 %, and 6 % of the total variability, respectively. It also suggests that the polynomial chaos expansion methodology is both novel and reliable when applied to uncertainty analysis of molten salt.

A Robust Optimization Model for Emergency Location Considering the Uncertainty and Correlation of Transportation Network Capacity

Emergencies often lead to the impairment of infrastructure systems, including transportation systems. It is necessary to analyze the uncertainty and correlation of transportation network capacity caused by emergencies, aiming at the problems of emergency facilities’ location and matching in emergency contexts. This study introduces novel concepts, such as flow distribution betweenness centrality (FD-BC) and the transport capacity effect coefficient (TC-EC). Furthermore, we introduce the ellipsoidal uncertainty set to characterize uncertainties in transport capacity. We construct a multi-criteria decision-making (MCDM) model and a multi-strength elitist genetic algorithm (multi-SEGA) to ensure the lower limit of transport capacity between demand and emergency points while minimizing decision-making costs. By designing an uncertain scenario example, we analyze the effect of the perturbation ratio and the uncertainty level on the robust location model. The following results were drawn: (1) Indicators FD-BC and TC-EC effectively indicated the importance of each section in the emergency transportation network. (2) The optimal value of the model’s objective function changed more significantly as the perturbation ratio and uncertainty level increased. (3) After reaching a certain uncertainty level, the robust model with an ellipsoidal uncertainty set became more conservative than the robust model with a box uncertainty set, which lacked practical significance. The research results guarantee the robustness of the emergency support system in uncertain conditions.

On a fair and risk‐averse urban air mobility resource allocation problem under demand and capacity uncertainties

AbstractUrban air mobility (UAM) is an emerging air transportation mode to alleviate the ground traffic burden and achieve zero direct aviation emissions. Due to the potential economic scaling effects, the UAM traffic flow is expected to increase dramatically once implemented, and its market can be substantially large. To be prepared for the era of UAM, we study the fair and risk‐averse urban air mobility resource allocation model (FairUAM) under passenger demand and airspace capacity uncertainties for fair, safe, and efficient aircraft operations. FairUAM is a two‐stage model, where the first stage is the aircraft resource allocation, and the second stage is to fairly and efficiently assign the ground and airspace delays to each aircraft provided the realization of random airspace capacities and passenger demand. We show that FairUAM is NP‐hard even when there is no delay assignment decision or no aircraft allocation decision. Thus, we recast FairUAM as a mixed‐integer linear program (MILP) and explore model properties and strengthen the model formulation by developing multiple families of valid inequalities. The stronger formulation allows us to develop a customized exact decomposition algorithm with both benders and L‐shaped cuts, which significantly outperforms the off‐the‐shelf solvers. Finally, we numerically demonstrate the effectiveness of the proposed method and draw managerial insights when applying FairUAM to a real‐world network.

Thermal effects of organic porous media on absorption and desorption behaviors of carbon dioxide

As a result of global warming, people are increasingly concerned about greenhouse gas emissions, particularly carbon dioxide (CO2). Many countries have been promoting carbon capture, storage (CCS) projects in order to alleviate climate degradation and achieve net zero carbon emissions. To study the thermal effects of organic porous media on CO2 absorption and desorption, molecular dynamics coupled with Monte Carlo (MDMC) were used in this study. A part of the CO2 molecules will be trapped within kerogen matrix due to its complex porous structure. The affinity of kerogen to CO2 facilitates CO2′s adsorption within the kerogen porous media, resulting in a heterogeneous distribution of CO2. The kerogen forms high potential energy peaks and low potential energy wells in the matrix, which provide preferred adsorption sites for CO2 in the porous space. The low stress state of CO2 also indicates that it prefers adsorption in the matrix as CO2 performs a lower potential energy state in the kerogen matrix than in the bulk phase. This study examines different thermal effects of kerogen, and results indicate that increasing CO2 thermal motion facilitates its absorption, while a high temperature matrix promotes CO2 desorption. Adsorbed layer provides resistance for CO2′s diffusion behaviors. The free energy of CO2′s diffusion is analyzed in relation to its mechanism, revealing that irregular thermal motion causes uncertainty in the adsorption capacity.

Primary Frequency Control of Multiple ON/OFF Load Clusters Considering Capacity Uncertainty and Lock-Time Constraint

Primary Frequency Control of Multiple ON/OFF Load Clusters Considering Capacity Uncertainty and Lock-Time Constraint

Performance-based seismic design of Ultra-High-Performance Concrete (UHPC) bridge columns with design example – Powered by explainable machine learning model

Ultra-high-performance concrete (UHPC) has rapidly become a material of choice in modern construction owing to its favorable properties, such as superior strength, toughness, and durability. Yet, accurate quantification of damage states using appropriate engineering demand parameters (EDPs) remains a significant challenge in the performance-based seismic design (PBSD) of UHPC columns. This gap is especially evident in the scarcity of research focused on the PBSD of UHPC columns. Therefore, this study aims to develop an explainable machine learning (ML) powered predictive model for the drift ratio limit states of UHPC bridge columns across four damage states. To achieve this, a fiber-based numerical model was developed and then validated against large-scale experimental results of UHPC columns tested under reverse cyclic loading. The Latin hypercube sampling method is employed to generate a comprehensive database of UHPC bridge columns (10,000 UHPC columns), considering uncertainties across a spectrum of design factors, including column geometry, material characteristics, reinforcement ratio, and axial load ratio. The drift ratios at the initiation of four damage states are determined using the numerical model. Subsequently, the power of the ML algorithm is leveraged to introduce drift ratio limit states for UHPC columns that capture the onset of four different damage states. The efficacy of the developed model is assessed using a range of statistical metrics, including the composite fitness score, DX% metrics, coefficient of determination, root mean squared error (RMSE), normalized RMSE, and mean absolute error, which demonstrated high predictive accuracy of the drift ratio limit states on both the training and unseen or test datasets. Furthermore, a model-agnostic Shapley Additive exPlanation (SHAP) is used to explain the output of the model and examine the influence of various design factors on drift ratio across the damage states. Notably, the axial load ratio and aspect ratio are found to be major factors in determining the drift ratios across the damage states. The developed model is deployed into a software tool in order to enable its practical application. Additionally, the implementation of the developed model in the context of PBSD is illustrated through a design example. Furthermore, the study proposed capacity uncertainty parameters to aid the fragility assessment of UHPC columns. Finally, the proposed model, along with capacity uncertainty parameters, is used for the fragility assessment of UHPC columns reinforced with varying steel bar grades. The results demonstrate the less vulnerability of UHPC columns reinforced with higher bar grade, yet the effect of bar grade lessens at severe damage levels.

Effective hydrogen supply chain management framework considering nonlinear multi-stage process uncertainties

The large amount of carbon emitted due to industrial development is posing serious climate change. Under these circumstances, hydrogen energy is being used as a major energy source and is attracting attention as an alternative energy to fossil fuels, characterized by high carbon emissions. While the use of hydrogen has the obvious benefit of a low carbon footprint, the hydrogen production process possesses a high carbon footprint difference depending on the source of utilized electricity. This study considers several situations arising in an electrolysis-based hydrogen supply chain network (HSCN). A multi-stage stochastic programming (SP) is modeled to consider the uncertainty of demand and transportation capacity generated in HSCN. Moreover, a typical stochastic model has a chain rule between the decision variables resulting from nonlinearity and uncertainty, and these features make it difficult to derive an effective solution. Thus, in this study, a new methodology, Weighted Scenario Sample Average Approximation (WSSAA), is proposed to derive an effective solution for the multistage SP model considering various scenarios under the hydrogen supply chain. While a general stochastic programming approach fails to generate feasible solutions with volatile HSCN uncertainties, the proposed WSSAA framework provides feasible decisions considering multiple scenarios. The effectiveness of the proposed model applied with WSSAA is demonstrated through comparative experiments over the models used in existing studies.

Assessment of load test program for reliability-based design of piles

Quantifying the uncertainty of the bearing capacity of piles is crucial in the context of reliability-based design (RBD) for pile foundations. The utilization of site-specific load test data plays a pivotal role in reducing the uncertainty associated with bearing capacity, thereby enhancing the overall design of pile foundations. However, prior to initiating a load test program, there exists uncertainty both in the outcomes of the program and the potential benefits it may yield. This research endeavors to develop a method that allows for assessing the effectiveness of a load test program before its execution. The structure of this paper is as follows: firstly, it introduces a framework for evaluating the utility of the pile load test (PLT) program. Subsequently, it constructs a pre-posterior analysis to examine the anticipated benefits derived from the load test program. Finally, the proposed methodology is elaborated upon through a detailed example. This paper is valuable for enhancing decision-making in optimizing pile load test programs.

Monte Carlo analysis of masonry structures under tsunami action: Reliability of lognormal fragility curves and overall uncertainty prediction

Tsunami vulnerability of coastal buildings has gained more and more interest in recent years, in the consciousness of what losses may be caused. The improvement of the available approaches for the quantitative estimation of the probability of building damage and for defining possible strategies for risk mitigation is an actual goal. In this framework, several authors have provided empirical fragility curves based on field surveys after tsunamis. Nevertheless, a predictive approach based on analytical fragility curves, which can be extended to many classes of buildings, is essential for the scopes of civil protection and risk mitigation. In this paper, an approach for the construction of fragility curves, proposed for masonry structures under tsunami waves, is discussed and refined in the part regarding the assignment of the uncertainties. Further, an assessment of the reliability of the lognormal fragility distribution is carried out based on a Monte Carlo simulation applied to 4 classes of buildings. Here, it is shown that Monte Carlo analysis allows a direct evaluation of the uncertainties without the need to resort to ambiguous regression analyses and rules of combination of the uncertainties of demand and capacity based on the regression analysis results or other uncertainty estimation approaches.

Solving a Multimodal Routing Problem with Pickup and Delivery Time Windows under LR Triangular Fuzzy Capacity Constraints

This study models a container routing problem using multimodal transportation to improve its economy, timeliness, and reliability. Pickup and delivery time windows are simultaneously formulated in optimization to provide the shipper and the receiver with time-efficient services, in which early pickup and delayed delivery can be avoided, and nonlinear storage periods at the origin and the destination can be minimized. Furthermore, the capacity uncertainty of the multimodal network is incorporated into the advanced routing to enhance its reliability in practical transportation. The LR triangular fuzzy number is adopted to model the capacity uncertainty, in which its spread ratio is defined to measure the uncertainty level of the fuzzy capacity. Due to the nonlinearity introduced by the time windows and the fuzziness from the network capacity, this study establishes a fuzzy nonlinear optimization model for optimization problem. A chance-constrained linear reformulation equivalent to the proposed model is then generated based on the credibility measure, which makes the global optimum solution attainable by using Lingo software. A numerical case verification demonstrates that the proposed model can effectively solve the problem. The case analysis points out that the formulation of pickup and delivery time windows can improve the timeliness of the entire transportation process and help to achieve on-time transportation. Furthermore, improving the confidence level and the uncertainty level increases the total costs of the optimal route. Therefore, the shipper and the receiver must prepare more transportation budget to improve reliability and address the increasing uncertainty level. Further analysis draws some insights to help the shipper, receiver, and multimodal transport operator to organize a reliable and cost-efficient multimodal transportation under capacity uncertainty through confidence level balance and transportation service and transfer service selection.

Dynamic Oligopolistic Competition with Uncertainty and Supply Disruption Effects

We consider a finite-horizon discrete-time dynamic model of oligopolistic competition, with uncertain supply. The firms (retailers) make their decisions on quantities (sales) and orders of goods from a nonstrategic manufacturer taking into account uncertainty in demand parameters and available supply capacity. The retailers need to satisfy the joint available supply capacity constraint. The model is described as a game played over an event tree with given transition probabilities. We find a normalized equilibrium for the game with coupling constraints. The two-step procedure to find this equilibrium is described. We provide the necessary conditions of the equilibrium and examine different scenarios of uncertainties in the model by numerical simulations.

Robust maximum flow network interdiction considering uncertainties in arc capacity and resource consumption

Robust maximum flow network interdiction considering uncertainties in arc capacity and resource consumption

Marginal Pricing in Adaptive Robust Unit Commitment Under Load and Capacity Uncertainty

Marginal Pricing in Adaptive Robust Unit Commitment Under Load and Capacity Uncertainty

Probabilistic inspection planning for fatigue cracks in floating production, storage, and offloading units

Probabilistic inspection planning for fatigue cracks in floating production, storage, and offloading units

Coordination of protection and operation in micro-grids with inverter based distributed generation using SAOA.

In the proposed protection coordination scheme, the depreciation of the operation time of the entire relay in the primary and backup protection modes for all possible fault locations is considered as the objective function. The limitations of this problem include the equations for calculating the operation time of the relays in both forward and reverse directions, the limitation of the coordination time interval, the limitation of the setting parameters of the proposed relays, the restriction of the size of the reactance that limits the fault current, and the limitation of the standing time of distributed generation per small signal fault. The operation time of the relays depends on the short circuit current passing through them, so it is necessary to calculate the network variables before the fault occurs. For this purpose, optimal daily power distribution should be used in the micro-grid, because micro-grids consist of storage and renewable resources. The proposed plan includes the uncertainties of consumption and generation capacity of renewable resources. Then, to achieve a reliable answer with a low standard deviation, the refrigeration optimization algorithm is used to solve the proposed problem. Finally, the proposed design is implemented on the standard test system in the MATLAB software, and then the capabilities of the proposed design are examined.

Dynamic Courier Capacity Acquisition in Rapid Delivery Systems: A Deep Q-Learning Approach

With the recent boom of the gig economy, urban delivery systems have experienced substantial demand growth. In such systems, orders are delivered to customers from local distribution points respecting a delivery time promise. An important example is a restaurant meal delivery system, where delivery times are expected to be minutes after an order is placed. The system serves orders by making use of couriers that continuously perform pickups and deliveries. Operating such a rapid delivery system is very challenging, primarily because of the high service expectations and the considerable uncertainty in both demand and delivery capacity. Delivery providers typically plan courier shifts for an operating period based on a demand forecast. However, because of the high demand volatility, it may at times during the operating period be necessary to adjust and dynamically add couriers. We study the problem of dynamically adding courier capacity in a rapid delivery system and propose a deep reinforcement-learning approach to obtain a policy that balances the cost of adding couriers and the cost-of-service quality degradation because of insufficient delivery capacity. Specifically, we seek to ensure that a high fraction of orders is delivered on time with a small number of courier hours. A computational study in the meal delivery space shows that a learned policy outperforms policies representing current practice and demonstrates the potential of deep learning for solving operational problems in highly stochastic logistic settings. History: This paper has been accepted for the Transportation Science Special Issue on Machine-Learning Methods and Applications in Large-Scale Route Planning Problems. Funding: This work was supported by Agencia Nacional de Investigación y Desarrollo [72180404]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0042 .

Uncertainty analysis of heat transfer of TMSR-SF0 simulator

The TMSR-SF0 simulator is an integral effect thermal-hydraulic experimental system for the development of thorium molten salt reactor (TMSR) program in China. The simulator has two heat transport loops with liquid FLiNaK. In literature, the 95% level confidence uncertainties of the thermophysical properties of FLiNaK are recommended, and the uncertainties of density, heat capacity, thermal conductivity and viscosity are ±2%, ±10, ±10% and ±10% respectively. In order to investigate the effects of thermophysical properties uncertainties on the molten salt heat transport system, the uncertainty and sensitivity analysis of the heat transfer characteristics of the simulator system are carried out on a RELAP5 model. The uncertainties of thermophysical properties are incorporated in simulation model and the Monte Carlo sampling method is used to propagate the input uncertainties through the model. The simulation results indicate that the uncertainty propagated to core outlet temperature is about ±10°C with a confidence level of 95% in a steady-state operation condition. The result should be noted in the design, operation and code validation of molten salt reactor. In addition, more experimental data is necessary for quantifying the uncertainty of thermophysical properties of molten salts.