Uncertainty Decomposition Research Articles

Regulation of Electric Vehicle Speed Oscillations Due to Uneven Drive Surfaces Using ISMDTC

An unbalance in the electromagnetic torque and the load torque occurs when Electric Vehicles (EVs) are driven through uneven terrains. This leads to non-periodic and time-varying speed oscillations. As a result, torsional vibrations increase and leads to passenger discomfort and mechanical stress on the EV body. The EV drive control should be designed to mitigate these speed oscillations. In this paper, an Integral Sliding Mode Control Based Direct Torque Control (ISM-DTC) of Induction Motor (IM) is proposed to inherit the intrinsic properties of disturbance rejection, robustness against parametric variations, operational uncertainties, and improve the conventional Proportional-Integral (PI)-based DTC (PIDTC) performance in uncertain EV drive conditions. The proposed control is integrated with PIDTC, which maintains the speed and acts as a nominal control. The non-linear ISM loop cancels out the speed fluctuations by balancing the electromagnetic torque with dynamic load torque demand. The proposed control cancels out the matched uncertainties without amplifying the unmatched uncertainties in system dynamics. An analysis of the uncertainty decomposition and control gain derivation is presented. The proposed ISMDTC is verified through simulations and experiments considering different scenarios of torque, reference speed variations, uncertainties, and the standard New European Driving Cycle (NEDC) and Urban Dynamometer Driving Schedule (US) drive test cycles.

Secondary Frequency Regulation from Variable Generation Through Uncertainty Decomposition: An Economic and Reliability Perspective

The rapid integration of variable generation (VG), such as photovoltaics (PV), necessitates an increase in the secondary frequency regulation (SFR) to handle the system intra-dispatch interval imbalance because of VG's variation. Although PV has the control capability to provide SFR, the main challenge is in guaranteeing the delivery of PV's energy and SFRs capacities in the automatic generation control (AGC) within each dispatch interval considering its uncertainty. This paper proposes a deliverable VG SFR provision model with endogenous VG's power uncertainty decomposition. First, the uncertainty of VG is decomposed using distributionally robust chance constraints through which the deliverable SFR provision is guaranteed. Next, the intra-interval frequency response of PV's SFR is validated with a user defined AGC model including the PV power plant. Finally, the economic benefits and the reliability improvements—such as the frequency deviation reduction with PV providing SFR—can be integrated and evaluated. The proposed model is tested in a modified 18-bus system and in the 240-bus simplified Western Electricity Coordinating Council test system. Results demonstrate that with the deliverable SFR from PV, the system cost and the frequency reliability can be improved simultaneously. PV's SFR performance can be guaranteed with the proposed model.

Information-based uncertainty decomposition in dual-channel microwave remote sensing of soil moisture

Abstract. The National Aeronautics and Space Administration (NASA) Soil Moisture Active-Passive (SMAP) mission characterizes global spatiotemporal patterns in surface soil moisture using dual L-band microwave retrievals of horizontal (TBh) and vertical (TBv) polarized microwave brightness temperatures through a modeled mechanistic relationship between vegetation opacity, surface scattering albedo, and soil effective temperature (Teff). Although this model has been validated against in situ soil moisture, there is a lack of systematic characterization of where and why SMAP estimates deviate from the in situ observations. Here, we assess how the information content of in situ soil moisture observations from the US Climate Reference Network contrasts with (1) the information contained within raw SMAP observations (i.e., “informational random uncertainty”) derived from TBh, TBv, and Teff themselves and with (2) the information contained in SMAP's dual-channel algorithm (DCA) soil moisture estimates (i.e., “informational model uncertainty”) derived from the model's inherent structure and parameterizations. The results show that, on average, 80 % of the information in the in situ soil moisture is unexplained by SMAP DCA soil moisture estimates. Loss of information in the DCA modeling process contributes 35 % of the unexplained information, while the remainder is induced by a lack of additional explanatory power within TBh, TBv, and Teff. Overall, retrieval quality of SMAP DCA soil moisture, denoted as the Pearson correlation coefficient between SMAP DCA soil moisture and in situ soil moisture, is negatively correlated with the informational uncertainties, with slight differences across different land covers. The informational model uncertainty (Pearson correlation of −0.59) was found to be more influential than the informational random uncertainty (Pearson correlation of −0.34), suggesting that the poor performance of SMAP DCA at some locations is driven by model parameterization and/or structure and not underlying satellite measurements of TBh and TBv. A decomposition of mutual information between TBh, TBv, and DCA soil moisture shows that on average 58 % of information provided by TBh and TBv to DCA estimates is redundant. The amount of information redundantly and synergistically provided by TBh and TBv was found to be closely related (Pearson correlations of 0.79 and −0.82, respectively) to the retrieval quality of SMAP DCA. TBh and TBv tend to contribute large redundant information to DCA estimates under surfaces or conditions where DCA makes better retrievals. This study provides a baseline approach that can also be applied to evaluate other remote sensing models and understand informational loss as satellite retrievals are translated to end-user products.

Future projection of low flows in the Chungju basin, Korea and their uncertainty decomposition

AbstractLow flow projections in response to global warming and the uncertainty decomposition into different components are performed with the focus on the Chungju basin, South Korea. Four downscaled climate simulations, two bias correction methods, and two hydrological models with two different potential evapotranspiration computation methods are applied to constitute the 32 ensemble members (4 × 2 × 4) of low flows projections. An analysis of the variance is used to decompose the total variance in the low flow projections into the contribution from three different sources. The result shows that hydrological models, particularly their structures, are the key factor that affects the low flow projections. They contribute more than 85% of the total uncertainty, and the projected change of low flow using different hydrological models can be of opposite signs, even under the same climate input data. On the other hand, the uncertainties related to climate simulation and bias correction are much smaller, comprising around 10 and 2%, respectively. The possible mechanisms behind the large uncertainty of projected low flow are investigated by comparing the relevant hydrological variables obtained from different hydrological simulations. The different representations in the hydrological models for the freezing of the soil layer during winter, which will undergo large changes as temperature increases, are likely to affect the projected change in low flow greatly. The difference in potential evapotranspiration methods also affects the low flow projections, but its contribution is relatively weaker than the effects of the hydrological model structure.

Model-wise uncertainty decomposition in multi-model ensemble hydrological projections

Model-wise uncertainty decomposition in multi-model ensemble hydrological projections

On the optimality of 2\xb0C targets and a decomposition of uncertainty

Determining international climate mitigation response strategies is a complex task. Integrated Assessment Models support this process by analysing the interplay of the most relevant factors, including socio-economic developments, climate system uncertainty, damage estimates, mitigation costs and discount rates. Here, we develop a meta-model that disentangles the uncertainties of these factors using full literature ranges. This model allows comparing insights of the cost-minimising and cost-benefit modelling communities. Typically, mitigation scenarios focus on minimum-cost pathways achieving the Paris Agreement without accounting for damages; our analysis shows doing so could double the initial carbon price. In a full cost-benefit setting, we show that the optimal temperature target does not exceed 2.5 °C when considering medium damages and low discount rates, even with high mitigation costs. With low mitigation costs, optimal temperature change drops to 1.5 °C or less. The most important factor determining the optimal temperature is the damage function, accounting for 50% of the uncertainty.

On the optimality of 2°C targets and a decomposition of uncertainty

On the optimality of 2°C targets and a decomposition of uncertainty

Robust control for fuzzy electric power steering system: A two-layer performance approach

This study investigates the angle tracking control of the electric power steering system, which is underactuated and with (possibly fast) time-varying uncertainties. We design the control based on constraint-following, that is, formulating the tracking goal as servo constraints. To tackle the uncertainty, especially the mismatched uncertainty, a robust control is proposed with two-layer performance: deterministically guaranteed and fuzzily optimized. Particularly, the control design is implemented in three steps. First, without considering uncertainty, a nominal control is designed. Second, an uncertainty decomposition technique is presented to account for uncertainty, which creatively allocates the mismatched uncertainty for the robust control design that also builds on the nominal system control. The robust scheme is deterministic without using any “if–then” rules and guarantees uniform boundedness and uniform ultimate boundedness for the system, that is, the deterministically guaranteed performance. Third, by using fuzzy set theory to describe uncertainty, a fuzzy-based performance index, including system performance and control cost, is introduced. A control parameter optimal design problem is formulated and analytically solved, that is, the fuzzily optimized performance. The effectiveness of the proposed approach is illustrated by rigorous proof and the simulation results on the electric power steering system.

On the optimality of 2°C targets: a decomposition of uncertainty. Underlying data and model.

On the optimality of 2°C targets: a decomposition of uncertainty. Underlying data and model.

Fuzzy set theory for optimal design in controlling underactuated dynamical systems with uncertainty

The fuzzy set theory for optimal control design of underactuated dynamical systems with uncertainty is proposed. The uncertainty is (possibly fast) time varying whose bound is unknown and lies in a prescribed set expressed by a fuzzy set. Control goals of uncertain dynamical systems are formulated as a series of constraints, which may be holonomic and nonholonomic. From the view of constraint-following control, we design an adaptive robust control based on a creative uncertainty decomposition, which divides the uncertainty into matched and mismatched terms. This decomposition renders the mismatched term to “disappear” in the stability analysis. The proposed control is able to drive the system to approximately follow the constraints and guarantee system performance (uniform boundedness and uniform ultimate boundedness), in the presence of the uncertainty. It is in deterministic form and not “if–then” fuzzy rules based. Because of the expressed fuzzy set of the uncertainty bounds, a performance index, which balances the conflict between system performance and control cost, can be constructed. An optimal design gain can be obtained by minimizing the performance index whose solution is guaranteed to always exist. Numerical results on a planar vertical takeoff and landing aircraft are presented for demonstration.

Assessment of the cascade of uncertainty in future snow depth projections across watersheds of mountainous, foothill, and plain areas in northern latitudes

Snowmelt is a major driver of the hydrological cycle in cold regions, as such, its accurate representation in hydrological models is key to both regional snow depth and streamflow prediction. The choice of a proper method for snowmelt representation is often improvised; however, a thorough characterization of uncertainty in such process representations particularly in the context of climate change has remained essential. To fill this gap, this study revisits and characterizes performance and uncertainty around the two general approaches to snowmelt representation, namely Energy-Balance Modules (EBMs) and Temperature-Index Modules (TIMs). To account for snow depth simulation and projection, two common Snow Density formulations (SNDs) are implemented that map snow water equivalent (SWE) to snow depth. The major research questions we address are two-fold. First, we examine the dominant controls of uncertainty in snow depth and streamflow simulations across scales and in different climates. Second, we evaluate the cascade of uncertainty of snow depth projections resulting from impact model parameters, greenhouse gas emission scenarios, climate models and their internal variability, and downscaling processes. We enable the Soil and Water Assessment Tool (SWAT) by coupling EBM, TIM, and two SND modules for examination of different snowmelt representation methods, and Analysis of Variance (ANOVA) for uncertainty decomposition and attribution. These analyses are implemented in mountainous, foothill, and plain regions in a large snow-dominated watershed in western Canada. Results show, rather counter-intuitively, that the choice of SND is a major control of performance and uncertainty of snow depth simulation rather than the choice between TIMs and EBMs and of their uncertain parameters. Also, analysis of streamflow simulations suggest that EBMs generally overestimate streamflow on main tributaries. Finally, uncertainty decompositions show that parameter uncertainty related to snowmelt modules dominantly controls uncertainty in future snow depth projections under climate change, particularly in mountainous regions. However, in plain regions, the uncertainty contribution of model parameters becomes more variable with time and less dominant compared with the other sources of uncertainty. Overall, it is shown that the hydro-climatic and topographic conditions of different regions, as well as input data availability, have considerable effect on reproduction of snow depth, snowmelt and resulting streamflow, and on the share of different uncertainty sources when projecting regional snow depth.

Impacts of changes in the watershed partitioning level and optimization algorithm on runoff simulation: decomposition of uncertainties

Hydrological modeling has provided key insights into the mechanisms of model state, such as the watershed partitioning level and optimization algorithm, and their impacts on the hydrological process, but the uncertainty of this impact is poorly understood. To this end, in this study, the effects of the watershed partitioning level and optimization algorithm for hydrological simulation uncertainty were assessed based on the semi-distributed TOPMODEL model, i.e., six watershed partitioning levels and three intelligent global optimization algorithms were used in the source region of the Yellow River. Meanwhile, the uncertainty contribution of the individual and interaction of the watershed partitioning levels and optimization algorithms on the hydrological process were dynamically evaluated using the variance decomposition method based on subsampling. Results showed that the impacts of the watershed partitioning level and optimization algorithm on the runoff simulation were particularly obvious for different characteristic periods. In the flood period, the optimization algorithm was the dominant factor affecting the runoff simulation uncertainty, with the proportion of up to 0.50, whereas the contribution of the watershed partitioning level was only 0.22. In the non-flood period, they contributed substantially to the uncertainty of the runoff simulation, accounting for about 0.30. Moreover, the interactions between the watershed partitioning level and optimization algorithm had a strong influence throughout the year, especially in the non-flood period, which may be because the hydrological model amplifies the output error and increases the interaction effect. Generally, the results shed important insight into reducing the uncertainty of the runoff simulation in future research.

A Framework to Quantify the Uncertainty Contribution of GCMs Over Multiple Sources in Hydrological Impacts of Climate Change

AbstractThe quantification of climate change impacts on hydrology is subjected to multiple uncertainty sources. Large ensembles of hydrological simulations based on multimodel ensembles (MMEs) have been commonly applied to represent overall uncertainty of hydrological impacts. However, as increasing numbers of global climate models (GCMs) are being developed, how many GCMs in MMEs are sufficient to characterize overall uncertainty is not clear. Therefore, this study investigates the influences of GCM quantity on quantifying overall uncertainty and uncertainty contributions of multiple sources in hydrological impacts. Large ensembles of hydrological simulations are obtained through the permutation of 3 greenhouse gas emission scenarios, 22 GCMs, 6 downscaling techniques, 5 hydrological models (HMs), and 5 sets of HM parameters, which enables to decompose uncertainty components using analysis of variance. The influences of GCM quantity are investigated by repeatedly conducting uncertainty decomposition for hydrological simulations from subsets with different numbers of GCMs. The results show that GCMs are the leading uncertainty sources in evaluating changes in annual and peak streamflows, while for changes in low flow, other uncertainty sources except HM parameters also have large contributions to overall uncertainty. Furthermore, on the condition of using no more than five GCMs, there are large possibilities that the overall uncertainty and GCMs' uncertainty contribution are underestimated. Using around 10 GCMs can ensure that the median of different combinations generates similar uncertainty components as the whole ensemble. Therefore, it is recommended to use at least 10 GCMs in studies of climate change impacts on hydrology to thoroughly quantify uncertainty.

Uncertainty decomposition in climate-change impact assessments: a Bayesian perspective

A climate-impact projection usually consists of several stages, and the uncertainty of the projection is known to be quite large. It is necessary to assess how much each stage contributed to the uncertainty. We call an uncertainty quantification method in which relative contribution of each stage can be evaluated as uncertainty decomposition. We propose a new Bayesian model for uncertainty decomposition in climate change impact assessments. The proposed Bayesian model can incorporate uncertainty of natural variability and utilize data in control period. We provide a simple and efficient Gibbs sampling algorithm using the auxiliary variable technique. We compare the proposed method with other existing uncertainty decomposition methods by analyzing streamflow data for Yongdam Dam basin located at Geum River in South Korea.

Bayesian uncertainty decomposition for hydrological projections

There is a considerable uncertainty in a hydrological projection, which arisen from the multiple stages composing the hydrological projection. Uncertainty decomposition analysis evaluates contribution of each stage to the total uncertainty in the hydrological projection. Some uncertainty decomposition methods have been proposed, but they still have some limitations: (1) they do not consider nonstationarity in data and (2) they only use summary statistics of the projected data instead of the full time-series and lack a principled way to choose the summary statistic. We propose a novel Bayesian uncertainty decomposition method which can alleviate such problems. In addition, the proposed method provides probabilistic statements about the uncertainties. We apply the proposed method to the streamflow projection data for Yongdam Dam basin located at Geum River in South Korea.

Incomplete-Information Games in Large Populations with Anonymity

The paper provides theoretical foundations for models of strategic interdependence under uncertainty that have a continuum of agents and a decomposition of uncertainty into a macro component and an agent-specific micro component, with a law of large numbers for the latter. This macro-micro decomposition of uncertainty is implied by a condition of exchangeability of agents' types, which holds at the level of the prior if and only if it also holds at the level of agents' beliefs, i.e., posteriors. Under an additional condition of anonymity in payoffs, agents' behaviours are fully determined by their macro beliefs about the cross-section distribution of types and other macro variables and about the cross-section distribution of other agents' strategies. Any probability distribution over cross-section distributions of types and other macro variables is compatible with a fully specified belief system, but not every macro belief function is compatible with a common prior. The paper gives necessary and sufficient conditions for compatibility of a macro belief function with a common prior.

Framework for emulation and uncertainty quantification of a stochastic building performance simulator

A good framework for the quantification and decomposition of uncertainties in dynamic building performance simulation should: (i) simulate the principle deterministic processes influencing heat flows and the stochastic perturbations to them, (ii) quantify and decompose the total uncertainty into its respective sources, and the interactions between them, and (iii) achieve this in a computationally efficient manner. In this paper we introduce a new framework which, for the first time, does just that. We present the detailed development of this framework for emulating the mean and the variance in the response of a stochastic building performance simulator (EnergyPlus co-simulated with a multi agent stochastic simulator called No-MASS), for heating and cooling load predictions. We demonstrate and evaluate the effectiveness of these emulators, applied to a monozone office building. With a range of 25–50 kWh/m2, the epistemic uncertainty due to envelope parameters dominates over aleatory uncertainty relating to occupants' interactions, which ranges from 6–8 kWh/m2, for heating loads. The converse is observed for cooling loads, which vary by just 3 kWh/m2 for envelope parameters, compared with 8–22 kWh/m2 for their aleatory counterparts. This is due to the larger stimuli provoking occupants' interactions. Sensitivity indices corroborate this result, with wall insulation thickness (0.97) and occupants' behaviours (0.83) having the highest impacts on heating and cooling load predictions respectively. This new emulator framework (including training and subsequent deployment) achieves a factor of c.30 reduction in the total computational budget, whilst overwhelmingly maintaining predictions within a 95% confidence interval, and successfully decomposing prediction uncertainties.

Uncertainty decomposition of quantum networks in SLH framework

SummaryThis paper presents a systematic method to decompose uncertain linear quantum input‐output networks into uncertain and nominal subnetworks, when uncertainties are defined in SLH representation. To this aim, two decomposition theorems are stated, which show how an uncertain quantum network can be decomposed into nominal and uncertain subnetworks in cascaded connection and how uncertainties can be translated from SLH parameters into state‐space parameters. As a potential application of the proposed decomposition scheme, robust stability analysis of uncertain quantum networks is briefly introduced. The proposed uncertainty decomposition theorems take account of uncertainties in all three parameters of a quantum network and bridge the gap between SLH modeling and state‐space robust analysis theory for linear quantum networks.

Using Multistage Design‐Based Methods to Construct Abundance Indices and Uncertainty Measures for Delta Smelt

AbstractPopulation abundance indices and estimates of uncertainty are starting points for many scientific endeavors. However, if the indices are based on data collected by different monitoring programs with possibly different sampling procedures and efficiencies, applying consistent methodology for calculating them can be complicated. Ideally, the methodology will provide indices and associated measures of uncertainty that account for the sample design, the level of sampling effort (e.g., sample size), and the capture or detection probabilities. We develop and demonstrate consistent methodology for multiple monitoring programs that sample different life stages of Delta Smelt Hypomesus transpacificus, a critically endangered fish species endemic to the San Francisco Estuary, whose abundance indices have been at the center of much controversy given the regulatory consequences of their listed status. Current indices use different and incomparable methods, do not account for gear selectivity, and do not provide measures of uncertainty. Using recently available information on gear‐specific, length‐based conditional probabilities of capture given availability, we develop new abundance indices along with measures of uncertainty by means of a single methodological approach. These new indices are highly correlated with existing ones, but the approach taken here illuminates different sources of bias and quantifies between‐year variation using probabilistic statements where the previous indices cannot. Decomposition of uncertainty into its constituent sources reveals that early life stage uncertainty is dominated by gear inefficiency while later life stage uncertainty is dominated by sample size, thus providing guidance for improvements to existing surveys. An additional result of general methodological interest is a demonstration, via simulation intended to reflect realistic data properties, that a lognormal distribution is preferable to the normal distribution for making probabilistic statements about the indices. The work here facilitates the fitting of models attempting to identify factors associated with the dynamics and decline of the species.

Energy sector uncertainty decomposition: New approach based on implied volatilities

The source(s) of uncertainty for energy sector companies is of interest for managers and investors, both trying to manage the uncertainty. In this paper, we suggest decomposing this uncertainty into crude oil and stock market uncertainty components. Using time-series data on implied volatility indexes, we estimate the weights of the components (55% and 45%, respectively) by applying a maximum likelihood method. We find that the model accounts for 69% of the variability in the changes of energy sector uncertainty. Furthermore, we report that during high public interest in crude oil, measured by internet interest using crude oil related search terms, the weight of the crude oil (stock market) component increases (decreases), but when the price of oil or implied volatilities of crude oil or stock markets are high, it decreases (increases). Thus, we contribute by showing how energy sector companies’ market uncertainty can be divided into separate components; by suggesting how the weights of the components can be estimated using implied volatilities; and by providing empirical evidence on the effects of public interest and general crude oil and stock market conditions on the obtained weights.