Distribution Of State Variables Research Articles

Determination of steady-states in a tubular biofilm bioreactor with axial dispersion

The paper presents the method of modelling and numerical simulation of bioreactors with biofilm and axial dispersion of the liquid. Such bioreactors belong to systems with distributed state variables. The mathematical model was compared with a model assuming perfect mixing and a model assuming piston-flow of the liquid. According to calculations performed, the piston flow of the liquid can be assumed for Peclet numbers above 40. In turn, Peclet numbers below 0.5 justify perfect-mixing approximation. It was shown that there may exist an optimal value of Peclet number for which a maximum degree of conversion of the limiting substrate at the bioreactor outlet is obtained. The existence of the optimal Peclet number depends on the operating conditions of the bioreactor.

Using Complicated Mathematical Model in the Control Loop For the Technological Process Control System

Optimal control for technological process with distributed state variables and with a large dead times in the object is discussed. Very important problem for creating control system with using the object model in the control loop are considered. It has been shown that heat flux calorimetry is an effective experimental technique for the development of an exothermic (or endothermic) chemical process model based upon the process kinetic model and hydrodynamic media inside object. Successful application of this approach for the creation of mathematical models and their further use in the corresponding control systems has been demonstrated for two different important industrial processes – sintering process in the preparation of cement clinker in the tubular rotating kiln and modification process of epoxy resins with butanediol-1,4 for further synthesis of epoxy-urethane polymers with improved physical and mechanical properties. The mathematical model of a technological object makes it possible to specify the optimal operating mode for each of the considered processes and implement the optimal control conditions.

Efficient approximate inference in Bayesian networks with continuous variables

Inference is one key objective in a Bayesian network (BN), and it aims to estimate the posterior distributions of state variables based on evidence (observations). While efficient analytical inference algorithms (either approximate or exact) for BN with discrete variables have been well-established in the literature, the inference in BN with continuous variables is still challenging if the BN is non-linear and/or non-Gaussian. In this case we can either discretize the continuous variable and utilize the inference approaches for discrete BN; or we have to use sampling-based methods such as MCMC for static BN and particle filter for dynamic BN. This paper proposes a network collapsing technique based on the concept of probability integral transform to convert a multi-layer BN to an equivalent simple two-layer BN, so that the unscented Kalman filter can be applied to the collapsed BN and the posterior distributions of state variables can be obtained analytically. For dynamic BN, the proposed method is also able to propagate the state variables to the next time step analytically using the unscented transform, based on the assumption that the posterior distributions of state variables are Gaussian. Thus the proposed method achieves a very fast approximate solution, making it particularly suitable for dynamic BN where inference and uncertainty propagation are required over many time steps.

Aeroelastic behavior of a typical section with shape memory alloy springs: Modeling nonhomogeneous distribution of state variables

In this paper, a two-degree-of-freedom (namely, plunge and pitch) aeroelastic typical section with shape memory alloy helical springs in the pitch degree-of-freedom is modeled. A linear aerodynamic model is employed to predict the unsteady loads. The shape memory springs model is based on classical models modified by the von Mises pure shear assumption. Nonhomogeneous distributions of shear strain, shear stress and martensitic fraction in the wire cross-section are represented by axi-symmetric annular regions. The numerical predictions of the effects of pseudoelastic hysteresis of shape memory alloy springs on the aeroelastic behavior of the typical section when both the homogeneous and nonhomogeneous cross-sectional distributions are considered in the simulations are compared with experimental data obtained in wind tunnel tests. The nonhomogeneous assumption results in good agreement between numerical predictions and experiments. Both the numerical and experimental results show that the pseudoelastic hysteresis of SMAs can be employed as a passive alternative to modify the behavior of aeroelastic systems.

Unified probabilistic gas and power flow

The natural gas system and electricity system are coupled tightly by gas turbines in an integrated energy system. The uncertainties of one system will not only threaten its own safe operation but also be likely to have a significant impact on the other. Therefore, it is necessary to study the variation of state variables when random fluctuations emerge in the coupled system. In this paper, a multi-slack-bus model is proposed to calculate the power and gas flow in the coupled system. A unified probabilistic power and gas flow calculation, in which the cumulant method and Gram–Charlier expansion are applied, is first presented to obtain the distribution of state variables after considering the effects of uncertain factors. When the variation range of random factors is too large, a new method of piecewise linearization is put forward to achieve a better fitting precision of probability distribution. Compared to the Monte Carlo method, the proposed method can reduce computation time greatly while reaching a satisfactory accuracy. The validity of the proposed methods is verified in a coupled system that consists of a 15-node natural gas system and the IEEE case24 power system.

A Corrective Control Approach Considering Load Fluctuation of the Power System

When power system operates in an insecure condition, corrective control measures should be takin in time to eliminate constrains violation. Few of current corrective control approaches take load fluctuation into consideration, which may result in invalid measures. The present paper proposes a novel corrective control approach which takes load fluctuation into consideration. Firstly, the probability distribution of state variables and sensitivity coefficient matrixes are obtained by probabilistic power flow. Then a corrective control model considering worst situation of branch power and bus voltage amplitude is proposed. Case study shows that the approach is valid and effective.

A Stochastic Method for Crop Models: Including Uncertainty in a Sugarcane Model

Core Ideas We propose an approach for simulating effects of parameter and input variable uncertainties in crop models. The GLUE was useful for estimating the parameter correlation matrix and the best set of parameters. The crop model output uncertainty varied with soil and climate conditions. Crop models are increasingly being used for different purposes, including evaluation of climate change impacts on crop yields and opportunities for adapting management to future conditions. However, past uses of these models have been criticized in part due to a failure of researchers to quantify uncertainties of crop yield prediction. We have developed a method for considering uncertainty in a crop model using a simple sugarcane (Saccharum spp.) model as a case study. A Bayesian Monte Carlo approach generalized likelihood uncertainty estimation was used to estimate model parameters, their uncertainties, and correlations among them using data from five growing seasons at four locations in Brazil where crops received adequate nutrients and good weed control. Some of the model parameters were assumed to be correlated random variables, based on the literature, and varied across their ranges of uncertainty to estimate posterior distributions of parameters. The mean parameter values, parameter ranges, and the parameter covariance‐correlation matrix are inputs to this Bayesian approach, which includes a Toeplitz–Cholesky factorization to generate correlated random variable samples and then simulate a distribution of state variables on a daily time step. Correlated random simulation, based on posterior distributions of parameters, was an effective method for including uncertainty in the crop growth and yield estimates. We demonstrated that uncertainty can be reduced with respect to model structure and parameter meaning because the optimization process is heavily dependent on prior knowledge of the parameters. Uncertainty varied with environment even though distributions of parameters remained the same across all environments.

Development of an optimal control scheme for the process of epoxy resins modification with a complicated mathematical model in the control loop.

The problem of optimal control for a highly exothermal technological process with distributed state variables and with a large dead time is discussed. The main steps of creating a flexible control system with using the object model in the control loop are considered. It is shown that heat flux calorimetry is an effective experimental technique for the development of a process model based upon corresponding multistage kinetic model. It can be also applied to multiphase reaction systems together with simplified hydrodynamic models for mass transfer phenomena description. A successful application of this approach for developing the process mathematical model and its further introduction to the corresponding control system has been demonstrated for an important industrial process ? modification of epoxy resins with butanediol-1,4 for further synthesis of epoxy-urethane polymers with improved physico-chemical and mechanical properties. The process mathematical model makes it possible to specify the optimal operating mode for each resin and implement the optimal control.

Totally analytical closure of space filtered Navier–Stokes for arbitrary Reynolds number: Part III. aFNS theory validation

ABSTRACTFor arbitrary Reynolds number Re, aFNS theory O(1; δ2; δ3) significance scaled state variable achieves analytical closure of rigorously space filtered thermal, multi-species Navier–Stokes (NS) conservation principle partial differential equation (PDE) system well-posed on bounded domains (Part I). Validation of boundary commutation error (BCE) and nonhomogeneous Dirichlet boundary condition (DBC) resolution strategies results in ADh-GWSh-BCEh-DBCh algorithm coupling with aFNS theory optimal Galerkin GWSh + θTS CFD algorithm (Part II), including accuracy/convergence assessments. For Reynolds numbers ranging E+02 <Re < 2E+04, aFNS theory fully coupled k = 1 basis Galerkin CFD code generated a posteriori data enable theory quantitative validation. For assured laminar Re range, NS no-slip BC reduced and coupled aFNS theory code predicted quasi-steady thermal-velocity transition to periodic unsteady is validated via linear stability predicted critical Re. For Re exceeding assured laminar, theory coupled CFD data quantify spatial filtering annihilation of (laminar) NS predicted large wave number spectral content. For sufficiently large Re, coupled CFD code a posteriori data document first principles prediction of unsteady periodic wall attached velocity profile transitioning-from-laminar, then separation, fully turbulent profile reattachment followed by relaminarization. These large Re CFD data as well enable validation of perturbation theory O(1; δ2; δ3) significance scaled state variable, ADh-GWSh-DBCh algorithm prediction of O(δ2) state variable non-homogeneous Dirichlet BC DOF data and in concert thoroughly quantify theory generated O(δ2; δ3) state variable distributions.

Dynamic stochastic optimal power flow of wind power and the electric vehicle integrated power system considering temporal-spatial characteristics

The intermittent volatility of wind power integrated into the grid poses a great threat to the stable operation of power systems on the supply side. Conversely, large-scale charging of electric vehicles (EVs) also brings new challenges to dispatch on the demand side. In response, the randomness and temporal-spatial correlations of stochastic wind power generation are considered in this paper. Additionally, the EV charging infrastructure is studied. A dynamic stochastic optimal power flow (DSOPF) for wind farms and EVs integrated power system based on the chance-constrained programming model is proposed. An optimal dispatch scheme is obtained by solving the dynamic optimal power flow. After that, dynamic probabilistic power flow based on cumulants is performed under the scheme to obtain the probability distribution of state variables. The upper and lower bounds of chance constraints are adjusted according to the probability distribution function until they are all satisfied. Illustrative examples demonstrate the effectiveness of DSOPF for firming the variable wind energy, and EV charging is performed on the Institute of Electrical and Electronics Engineers systems. On this basis, different EV charging modes and the temporal-spatial correlations are specifically discussed.

Interpolation of final geometry and result fields in process parameter space

Different routes to produce a product in a bulk forming process can be described by a limited set of process parameters. The parameters determine the final geometry as well as the distribution of state variables in the final shape. Ring rolling has been simulated using different parameter settings. The final state variable fields have been subjected to Principal Component Analysis. Interpolation of amplitudes in process parameter space gives a good representation of the fields and is useful as metamodel of the process.

An Anatomy of the Equity Premium

This paper introduces a decomposition of the market return in terms of higher-order realized, and option-implied risk aversion, connecting it to level, slope, and curvature of the implied volatility surface. Empirically, second-order risk aversion -- loss aversion -- explains most of the market return. Signals revealed by this risk anatomy provide predictive power out-of-sample for realized returns in particular for longer maturities. The decomposition also shows that compensation for disaster risk is not prominently featured in the market return. Furthermore it highlights that models with identically and independently distributed state variables are not suited to represent in particular longer-maturity returns.

Blind False Data Injection Attack Using PCA Approximation Method in Smart Grid

Accurate state estimation is of paramount importance to maintain normal operations of smart power grids. However, recent research shows that carefully produced attacks with the knowledge of the grid topology, i.e., Jacobian matrix, can bypass the bad data detection (BDD) system. The BDD is used to ensure the integrity of state estimation to filter faulty measurements introduced by device malfunctions or malicious attacks. However, to construct the false data injection attack vectors, a common assumption in most prior works on false data injection attacks is that the attacker has complete knowledge about the power grid topology and transmission-line admittances. By contrast, this paper studies the general problem of blind false data injection attacks using the principal component analysis approximation method without the knowledge of Jacobian matrix and the assumption regarding the distribution of state variables. The proposed attack is proven to be approximately stealthy. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> The performance of the proposed attack is analyzed. Simulations confirm the performance of the proposed method.

Capacity allocation of hybrid solar-wind energy system based on discrete probabilistic method

Complementary renewable energies like wind and solar power may be more sufficient to satisfy reliability requirements. This paper proposes a quantitative capacity allocation method of a hybrid wind and solar energy system. First, discrete probability distributions are established to model the random factors including the volatility of power outputs and the failure of components. Then a multiobjective optimization model is formulated with objectives of minimization of the total investment, the nodal voltages violating limits probability, and power supply inadequacy probability. For the purpose of fast probability computing with a satisfactory precision degree, an innovative probabilistic load flow algorithm is introduced, which deals with means and increments of random variables separately and uses cumulants as well as Gram--Charlier series to obtain probabilistic distributions of state variables. A modified parallel elitist nondominated sorting genetic algorithm II is used to search the Pareto optimal configuration solutions.

Improved Probabilistic Load Flow Method to Consider Random Generator Outages

In conventional cumulant method of probabilistic load flow (PLF), random generator outages are usually simulated by discrete distributions of nodal power injections, but that will lead to significant error in AC load flow model. An improved PLF method base on AC model is proposed in this paper, which considers random generator outages and loads uncertainties. Cumulant and Gram-Charlier series expansion were applied to deal with the random variations of loads, instead of convolution calculations. According to the characteristics and focused aspects of power grid, certain generators were selected to form event group of generator outages and each event was analysed by exact load flow.Then total probability theorem was introduced to obtain the probabilistic distributions of node voltages and line flows that considered random factors of loads and generators.The case study of IEEE 39-bus system shows that the random generator outages remarkably affect the probabilistic distributions of state variables. The proposed method can avoid the error caused by generator outages in conventional cumulant method. Furthermore, the result of proposed method is consistent with that of Monte Carlo simulation, while computation speed is much faster.

Consistent Pricing and Hedging Volatility Derivatives with Two Volatility Surfaces

Abstract Using the joint characteristic function of equity price and state variables, we can price contingent claims on both equity and VIX consistently. Based on linear approximation of jump size, we show that one factor models implies all VIX future contract of different maturities are perfectly correlated in contrast to market observations. In the examples of multi-factor model, we demonstrate how to calculate the optimal hedging ratio for VIX future to hedge VIX option. We derived the unconditional correlation term structure of VIX future implied by the model based on the stationary distribution of state variables. We show multifactor models that are calibrated to the two voaltility surfaces will produce very different hedge ratios for VIX options.

Virtual 3D Microstructures with Specified Characteristics of State Variable Distributions

For a wide variety of model calculations a hypothetical 3D microstructure is required as input. Although experimental data are frequently used to this purpose, 3D microstructures are difficult to measure experimentally. In order to circumvent these difficulties, a virtual microstructure generator to simulate a specific 3D material microstructure is proposed. Such a virtual microstructure could serve as input for different types of models, would allow a faster model prototyping, would help to explore the boundary conditions of models and reduces the number of unnecessary experimental measurements. In the current paper, the method to generate and to control the grain size distribution as well as texture are discussed.

A Control‐oriented Dynamic Model Adapted to Variant Steam‐to‐carbon Ratios for an SOFC with Exhaust Fuel Recirculation

AbstractThe steam‐to‐carbon ratio (S/C) is a typical disturbance parameter in the operation of solid oxide fuel cell (SOFC) power generation system. A planar SOFC with a pre‐reformer and exhaust fuel recirculation system is investigated in this work. A lumped, nonlinear dynamic model is developed for the SOFC with consideration both of the spatial effect and the variant S/Cs. The dynamic model is deduced based on a fitting function so‐called Exponential Association Function, which is employed to describe the spatial distribution of state variables in SOFC. Three parameters of the fitting function are identified to integrate the spatial effect and S/C effect in the model. The parameters of Exponential Association Function are determined by function fitting on three‐dimensional numerical data at the sample operation points. Carbon formation activity is analysed using the simulation results and thermodynamic data. Dynamic simulation is implemented with the help of software MATLAB/SIMULINK. The results show that the developed model has good performance in predicting the responses of the state variables and catching the changes of S/C.

Numerical and technological properties of bubble column bioreactors for aerobic processes

This paper describes the method of modelling and numerical simulation of bubble column bioreactors in which the process of aerobic biodegradation of carbonaceous substrate occurs. Such bioreactors belong to systems with distributed state variables. Determining steady states of such objects results in solving non-linear boundary-value problems. The bioreactors with axial dispersion and piston flow with biomass recirculation were analysed. The effectiveness of selected algorithms used to determine the steady states of such bioreactors were compared; the numerical properties of mathematical models of analysed bioreactors were specified, the branches of steady states in bioreactors with axial dispersion and piston flow were determined and the application areas of such bioreactors were defined.

Numerical simulation of ram extrusion in short-fiber-reinforced fresh cementitious composites

A series of ram extrusion tests was carried out on a short-fiber-reinforced, semisolid, fresh cementitious composite. An elastoviscoplastic constitutive model is proposed for the extrudable fresh cementitious composite. It features the associative flow rule, a nonlinear strain rate-hardening law, and the von Mises yield criterion. The model is then implemented in ANSYS/LS-DYNA explicit finite element code. Various ram extrusion processes of the fresh cementitious composite were simulated. It has been found that the extrusion load versus imposed displacement predictions agree well with the experimental results. The fresh paste flow, through the die entry and the die-land, is then interpreted in light of the evolution of the deformation and distribution of state variables, mainly based on numerical results and the ram extrusion mechanism. The effects of extrusion ratio and extrusion velocity on extrusion load are also investigated, based on the mechanical properties of the fresh cementitious composite. The study indicates that the numerical procedure established, together with the constitutive model proposed, is applicable for describing ram extrusion of short-fiber-reinforced fresh cementitious composites, which might provide a numerical rheometric tool from which ram extrusion of elastoviscoplastic paste-like materials can be examined and quantified.