Nonlinear dimension reduction based neural modeling for distributed parameter processes

Many chemical processes are nonlinear distributed parameter systems with unknown uncertainties. For this class of infinite-dimensional systems, the low-order model identification from process data is very important in practice. The dimension reduction with a principal component analysis (PCA) is only a linear approximation for nonlinear problem. In this study, a nonlinear dimension reduction based low-order neural model identification approach is proposed for nonlinear distributed parameter processes. First, a nonlinear principal component analysis (NL-PCA) network is designed for the nonlinear dimension reduction, which can transform the high-dimensional spatio-temporal data into a low-dimensional time domain. Then, a neural system can be easily identified to model this low-dimensional temporal data. Finally, the spatio-temporal dynamics can be reproduced using the nonlinear time/space reconstruction. The simulations on a typical nonlinear transport-reaction process show that the proposed approach can achieve a better performance than the linear PCA based modeling approach.     

A Bayesian latent model with spatio-temporally varying coefficients in low birth weight incidence data

In spatial epidemiology studies, the effects of covariates on adverse health outcomes could vary over space and time so examining the spatio-temporally varying effects is useful. In particular, the association between covariates and health outcomes could have locally different temporal patterns. In this article, we develop a Bayesian spatio-temporal latent model to identify spatial clusters in each of which covariate effects have homogeneous temporal patterns as well as estimate heterogeneous temporal effects of covariates depending on spatial groups. We compare the proposed model to several alternative models to assess the performance of the proposed model in terms of a range of model assessment measures. Low birth weight incidence data in Georgia for the years 1997-2006 are used.     

A Stationary Spatio-Temporal GARCH Model

We introduce a lagged nearest-neighbour, stationary spatio-temporal generalized autoregressive conditional heteroskedasticity (GARCH) model on an infinite spatial grid that opens for GARCH innovations in a space-time ARMA model. This is illustrated by a real data application to a classical dataset of sea surface temperature anomalies in the Pacific Ocean. The model and its translation invariant neighbourhood system are wrapped around a torus forming a model with finite spatial domain, which we call circular spatio-temporal GARCH. Such a model could be seen as an approximation of the infinite one and simulation experiments show that the circular estimator with a straightforward bias correction performs well on such non-circular data. Since the spatial boundaries are tied together, the well-known boundary issue in spatial statistical modelling is effectively avoided. We derive stationarity conditions for these circular processes and study the spatio-temporal correlation structure through an ARMA representation. We also show that the matrices defined by a vectorized version of the model are block circulants. The maximum quasi-likelihood estimator is presented and we prove its strong consistency and asymptotic normality by generalizing results from univariate GARCH theory.     

Projections of cancer mortality risks using spatio-temporal P-spline models

Cancer mortality risk estimates are essential for planning resource allocation and designing and evaluating cancer prevention and management strategies. However, mortality figures generally become available after a few years, making necessary to develop reliable procedures to provide current and near future mortality risks. In this work, a spatio-temporal P-spline model is used to provide predictions of mortality/incidence counts. The model is appropriate to capture smooth temporal trends and to predict cancer mortality/incidence counts in different regions for future years. The prediction mean squared error of the forecast values as well as an appropriate estimator are derived. Spanish prostate cancer mortality data in the period 1975-2008 will be used to illustrate results with a focus on cancer mortality forecasting in 2009-2011.     

Robust probabilistic principal component analysis for process modeling subject to scaled mixture Gaussian noise

Conventionally, for probabilistic principal component analysis (PPCA) based regression models, noise with a Gaussian distribution is assumed for both input and output observations. This assumption makes the model to be vulnerable to large random errors, known as outliers. In this article, unlike the conventional noise assumption, a mixture noise model with a contaminated Gaussian distribution is adopted for probabilistic modeling to diminish the adverse effect of outliers, which usually occur due to irregular process disturbances, instrumentation failures or transmission problems. This is done by downweighing the effect of the noise component which accounts for contamination on output prediction. Outliers are common in process industries; therefore, handling this issue is of practical importance. In comparison with conventional PPCA based regression model, prediction performance of the developed robust probabilistic regression model is improved in presence of data contamination. To evaluate the model performance two case studies were carried out. A simulated set of data with specific characteristics to highlight the presence of outliers was used to demonstrate the robustness of the developed model. The advantages of this robust model are further illustrated via a set of real industrial process data.     

微粒群算法优化化工建模训练集

提出两种均以微粒群(PSO)算法对原始训练集随机抽样优化,再结合机器学习算法建立预测模型的PSO算法优化化工建模训练集的思路。思路1首先以模型交叉验证的均方误差函数mse最小为目标优化训练集,再通过对验证集预测,从平行运行得到的多个优化训练集中确定最优训练集用于建模。思路2借鉴提高BP神经网络泛化能力的初期终止(early stop)法,以对验证集预测的mse最小为目标优化训练集,再通过对测试集预测,从平行运行得到的多个优化训练集中确定最优训练集用于建模。通过仿真实验研究和对某炼油厂调和汽油生产数据的具体分析应用,表明本文思路可以较大幅度提高模型的预测准确性,在化工建模中具有推广应用价值。     

Conway–Maxwell–Poisson Autoregressive Moving Average Model for Equidispersed,Underdispersed, and Overdispersed Count Data

In this work, we propose a dynamic regression model based on the ConwayŮMaxwell–Poisson (CMP) distribution with time-varying conditional mean depending on covariates and lagged observations. This new class of ConwayŮMaxwell–Poisson autoregressive moving average (CMP-ARMA) models is suitable for the analysis of time series of counts. The CMP distribution is a two-parameter generalization of the Poisson distribution that allows the modeling of underdispersed, equidispersed, and overdispersed data. Our main contribution is to combine this dispersion flexibility with the inclusion of lagged terms to model the conditional mean response, inducing an autocorrelation structure, usually relevant in time series. We present the conditional maximum likelihood estimation, hypothesis testing inference, diagnostic analysis, and forecasting along with their asymptotic properties. In particular, we provide closed-form expressions for the conditional score vector and conditional Fisher information matrix. We conduct a Monte Carlo experiment to evaluate the performance of the estimators in finite sample sizes. Finally, we illustrate the usefulness of the proposed model by exploring two empirical applications.     

Influence of Operating Parameters on the Average Spout Width in Two‐Dimensional Spouted Beds

In this work a set of experiments were performed in a two‐dimensional spouted bed to study the effect of different operating conditions on the spout cavity width. The measurement of spout‐annulus interface along the bed level was made by visual observations on a flat face column. A numerical integration formula was used to calculate the average spout width. The experimental runs were performed with different materials, bed dimensions, static bed heights, fluid velocities and gas inlet orifice width. The influences of these variables on average spout width were verified through a statistical analysis. An empirical correlation is proposed to predict the average spout width. The empirical model parameters were found through a statistical analysis.     

Water and mercaptan adsorption on 13X zeolite in natural gas purification process

The aim of this work is to model the adsorption process used for mercaptan and water removal from natural gas. Three fixed beds containing Zeolite molecular sieve type 13X, are used in this plant. In this operation, two beds are in process for adsorption purposes and the other one is regenerated simultaneously. This system is also operated under isothermal condition. In modeling of this process, rate of adsorption is approximated by linear driving force (LDF) expression, and the extended Langmuir isotherm is used to describe adsorption equilibrium. The set of partial differential equations of dynamic model is solved by Crank-Nicolson method. The effect of equations of state is also studied and the best equation fitting the industrial data is selected. Also, concentration profile is presented versus bed length at various times. The influences of pressure, inlet concentration and bed height on the breakthrough time are also investigated.     

Quantitative modeling of scratch-induced deformation in amorphous polymers

In order to predict scratch performance of polymers, the present study focuses on quantitative assessment of various scratch-induced deformation mechanisms based on a set of model amorphous polymers via numerical modeling. A modification of Ree-Eyring theory is used to account for the rate dependent behavior of the model polymers at high strain rates using the experimental data obtained at low strain rates. By incorporating the rate and pressure dependent constitutive and frictional behaviors in the finite element methods (FEM) model, good agreement has been found between FEM simulation and experimental observations. The results suggest that, by including appropriate constitutive relationship and frictional model in the numerical analysis, the scratch behavior of polymers can be quantitatively predicted with reasonable success. Usefulness of the present numerical modeling for designing scratch resistant polymers is discussed.     

Nonlinear model predictive control for distributed parameter systems using data driven artificial neural network models

In this work the radial basis function neural network architecture is used to model the dynamics of Distributed Parameter Systems (DPSs). Two pure data driving schemes which do not require knowledge of the governing equations are described and compared. In the first method, the neural network methodology generates the full model of the system that is able to predict the process outputs at any spatial point. Past values of the process inputs and the coordinates of the specific location provide the input information to the model. The second method uses empirical basis functions produced by the Singular Value Decomposition (SVD) on the snapshot matrix to describe the spatial behavior of the system, while the neural network model is used to estimate only the temporal coefficients. The models produced by both methods are then implemented in Model Predictive Control (MPC) configurations, suitable for constrained DPSs. The accuracies of the modeling methodologies and the efficiencies of the proposed MPC formulations are tested in a tubular reactor and produce encouraging results.     

An alternative approach to estimating parameters in creep models of high‐density polyethylene

Polyethylene (PE) is increasingly used in structural applications due to its light weight and rust‐resistant nature. With growing demand for the use of PE as a structural material, there is a need for mathematical models that describe the mechanical behavior of this material. Curve fitting using a linear time‐dependent model is a common approach for modeling creep of PE at the macrostructural level. However, besides the point estimates of the model parameters and the (visual) fit of the model to experimental data, little else is learnt from the curve‐fitting approach. This work presents a rigorous statistical approach for modeling creep compliance of PE. Four high‐density PE resins used over a wide range of applications are studied. Linear viscoelastic modeling using the multi‐Kelvin element theory is examined in two forms: model linear in parameters and model nonlinear in parameters. With the application of valid statistical techniques, complex relationships between model parameters, largely unstudied before, are observed, such as evidence of a high degree of correlation among material parameters of the creep model. POLYM. ENG. SCI., 2011. © 2010 Society of Plastics Engineers.     

A new data-based methodology for nonlinear process modeling

A new data-based method for nonlinear process modeling is developed in this paper. In the proposed method, both distance measure and angle measure are used to evaluate the similarity between data, which is not exploited in the previous work. In addition, parametric stability constraints are incorporated into the proposed method to address the stability of local models. Furthermore, a new procedure of selecting the relevant data set is proposed. Literature examples are presented to illustrate the modeling capability of the proposed method. The adaptive capability of the proposed method is also evaluated.     

A bidirectional between‐set statistical analysis method and its applications

In this work, a bidirectional statistical modeling and analysis approach is developed to relate two data tables ( X ₁ and X ₂) under the supervision of each other. Different from quality prediction where the interest was to interpret one set of variables by another set, the current task lies in modeling simultaneously both data spaces in bidirectional fashion ( X ₁ ? X ₂) responding to different between‐set relationships. It is performed in two steps. The first step aims at a bidirectional latent variable (Bi‐LV) extraction and preparation, by which the between‐set covarying relationship is preliminarily set up. In the second step, where a joint postprocessing is performed on the Bi‐LV modeling result (here termed Bi‐JPLV algorithm), different types of systematic variations are decomposed in each space. Correlated and unique variations are discriminated and evaluated in specific model parameters separately revealing between‐set similarity and dissimilarity, respectively. The proposed method gives a good interpretation of the underlying information within each data space from a bidirectional viewpoint, revealing practical application potential. The feasibility and performance of the proposed method are illustrated with both numerical and real industrial cases. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

电解质溶液的分子热力学模型

本文以扰动理论为基础建立了含极性组分和电解质的混合物的状态方程.混合物的Helmholtz能由硬球、静电和吸引项三部分组成.对于无电解质的混合物,本状态方程还原成Hu等近期开发的方程.用Bromley、Meissner、pitzer、Chen和本文摸型对25个二元电解质水溶液(最高浓度达20mol/kg)298.15K时的离子平均活度系数进行了关联,本文模型的精度最高.另外,用298.15K回归出的参数对其它温度下的离子平均活度系数进行了预测,结果表明模型参数与温度的关系较小.     

SOLUTION OF POPULATION BALANCE EQUATIONS IN EMULSION POLYMERIZATION USING METHOD OF MOMENTS

In this work, the method of moments is used for solution of population balance equations appearing in modeling of emulsion polymerization (EP). The zero-one model without coagulation effect and the pseudo-bulk model including coagulation effect are investigated as two common approaches for modeling EP processes. The fixed quadrature method is used to close the set of moment equations, and the maximum entropy approach is applied to reconstruct the particle size distribution from a finite number of its moments. Comparing the results with those obtained by the high-precision finite volume technique indicates that, despite the low computational load of the moment method, it has an acceptable accuracy. These features support use of the moment technique for other applications such as on-line control or optimization in particulate processes.     

基于LTSA的FS-SVDD方法及其在化工过程监控中的应用

基于支持向量数据描述(SVDD)方法的非高斯过程监控和故障诊断具有众多优点。然而在对SVDD离线建模时需要在整个训练样本集上操作,对大样本集计算量相当大,也不利于在线操作时模型的更新。对此提出一种基于特征样本的SVDD(FS-SVDD),采用特征样本提取方法用少数几个特征样本代替原始数据集进行训练,显著降低了建模复杂度。同时,针对传统的线性降维算法如主成分分析(PCA)存在的提取过程数据非线性结构能力不足的缺点,首先用局部切空间排列(LTSA)方法提取出低维子流形,进行有效的维数约减;接着在这个低维子流形上执行SVDD算法;最后,利用相应统计指标进行过程监控。在TE过程上的仿真表明上述方法的有效性。     

A simplified thermodynamic modeling procedure for predicting asphaltene precipitation

In this work, a simplified thermodynamic modeling procedure for determination of the amount of asphaltene precipitation is presented. The onset of asphaltene precipitation in the presence of different solvents is predicted by applying the molecular solubility model. Since asphaltene molecular weight varies in different solvents, the molecular weight of asphaltene has been tuned by experimental data. The tuned molecular weight is used to predict the amount of precipitated asphaltene. The Flory–Huggins statistical thermodynamics theory is applied to derive the Gibbs free energy relationship. A necessary and sufficient condition is defined to minimize the Gibbs free energy relation. By solving the set of equations derived from the minimization, the weight percent of precipitated asphaltene has been determined. The advantage of this model is that one does not need to perform expensive and time consuming experiment in order to obtain molecular weight data. The other improvement of this model compared to the other models is the requirement of a minimum amount of experimental data to find the unknown parameters. It also has the advantage of obtaining solubility parameters through thermodynamics relationships rather than using the relation for regular solution when the asphaltene solution is a non-regular solution. The results of this model are in good agreement with the experimental data.