Model Creation

All regression methods aim at the minimization of residuals, for instance minimization of the sum of the squared residuals. It is essential to focus on minimal prediction errors for new cases—the test set—but not (only) for the calibration set from which the model has been created. It is relatively easy to create a model— especially with many variables and eventually nonlinear features—that very well fits the calibration data however, it may be useless for new cases. This effect of overfitting is a crucial topic in model creation. Definition of appropriate criteria for the performance of regression models is not trivial. About a dozen different criteria— sometimes under different names—are used in chemometrics, and some others are waiting in the statistical literature for being detected by chemometricians a basic treatment of the criteria and the methods how to estimate them is given in Section 4.2. 

The data set is split into a calibration set used for model creation and optimization and a test set (prediction set) to obtain a realistic estimation... 

CV or bootstrap is used to split the data set into different calibration sets and test sets. A calibration set is used as described above to create an optimized model and this is applied to the corresponding test set. All objects are principally used in training set, validation set, and test set however, an object is never simultaneously used for model creation and for test. This strategy (double CV or double bootstrap or a combination of CV and bootstrap) is applicable to a relatively small number of objects furthermore, the process can be repeated many times with different random splits resulting in a high number of test-set-predicted values (Section 4.2.5). 

Data Sources I Data 1 Harmonisation I (Real-time) 1 Sensor Fusion 1 Model Creation 1 1... 

It is, at this point, important to understand the difference between unsupervised methods and supervised methods. With the former, there is no indication given to the model creation program (e.g. PCA, self-organising maps) of where any of... 

Instrument calibration or models creation (Recalibration module), this module is used when the existing models are not fitting well with the sample composition. In this case, it is necessary to create a new model on the base of a set of relevant spectra (minimum of 20 spectra). The parameters values obtained by laboratory methods (COD, TOC, BOD...) are included in the data base in order to found the more suitable model. 

SAS The SAS Institute support organization has recently published resources for both validation (21) and actual IQ/OQ guidance (22). This should certainly be reviewed as a plausible starting point for the OQ. The same advice regarding analyses from standards organizations (15) applies. Please note that both S-Plus and SAS provide a wide range of capabilities for model creation, data analysis, presentation, and interfacing to databases and other software. It is incumbent on the user community to identify, at least initially, the capabilities that will be utilized in the user requirements documentation. Such software-specific capability should then be appropriately tested in the OQ. 

CIMOSA model creation processes, namely instantiation, derivation and generation, define how generic building blocks and partied models are used to create particidar enterprise models. 

Beyond FEM, BEM, and FDM, there are other calculation systems that are based on problem-specific model creation. These systems, however, are usually applied only in conjunction with an associated model. Two examples are the calculation of suspensions and the determination and layout of weld contacts. 

A human controls part model creation procedures by interactive communication. 

The viewpoint of an engineer is often changed during model creation sessions depending on the actual region of the object under work or analysis. In Figure 1-15d, the viewpoint has been... 

Figure 2-17 summarizes the general characteristics and construction of shape model entities. Let us suppose that a model creation starts with an empty model space. The first entity is point P as defined by its coordinates. Both line Lj and closed contour Cj entities are defined using P as the starting point. We say that Lj and Q are higher-level entities than P. Contour Cj consists of six straight-line entities. Any component element of Cj can be modified or deleted and new elements can be inserted. Entities Lj and Cj are input parameters for the definition of a solid prism entity. This solid is the only component entity of the solid model representation of Part 1. Contour C2 is taken from Part 1 for the definition of Part 2. Line L2 is defined as an extension of an edge of Part 1. Similarly to Part 1, the shape of Part 2 is... 

In Figure 3-44, S3 is constrained as a rotational surface. This constraint is placed by the model-creation procedure. It prevents modification of the analytic shape of the rotational surface at development and application of the model. When the new surface S2 is integrated in the model, end surface continuity conditions at the connection of surfaces S2 and S3 can be established and maintained only by the modification of S2-... 

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