Multidimensional Uncertainties Research Articles

Net-zero carbon emission oriented Bi-level optimal capacity planning of integrated energy system considering carbon capture and hydrogen facilities

The integrated energy system (IES) is considered an efficient energy provision paradigm to improve the utilization efficiency of renewable generation (RG), reduce energy cost and improve energy supply reliability. However, the multi-dimensional uncertainties and the hydrogen utilization have posed enormous challenges to the optimal planning of the IES. This paper proposes a net-zero carbon emission oriented bi-level optimal planning model for the IES with full consideration of the multiple operational uncertainties in the IES (RG, multiple demands). The upper level is an optimal capacity configuration model, and the economic costs, energy selling profits, the penalty for power abandonment and energy supply shortage are settled as the objectives. The lower level is an optimal energy dispatch model with the objective function of minimizing the total operating cost of the IES on typical days. An integrated energy system framework consisting of multiple energy flows is formulated in the presence of carbon capture system (CCS) and hydrogen-to-power (H2P) facilities. To fully characterize the uncertainties of RG and multiple demands, a data-driven scenario generation method is adopted to expand the operational scenarios, in which probability distribution assumptions and prior knowledge are not necessary. Finally, the effectiveness of the proposed solution is extensively demonstrated through numerical simulation, and a sensitivity analysis is carried out to assess the impact of changes in electricity and gas prices on the IES planning results.

Advanced virtual modelling aided stochastic nonlinear dynamic stability analysis of the GPLR-FGP plate in thermal environments

This paper explores the crucial yet challenging task of stochastic nonlinear dynamic buckling investigations of the GPLR-FGP plate under biaxial impacts in thermal environments with multi-dimensional uncertainties for the first time. An advanced virtual modelling technique, namely the Extended Support Vector Regression (XSVR) with a fresh S-spline polynomial kernel, is newly developed to alternatively depict the underpinned and sophisticated relationship between the inevitable system uncertainties and concerned nonlinear buckling response in an efficient fashion. Adequate statistical information of stability performance is furnished for the safety assessment and reliability-based design of the GPLR-FGP composite. The superior competence, advisable exactness, and appealing efficiency of the proposed uncertainty quantification framework are vividly demonstrated through benchmark tests and comprehensive numerical experiments against established machine learning algorithms. Moreover, the user-friendly modularity feature, and unique capabilities of expeditious information update and responsiveness highlight the versatile applicability of the proposed technique in realistic structural implementation under swiftly changing environments.

Optimum investment strategy for hydrogen-based steelmaking project coupled with multiple uncertainties

The large-scale application of hydrogen steelmaking technology is expected to substantially accelerate the decarbonization process of the iron and steel industry. However, hydrogen steelmaking projects are still in the experimental or demonstration stage, and scientific investment decision-making methods are urgently needed to support the large-scale development of the technology. When assessing the investment value, existing studies usually only consider the intrinsic project value under a specific pathway, while ignoring the option value under realistic multiple uncertainties in terms of technology, market, and policy, leading to an underestimation of the investment value. To address this issue, this study constructs a real options model to explore the optimal investment timing and revenue of the hydrogen steelmaking project, by taking into account multi-dimensional uncertainties stemming from price fluctuations in the steel market, the development of the carbon market, and technological advances. Additionally, the impacts of various subsidy policies on the investment strategy are also investigated. Least Squares Monte Carlo method is applied to overcome computational challenges posed by dynamic programming under multi-dimensional uncertainties. The results show that: (i) Investment is not recommended based on current crude steel price and hydrogen price. (ii) When the annual reduction rate of hydrogen price reaches 5%, the optimal investment timing would advance to 2036. (iii) On this basis, with the introduction of a 20% green hydrogen subsidy policy, the optimal investment timing would be further brought forward to 2033. The implementation of tax incentives would significantly increase the investment value. The investment value would surge from 170 million CNY to 262 million CNY as the tax rate decreases from 20% to zero. The findings could provide reasonable suggestions for investment decisions under realistic volatile environments, as well as scientific references for policy design, thus facilitating the large-scale and high-level development of hydrogen-based steelmaking technology.

Safe Motion Planning and Control Framework for Automated Vehicles with Zonotopic TRMPC

Model mismatches can cause multi-dimensional uncertainties for the receding horizon control strategies of automated vehicles (AVs). The uncertainties may lead to potentially hazardous behaviors when the AV tracks ideal trajectories that are individually optimized by the AV's planning layer. To address this issue, this study proposes a safe motion planning and control (SMPAC) framework for AVs. For the control layer, a dynamic model including multi-dimensional uncertainties is established. A zonotopic tube-based robust model predictive control scheme is proposed to constrain the uncertain system in a bounded minimum robust positive invariant set. A flexible tube with varying cross-sections is constructed to reduce the controller conservatism. For the planning layer, a concept of safety sets, representing the geometric boundaries of the ego vehicle and obstacles under uncertainties, is proposed. The safety sets provide the basis for the subsequent evaluation and ranking of the generated trajectories. An efficient collision avoidance algorithm decides the desired trajectory through the intersection detection of the safety sets between the ego vehicle and obstacles. A numerical simulation and hardware-in-the-loop experiment validate the effectiveness and real-time performance of the SMPAC. The result of two driving scenarios indicates that the SMPAC can guarantee the safety of automated driving under multi-dimensional uncertainties.

Sizing isolated mini-grids in Kenya: Risk transfer to deal with multidimensional uncertainties and constraints

Isolated mini-grids (MG) can be an efficient option for rural electrification worldwide. Nonetheless, a large share of MG fail after a few years and inadequate sizing has been identified as a major risk. Academia, public authorities and funding agencies tend to consider the sizing of mini-grids mostly from a technical and economic angle, looking to optimize performance for MG developers and operators with tools such as HOMER. This paper proposes a different approach. We study the strategies adopted by different MG stakeholders to deal with their own uncertainties and constraints in the sizing process. Based on field work in Kenya, we detail how MG funders and regulators transfer risks to private MG developers and operators. As a result, the latter face risks regarding demand estimation, funding and regulatory aspects when sizing MGs. In turn, they adapt their methods and business models, sometimes transferring risks to end users. While flexible sizing might be a solution, we show that regulatory and funding issues limit MG modularity, leading low-income customers to eventually bear the consequences of ill-suited sizing.

A robust investment decision to deploy bioenergy carbon capture and storage—exploring the case of Stockholm Exergi

The upscaling of novel carbon dioxide removal, such as bioenergy carbon capture and storage (BECCS), to gigatonne scales is an urgent priority if global warming is to be limited to well below 2 °C. But political, economic, social, technological, environmental and regulatory uncertainty permeates BECCS projects and deters investors. To address this, we explore options to improve the robustness of BECCS deployment strategies in the face of multi-dimensional uncertainties. We apply Dynamic Adaptive Planning (DAP) through expert interviews and Robust Decision Making (RDM) through exploratory modelling, two decision making under deep uncertainty methods, to the case of Stockholm Exergi, an early mover aiming to deploy BECCS at a combined heat and power plant in the capital of Sweden. The main contributions of the research are to 1) illustrate how a quantification of robustness against uncertainty can support an investment decision to deploy BECCS 2) comprehensively cover uncertain vulnerabilities and opportunities of deploying BECCS, and 3) identify critical scenarios and adaptations to manage these uncertainties. The main conclusions are: investing in BECCS is relatively robust if assessing performance across many scenarios and if comparing the worst-cases of either investing, or not doing so. Not investing could miss out on up to € 3.8 billion in terms of net present value. The critical uncertainties of BECCS can be managed by strengthening biomass sustainability strategies and by gaining support for negative emission trading regulation on carbon markets, e.g., voluntary or Paris Agreement Article 6. Even in vulnerable scenarios of average electricity prices above 82 €/MWh, if trading regulation is implemented before 2030 and if negative emission prices exceed 151 €/CO2, investing in BECCS performs better than not doing so in 96% of cases. We suggest that facility-level parameters and cost-reductions are of little importance for BECCS investments and upscaling. It is regulatory certainty of operating revenues, e.g., through negative emission markets, that needs to be provided by policymakers.

Collision Risk Assessment for Intelligent Vehicles Considering Multi-Dimensional Uncertainties

Collision Risk Assessment for Intelligent Vehicles Considering Multi-Dimensional Uncertainties

Robust Cyber-Physical Co-Planning for Multi-Energy Ship Operation under Multi-dimensional Uncertainties

Robust Cyber-Physical Co-Planning for Multi-Energy Ship Operation under Multi-dimensional Uncertainties

Dynamically orthogonal narrow-angle parabolic equations for stochastic underwater sound propagation. Part I: Theory and schemes.

Robust informative acoustic predictions require precise knowledge of ocean physics, bathymetry, seabed, and acoustic parameters. However, in realistic applications, this information is uncertain due to sparse and heterogeneous measurements and complex ocean physics. Efficient techniques are thus needed to quantify these uncertainties and predict the stochastic acoustic wave fields. In this work, we derive and implement new stochastic differential equations that predict the acoustic pressure fields and their probability distributions. We start from the stochastic acoustic parabolic equation (PE) and employ the instantaneously-optimal Dynamically Orthogonal (DO) equations theory. We derive stochastic DO-PEs that dynamically reduce and march the dominant multi-dimensional uncertainties respecting the nonlinear governing equations and non-Gaussian statistics. We develop the dynamical reduced-order DO-PEs theory for the Narrow-Angle parabolic equation and implement numerical schemes for discretizing and integrating the stochastic acoustic fields.

Cyber-physical system planning for VPPs supporting frequency regulation considering hierarchical control and multidimensional uncertainties

Renewable energy resources with uncertain output are being connected to the power grid, which puts great pressure on the grid frequency regulation (FR). Virtual power plants (VPPs), which aggregate numerous flexible resources, have significant potential for participation in FR services. However, the FR capability of VPPs is often unreliable due to uncertain resource potential and unreliable communications, which limits their FR applications. Therefore, a cyber-physical system (CPS) planning method considering multidimensional uncertainties for hierarchical VPPs to provide reliable FR capacity is proposed in this paper. Firstly, a fast and reliable hierarchical architecture for VPPs is presented. Then, the reliable capacity model of VPPs for service planning is established within this architecture. The minimum probability scenario method based on the Pauta criterion and the failure mode and effects analysis (FMEA) method are used to quantify the impact of information-physical uncertainty in the model. Based on this, a CPS planning model for VPPs with the objective of minimizing investment and the constraints of normal capacity, reliable capacity and delay under various scenarios is constructed. By linearizing the model, the optimal solution for coordinating flexible resource pool composition, edge terminal allocation and communication can be solved. Numerical simulations on the improved IEEE 33-node and 123-node systems demonstrate the effectiveness of the proposed method.

BOOM! Tephrochronological dataset and exploration tool of the Southern (33–46° S) and Austral (49–55° S) volcanic zones of the Andes

Tephrochronology studies the deposits of explosive volcanic eruptions in the stratigraphic record. The Southern (SVZ, 33–46° S) and Austral (AVZ, 49–55° S) Volcanic Zones of the Andes are two very active volcanic zones where tephrochronology is of great use. There, it can be used to improve chronologies of paleoenvironmental records in Patagonia, an area providing valuable records at global scale; as well as to identify areas likely to be affected by volcanic eruptions in the future, essential for producing volcanic hazard maps. The close proximity of many volcanic centers with recurrent explosive activity, which have very similar geochemical compositions, and very often poor age constraints, represent a challenge for the study of tephrochronology in the region. In addition to this, the ever-growing amount of tephrochronological information in the area, dispersed in different types of publications which vary greatly in format, makes the integration of the data produced by different actors, and consecutively its interpretation, increasingly difficult. Here we address this issue by compiling the BOOM! dataset, which integrates ∼30 years of research on 32 active volcanic centers and 132 different eruptions, which took place during the last 20,000 years. To help users find and reuse data in the large dataset, we developed an online platform which provides user-friendly tools for exploring it, and helps users download subsets of it. To integrate this very heterogeneous information, special attention was given to include information which allows users to evaluate data quality and comparability, as well as to provide tools in the explorer for users to filter data by different criteria. The integration of this dataset opens new perspectives for the development of novel visualizations of tephrochronological data, for example, to better understand the multidimensional uncertainties associated with it. For example, uncertainties associated with analytical precision, with age estimates of both tephra deposits and volcanic eruptions, and of tephra classification. Additionally, it allows for the use of robust statistical tools to correlate tephra deposits, including those based on machine learning algorithms, which are here explored.

Enhancing deep neural networks for multivariate uncertainty analysis of cracked structures by POD-RBF

An efficient Monte Carlo (MC) simulation method is proposed to address multivariate uncertainties in the dynamic fracture analysis of cracked structures. Deep neural networks (DNN) based on model order reduction are special surrogate models for enhancing the sampling efficiency of MC simulation. Proper orthogonal decomposition-radial basis functions (POD-RBF) bridge the original full model and the DNN, enabling the training datasets of the neural network to be evaluated rapidly from a reduced-order model. The full-order model snapshot of the cracked structure is obtained using the scaled boundary finite element method (SBFEM). We innovatively tackle multidimensional uncertainties, including individual crack lengths, material parameters, and their combinations. Numerical examples show that the POD-RBF-DNN-MC surrogate model benefits from the uncertainty analysis of large scale and multidimensional random input variables. The method is simpler than full-order sampling and eliminates the scale problem of POD-RBF. In addition, the POD-RBF-DNN-MC surrogate model is more efficient than full-order MC, POD-RBF-MC only, and DNN-MC only, with respect to accelerating the stochastic response analysis based on MC. Finally, we validate the proposed algorithm and show that it significantly improves the efficiency of uncertainty analysis.

Robust Long-Term Hand Grasp Recognition With Raw Electromyographic Signals Using Multidimensional Uncertainty-Aware Models.

Hand grasp recognition with surface electromyography (sEMG) has been used as a possible natural strategy to control hand prosthetics. However, effectively performing activities of daily living for users relies significantly on the long-term robustness of such recognition, which is still a challenging task due to confused classes and several other variabilities. We hypothesise that this challenge can be addressed by introducing uncertainty-aware models because the rejection of uncertain movements has previously been demonstrated to improve the reliability of sEMG-based hand gesture recognition. With a particular focus on a very challenging benchmark dataset (NinaPro Database 6), we propose a novel end-to-end uncertainty-aware model, an evidential convolutional neural network (ECNN), which can generate multidimensional uncertainties, including vacuity and dissonance, for robust long-term hand grasp recognition. To avoid heuristically determining the optimal rejection threshold, we examine the performance of misclassification detection in the validation set. Extensive comparisons of accuracy under the non-rejection and rejection scheme are conducted when classifying 8 hand grasps (including rest) over 8 subjects across proposed models. The proposed ECNN is shown to improve recognition performance, achieving an accuracy of 51.44% without the rejection option and 83.51% under the rejection scheme with multidimensional uncertainties, significantly improving the current state-of-the-art (SoA) by 3.71% and 13.88%, respectively. Furthermore, its overall rejection-capable recognition accuracy remains stable with only a small accuracy degradation after the last data acquisition over 3 days. These results show the potential design of a reliable classifier that yields accurate and robust recognition performance.

An application of approximate dynamic programming in multi-period multi-product advertising budgeting

<p style='text-indent:20px;'>Advertising has always been considered a key part of marketing strategy and played a prominent role in the success or failure of products. This paper investigates a multi-product and multi-period advertising budget allocation, determining the amount of advertising budget for each product through the time horizon. Imperative factors including life cycle stage, <inline-formula><tex-math id="M1">\begin{document}$ BCG $\end{document}</tex-math></inline-formula> matrix class, competitors' reactions, and budget constraints affect the joint chain of decisions for all products to maximize the total profits. To do so, we define a stochastic sequential resource allocation problem and use an approximate dynamic programming (<inline-formula><tex-math id="M2">\begin{document}$ ADP $\end{document}</tex-math></inline-formula>) algorithm to alleviate the huge size of the problem and multi-dimensional uncertainties of the environment. These uncertainties are the reactions of competitors based on the current status of the market and our decisions, as well as the stochastic effectiveness (rewards) of the taken action. We apply an approximate value iteration (<inline-formula><tex-math id="M3">\begin{document}$ AVI $\end{document}</tex-math></inline-formula>) algorithm on a numerical example and compare the results with four different policies to highlight our managerial contributions. In the end, the validity of our proposed approach is assessed against a genetic algorithm. To do so, we simplify the environment by fixing the competitor's reaction and considering a deterministic environment.</p>

Operation and Planning of Energy Hubs Under Uncertainty—A Review of Mathematical Optimization Approaches

Co-designing energy systems across multiple energy carriers is increasingly attracting attention of researchers and policy makers, since it is a prominent means of increasing the overall efficiency of the energy sector. Special attention is attributed to the so-called energy hubs, i.e., clusters of energy communities featuring electricity, gas, heat, hydrogen, and also water generation and consumption facilities. Managing an energy hub entails dealing with multiple sources of uncertainty, such as renewable generation, energy demands, wholesale market prices, etc. Such uncertainties call for sophisticated decision-making techniques, with mathematical optimization being the predominant family of decision-making methods proposed in the literature of recent years. In this paper, we summarize, review, and categorize research studies that have applied mathematical optimization approaches towards making operational and planning decisions for energy hubs. Relevant methods include robust optimization, information gap decision theory, stochastic programming, and chance-constrained optimization. The results of the review indicate the increasing adoption of robust and, more recently, hybrid methods to deal with the multi-dimensional uncertainties of energy hubs.

Reliability modelling considering multi-dimensional cognitive uncertainties based on uncertainty theory

Aiming at the multi-dimensional cognitive uncertainties in performance degradation modelling for small samples, a reliability assessment method is proposed based on uncertainty theory. First, a degradation model is established based on the uncertain process, which considers cognitive uncertainties from the time fluctuation, the measurement error, and the individual differences in initial value and degradation rate, and the reliability function is derived. Then, a two-step parameter estimation method for the degradation model is proposed based on the α-path and the least square, which is verified by numerical simulation. Finally, the effectiveness and superiority of the proposed method are verified by the cases of GaAs lasers and magneto-optic data storage disks, and parameter sensitivity analysis is conducted. The results indicate that uncertainty affects product reliability greatly. For small samples, thedegradation models considering multi-dimensional uncertainties based on the Liu process has smaller fitting errors than that based on the Wiener process.

Robust optimal capacity planning of grid-connected microgrid considering energy management under multi-dimensional uncertainties

Microgrid is considered an efficient paradigm for managing the massive number of distributed renewable generation and storage facilities. The optimal microgrid capacity planning is a non-trivial task due to the impact of randomness and uncertainties of renewable generation sources, and the adopted energy management strategies. In this paper, an optimal capacity planning model for the grid-connected microgrid is developed fully considering the renewable generation uncertainties through efficient scenario generation and reduction based on the deep convolutional generative adversarial network (DCGAN) and improved k-medoids clustering algorithm, as well as the microgrid energy management strategy. The proposed solution optimizes the capacity planning for the maximization of renewable energy utilization efficiency, and minimizes the economic cost and carbon emissions. The proposed solution is assessed using a case study of a microgrid (MG) project in northern China through a comparative study and the numerical results confirm the cost-effectiveness of the proposed solution.

Integrated Planning of Cyber-Physical Active Distribution System Considering Multidimensional Uncertainties

The integration of cyber technologies is transforming the power distribution network into a cyber-physical active distribution system (CPADS), and brings more flexibility to its operation. However, various uncertainties from the cyber space and physical space are emerging and coupled with each other, which results in significant challenges for the distribution network planning and operation. Thus, a bilevel integrated planning model accounting for multidimensional uncertainties from both the cyber space and physical space is proposed for the CPADS in this paper. With the goal of minimizing the annual investment and operation costs, the model comprehensively considers the location and selection of active-management elements (e.g., electrical storage systems, capacitor banks, and switches), investment constraints, power flow constraints, and operation constraints for all the active-management elements, etc. Moreover, based on the typical cyber system failure scenario represented by information link failure (ILF), a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N-k</i> uncertainty set considering the failure probability distribution is proposed, while the uncertainties of renewable energy and load demand are characterized by box-like uncertainty sets. Finally, the proposed planning model is recast into a multi-stage robust optimization model which can be divided into a master problem and two-step subproblems (SP-1 and SP-2) to be solved by the column and constraint generation (CCG) algorithm. Case studies and comparative analysis on the PG 69 distribution system are performed to verify the effectiveness of the proposed method.

A novel deep-learning based surrogate modeling of stochastic electric vehicle traffic user equilibrium in low-carbon electricity–transportation nexus

The increasing penetration of electric vehicles (EV) and fast charging stations (FCS) is tightly coupling the operation of power and transportation systems. In this context, the characterization of the EV flows and charging demand in response to varying traffic conditions and coordinated optimization strategies play a vital role. Previous work on the computation of stochastic traffic user equilibrium (TUE) involve non-linearities in the traffic link and FCS congestion representations and are generally inefficient in dealing with the multi-source uncertainties associated with the operating conditions of the traffic network (TN) and power distribution network (PDN). To address this, this paper proposed a novel deep learning (DL) based surrogate modeling method, leveraging the strength of edge-conditioned convolutional network (ECCN) and deep belief network (DBN). ECCN enables automatic extraction of spatial dependencies, taking into account both node and edge features characterizing the operation of TN. DBN leverages the value of the extracted features and achieves an accurate mapping between the latter to the EV charging demand and EV flows in the TUE, while adaptively generalizing to the multi-dimensional uncertainties. Case studies on three test systems of different scales (including a real-world case involving the matched TN and PDN of Nanjing city) demonstrate that the proposed surrogate model achieves a higher solution accuracy with respect to the state-of-the-art DL-based methods, and exhibits favorable computational performance. Quantitative results also corroborate the benefits brought by the proposed coordinated spatial optimization of EV flows and charging demand on the operation of both TN and PDN.

Impacts of Multi-Dimensional Geometrical Uncertainties on Field Characteristics of Traveling-Wave Tube in Data-Driven Perspective

Recent prominent analyses on impacts of fabrication errors tend to start from Pierce parameters by assuming a normal distribution on them. We manage to analyze the complicated effects of multi-dimensional uncertainties directly from geometrical tolerances and present a general pattern for multi-dimensional geometrical uncertainty analysis on field characteristics. Aided by artificial neural networks (ANNs) which would get hold of the cost surface quickly and serve as rapid interfaces with a calculation speed several orders faster than full-wave code, Monte Caro analysis is accessible and effective to simulate the actual probabilistic distributions through a large-volume sampling on neural networks. Under such data-driven perspective which circumvents sophisticated theoretical analysis, the variations of geometrical parameters are analyzed as an entirety from the viewpoint of distribution. The dynamics of features of distributions of three field characteristics as well as geometrical parameters are therefore possible to be delved and analyzed. Such an analysis pattern is general since none of the steps presented cannot be readily transplanted to other topologies.