Validation, model

Model validation is the process by which the least-squares model is examined to determine whether it is sufficiently good. Although many aspects can be formalised mathematically, some amount of intuition and experience is required in order to 

Model validation consists of three parts (1) testing the residuals, (2) testing the adequacy of the model, and (3) taking corrective action. Each of these three parts will now be examined in greater detail. 

It has been shown that for ordinary, least-squares analysis to hold, four assumptions are required about the distribution of the errors. These assumptions must be verified in order to determine the validity of the method. To refi esh, the four key assumptions are  

The errors are homoscedastic, that is, they have the same variance. 

Since the true errors cannot be known, the residuals obtained from regression analysis are used instead. The following tests can be performed to determine the 

Several procedures are available to determine the reliability and statistical significance of the model. The performance of regression models is commonly measured by the explained variance for the response variable y, denoted R, and the residual standard deviation (S ), calculated using the following equations  

Both statistical parameters provide a measure of how well the model can predict new outcomes, however is a more robust estimates of the predictive ability of models because, unlike R does not depend on the number of data points in the 

Cross-validation methods are often also applied. This involves omitting in turn one (leave-one-out) or more (leave-many-out) data points from the training set, generating a QSPR model using the remaining data points, and then predicting the properties of the data point(s) omitted. However, it has often been shown that the use of only this criterion gives an overly optimistic estimate of the predictivity of models [29]. 

The statistics of prediction of an independent external test set provide the best estimate of the performance of a model. However, the splitting of the data set in training set (used to develop the model) and the test set (used to estimate how well the model predicts unseen data) is not a suitable solution for small-sized data sets and an extensive use of internal validation procedures is recommend. 

For unimodal and symmetrical distributions, data point with deviations at least twice greater than the standard deviation of the data are usually considered outliers. Outliers that cause a poor fit degrade the predictive value of the model however, care must be taken when excluding these outliers. They can be a clue in incorrectly measured experimental property or in the inadequacy of the model in capturing some important attribute of the material. Indeed, important microscopic properties of the material have not been accounted for in the model and/or the outlier represents an extreme point for this property. 

Numerical models should be tested to prove their predictive power. The next two sections contain a discussion of general validation issues and an assessment of the model described above using available data on Czochralski silicon growth in 

The necessary stages of the code development are verification (an assessment of the correctness of the model implementation) and validation (an assessment of the adequacy of the model to the real world) [47]. 

Verification Verification is primarily a mathematical issue [47]. The major sources of errors in the numerical solution have been listed in ref [48] insufficient spatial and temporal discretization convergence insufficient convergence of an iterative procedure computer round-off computer programming errors. Errors of the latter type are the most difficult to detect and fix when the code executes without an obvious crash, yielding moderately incorrect results [48]. The study reported in ref. [49] revealed a surprisingly large number of such faults in the tested scientific codes (in total, over a hundred both commercial and research codes regularly used by their intended users). 

Verification is performed by comparison of the numerical results with highly accurate (benchmark) solutions such as 1) exact analytical solutions 2) benchmark solutions of ordinary differential equations (ODE) or 3) benchmark solutions of partial differential equations. The usual use of ODE solution is based on exploiting the symmetry properties one can solve an essentially one-dimensional problem (for example, having spherical symmetry) using a general three-dimensional grid. There are a few well-known multidimensional benchmark solutions such as laminar convection in a square cavity [50, 51] and the flow over a backward-facing step with heat transfer [52]. 

Validation Validation is the second step in the assessment of the software quality. It should be stressed that verification should not be skipped successfiil validation 

Unquestionably one of the most important aspects of all calibration methods is model validation. Several questions need to be answered  

NIR models are validated in order to ensure quality in the analytical results obtained in applying the method developed to samples independent of those used in the calibration process. Although constructing the model involves the use of validation techniques that allow some basic characteristics of the model to be established, a set of samples not employed in the calibration process is required for prediction in order to conhrm the goodness of the model. Such samples can be selected from the initial set, and should possess the same properties as those in the calibration set. The quality of the results is assessed in terms of parameters such as the relative standard error of prediction (RSEP) or the root mean square error of prediction (RMSEP). 

The primary reformer models has been validated by comparing calculated to measured results, and by comparing predicted to observed results. Three cases of calculated versus measured results are presented, one for naphtha feed, and the other for butane feed. One case of predicted versus observed results is presented, for a naphtha feed. The on-line, closed-loop optimization system continuously supplies validation results, by reporting differences (biases) between calculated and measured results on every optimization cycle. 

These results, along with calculated parameters, can be monitored by trending their values as a function of time. 

The first two validation cases are Parameter cases, while the third is a Reconcile case. In the first two cases only primary reformer calculations are 

In order to validate the different approaches it is necessary to compare the results with experimental data. In addition, the IBC method relies on empirical 

Less experimental work has been performed for axial impellers. Kresta and Wood [48] performed LDV measurements of mean and fluctuating radial, axial and tangential velocities in cylindrical tanks with a 45 -pitched, four blade turbine at 400 rpm. A review of experimental investigations of turbulent flow in closed and free-surface unbaffled tanks stirred by radial impellers can be found in Ciofalo et al [12]. 

Experimental investigations of wall heat transfer in stirred tank reactors have been reported by Engeskaug et al [23], Oldshue [65], Hewitt et al [40], among others. 

The 10 simulations confirmed that the 10 procedure is capable of predicting the near impeller flow and turbulence fields with a reasonable accuracy, thus to some extent reducing the need for empirical information. Hence, the lO method is often preferred compared to the IBC method although it was 1—4 times more cpu demanding for one of the particular cases referred. 

Lane et al [49] did compare the performance of simulations with the SM and the MRF approach in predicting flow fields within a standard stirred tank equipped with a Rushton turbine. Reasonable agreement with experimental data in terms of mean velocities is obtained with both methods. Nevertheless, the MRF method provides a saving in computational time of about an order of magnitude. 

The primary pore size distributions of the cases A and B in Table 3.5 are experimentally determined by mercury injection porosimetry (MIP) (Fermeglia and Pricl, 2009) on the instrument of PoreMaster GT 60. The MIP enables the measurements of both the pressure required to force mercury into the pores of CLs and the intruded Hg volume at each pressure. The employed equipment operates from 13 kPa to a pressure of 410 MPa, equivalent to the pores with the diameters, d, ranging from 100 [xm to 0.0036 xm. On the other hand, the 3 V method provides a tool to theoretically calculate the agglomerate volume depending on the probe radius. In analogy to the 

In order to mimic the feature of the CLs, the TEM sample is prepared by mixing the Pt/C electrocatalysts (40 wt%, BASF) in the Isopropanol-Nafion solution, in which the Nafion content is 

In order to validate the different approaches it is necessary to compare the results with experimental data. In addition, the IBC method relies on empirical data in order to implement the momentum source induced by the stirrer. Brucato et al. [10] give a review of the different methods of measuring the velocity field. The most commonly used measurement technique is the Laser Doppler Velocimetry (LDV). 

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Iteration of the steps, descriptor selection, model building, and model validation in combination with an optimi ation algorithm allows one to select a descriptor subset having maximum predictivity. 

The abbreviation QSAR stands for quantitative structure-activity relationships. QSPR means quantitative structure-property relationships. As the properties of an organic compound usually cannot be predicted directly from its molecular structure, an indirect approach Is used to overcome this problem. In the first step numerical descriptors encoding information about the molecular structure are calculated for a set of compounds. Secondly, statistical methods and artificial neural network models are used to predict the property or activity of interest, based on these descriptors or a suitable subset. A typical QSAR/QSPR study comprises the following steps structure entry or start from an existing structure database), descriptor calculation, descriptor selection, model building, model validation. 

Model Validity Probabilistic failure models cannot be verified. Physical phenomena are observed in experiments and used in model correlations, but models are, at best, approximations of specific accident conditions. 

Electric Power Research InsHtute, "Preliminary Results from the EPRI Plume Model Validation Project—Plains Site." EPRI EA-1788, RP 1616. Palo Alto, CA. Interim Report. Prepared by TRC Environmental Consultants, 1981. 

IMES was developed to assist in the selection and evaluation of exposure assessment models and to provide model validation and uncertainty information on various models and their applications. IMES is composed of 3 elements 1) Selection - a query system for selecting models in various environmental media, 2) Validation - a database containing validation and other information on applications of models, and 3) Uncertainty - a database demonstrating apfhieatum nl a mode uncertainty protocol. 

Drish, W. F., and Singh, S. (1992). Train Energy Model Validation Using Revenue Service Mixed Intermodal Train Data. Chicago Association of American Railroads. 

The structure and mathematical expressions used in PBPK models significantly simplify the true complexities of biological systems. If the uptake and disposition of the chemical substance(s) is adequately described, however, this simplification is desirable because data are often unavailable for many biological processes. A simplified scheme reduces the magnitude of cumulative uncertainty. The adequacy of the model is, therefore, of great importance, and model validation is essential to the use of PBPK models in risk assessment. 

Considerable numbers of the numerical solutions of full-Hlm EHL for different surface geometries, such as the smooth surfaces, surfaces with single asperity, and sinusoidal waviness, were published over the past years. They provide good reference data for the purpose of model validation. 

The model validation in mixed lubrication should be made under the conditions when asperity contacts coexist with lubrication. Choo et al. [45] measured film thickness on the surface distributed with artificial asperities. The experi-... 

The traditional approach to optimize a process is schematically shown in Figure 2 its principle elements are the development of a model, model validation, definition of an objective function and an optimizing algorithn. The "model" can be (a) theoretical, (b) empirical or (c) a combination of the two. 

The validity of the model is tested against the experiment. A ISOOcc canister, which is produced by UNICK Ltd. in Korea, is used for model validation experiment. In the case of adsorption, 2.4//min butane and 2.4//min N2 as a carrier gas simultaneously enter the canister and 2.1//min air flows into canister with a reverse direction during desorption. These are the same conditions as the products feasibility test of UNICK Ltd. The comparison between the simulation and experiment showed the validity of our model as in Fig. 5. The amount of fuel gas in the canister can be predicted with reasonable accuracy. Thus, the developed model is shown to be effective to simulate the behavior of adsorption/desorption of actual ORVR system. 

QSAR model validation is an essential task in developing a statistically vahd and predictive model, because the real utility of a QSAR model is in its ability to predict accurately the modeled property for new compounds. The following approaches have been used for the vahdation of QSAR Eqs. 1-20 ... 

The PBPK model for a chemical substance is developed in four interconnected steps (1) model representation, (2) model parametrization, (3) model simulation, and (4) model validation (Krishnan and Andersen 1994). In the early 1990s, validated PBPK models were developed for a number of toxicologically important chemical substances, both volatile and nonvolatile (Krishnan and Andersen 1994 Leung 1993). PBPK models for a particular substance require estimates of the chemical substance-specific... 

PARAMETER ESTIMATION AND MODEL VALIDATION 17.4.1 Experimental Data... 

Roy, R. P, R. C. Dykuizen, M. G. Su, and P. Jain, 1988, The Stability Analysis Using Two-Fluid SAT Code for Boiling Flow Systems, Vol 1, Theory Vol. 4, Experiments and Model Validation, EPRI NP-6103-CCM, Palo Alto, CA. (6)... 

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