Model distortion

There have been several attempts to modify the Gaussian curve in order to better model distorted chromatographic concentration profiles. This might be useful if model-based fitting is applied to asymmetrical chromatograms. The following skewed Gaussian function is often suitable. 

The concept of time-dependent model distortion becomes clearer through considering a typical modelling approximation. For example, steam flow, W, through a valve might be modelled as proportional to the upstream pressure, p, and valve opening, y ... 

Another way of expressing the idea of model distortion is to regard the recorded plant transients as continuous, indirect measurements of the model s constant parameters. If these new, inferential measurements of the model parameters fall outside the ranges set by previous, more direct measurements then there is an inconsistency. We should reject the model in its current state and seek to improve it. By this formulation, it becomes clear that the model distortion approach consists of mapping the complex dynamic behaviour of recorded plant variables onto the simple... 

Following the model-distortion idea described above, let us vary dynamically those parameters hitherto deemed constant. The values of the state variables will now be different from those of the nominal model, with the difference dependent on the extent of the variation in the parameters. Letting the new states be denoted by the n-dimensional vector, X, they will follow the equation... 

Before considering methods of finding a, let us review how the concept of model distortion has allowed us to move from comparison between model and plant to a comparison between two models, in one of which we allow the nominally constant parameters to be varied. Suppo.se we drive the system to follow the recorded transients exactly. Using the superscript 0 to label the vectors associated with exact matching, the parameter variations will be given by (/), the states by X"(/) and the outputs by Y (f). Exact matching implies ... 

Time-domain technique for the solution of the model distortion equations... 

An estimate for giving full weight to knowledge derived from the results of the transients used as the basis for the model-distortion exercise would be... 

Mathematical model distortion. Usually, it is difficult to accurately describe the complex hydrogeological conditions and mining system with mathematic expressions. So to establish the mathematical model is hard, and slightly carelessness can make mathematical model distortion. 

In photographic work deflections of these components from their ideal values cause the systematic model distortion. 

---