Laminar flamelet modeling of a turbulent CH4/H2/N2 jet diffusion flame using artificial neural networks

The laminar flamelet concept is used in the prediction of mean reactive scalars in a non-premixed turbulent CH₄/H₂/N₂ flame. First, a databank for temperature and species concentrations is developed from the solutions of counter-flow diffusion flames. The effects of flow field on flamelets are considered by using mixture fraction and scalar dissipation rate. Turbulence-chemistry interactions are taken into account by integrating different quantities based on a presumed probability density function (PDF), to calculate the Favre-averaged values of scalars. Flamelet library is then generated. To interpolate in the generated library, one artificial neural network (ANN) is trained where the mean and variance of mixture fraction and the scalar dissipation rate are used as inputs, and species mean mass fractions and temperature are selected as outputs. The weights and biases of this ANN are implemented in a CFD flow solver code, to estimate mean values of the scalars. Results reveal that ANN yields good predictions and the computational time has decreased as compared to numerical integration for the estimation of mean thermo-chemical variables in the CFD code. Predicted thermo-chemical quantities are close to those from experimental measurements but some discrepancies exist, which are mainly due to the assumption of non-unity Lewis number in the calculations.     

Adaptive network fuzzy inference system modeling for the input selection and prediction of anaerobic digestion effluent quality

This paper presents the development and evaluation of three adaptive network fuzzy inference system (ANFIS) models for a laboratory scale anaerobic digestion system outputs with varied input selection approaches. The aim was the investigation of feasibility of the approach-based-control system for the prediction of effluent quality from a sequential upflow anaerobic sludge bed reactor (UASBR) system that produced a strong nonlinearship between its inputs and outputs. As ANFIS demonstrated its ability to construct any nonlinear function with multiple inputs and outputs in many applications, its estimating performance was investigated for a complex wastewater treatment process at increasing organic loading rates from 1.1 to 5.5 g COD/L d. Approximation of the ANFIS models was validated using correlation coefficient, MAPE and RMSE. ANFIS was successful to model unsteady data for pH and acceptable for COD within anaerobic digestion limits with multiple input structure. The prediction performance showed a high feasibility of the model-based-control system on the anaerobic digester system to produce an effluent amenable for a consecutive aerobic treatment unit.     

Application of artificial neural networks for the prediction of roll force and roll torque in hot strip rolling process

This paper introduces an artificial neural network (ANN) application to a hot strip mill to improve the model’s prediction ability for rolling force and rolling torque, as a function of various process parameters. To obtain a data basis for training and validation of the neural network, numerous three dimensional finite element simulations were carried out for different sets of process variables. Experimental data were compared with the finite element predictions to verify the model accuracy. The input variables are selected to be rolling speed, percentage of thickness reduction, initial temperature of the strip and friction coefficient in the contact area. A comprehensive analysis of the prediction errors of roll force and roll torque made by the ANN is presented. Model responses analysis is also conducted to enhance the understanding of the behavior of the NN model. The resulted ANN model is feasible for on-line control and rolling schedule optimization, and can be easily extended to cover different aluminum grades and strip sizes in a straight-forward way by generating the corresponding training data from a FE model.     

Prediction of multivariate time series by autoregressive model fitting

Suppose the stationary r-dimensional multivariate time series {y_t} is generated by an infinite autoregression. For lead times h≥1, the linear prediction of y_t+h based on y_t, y_t−1,… is considered using an autoregressive model of finite order k fitted to a realization of length T. Assuming that k → ∞ (at some rate) as T → ∞, the consistency and asymptotic normality of the estimated autoregressive coefficients are derived, and an asymptotic approximation to the mean square prediction error based on this autoregressive model fitting approach is obtained. The asymptotic effect of estimating autoregressive parameters is found to inflate the minimum mean square prediction error by a factor of (1 + kr/T).     

Prediction Problems for Square-Transformed Stationary Processes

This paper discusses the prediction problems for square-transformed process, Y _t = X _t ², where X _t is a stationary process with spectral density g(). The square-transformation is important in prediction of the volatility of ARCH models. First, we evaluate the mean square prediction error for square-transformed process when the predictor is constructed from the true spectral density g(). However, it is often that the true structure g() is not completely specified. Hence, we consider the problem of misspecified prediction when a conjectured spectral density f (), , is fitted to g(). Then, constructing the best linear predictor based on f (), we can evaluate the prediction error for square-transformed process. Also, we consider a bias adjusted prediction problem for the above two cases. Furthermore, we may suppose that X _t is a non-Gaussian process. Then, we evaluate the mean square prediction errors when the best linear predictor is constructed by the true spectral density g() and the conjectured spectral density f (), respectively. Since is usually unknown we estimate it by a quasi-MLE . The second-order asymptotic approximations of the mean square errors of the predictors based on g() and f () are given. Finally, we provide some numerical examples, which show some unexpected features.     

A Generalization on the Difference Between an Integer and Its Inverse Modulo Q

The main purpose of this paper is to use the properties of the Gauss sums, primitive characters and the mean value of Dirichlet L-functions to study the hybrid mean value of the error term E（n, l, c, q） and the hyper-Kloosterman sums K（h,n＋1,q）, the asymptotic property of the mean square value ∑^p c=1 E^2（n, 1, c, p）, and give two interesting mean value formulae.     

New approach to applying neural network in nonlinear dynamic model

In this work, radial basis function neural network (RBF-NN) is applied to emulate an extended Kalman filter (EKF) in a data assimilation scenario. The dynamical model studied here is based on the one-dimensional shallow water equation DYNAMO-1D. This code is simple when compared with an operational primitive equation models for numerical weather prediction. Although simple, the DYNAMO-1D is rich for representing some atmospheric motions, such as Rossby and gravity waves. It has been shown in the literature that the ability of the EKF to track nonlinear models depends on the frequency and accuracy of the observations and model errors. In some cases, just fourth-order moment EKF works well, but will be unwieldy when applied to high-dimensional state space. Artificial Neural Network (ANN) is an alternative solution for this computational complexity problem, once the ANN is trained offline with a high order Kalman filter, even though this Kalman filter has high computational cost (which is not a problem during ANN training phase). The results achieved in this work encourage us to apply this technique on operational model. However, it is not yet possible to assure convergence in high dimensional problems.     

Artificial neural network for discrete model order reduction with substructure preservation

This paper presents a new technique for model order reduction (MOR) that is based on an artificial neural network (ANN) prediction. The ANN-based MOR can be applied for different scale systems with substructure preservation. In the proposed technique, the ANN is implemented for predicting the unknown elements of the reduced order model. Prediction of the ANN architecture is based on minimizing the cost function obtained by the difference between the actual and desired system behaviour. The ANN prediction process is pursued while maintaining the full order substructure in the reduced model. The proposed ANN-based model order reduction method is compared to recently published work on MOR techniques. Simulation results verify the validity of the new MOR technique.     

On Minimum Stars and Maximum Matchings

We discuss worst-case bounds on the ratio of maximum matching and minimum median values for finite point sets. In particular, we consider ``minimum stars,' which are defined by a center chosen from the given point set, such that the total geometric distance L <sub>S</sub> to all the points in the set is minimized. If the center point is not required to be an element of the set (i.e., the center may be a Steiner point), we get a ``minimum Steiner star' of total length L _SS . As a consequence of triangle inequality, the total length L _M of a maximum matching is a lower bound for the length L _SS of a minimum Steiner star, which makes the worst-case value ρ(SS,M) of the value L _SS /L _M interesting in the context of optimal communication networks. The ratio also appears as the duality gap in an integer programming formulation of a location problem by Tamir and Mitchell. In this paper we show that for a finite set that consists of an even number of points in the plane and Euclidean distances, the worst-case ratio ρ(S,M) cannot exceed . This proves a conjecture of Suri, who gave an example where this bound is achieved. For the case of Euclidean distances in two and three dimensions, we also prove upper and lower bounds for the worst-case value ρ(S,SS) of the ratio L _S /L _SS , and for the worst-case value ρ(S,M) of the ratio L _S /L _M . We give tight upper bounds for the case where distances are measured according to the Manhattan metric: we show that in three-dimensional space, ρ(SS,M) is bounded by 3/2, while in two-dimensional space L _SS =L _M , extending some independent observations by Tamir and Mitchell. Finally, we show that ρ(S,SS) is 3/2 in the two-dimensional case, and 5/3 in the three-dimensional case. Received January 1, 1999, and in revised form July 15, 1999.     

On the mean square error of maximum likelihood estimates of the distribution density of sufficient statistics of the multivariate normal distribution

The extensive use of maximum likelihood estimates underscores the importance of the problem of statistical estimation of their errors. These estimates are of utmost importance in cases where the family of normal distributions and the families related to the normal distributions are considered [1, 2, 4]. The mean square errors of the maximum likelihood estimates of the normal density were investigated in the author's paper [3]. The mean square errors of statistical estimates of some families of densities related to the normal distributions were considered in the papers [4–6]. In the present paper, we obtain an asymptotic expansion of the mean square error of the maximum likelihood estimates of the densities of the joint distribution of sufficient statistics of the family of multivariate normal distributions. The results obtained allow us to construct the mean square errors of the maximum likelihood estimates for the chi-square density and Wishart's density. Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 4–11, Perm. 1990.     

Shape optimal design of arch dams using an adaptive neuro-fuzzy inference system and improved particle swarm optimization

An efficient methodology is proposed to find the optimal shape of arch dams including fluid–structure interaction subject to earthquake ground motion. In order to reduce the computational cost of optimization process, an adaptive neuro-fuzzy inference system (ANFIS) is built to predict the dam effective response instead of directly evaluating it by a time-consuming finite element analysis (FEA). The presented ANFIS is compared with a widespread neural network termed back propagation neural network (BPNN) and it appears a better performance generality for estimating the dam response. The optimization task is implemented using an improved version of particle swarm optimization (PSO) named here as IPSO. In order to assess the effectiveness of the proposed methodology, the optimization of a real world arch dam is performed via both IPSO–ANFIS and PSO–BPNN approaches. The numerical results demonstrate the computational advantages of the proposed IPSO–ANFIS for optimal design of arch dams when compared with the PSO–BPNN approach.     

Prediction of multivariate chaotic time series via radial basis function neural network

In this article, a new multivariate radial basis functions neural network model is proposed to predict the complex chaotic time series. To realize the reconstruction of phase space, we apply the mutual information method and false nearest‐neighbor method to obtain the crucial parameters time delay and embedding dimension, respectively, and then expand into the multivariate situation. We also proposed two the objective evaluations, mean absolute error and prediction mean square error, to evaluate the prediction accuracy. To illustrate the prediction model, we use two coupled Rossler systems as examples to do simultaneously single‐step prediction and multistep prediction, and find that the evaluation performances and prediction accuracy can achieve an excellent magnitude. © 2013 Wiley Periodicals, Inc. Complexity, 2013.     

Hilbert space representations of general discrete time stochastic processes

We show that under mild conditions the joint densities Px₁,…,x_n) of the general discrete time stochastic process X_n on $\text{pH}$ can be computed via

$\text{Px}{}_1\text{,…,x}{}_{\mathrm{n}}\text{(x}{}_1\text{,…,x}{}_{\mathrm{n}}\text{) = 6?T(x}{}_1\text{)…T(x}{}_{\mathrm{n}}\text{)6}{}^2$

where ? is in a Hilbert space $\text{pH}$, and T (x), x ? $\text{pH}$ are linear operators on $\text{pH}$. We then show how the Central Limit Theorem can easily be derived from such representations.     

Artificial neural network modeling techniques applied to the hydrodesulfurization process

Reduction of harmful emissions in the combustion of fossil fuels imposes tighter specifications limiting the sulfur content of fuels. Hydrodesulfurization (HDS) is a key process in most petroleum refineries in which the sulfur is mostly eliminated. The modeling and simulation of the HDS process are necessary for a better understanding of the process operation; it is also a requirement to optimize process operation. The objective of this work is to explore the use of different artificial neural network (ANN) architectures in creating various models of the HDS process for the prediction of sulfur removal from naphtha. A database was build using daily records of the HDS process from a Mexican refinery. Accuracy of the predictions was quantified by the root of the mean squared difference between the measured and the predicted sulfur content in the desulfurized naphtha, along with the coefficient of correlation as a measure of the goodness of fit. Results show that the ANN models can be used as practical tools for predictive purposes. One particular example is the ability to anticipate such situations, in the process, that could increase alertness because some variables are deviating from acceptable limits.     

Proper forcing axiom and selective separability

We continue the study of Selectively Separable (SS) and, a game-theoretic strengthening, strategically selectively separable spaces (SS⁺) (see Barman, Dow (2011) [1]). The motivation for studying SS⁺ is that it is a property possessed by all separable subsets of Cp(X) for each σ-compact space X. We prove that the winning strategy for countable SS⁺ spaces can be chosen to be Markov. We introduce the notion of being compactlike for a collection of open sets in a topological space and with the help of this notion we prove that there are two countable SS⁺ spaces such that the union fails to be SS⁺, which contrasts the known result about SS spaces. We also prove that the product of two countable SS⁺ spaces is again countable SS⁺. One of the main results in this paper is that the proper forcing axiom, PFA, implies that the product of two countable Fréchet spaces is SS, a statement that was shown in Barman, Dow (2011) [1] to consistently fail. An auxiliary result is that it is consistent with the negation of CH that all separable Fréchet spaces have π-weight at most ω₁.     

Time-varying minimum cost flow problems

In this paper, we study a minimum cost flow problem on a time-varying network. Let N(V,A,l,b,c_r,c_w) be a network with an arc set A and a vertex set V. Each a∈A is associated with three integer parameters: a positive transit time b(a,t), an arbitrary transit cost c_r(a,t), and a positive capacity limit l(a,t). Each x∈V is associated with two integer parameters: a waiting cost c_w(x,t) and a vertex capacity l(x,t). All these parameters are functions of the discrete time t=0,1,2,… The objective is to find an optimal schedule to send a flow from the origin (the source vertex) to its destination (the sink vertex) with the minimum cost, subject to the constraint that the flow must arrive at the destination before a deadline T. Three versions of the problem are examined, which are classified depending on whether waiting at the intermediate vertices of the network is strictly prohibited, arbitrarily allowed, or bounded. Three algorithms with pseudopolynomial time complexity are proposed, which can find optimal solutions to the three versions of the problem, respectively.     

The signed star domination numbers of the Cartesian product graphs

Let G be a graph with vertex set V(G) and edge set E(G). A function f:E(G)→{-1,1} is said to be a signed star dominating function of G if for every v∈V(G), where E_G(v)={uv∈E(G)|u∈V(G)}. The minimum of the values of , taken over all signed star dominating functions f on G, is called the signed star domination number of G and is denoted by γ_SS(G). In this paper, a sharp upper bound of γ_SS(G×H) is presented.     

基于EEMD-Elman-Adaboost的中美股票价格预测研究

针对股票价格序列高度非正态、非线性、非平稳等复杂特征,文章以Elman神经网络为基础,引入集合经验模态分解(EEMD)与Adaboost算法,对中美股票的日收盘价进行预测。首先,利用EEMD算法将样本分解为多个本征模函数分量和1个残差分量。其次,用Adaboost算法优化Elman神经网络,对各个分量进行预测。最后,将各分量预测结果进行求和,作为最终预测结果。研究结果表明:EEMD-Elman-Adaboost模型对中美股票价格预测的均方根误差、平均相对误差、平均绝对误差均比现有的BP、Elman、EMD-Elman、EEMD-Elman模型小,新组合模型融合了EEMD、Elman神经网络、Adaboost算法的优点,具有更强的泛化能力和跟随能力。     

Estimation of a smooth quantile function under the proportional hazards model

The problem of estimating a smooth quantile function, Q(·), at a fixed point p, 0 < p < 1, is treated under a nonparametric smoothness condition on Q. The asymptotic relative deficiency of the sample quantile based on the maximum likelihood estimate of the survival function under the proportional hazards model with respect to kernel type estimators of the quantile is evaluated. The comparison is based on the mean square errors of the estimators. It is shown that the relative deficiency tends to infinity as the sample size, n, tends to infinity.     

On stable estimation of a function of a parameter

Given the function f and the vector-statistic t_N which is a mean square consistent estimator of a parameter a, the problem is to estimate f(a). The criteria for the mean square consistency of the estimator f(t_N) are considered. In the case where the estimator f(t_N) is not mean square consistent, a class of estimators of f(a) is proposed, and it is proved that the estimators of the class are mean square consistent for all distribution of t_N. Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 44–55, Perm, 1990.