Identification of the movement of water in unsaturated soils: the problem of identifiability of the model

Abstract The estimation of model parameters using non-linear regression techniques is one of the aspects of inverse modelling and is known as the identification problem, the solution of which may be non-unique. The main causes of this non-uniqueness are the structure of the model and the design of the input signal. It will be shown that the parameters can be estimated only if a model with different parameter values yields different output signals. A model that has this feature is called identifiable. As an example, the identification of a model for the movement of water in unsaturated soils is used. This model appears to be non-identifiable, which results in non-unique solutions.

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