Extrapolation Capability Research Articles

Bottom-up optimization approach and nonlinear model for oilfield output programming

In the process of oilfield development, it is unable to separate the marginal effect of each developing measure from the aggregate effect of all developing measures, so both marginal analysis method and Markowitz portfolio theory are helpless for the oilfield output programming. Function Simulation is proved to be a feasible tool to model the input-output relationship of oilfield development. By training with historical development data, it possesses extrapolation capability in some range, which forms the basis for the oilfield output programming. The purpose of this paper is to report on the use of bottom-up optimization mechanism which is embedded by Function Simulation to optimize the distribution of output in oilfield. Following presentation of the features of oilfield development, the top-down approach and the Function Simulation as a tool for oilfield output programming are reviewed. The process of designing the bottom-up optimization framework embedded with Function simulations, determining the embedding protocol and coordinating the corresponding relationship between the subentry outputs and the subentry costs is described. Subsequently, models and an example are given. Finally, the paper concludes that above optimization method is suitable to solve a class of programming problems.

On-line estimation of cell growth from agitation speed in DO-stat culture of a filamentous microorganism,Agaricus blazei

A simple, but effective on-line method for estimating the mycelial cell mass concentration from agitation speed data, a most readily-available process variable, has been developed for DO-stat cultures ofAgaricus blazei. The dynamic change of dissolved oxygen concentration (DOC) in the initial transient period and the change in yield were considered in the development of the estimation algorithm or estimator. Parameters in the estimation algorithm were calculated from the agitation speed data at 20% of DOC. The proposed estimator could accurately predict the cell mass concentration regardless of DOC levels in the tested range of 10–40%, showing a good extrapolation capability.

Evaluation of Physiologically Based Pharmacokinetic Models in Risk Assessment: An Example with Perchloroethylene

One of the more problematic aspects of the application of physiologically based pharmacokinetic (PBPK) models in risk assessment is the question of whether the model has been adequately validated to provide confidence in the dose metrics calculated with it. A number of PBPK models have been developed for perchloroethylene (PCE), differing primarily in the parameters estimated for metabolism. All of the models provide reasonably accurate simulations of selected kinetic data for PCE in mice and humans and could thus be considered to be “validated” to some extent. However, quantitative estimates of PCE cancer risk are critically dependent on the prediction of the rate of metabolism at low environmental exposures. Recent data on the urinary excretion of trichloroacetic acid (TCA), the major metabolite of PCE, for human subjects exposed to lower concentrations than those used in previous studies, make it possible to compare the high- to low-dose extrapolation capability of the various published human models. The model of Gearhart et al., which is the only model to include a description of TCA kinetics, provided the closest predictions of the urinary excretion observed in these low-concentration exposures. Other models overestimated metabolite excretion in this study by 5- to 15-fold. A systematic discrepancy between model predictions and experimental data for the time course of the urinary excretion of TCA suggested a contribution from TCA formed by metabolism of PCE in the kidney and excreted directly into the urine. A modification of the model of Gearhart et al. to include metabolism of PCE to TCA in the kidney at 10% of the capacity of the liver, with direct excretion of the TCA formed in the kidney into the urine, markedly improved agreement with the experimental time-course data, without altering predictions of liver metabolism. This case study with PCE demonstrates the danger of relying on parent chemical kinetic data to validate a model that will be used for the prediction of metabolism.

Introducing the bounded derivative network—superceding the application of neural networks in control

The Bounded Derivative Network (BDN), the analytical integral of a neural network, is a natural and elegant evolution of universal approximating technology for use in automatic control schemes. This modeling approach circumvents the many real problems associated with standard neural networks in control such as model saturation (zero gain), arbitrary model gain inversion, ‘black box’ representation and inability to interpolate sensibly in regions of sparse excitation. Although extrapolation is typically not an advantage unless the understanding of the process is complete, the BDN can incorporate process knowledge in order that its extrapolation capability is inherently sensible in areas of data sparsity. This ability to impart process knowledge on the BDN model enables it to be safely incorporated into a model based control scheme.

Testing the generalization of artificial neural networks with cross-validation and independent-validation in modelling rice tillering dynamics

Neural networks (NN) rely on the inner structure of available data sets rather than on comprehension of the modeled processes between inputs and outputs. Therefore, neural networks have been regarded as highly empirical models with limited extrapolation capability to situations outside the range of the training and validation data sets. In this study, the generalization ability of neural networks in predicting rice tillering dynamics was tested and several techniques inducing the generalization ability of neural networks were compared. We compared the performance of cross-validated neural networks with independent-validated neural networks and found that neural networks were able to extrapolate and predict tillering dynamics if the data were within the range of inputs of the training set. An inadequate training set resulted in overfitting of available data and neural networks that were not generalizable. The training set size required to enable a neural network to generalize and predict rice tillering dynamics was found to be at least 9 times as many training patterns for each weight. When a large number of variables are included in the input vector of a neural network with inadequate amounts of training data, we strongly recommend that the dimension of the input vector is reduced using principle component analysis (PCA), correspondence analysis (CA) or similar techniques to decrease the number of weights before the training procedure to improve the generalization ability of the NN. If the amount of training data still is not sufficient after the dimension of the input vector is reduced, regularization techniques, such as early stopping, jittering, and especially the embedment of estimated results by a theoretical model into the training set, should be used to improve the generalization ability of the neural network. The generalization of neural networks presents a wide spectrum of problems, and the proposed approaches are not confined strictly to modelling rice tillering dynamics but can be applied to other agricultural and ecological systems.

Artificial neural network modelling of oil sands extraction processes

Although the artificial neural network (ANN) approach has been used in various disciplines of engineering since the 1980s, its use in the oil sands extraction industry is quite new and has great potential. This paper demonstrates two important ANN modelling techniques that will be very useful to the oil sand industry through a case study. First, the ANN pattern recognition approach is illustrated to categorize a large oil sand processing database consisting of experimental data from the last 20 years. Second, within each category, the authors demonstrate how to follow a general protocol to build ANN models that are capable of predicting the primary recovery and the primary froth quality for the oil sand treatment process with fairly good accuracy. To verify the reliability of the ANN models, besides the regular statistical and graphical analysis, the authors also conducted a sensitivity analysis to test the response logic, parameter interaction, and extrapolation capability of the ANN models. As shown in the paper, these tests are both satisfactory and interesting. With sufficient accuracy and robustness in performance, these ANN models can be used to evaluate both the qualitative and the quantitative response of the oil sand treatment process to the known key parameters, which, in turn, can then be used to optimize the oil sand treatment process. Furthermore, these ANN models can be linked with the geological survey results to estimate the production potential of an oil sand ore field and to manage the cost of stockpiling the chemicals for the treatment process.Key words: oil sand processing, artificial neural network, pattern recognition.

Modeling Some Alcohol/Alkane Binary Systems Using the SAFT Equation of State with a Semipredictive Approach

An approach proposed in an earlier work for modeling n-alkane + n-alkane systems (Benzaghou, S.; Passarello, J. P.; Tobaly, P. Fluid Phase Equilib. 2001, 180, 1) is extended to the VLE (vapor-liquid equilibrium; vapor pressure and liquid-phase molar volume) representation of n-alkane + 1-alcohol binary systems using the SAFT equation. The original approach was based on molecular assumptions that consider all n-alkanes to be composed of identical segments. These assumptions are here extended to the 1-alkanol chemical series. The thermodynamic representation of the chemical series of pure 1-alkanols thus requires only four adjustable parameters. The values of the corresponding parameters were determined by fitting the data of the series of light 1-alkanols (1-propanol to 1-octanol). The extrapolation capability of this method was then tested. The VLE thermodynamic properties of pure heavy 1-alcohols (up to 1-octadecanol) and 1-alcohol + n-alkane mixtures were predicted without any additional binary parameters. The model predicts the experimental data within a few percent.

Parameter estimation based model of water-to-water heat pumps with scroll compressors and water/glycol solutions

A recently developed parameter estimation-based steady state simulation model of water-to-water reciprocating vapor compression heat pumps (Jin H, Spitler JD, ASHRAE Trans. 2002; 108(1)) is built up from models of individual components. Various unspecified parameters for individual components are estimated from catalogue data for the overall unit performance. This approach has been shown to give better accuracy and extrapolation capability than polynomial fit models. It has also been shown to give accuracy similar to more detailed deterministic models that require additional information not typically available to an engineer performing energy analysis. This paper covers two important extensions to the model — scroll compressors and glycol/water mixtures. A five-parameter (including intake volumetric flow rate, built-in compression ratio, leakage coefficient and two efficiency-related parameters) scroll compressor model replaces the reciprocating compressor model previously used. While necessary in some applications for providing protection from freezing, water/glycol solutions adversely impact heat transfer performance. A procedure for adjusting the model parameters to account for the change in working fluids is presented. In addition, a preliminary field validation of the modified water-to-water heat pump model is presented. The heat pump utilized both a scroll compressor and a propylene glycol/water mixture as the working fluid.

Use of the DIPPR Database for Development of Quantitative Structure−Property Relationship Correlations: Heat Capacity of Solid Organic Compounds

Two group-contribution methods have been developed to estimate heat capacities of organic solids at ambient pressure. The power-law (PL) method utilizes an empirical temperature dependence, while the partition function (PF) method is based on the Einstein−Debye partition function for crystals with a modified frequency distribution function. Both methods have a fixed temperature functionality but utilize group contributions to obtain the compound-specific constants in the predictive equations. The training set for the group-contribution correlations consisted of 455 compounds and 7967 heat capacity data points. Both methods can be used for temperatures above 50 K, and they correlate the training set to within approximately 9.4 J·mol-1·K-1, corresponding to an average deviation of 6.8% for the PL method and 8.0% for the PF method. The PL method gives better results at lower temperatures, and the PF method at higher temperatures. Tests on the methods' extrapolation capabilities suggest that at 298 K they hav...

地球統計学による地下水のイオン成分濃度の時空間分布モデリング

Environmental data acquired by periodic or continuous measurements at many points are expressed in the spatio-temporal region. Therefore, it is necessary to combine a spatial analysis and a time-series analysis for characterizing data distribution. This study adopts geostatistics to construct a distribution model, which can consider spatio-temporal correlation structures peculiar to the regionalized data and has ability to predict the near future values. The concentration data of seven ion components, Na+, Mg2+, K+, Ca2+, C1-, SO2-4, and HCO-3 contented in the groundwater in the Kumamoto city area, southwest Japan, were chosen for a case study of hydrologic environmental related problem. These data were sampled two times per year between 1994 and 2000 at the 31 groundwater observation wells. Omnidirectional semivariograms of univariate and cross-semivariograms of two variates were made and approximated by polynomials. They clarified two features of correlation structures of the components, which are monotonous increase type and periodic change type of semivariances between data pair with increase of distance and time interval. Through the cross-validation from the two viewpoints, (1) temporal extrapolation capability of ordinary kriging and ordinary co-kriging and (2) validness for considering both the spatial and temporal directions, it was demonstrated that the kriging methods can estimate properly the ion component concentrations and produce less smoothing effect. The concentrations in four June times in 1994, 1996, 1998, and 2000 were estimated and characteristics of fluctuation patterns of each component were detected. A cluster analysis of the hexadiagrams using the seven ion component concentrations estimated in each observation year clarified the zones having similar water quality. The lithologies and groundwater flows in the shallow depths are regarded as influence factors on water quality. In addition, the temporal changes of water qualities were found to be interpretable by a combination of the precipitation and groundwater flows. Water management is specially required for the portions where the qualities are changeable.

A Fuzzy ARTMAP-Based Quantitative Structure−Property Relationship (QSPR) for Predicting Physical Properties of Organic Compounds

A modified fuzzy ARTMAP neural-network-based QSPR for predicting normal boiling points, critical temperatures, and critical pressures of organic compounds was developed. Seven or eight molecular descriptors (the sum of atomic numbers; five valence connectivity indices; and the second-order kappa shape index, without or with the dipole moment) were used to describe the topological and electronic features of a heterogeneous set of 1168 organic compounds. Optimal training and testing sets were selected with fuzzy ART. The fuzzy ARTMAP models with eight descriptors as input provided the best predictive and extrapolation capabilities compared to optimal back-propagation models and group contribution methods. The absolute mean errors of predictions for the normal boiling point (1168 compounds), the critical temperature (530 compounds), and the critical pressure (463 compounds) were 2.0 K (0.49%), 1.4 K (0.24%), and 0.02 MPa (0.52%), respectively. A composite model for simultaneously estimating the three propert...

Improved correlations for heavy n-paraffin physical properties

Critical properties and acentric factors are essential input parameters for equation-of-state models. Experimental data for such properties are limited for heavy hydrocarbons; this necessitates the use of property correlations based on data for lighter members of the homologous series under study. However, inaccurate estimates of the critical properties and the acentric factors often translate to erroneous phase behavior predictions and computational failures. Recent experimental measurements extend the available data on critical properties of n-paraffins up to n-C 36; using this information, we have examined a number of existing correlations for predicting n-paraffin physical properties. Careful evaluation of the quality and the extrapolation capability of each correlation indicates that the asymptotic behavior correlation (ABC) is well suited for the task. Accordingly, we have updated the ABC using the recent experimental data. The accuracy of the updated correlations for describing experimental critical temperature, critical pressure, acentric factor, critical compressibility, and normal boiling point temperature for normal paraffins is 0.2, 0.8, 0.4, 0.6, and 0.1%, respectively, over the range from C 3 to n-C 36.

Hybrid neural network approach in description and prediction of dynamic behavior of chaotic chemical reaction systems

A chaotic system with available prior knowledge is identified with both the sequential hybrid neural network and the standard Artificial Neural Network (ANN). The identified models are validated with phase portrait, return map, the largest Lyapunov exponent and correlation dimension instead of using Sum of Square Errors (SSE). Interpolation and Extrapolation capability of the models are compared. This is demonstrated for nonisothermal, irreversible, first-order, series reaction A≇B≇C in a CSTR.

Prediction of Phase Equilibria and Volumetric Behavior of Fluids with High Concentration of Hydrogen Sulfide

A systematic study of the properties of hydrogen sulfide and its mixtures with hydrocarbons is presented, using the modified and volume translated (t-mPR) as well as the Jhaveri and Youngren volume translated (J-PR) Peng-Robinson equation of state (EoS). Hydrogen sulfide vapor pressure and saturated liquid volume predictions are presented with both EoS. Volumetric predictions with the J-PR EoS are improved when a shift parameter for H2S is incorporated. A simple generalized correlation of the interaction parameters of H2S/n-alkane binary mixtures as a function of the hydrocarbon acentric factor is proposed. The correlation can also be applied to i-alkanes and provides good extrapolation capability to larger alkanes. Interaction parameters for H2S with other hydrocarbons are also given. Application to synthetic multicomponent mixtures and to reservoir oils with high content of H2S gives very satisfactory results.

Processing modelling development through artificial neural networks and hybrid models

Developing fully mechanistic models for bioprocess is expensive and time-consuming. On the other hand, using pure ‘black-box’ approaches can lead to a misuse of available information, because there are aspects of the process that can be accurately described by simple equations as, for example, mass balances. This work analyses the use of different types of ‘black-box’ and hybrid models to outline the dynamics of a batch beer production. The hybrid models, combine mechanistic equations with ‘black-box’ techniques (reserved only for the unclear parts of the system), in order to achieve an efficient use of the available information. The hybrid models can also be called ‘grey-box’ approaches. To generate the hybrid models, different level of information is introduced into the ‘black-box’ models, allowing for an interesting model performance comparison in the end. Results demonstrate that the ‘black-box’ models present a good performance in the range of process conditions used to develop them. However, the inclusion of mechanistic knowledge into the hybrid models increase the model extrapolative capability. In this work, artificial neural networks (ANN) are used as the main technique for both the ‘black-box’ models and the ‘black-box’ parts in the hybrid models.

HYBRID NEURAL APPROACHES FOR MODELLING DRYING PROCESSES FOR PARTICULATE SOLIDS

ABSTRACT This work presents methods for synthesizing drying process models for particulate solids that combine prior knowledge with artificial neural networks. The inclusion of prior knowledge is investigated by developing two applications with the data from two indirect rotary steam dryers. The first application consisted in the modelling of the drying process of soya meal in a batch indirect rotary dryer, The external and internal mass transfer resistances were associated in the hidden layer of the network to linear and sigmoidal nodes, respectively. The second application consisted in the modelling of the drying process of soya meal in a continuos indirect rotary dryer. The model was constructed using the Semi-parametric Design Approach. The model predicts the evolution of solid moisture content and temperature as a function of the solid position in the dryer. The results show that the hybrid model performs better than the pure “ black box” neural network and default models. They also shows that prior knowledge enhances the extrapolation capabilities of a neural network model,

Superresolution capabilities of the Gerchberg method in the band‐pass case: An eigenvalue analysis

This article first provides a general introduction to the Gerchberg superresolution algorithm. Some specific properties of this algorithm, when applied to 2D band-pass images, are then studied by means of an eigenvalue analysis of the imaging operator. The main feature derived is the capability to recover the dc component of the unknown object that has to be reconstructed from the noisy image available. This aspect is important with band-pass images of strictly positive objects, in that recovering the low-frequency and dc components in this case is tantamount to suppressing intolerable artifacts. A set of eigenpairs of the imaging operator was calculated numerically. From the dominant eigenvalues, the spectrum extrapolation capabilities of the method can be derived. From the behavior of the eigenfunctions, the capability of the method to recover the dc component of the original object can be evaluated. Some of the calculated eigenfunctions are shown as examples. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 181–188, 1998

Superresolution capabilities of the Gerchberg method in the band‐pass case: An eigenvalue analysis

This article first provides a general introduction to the Gerchberg superresolution algorithm. Some specific properties of this algorithm, when applied to 2D band-pass images, are then studied by means of an eigenvalue analysis of the imaging operator. The main feature derived is the capability to recover the dc component of the unknown object that has to be reconstructed from the noisy image available. This aspect is important with band-pass images of strictly positive objects, in that recovering the low-frequency and dc components in this case is tantamount to suppressing intolerable artifacts. A set of eigenpairs of the imaging operator was calculated numerically. From the dominant eigenvalues, the spectrum extrapolation capabilities of the method can be derived. From the behavior of the eigenfunctions, the capability of the method to recover the dc component of the original object can be evaluated. Some of the calculated eigenfunctions are shown as examples. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 181–188, 1998

Modelling pressure drop in water treatment

Industrial concern regarding the use of ‘black box’ models has understandably limited their routine application. In an attempt to overcome some of these concerns the technique of hybrid modelling (Thompson M. L. and Kramer, M. A., AIChE Journal, 1991, 40, 1328–1340) has become a popular alternative. It has been applied to many different processes and has shown a marked improvement on the now more traditional data-based models such as artificial neural networks (Psichogios D. C. and Ungar L. H., AIChE Journal, 1992, 38, 1499–1511) and NARMAX (Billings S. A., Gray J. O. and Owens D. H., Nonlinear Systems Design. Peter Peregrinus Ltd, 1984) structures. Hybrid models consist of a ‘black box’ model combined with a model of predefined structure (often mechanistic/first principles model) thereby gaining the advantages of both modelling techniques, namely the non-linear capabilities of a generally structured neural network and the extrapolation capabilities of a more rigid model. In this paper the ability of two different hybrid modelling techniques, combining an artificial neural network with a model of appropriate structure, to predict loss of head of pressure profiles in a water treatment plant, are compared. Data were obtained at 15-min intervals from on-line plant sensors. The input variables used were incoming water flowrate, raw water turbidity, supernatant return flowrate, pH of water entering the filters and solids build up on the filters. Results show the serial structure to be more robust allowing extrapolation outside the range of the training data set as compared to the parallel arrangement yielding a 20% reduction in RMS validation error.

A PDP constructive algorithm for system modelling

A new constructive algorithm is presented for building neural networks that learn to reproduce output temporal sequences based on one or several input sequences. This algorithm builds a network for the task of system modelling, dealing with continuous variables in the discrete time domain. The constructive scheme makes it user independent. The network's structure consists of an ordinary set and a classification set, so it is a hybrid network like that of Stokbro et al. [6], but with a binary classification. The networks can easily be interpreted, so the learned representation can be transferred to a human engineer, unlike many other network models. This allows for a better understanding of the system structure than just its simulation. This constructive algorithm limits the network complexity automatically, hence preserving extrapolation capabilities. Examples with real data from three totally different sources show good performance and allow for a promising line of research.