Distribution Of State Variables Research Articles

Dynamic linkages in agricultural and energy markets: A quantile impulse response approach

AbstractThis article investigates the dynamic linkages between agricultural and energy markets, with a focus on an econometric analysis of multivariate stochastic dynamics based on the joint distribution of state variables. The analysis relies on a quantile approach followed by the evaluation of a copula. Applied to nonlinear price dynamics, the approach is flexible and supports a general evaluation of impulse response functions representing how prices adjust over time and across markets in response to a given shock. The analysis allows for arbitrary distribution functions; it captures own‐price and cross‐price dynamics that can depend on the nature of shocks; and it also allows current changes to affect all moments of the future price distributions. The usefulness of the approach is illustrated in an econometric investigation of dynamic linkages in US corn, ethanol, and crude oil markets. We show how price adjustments can vary across quantiles, reflecting different speeds of adjustments depending on market conditions. We find evidence of nonlinear dynamics specific to the tails of the price distributions. We uncover evidence of positive contemporaneous codependence, especially tail dependence. We show how price shocks affect mean, variance, skewness as well as kurtosis of future price distributions. These results stress the importance of going beyond a standard mean‐variance analysis. They also shed new light on the deep linkages existing in the food‐fuel nexus.

Research on Global Optimization Algorithm of Integrated Energy and Thermal Management for Plug-In Hybrid Electric Vehicles.

Power distribution and battery thermal management are important technologies for improving the energy efficiency of plug-in hybrid electric vehicles (PHEVs). In response to the global optimization of integrated energy thermal management strategy (IETMS) for PHEVs, a dynamic programming algorithm based on adaptive grid optimization (AGO-DP) is proposed in this paper to improve optimization performance by reducing the optimization range of SOC and battery temperature, and adaptively adjusting the grid distribution of state variables according to the actual feasible region. The simulation results indicate that through AGO-DP optimization, the reduction ratio of the state feasible region is more than 30% under different driving conditions. Meanwhile, the algorithm can obtain better global optimal driving costs more rapidly and accurately than traditional dynamic programming algorithms (DP). The computation time is reduced by 33.29-84.67%, and the accuracy of the global optimal solution is improved by 0.94-16.85% compared to DP. The optimal control of the engine and air conditioning system is also more efficient and reasonable. Furthermore, AGO-DP is applied to explore IETMS energy-saving potential for PHEVs. It is found that the IETMS energy-saving potential range is 3.68-23.74% under various driving conditions, which increases the energy-saving potential by 0.55-3.26% compared to just doing the energy management.

Asymptotic Learning Requirements for Stealth Attacks on Linearized State Estimation

Information-theoretic stealth attacks are data injection attacks that minimize the amount of information acquired by the operator about the state variables, while simultaneously limiting the Kullback-Leibler divergence between the distribution of the measurements under attack and the distribution under normal operation with the aim of controling the probability of attack detection. For Gaussian distributed state variables, attack construction requires knowledge of the second order statistics of the state variables, which is estimated from a finite number of past realizations using a sample covariance matrix. Within this framework, the attack performance is studied for the attack construction with the sample covariance matrix. This results in an analysis of the amount of data required to learn the covariance matrix of the state variables used on the attack construction. The ergodic attack performance is characterized using asymptotic random matrix theory tools, and the variance of the attack performance is bounded. The ergodic performance and the variance bounds are assessed with simulations on IEEE test systems.

Probabilistic energy flow analysis of the integrated electricity and gas system considering multiform uncertainties

The coupling of electricity and gas systems has been ever-augmented with the wide deployment of gas-fired generators, which facilitates the conception of the integrated electricity and gas system (IEGS). Probabilistic energy flow (PEF) analysis is usually conducted to assess the operating status of the IEGS by calculating the probability distribution of state variables (e.g., gas pressure, gas flow, voltage, and power flow). However, multiform time-variant uncertainties can simultaneously reside in the IEGS, including discrete (e.g., the component failure or functioning) and continuous ones (e.g., renewable energy outputs). Existing PEF analysis works cannot completely deal with time-variant multiform uncertainties featured with different mathematical characteristics. This limitation hinders the estimation of potential operating risks of the IEGS. To address this, this paper proposes a generalized framework for analyzing the probabilistic energy flow of the IEGS considering multiform uncertainties. Firstly, both time-varying random working states and variable outputs of components are represented as probabilistic models utilizing the Lz- transform technique. The probabilistic model is composed of some representative states depicting possible realizations of the component's performance and corresponding probabilities. On this basis, the optimal energy flow (OEF) operator is defined to aggregate probabilistic models of different components to determine probabilistic models of energy flows in the IEGS. Furthermore, multidimensional indices are constructed to comprehensively explore the probabilistic features of energy flows and the impact of probabilistic energy flows on the system performance. In this paper, the system performance mainly refers to the energy-serving capability of the IEGS. Specifically, probabilistic distribution characteristics of energy flows are explicitly displayed by relevant expectations, standard deviations as well as skewnesses. Indices such as the nodal expected gas and electricity not supplied are adopted to evaluate the influence of the probabilistic energy flow on the system performance. Numerical studies reveal that energy flows through different pipelines or power lines present diversified statistical characteristics, which indicates that they are influenced by multiform uncertainties to different extents.

Probabilistic Load Flow for Wind Integrated Power System Considering Node Power Uncertainties and Random Branch Outages

This paper proposes an analytical probabilistic load flow (PLF) approach that considers conventional generator outages, load variability, and random branch outages. The branch outages are modeled as 0-1 distributions of fictitious power injections at the appropriate nodes. The distribution of state variables and line power flows is then obtained using a combined Cumulant and Gram-Charlier series expansion approach. The proposed PLF performs contingency sequencing with fuzzy logic to eliminate random line checking and avoid masking mistakes faced by performance index-based algorithms. The Jacobian inverse calculation in the traditional Cumulant method is eliminated to conserve storage space and speed up the computation using the Gauss-Jordan method. The correlations among loads and wind power generations has been modeled using the Nataf transformation process. Results of 24-bus and 259-bus equivalent systems of the Indian southern and western power grids are analyzed and validated with those obtained using the Monte Carlo simulation method. The suggested method's efficacy is justified by its accuracy and low computational burden.

Impacts of Observation Forward Operator on Infrared Radiance Data Assimilation with Fine Model Resolutions

Abstract All-sky radiance assimilation often has non-Gaussian observation error distributions, which can be exacerbated by high model spatial resolutions due to better resolved nonlinear physical processes. For ensemble Kalman filters, observation ensemble perturbations can be approximated by the linearized observation operator (LinHx) that uses the observation operator Jacobian of ensemble mean rather than the full observation operator (FullHx). The impact of observation operator on infrared radiance data assimilation is examined here by assimilating synthetic radiance observations from channel 1025 of GIIRS with increased model spatial resolutions from 7.5 km to 300 m. A tropical cyclone is used, while the findings are expected to be generally applied. Compared to FullHx, LinHx provides larger magnitudes of correlations and stronger corrections around observation locations, especially when all-sky radiances are assimilated at fine model resolutions. For assimilating clear-sky radiances with increasing model resolutions, LinHx has smaller errors and improved vortex intensity and structure than FullHx. But when all-sky radiances are assimilated, FullHx has advantages over LinHx. Thus, for regimes with more linearity, LinHx provides stronger correlations and imposes more corrections than FullHx; but for regimes with more nonlinearity, LinHx provides detrimental non-Gaussian prior error distributions in observation space, unrealistic correlations, and overestimated corrections, compared to FullHx. Significance Statement Assimilating satellite radiances has been essential for numerical weather prediction. All-sky radiance assimilation can improve the analyses and forecasts of tropical cyclones, but it often has non-Gaussian observation error distributions. With increased model resolutions, nonlinear physical processes can be better resolved, which leads to non-Gaussian error distributions of state variables. Nonlinearity and non-Gaussianity impose great challenges for data assimilation (DA), since most DA theories assume linear processes and Gaussian error distributions. As the spatial resolutions of observations and numerical models will keep increasing, the potential issues of assimilating high-spatial-resolution observations given fine model resolutions need to be examined. The linearized observation forward operator, as an alternative to remedy non-Gaussianity for radiance DA, is investigated. With model resolution increasing from 7.5 km to 300 m, the linearized observation operator has advantages over the full observation operator for assimilating clear-sky radiances, but the opposite is true for assimilating all-sky radiances.

Graph Attention Enabled Convolutional Network for Distribution System Probabilistic Power Flow

Probabilistic power flow (PPF) is pivotal to quantifying the state uncertainties of distribution power systems. However, it is very challenging due to underlying complex correlations among renewable outputs. To address this problem, a graph attention enabled convolutional network (GAECN) is proposed to approximate PPF in this article. Specifically, the graph convolutional layer of GAECN is used to aggregate the correlations among the nodal power injections during the training process. Within this layer, a full self-adaptive graph convolutional operation is proposed to automatically capture and learn the implicit correlation for achieving significantly enhanced accuracy of PPF. This layer is then followed by the convolutional neural network to capture the uncertain generation of renewable energy to achieve the robust computation of system state variable distributions. The simulation results demonstrate the accuracy and efficiency of the proposed method in IEEE 33, PG&E 69-node, 118-node, and practical 76-node distribution systems.

Review of the limitations and potential empirical improvements of the parametric group method of data handling for rainfall modelling

This study furthers the utilisation of the parametric group method of data handling (GMDH) in assessing the possibility of rainfall modelling and prediction, using publicly available temperature and rainfall data. In using ordinary GMDH approaches, the modelling is inconclusive with no clear consistency demonstrated through coefficients of determination and analysis of variance. Hence, an empirical assessment has been undertaken to provide an explanation of the inconsistency. In doing so, state variable distribution, their classification within the fuzzy context, and the need to integrate the principle of incompatibility into the GMDH modelling format are all assessed. The mathematical foundations of GMDH are discussed within the heuristic framework of data partitioning, partial description synthesis, the limitations of the least-squares coefficient of determination, incompleteness theorem, and the necessity for an external criterion in the selection procedure for polynomials. Methods for modelling improvement include the potential for hybridisation with least square support vector machines (LSSVM), the application of filters for parameter estimation, and the combination with signal processing techniques, ensemble empirical mode decomposition (EEMD), wavelet transformation (WT), and wavelet packet transformation (WPT). These have been investigated in addition to the implementation of enhanced GMDH (eGMDH) and fuzzy GMDH (FGMDH). The inclusion of exogenous data and its application within the GMDH modelling paradigm are also discussed. The study concludes with recommendations to enhance the potential for future rainfall modelling study success using parametric GMDH.

Sparse Data Injection Attacks on Smart Grid: An Information-Theoretic Approach

Sparse data injection attacks are data injection attacks that target a limited number of sensors in the smart grid paradigm. In this paper, sparse attack construction strategy is proposed for the information-theoretic stealth attacks, in which the attacker minimizes the amount of information acquired by the operator about the power system from the observations and the probability of being detected simultaneously. For Gaussian distributed state variables, closed-form expression is proposed for the optimal Gaussian sparse attacks when the attacker targets deterministic observations and gets access to the full system information. Based on that, two target observation selection strategies are introduced to find the vulnerable observations in the system, in which the algorithms take different tradeoff strategies between performance and computational time. Furthermore, a locally perfect stealthy attack construction strategy is proposed for the case in which the attacker only has partial system information but gets access to real-time realizations of the local state variables. The optimality of Gaussian sparse attacks and the performance of the selection strategies are validated on the IEEE 30 Bus and 118 Bus test systems.

Recurrent Neural Networks (RNNs) with dimensionality reduction and break down in computational mechanics; application to multi-scale localization step

Artificial Neural Networks (NNWs) are appealing functions to substitute high dimensional and non-linear history-dependent problems in computational mechanics since they offer the possibility to drastically reduce the computational time. This feature has recently been exploited in the context of multi-scale simulations, in which the NNWs serve as surrogate model of micro-scale finite element resolutions. Nevertheless, in the literature, mainly the macro-stress–macro-strain response of the meso-scale boundary value problem was considered and the micro-structure information could not be recovered in a so-called localization step. In this work, we develop Recurrent Neural Networks (RNNs) as surrogates of the RVE response while being able to recover the evolution of the local micro-structure state variables for complex loading scenarios. The main difficulty is the high dimensionality of the RNNs output which consists in the internal state variable distribution in the micro-structure. We thus propose and compare several surrogate models based on a dimensionality reduction: (i) direct RNN modeling with implicit NNW dimensionality reduction, (ii) RNN with PCA dimensionality reduction, and (iii) RNN with PCA dimensionality reduction and dimensionality break down, i.e. the use of several RNNs instead of a single one. Besides, we optimize the sequential training strategy of the latter surrogate for GPU usage in order to speed up the process. Finally, through RNN modeling of the principal components coefficients, the connection between the physical state variables and the hidden variables of the RNN is revealed, and exploited in order to select the hyper-parameters of the RNN-based surrogate models in their design stage.

EXISTENCE OF STATIONARY EQUILIBRIUM IN AN INCOMPLETE‐MARKET MODEL WITH ENDOGENOUS LABOR SUPPLY

AbstractIn this article, I first study an income fluctuation problem with endogenous labor supply. Let β be the agent's time discount factor and be the constant gross rate of return on assets. For , I show that the agent's wealth either approaches infinity almost surely or converges to a finite level almost surely. For , I prove the existence, uniqueness, and stability of the stationary distribution of state variables. I then show the existence of the stationary general equilibrium in an incomplete‐market model with endogenous labor supply.

Determination of State Variables in Textile Composite with Membrane During Complex Heat and Moisture Transport

Abstract The cotton-based composite is equipped with a single/double semipermeable membrane made of polyurethane (PU) (100%), which blocks liquid transport to the surrounding environment. The complex problem analyzed involves the coupled transport of water vapor within the textile material, transport of liquid water in capillaries, as well as heat transport with vapor and liquid water. The problem can be described using the mass transport equation for water vapor, heat transport equation, and mass transport equation for liquid moisture, accompanied by the set of corresponding boundary and initial conditions. State variables are determined using a complex multistage solution procedure within the selected points for each layer. The distributions of state variables are determined for different configurations of membranes.

Exact model for the response of moderately thick laminates to transverse forces

Under the premise of homogeneous force, or curvature-gradient, distribution, a solution for transverse-shear strains and stresses, warping functions, and through-thickness displacements is derived by satisfying all relations and conditions of linear elasticity. Only for calculating the substitute-plate transverse-stiffness matrix the principle of the minimum of the total potential energy is used as a scheme for correctly combining energetically conjugate components of stresses and strains for the entries of the substitute-plate transverse stiffness matrix. The model is valid for all laminate and sandwich designs. The said premise renders the model a point theory rather than a structural theory, so that it is a complement to the classical theory of laminated plates in the sense of mapping substitute-plate properties and distribution of state variables through the laminate thickness. This paper explains the modeling ideas and derivations in detail. Predictions of the responses for a set of sample laminates of varying complexity, and comparison of stiffness values with those obtained by a dedicated FEM formulation, verify the model.

A numerical study on interface shearing of granular Cosserat materials

This article presents the interface shearing behaviour of a granular soil layer in contact with a bounding structure under motion. For this purpose, an elasto-plastic Cosserat continuum model (EPCCM) and finite element method (FEM) in the updated Lagrange frame are employed. Plane quasi-static shearing of a granular soil layer, bounded by upper and lower rigid boundaries with different surface roughness conditions, is simulated under free dilatancy and constant vertical pressure. Herein, the additional Cosserat kinematical boundary constraints along the bounding surfaces allow a more detailed description of the surface roughness. Specific emphasis is given to the effects of surface roughness as well as the boundary conditions of the entire system on the shear behaviour of layer. According to the obtained results, the shear band location is different in an infinite or finite shear layer depending on the adopted boundary constraints. Further numerical simulations of plane interface shearing are also carried out here using discrete element method (DEM), complementary to Cosserat FE analyses, to better understand the micro-mechanics of granular media near interfaces. FE results are compared with those of experiments as well as DEM simulations and reasonable agreements are seen. The evolution and distribution of state variables and polar quantities in DEM simulations are in proper accordance with the predictions of Cosserat FE model.

Sensitivity of a Continuum‐Scale Porous Media Heat and Mass Transfer Model to the Spatial‐Discretization Length‐Scale of Applied Atmospheric Forcing Data

AbstractFundamental process understanding and description of heat, mass, and momentum exchanges across the land‐atmosphere interface in model boundary forcing parameterizations is critical to the simulation of near‐surface soil moisture dynamics (e.g., bare‐soil evaporation). This study explores the sensitivity of a continuum‐scale porous media heat and mass transfer model to the spatial‐discretization length‐scales (i.e., spatial‐resolution) of near‐surface atmospheric data; the goal is to determine how much data are needed to force the model and adequately capture evaporative water losses and subsurface state variable distributions. The requisite atmospheric forcing data were taken from the high‐resolution, precision bare‐soil evaporation experiments of Trautz et al. (2018, https://doi.org/10.1029/2018WR023102). Simulation results demonstrated that shallow subsurface mass and heat transfer dynamics can be adequately captured with forcing data averaged over large length‐scales, or a minimal number of measurements, provided that soil conditions are properly described. The soil moisture spatial distributions were found to be insensitive to horizontal variations in the forcing data. The model failed to capture small‐scale trends observed experimentally; this did not impact the accuracy of total evaporative water loss estimates however. These results indicate that in future physical experimental efforts conducted at 1–10‐m length‐scales, there is no need to focus on the generation of high‐spatial resolution atmospheric measurements—time and effort would be better spent in characterizing soil conditions and properties. Even though a theoretical foundation was not provided to directly extrapolate this work to the field scale, these findings have practical value in designing field data collection strategies.

A General Formulation of Linear Power Flow Models: Basic Theory and Error Analysis

Linear power flow models are widely used in power systems to simplify the nonlinear power flow equations. The DC power flow model is one of the representatives. There are many other linear power flow models that improve the DC power flow model with the inclusion of $\boldsymbol{Q}$ and $\boldsymbol{v}$ . However, existing linear models are derived based on empirical mathematical approximation without a general methodology guidance. In this paper, we found that the fundamental difference among different linear power flow models lies in the formulation of “independent variables.” Based on this finding, a general formulation of linear power flow models is proposed. The linearization error is theoretically analyzed. In particular, the case when $\boldsymbol{ \theta }$ and $\boldsymbol{v^{\scriptscriptstyle k}}$ are regarded as independent variables is thoroughly investigated. Method for finding the linear power flow with the minimum error is presented. The formulation of the independent variables associated with the minimum linearization error is determined by the distribution of state variables $\boldsymbol{v}$ and $\boldsymbol{\theta }$ . It is shown that the linearization error when $\boldsymbol{v^{\scriptscriptstyle 2}}$ is regarded as an independent variable is normally smaller than that for $\boldsymbol{v}$ because of the special properties of the distribution of $\boldsymbol{v}$ in power grids.

Comparing ERT- and scaling-based approaches to parameterize soil hydraulic properties for spatially distributed model applications

Optimal management of water resources depends on the prediction capability of process-based hydrological models. New generation Richards equation-based distributed models provide detailed descriptions of hydrological processes that, however, depend highly on the proper assessment of the spatial variability of soil hydraulic properties (SHPs). Field surveys and sampling campaigns commonly provide sparse local scale measurements of SHPs. Nevertheless, the challenge is to transfer this information from the “observation scale” to the “model scale” by increasing as much as possible the prediction efficiency with affordable practical burdens. The performances of two parameterization approaches are compared in this study in terms of outputs of water budget simulated by the HydroGeoSphere (HGS) model in a small catchment. The first approach relies on knowledge of soil hydraulic data from soil cores (centimeter scale) collected in many locations of the study site and the application of the Miller-Miller scaling technique enabling the spatial variability of the so-called “aggregated” SHPs to be described over the spatial domain of interest. The second approach, instead, estimates a set of “equivalent” SHPs through the numerical inversion of geophysical data measured with the electrical resistivity tomography (ERT) during an infiltration experiment (meter scale) performed in only one plot-transect of the study catchment. The SHPs obtained by these two approaches are then assigned to each numerical grid cell in HGS to simulate the catchment-scale soil water budget at daily time resolution. Within the framework of a functional evaluation, we compare the performance of these two soil hydraulic parameterization approaches in terms of streamflow (viewed as a lumped flux) and near-surface soil effective saturation patterns (viewed as distributed state variables). Better comparisons between observed and simulated streamflow values are obtained when the study site is parameterized using the “equivalent” SHPs. Conversely, the HGS water budget simulations using the “aggregated” SHPs are more effective when one should describe the spatial patterns of near-surface soil moisture values. This study highlights the pros and cons and potential flaws when choosing two different parameterization techniques in spatially distributed modeling applications.

The binding interactions that maintain excitation-contraction coupling junctions in skeletal muscle.

Calcium for contraction of skeletal muscles is released via tetrameric ryanodine receptor (RYR1) channels of the sarcoplasmic reticulum (SR), which are assembled in ordered arrays called couplons at junctions where the SR abuts T tubules or plasmalemma. Voltage-gated Ca2+ (CaV1.1) channels, found in tubules or plasmalemma, form symmetric complexes called CaV tetrads that associate with and activate underlying RYR tetramers during membrane depolarization by conveying a conformational change. Intriguingly, CaV tetrads regularly skip every other RYR tetramer within the array; therefore, the RYRs underlying tetrads (named V), but not the voltage sensor-lacking (C) RYRs, should be activated by depolarization. Here we hypothesize that the checkerboard association is maintained solely by reversible binary interactions between CaVs and RYRs and test this hypothesis using a quantitative model of the energies that govern CaV1.1-RYR1 binding, which are assumed to depend on number and location of bound CaVs. A Monte Carlo simulation generates large statistical samples and distributions of state variables that can be compared with quantitative features in freeze-fracture images of couplons from various sources. This analysis reveals two necessary model features: (1) the energy of a tetramer must have wells at low and high occupation by CaVs, so that CaVs positively cooperate in binding RYR (an allosteric effect), and (2) a large energy penalty results when two CaVs bind simultaneously to adjacent RYR protomers in adjacent tetramers (a steric clash). Under the hypothesis, V and C channels will eventually reverse roles. Role reversal justifies the presence of sensor-lacking C channels, as a structural and functional reserve for control of muscle contraction.

An anatomy of the market return

This paper introduces a model free decomposition of S&P 500 forward market index returns in terms of realized and implied dispersion, downside, and tail risk using option portfolios. The decomposition lends itself by construction to learn about the different sources of risk in the market return and subsequently to visual and formal diagnosing of asset pricing models. It utilizes a novel conditional frequency analysis on the basis of available options rather than the times series of the S&P 500. Empirically, downside risk accounts for most of the forward market return, while symmetric tail risk is not prominently featured. The predictable, persistent part of the realized return is small. Nevertheless, signals revealed by this risk anatomy provide predictive out of sample power for realized returns, in particular for longer maturities. Furthermore, it indicates that models with identically and independently distributed state variables are generally misspecified in this market, and that care must be taken when calibrating disaster risk models. A formal test based on the risk anatomy rejects a model with time-varying disaster intensity.

Evaluating and Improving a PDF Cloud Scheme Using High‐Resolution Super Large Domain Simulations

AbstractCloud schemes, which use probability density functions (PDFs) to describe the subgrid‐scale variability of thermodynamic state variables, rely heavily on large eddy simulation (LES) data to provide information on the distributions of state variables in a turbulent domain. Until recently, LES simulations were commonly limited to small domains and highly idealized prototype regimes, but super large domain realistically forced simulations are now available, which contain previously excluded synoptic scale variability and orographic effects. Thanks to these advances PDF cloud schemes can be confronted with much more realistic distributions of thermodynamic states and clouds on the horizontal scales they were developed for. One example of super large domain LES is a library of recent Germany‐wide simulations with a 100‐m resolution. We use these simulations to study how a PDF cloud scheme, which represents variability through a beta function of total water, represents cloud fraction and the total and liquid water distribution. Special emphasis is placed on studying how various closures, which limit the possible shape of the beta function, affect the resulting cloud fraction. Our analysis shows that the PDF cloud scheme leads to much smaller cloud fraction errors than a classic parameterization that relates cloud fraction to relative humidity and that the PDF scheme is suitable for model resolutions from 5 to 100 km. The PDF cloud scheme performance is increased by introducing a zero‐buoyancy relationship between water vapor and temperature to approximate the orientation of their joint PDF.