Stochastic Uncertainty Research Articles

Interval Prediction Model of Deformation Behavior for Dam Safety during Long-Term Operation Using Bootstrap-GBDT

Accurate and reliable prediction on structural deformation is a powerful means to evaluate the safety state of dams during long-term operation. This work is a contribution to the quantification of the cognitive and stochastic uncertainties in prediction models for the dam performance using measured time series, through constructing the prediction interval (PI) by an innovative model combined with the gradient boosting decision tree (GBDT) and the bootstrap method. The constructed PI, improved by the kernel density estimation (KDA), consists of an upper bound and a lower bound of the interval to provide a confidence level for dam deformation prediction. The bootstrap method combined with multiple GBDT is utilized to estimate the variance of the model bias, mainly derived from the cognitive uncertainties. The variance of random noise can be furtherly estimated through training the combined model to fit the residuals so as to indicate the stochastic uncertainties. The effectiveness of the newly proposed model is validated employing measured data of the Jinping Ι arch Dam. The results indicate that the methodology can obtain high-quality PIs and accurate prediction values and thus can provide strong support for better appraising dam performance during long-term operation.

Optimization of integrated load dispatch in multi-fueled renewable rich power systems using fractal firefly algorithm

This manuscript applied fractal firefly optimization technique to the integrated load dispatch (ILD) problem involving loads allocation to power generating units with the minimum total fuel cost and emissions while handling the constraints for large-scale multi-fueled power plants and integration of stochastic wind to provide sustainable energy. The penetration of wind energy into conventional grids has resolved power system scheduling issues at the cost of rise in the stiffness of nonconvex ILD optimization problem. In order to enhance the dispatch performance with significant penetration of wind energy, an effective framework of fractal heritage is introduced inspired by Firefly algorithm. In order to validate the efficacy and flexibility of the proposed algorithm, sundry non-convex ILD optimization scenarios with valve-point effects, capacity constraints, multi-fuels power plants and Weibull's distributed stochastic wind uncertainty is implemented. The results reveal stupendous performance in term of the minimum fuel cost with higher efficiency and finer convergence rate than that of conventional algorithms.

Mitigating stochastic uncertainty from weather routing for ships with wind propulsion

Reducing the shipping sector's contribution to climate change requires urgent emission reductions this decade. Both weather routing and wind propulsion offer immediate solutions, where combining sails with efficient routing amplifies the performance of each technology. However, while large emission savings are theoretically available, the impact of stochastic uncertainty from wind forecasts is unknown. Here, we present a novel approach that exploits fuel consumption calculations from over a thousand departures across three routes to characterise stochastic uncertainty. We show that routes with ideal wind conditions and long voyage times are most sensitive to uncertain forecast inputs, reducing savings from Flettner rotors and weather routing by up to 44% when a priori weather routing strategies are used. This paper further shows how an adaptive weather routing strategy can be used as an accurate prediction tool to reduce uncertainty on all routes investigated, reliably amplifying carbon savings from Flettner rotors by between 1.16 and 2.48 times typical great circle route savings. Overall, this paper provides greater assurance around the previously estimated carbon savings that serves to strengthen confidence in a wind-assisted decarbonisation strategy and its potential to provide essential emission reductions this decade.

An Autoregressive-Based Kalman Filter Approach for Daily PM2.5 Concentration Forecasting in Beijing, China.

With the acceleration of urbanization, air pollution, especially PM2.5, has seriously affected human health and reduced people's life quality. Accurate PM2.5 prediction is significant for environmental protection authorities to take actions and develop prevention countermeasures. In this article, an adapted Kalman filter (KF) approach is presented to remove the nonlinearity and stochastic uncertainty of time series, suffered by the autoregressive integrated moving average (ARIMA) model. To further improve the accuracy of PM2.5 forecasting, a hybrid model is proposed by introducing an autoregressive (AR) model, where the AR part is used to determine the state-space equation, whereas the KF part is used for state estimation on PM2.5 concentration series. A modified artificial neural network (ANN), called AR-ANN is introduced to compare with the AR-KF model. According to the results, the AR-KF model outperforms the AR-ANN model and the original ARIMA model on the predication accuracy; that is, the AR-ANN obtains 10.85 and 15.45 of mean absolute error and root mean square error, respectively, whereas the ARIMA gains 30.58 and 29.39 on the corresponding metrics. It, therefore, proves that the presented AR-KF model can be adopted for air pollutant concentration prediction.

Uncertainty propagation scheme for two-step Monte Carlo neutronic simulations applied to the stochastic uncertainty of the intermediate radiation source in SRC-UNED

Two-step Monte Carlo (MC) neutronic simulations are widely used for nuclear analyses required in fusion facilities. This is the case of ITER nuclear analyses beyond the bio-shield, where it is necessary to couple two models (Tokamak and Tokamak Complex) which share the bio-shield as a common interface. Here, the radiation transport is performed through the characterization of the radiation field that relates both models. SRC-UNED code allows coupling two MC simulations by defining and sampling the realistic intermediate radiation sources that represent the radiation crossing the ITER bio-shield. Nonetheless, the coupling of MC simulations has some disadvantages. One of the main ones is that the stochastic uncertainty due to the first MC simulation is not propagated during the second one. Consequently, the quality of the intermediate radiation source is not quantified. Typical schemes for stochastic uncertainty propagation require evaluating the covariance matrix of the intermediate radiation source, which is prohibitive in SRC-UNED real applications since it would require high computational memory resources to store the necessary information. To overcome this limitation, a scheme based on the direct estimation of the standard deviation is proposed, implemented and verified for SRC-UNED. This method enables the stochastic uncertainty to be quantified and propagated, from the intermediate radiation source to the nuclear response, in real cases such as ITER Torus Cryopumps analysis.

Coupling Fuzzy Bi-Level Chance Constraint Programming and Spatial Analysis for Urban Ecological Management

In this study, a fuzzy bi-level chance constraint programming (FBCP) model is developed for urban ecological management in Xiamen, China. FBCP has advantages in balancing trade-offs between multiple decision makers and can address fuzzy and stochastic uncertainty in ecosystem management. It also can reflect the impact of different violation risk levels and emission reduction measures on system benefit, ecosystem service value, and land resource allocation. Then, the conversion of land use and its effects at small regional extent (CLUE-S) model is employed to provide the spatial allocation of future land resources under different scenarios. Results reveal that (i) carbon fixation and climate regulation are the major contributors to the ecosystem service value, with a proportion of [15.4, 15.6]% and [18.5, 18.8]%, respectively; (ii) the main environmental problem in Xiamen is the water pollution caused by the excessive discharge of commercial and residential land, with COD and NH3-N account for [68.81, 69.33]% and [67.65, 68.20]% of the total discharge of the city, respectively; (iii) the violation risk p level is the most impact factor, and the schemes with high system benefit would face greater default risk and lower ecological quality; (iv) FBCP model considers the trade-off between economic benefit and ecological quality, while the fuzzy chance constraint programming (FCP) model achieves a high system benefit at the expense of the environment. These findings help decision makers to understand the impact of parameter uncertainty and pollutant discharge policies on system benefit, and adjust land-use patterns to weigh ecological environment protection with urban economic development.

Safe, learning-based MPC for highway driving under lane-change uncertainty: A distributionally robust approach

We present a case study applying learning-based distributionally robust model predictive control to highway motion planning under stochastic uncertainty of the lane change behavior of surrounding road users. The dynamics of road users are modeled using Markov jump systems, in which the switching variable describes the desired lane of the vehicle under consideration and the continuous state describes the pose and velocity of the vehicles. We assume the switching probabilities of the underlying Markov chain to be unknown. As the vehicle is observed and thus, samples from the Markov chain are drawn, the transition probabilities are estimated along with an ambiguity set which accounts for misestimations of these probabilities. Correspondingly, a distributionally robust optimal control problem is formulated over a scenario tree, and solved in receding horizon. As a result, a motion planning procedure is obtained which through observation of the target vehicle gradually becomes less conservative while avoiding overconfidence in estimates obtained from small sample sizes. We present an extensive numerical case study, comparing the effects of several different design aspects on the controller performance and safety.

Optimized adaptive filtering for fault estimation of the dynamics of high-speed train based on robust extended Kalman filter

In this paper, an optimized adaptive robust extended Kalman filter is proposed based on random weighting factors and an improved whale optimization algorithm for fault estimation of the dynamics of high-speed trains with constant time delays, drastically changing noise and stochastic uncertainties. Robust upper bounds are proposed to improve the performance of the extended Kalman filter by decreasing the influence of the linearization error on filtering for the dynamics of high-speed trains with constant time delays, and its robustness is proven to guarantee the feasibility of the proposed upper bounds. Furthermore, considering drastically changing noise with unknown statistics, a random weighting adaptive algorithm is proposed to implement unbiased noise estimation so that the robust extended Kalman filter can still be implemented well. In addition, a differential evolution algorithm and adaptive parameter are introduced to improve the performance of the whale optimization algorithm so that the stochastic uncertainties are optimized, and the influence of the stochastic uncertainties on filtering is further decreased. The simulation results in the three conditions show that, compared with the variational Bayes adaptive iterated extended Kalman filter, using the proposed method, the position, speed and fault estimation errors are decreased by 31.8%, 33.2% and 28.3%, respectively, on average, which depends on more accurate noise estimation.

Stochastic Coded Offloading Scheme for Unmanned-Aerial-Vehicle-Assisted Edge Computing

Unmanned aerial vehicles (UAVs) have gained wide research interests due to their technological advancement and high mobility. The UAVs are equipped with increasingly advanced capabilities to run computationally intensive applications enabled by machine learning techniques. However, because of both energy and computation constraints, the UAVs face issues hovering in the sky while performing computation due to weather uncertainty. To overcome the computation constraints, the UAVs can partially or fully offload their computation tasks to the edge servers. In ordinary computation offloading operations, the UAVs can retrieve the result from the returned output. Nevertheless, if the UAVs are unable to retrieve the entire result from the edge servers, i.e., straggling edge servers, this operation will fail. In this article, we propose a coded distributed computing (CDC) approach for computation offloading to mitigate straggling edge servers. The UAVs can retrieve the returned result when the number of returned copies is greater than or equal to the recovery threshold. There is a shortfall if the returned copies are less than the recovery threshold. To minimize the cost of the network, energy consumption by the UAVs, and prevent over and under subscription of the resources, we devise a two-phase stochastic coded offloading scheme (SCOS). In the first phase, the appropriate UAVs are allocated to the charging stations amid weather uncertainty. In the second phase, we use the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$ </tex-math></inline-formula> -stage stochastic integer programming (SIP) to optimize the number of computation subtasks offloaded and computed locally, while taking into account the computation shortfall and demand uncertainty. By using a real data set, the simulation results show that our proposed scheme is fully dynamic and minimizes the cost of the network and UAV energy consumption amid stochastic uncertainties.

ANALYTICAL MODEL OF ORGANIZATION OF FREIGHT TRANSPORTATION IN COMPLEX TRANSPORT SYSTEM OF MEGALOPOLIS

The article presents an analytical model that allows designing information and analytical platforms for managing freight transportation in complex transport systems. The developed model is based on the principles of synthesis of methods for controlling the structural dynamics of complex systems and solves the problems of finding the optimal balance between the information situation of the object and the subject of design. The principles of mathematical modeling of processes on an information and analytical platform were formed, namely: the implementation of an object-oriented approach when forming an information space of possible solutions and dismemberment into subsystems and levels based on the principle of homogeneity of technology and heterogeneity of information states. On the basis of the formed approach, an information and analytical platform has been developed in the freight transportation management system, which allows you to objectively reflect the change in system variables over time for a particular process from the standpoint of multivariable forecasting, while the tools for simulating the production of solutions can be transformed in relation to a particular process, depending on the information situation corresponding to the conditions of the freight transportation process.&#x0D; Purpose. Development of an analytical model for building an information and analytical platform for managing the system of road freight transportation in a large agglomeration or metropolis.&#x0D; Methodology. Mathematical methods of decision theory under conditions of stochastic uncertainty, which makes it possible to develop optimal control strategies in a complex system.&#x0D; Results. Mathematical model and algorithms for the organization of road freight transportation in the context of the flow of unstructured information of the external environment.&#x0D; Practical implications. The transport system of a metropolis or large agglomeration, in which the indicators of its effectiveness are influenced by a large number of external and internal factors and at the same time there is a significant dynamic of the studied indicators.

The Genesis of Uncertainty: Structural Analysis of Stochastic Chaos in Finance Markets

The presented article is methodological in nature and is devoted to the analysis of observation series of financial asset quotation changes in capital markets. The most important feature of these processes is their instability, which manifests itself in high sensitivity to seemingly minor disturbing factors. This phenomenon is well-studied in the theory of nonlinear dynamical systems and is described by models of deterministic chaos. However, for the processes considered in the article, the dynamic instability of the immersion environment is exacerbated by stochastic uncertainty caused by random fluctuations in the pricing process. As a result, describing observation series of quotations of financial assets is difficult because it involves stochastic chaos. This article analyzes and classifies chaotic series of observations to help model and forecast related processes.

Robust state estimation and fault detection for Autonomous Underwater Vehicles considering hydrodynamic effects

Autonomous Underwater Vehicles (AUVs) are designed to operate in complex external environments, making fault detection crucial to overall safety. While a general kinetic model can be applied to describe the dynamics of an AUV, obtaining accurate parameters for the dynamic model is challenging due to the complexity of the outline structure of the AUV and external influence factors. In addition, environmental influence on model parameters is usually time-varying and stochastic, which is different from simple model uncertainties. In this paper, we model external perturbations as stochastic model uncertainties that share some characteristics with noise. We also apply an improved robust filtering method to estimate system states and alleviate the effects of stochastic system uncertainties. Based on the proposed filtering approach, a residual signal is computed based on reconstruction errors of the observations and smoothed using a sliding-window technique, which is directly applied to the fault detection problem. Finally, simulation experiments demonstrate the effectiveness of the proposed method in detecting actuator faults in several cases.

Bayesian modeling of the temporal evolution of seismicity using the ETAS.inlabru package

The epidemic type aftershock sequence (ETAS) model is widely used to model seismic sequences and underpins operational earthquake forecasting (OEF). However, it remains challenging to assess the reliability of inverted ETAS parameters for numerous reasons. For example, the most common algorithms just return point estimates with little quantification of uncertainty. At the same time, Bayesian Markov chain Monte Carlo implementations remain slow to run and do not scale well, and few have been extended to include spatial structure. This makes it difficult to explore the effects of stochastic uncertainty. Here, we present a new approach to ETAS modeling using an alternative Bayesian method, the integrated nested Laplace approximation (INLA). We have implemented this model in a new R-Package called ETAS.inlabru, which is built on the R packages R-INLA and inlabru. Our study has included extending these packages, which provided tools for modeling log-Gaussian Cox processes, to include the self-exciting Hawkes process that ETAS is a special case of. While we just present the temporal component here, the model scales to a spatio-temporal model and may include a variety of spatial covariates. This is a fast method that returns joint posteriors on the ETAS background and triggering parameters. Using a series of synthetic case studies, we explore the robustness of ETAS inversions using this method of inversion. We also included runnable notebooks to reproduce the figures in this article as part of the package's GitHub repository. We demonstrate that reliable estimates of the model parameters require that the catalog data contain periods of relative quiescence, as well as triggered sequences. We explore the robustness of the method under stochastic uncertainty in the training data and show that the method is robust to a wide range of starting conditions. We show how the inclusion of historic earthquakes prior to the modeled time window affects the quality of the inversion. Finally, we show that rate-dependent incompleteness of earthquake catalogs after large earthquakes have a significant and detrimental effect on the ETAS posteriors. We believe that the speed of the inlabru inversion, which includes a rigorous estimation of uncertainty, will enable a deeper exploration of how to use ETAS robustly for seismicity modeling and operational earthquake forecasting.

The uncertainty in mega-regional SEA and its coping methods in China's practice

Mega-regional strategic environmental assessment (RSEA) aims to provide decision-makers with scientific estimations and protective recommendations for regional development by taking inter-provincial space as work scopes, focalizing regional development as evaluation objects, and evaluating long-term ecological environmental impacts. Huge uncertainties inevitably exist in RSEA, affecting a reliable assessment. However, past literature offers limited guidance on how to systematically identify and address uncertainties in RSEAs. Thus, in light of uncertainty research in other environmental domains, an uncertainty typology of RSEA is constructed based on Simon's administrative model (1957) and Koernoev & Devuyst's decision situation (2016). Three uncertainty types including stochastic, epistemic, and technical uncertainties are developed to respectively interpret the variability-, knowledge-, and technic-related uncertainties. Various coping methods are identified, such as scenario analysis, modeling simulation, worst-case principles, adaptive management, etc. Then, practitioners' perception towards the uncertainty typology is investigated by a questionnaire survey, and the application of uncertainty coping approaches in RSEA practice is examined through case studies. Subsequently, the enlightenment of uncertainty handling in China's RSEA is proposed.

Collaborative Decision Making (CDM) in Emergency Caused by Captain Incapacitation

The authors present a new approach to decision-making to ensure the proper collaboration of different personnel. Models are used in intelligent integrated decision support systems, especially for actions in emergencies. Behavioral deterministic models are used for synchronization actions of all operators, to support and timely predicting of operators' actions in an emergency. To determine the quantitative characteristics of risk levels, models for collaborative decision making (CDM) under uncertainty by the operators (pilots, air traffic controllers, flight/dispatch), and other invited specialists, have been developed. The decision-making modeling of a group of operators in case of an emergency situation such as “pilot incapacitation” was presented. The methodological basis for CDM in certainty is network planning, in conditions of Stochastic uncertainty – is a decision tree, in conditions of non-stochastic uncertainty – is a matrix of decisions, and outcomes are made this using the expert judgment method for obtaining quantity estimations.

Integration of design and control for renewable energy systems with an application to anaerobic digestion: A deep deterministic policy gradient framework

In recent years, the urgent need to develop sustainable processes to curb the effects of climate change has gained global attention and led to the transition into green technologies, such as Anaerobic Digestion Systems (AD). As these technologies present a complex dynamic behavior, there is a motivation to seek for new ways to optimize these systems. This study presents a Deep Deterministic Policy Gradient (DDPG) strategy for integration of process design and control. DDPG is a state-of-the-art reinforcement learning algorithm used to search for optimal solutions. The proposed approach considers stochastic disturbances and parametric uncertainty. Also, a penalty function included in the reward function is considered to account for process constraints. The proposed approach was tested in AD systems involving Tequila vinasses. Two reactor AD configurations were explored under multiple scenarios using the proposed DDPG strategy. While the two-stage AD system required a larger capital investment in exchange of higher amounts of biogas being produced, the single-stage AD system required less investment in capital costs in exchange of producing less biogas and therefore lower revenues than the two-stage system. The results showed that DDPG was able to identify optimal design and control profiles thus making it an attractive method for optimal process design and operations management of renewable systems.

Construction of an economic environment scheduling system based on the multi-objective fuzzy optimization model

Abstract To integrate the combination of electric vehicles and wind power of the transmission system, a wind farm environment multi-objective transmission model considering plug-in electric vehicles was established. The fuzzy optimal scheduling model for the environment and economy target of wind farm power system considering grid interconnection of electric vehicles designed by the author has the following characteristics: A fuzzy multi-objective dynamic scheduling model for the design of wind farm power system considering grid connection of plug-in electric vehicle is established, and the original 10 systems are taken as an example for power system design. The results show that the better model shows that the electric vehicle grid connection can greatly reduce the disadvantage of wind power stochastic uncertainties of system scheduling. The model can be used under different conditions further analyzing the rationality of the model determined by the author. An improved particle swarm optimization algorithm is used to solve this problem. The model takes the environmental and economic benefits into account, which improves the efficiency of the model.

Two-stage robust optimal operation of AC/DC distribution networks with power electronic transformers

Power electronic transformers (PET) are a new type of power electronic equipment with a multi-port flexible dispatch function, which can play the role of a power hub in a system composed of multiple AC-DC hybrid distribution grids for interactive sharing of power in multiple regions. In this study, a two-stage robust optimization operation model of a hybrid AC-DC distribution network with PET is proposed based on PET power transmission and transformation characteristics. The stochastic uncertainty of the distributed renewable energy output in the AC-DC grid is handled by a two-stage robust optimization method to determine the minimum total system operation cost under the worst case of distributed renewable energy output. Finally, a constrained column generation algorithm is used to solve the two-stage robust optimization model in the min-max-min form and verifies the validity of the model in this study.

Network flexibility regulation by renewable energy hubs using flexibility pricing-based energy management

This article presents the energy management of electrical and thermal networks in the presence of renewable energy hubs to regulate the flexibility of these networks based on flexible pricing services. Hubs consist of renewable sources and bio-waste units in addition to energy storage and responsive loads. The bio-waste unit produces electrical and thermal energy simultaneously. The proposed scheme minimizes the difference between the network's energy cost and the hub's flexibility income. It is subject to the optimal power flow equations and flexibility limitation in networks, operation model of resources, storage, and responsive loads in form of energy hub, and hub flexibility model. Unscented transformation-based stochastic optimization models uncertainties of load, renewable power, and energy price. Finally, the numerical results demonstrate the capability of the proposed scheme in extracting the optimal state of flexibility, operation, and economic situation of electric and thermal networks with optimal energy management of renewable hubs based on flexible pricing services. The inclusion of renewable resources, storage generators, and responsive loads into a renewable hub improves the economic situation by 32.9% and the status of operation indicators of the energy networks by 22.4–42% in condition of 100% flexibility.

The Impact of Uncertainty Shocks to Consumption under Different Confidence Regimes Based on a Stochastic Uncertainty-in-Mean TVAR Model

Exogenous uncertainty shocks may have different effects on domestic and foreign consumption under different consumer confidence regimes. In this paper, we specify a threshold vector autoregressive (TVAR) model with different consumer confidence regimes to study the response of endogenous macroeconomic variables to exogenous shocks. The evidence shows that in China, compared to high consumer confidence, low consumer confidence dampens consumption both at home and abroad. However, low consumer confidence benefits exports, the source of foreign consumption. A forecast error variance decomposition analysis further confirms the difference in the effects under different consumer confidence regimes. A comparative analysis shows that consumer confidence is much more influential in the US than in China. Our findings differ from those of earlier works, as we introduce stochastic uncertainty to both the mean and heteroscedasticity and apply counterfactual analysis to show the hazard of ignoring stochastic uncertainty in the traditional threshold vector autoregression. Finally, from the ex ante and ex post perspectives, we provide managerial implications for the authorities to tackle economic issues based on different consumer confidence regimes.