In the presence of abundant quantitative data and sufficient knowledge, it is straightforward to employ sophisticated quantitative modelling approaches and tractable computational tools to first build quantitative models by presuming the model structures and then fit the numeric parameters of these models.
The matrix coefficients have a fixed structure and it is now interesting to obtain the parameters required by the model structure.
Figure 4b shows distributions of the maximum (red) and minimum (blue) eigenvectors of the tensor caused by the model structure (Fig. 3) whose density contrast is −200 kg/m3.
Figure 4a shows distributions of the maximum (red) and minimum (blue) eigenvectors of the gravity gradient tensor caused by the model structure (Fig. 3) whose density contrast (Δρ = ρ 1 − ρ 2) is 200 kg/m3.
Model structure directly incorporated data for recorded test volumes as part of the testing assumptions explicitly captured by the model structure (please refer to "Model 1" in Additional file 1).
This effect can be attributed to the choice of the objective function rather than to limitations induced by the model structure: since the standard deviations are higher during the first 30 minutes, higher deviations are tolerated in this time interval.
In the smaller-dimensional world described by the model structure and its parameters, new experiments are easier to conceive, hypotheses can be tested with greater clarity, and knowledge can be extended with inexpensive computational effort [ 1].
Hence, with the measured output denoted as y, the assumption is that (4) y (t ) = y ^ (t, θ ) + ν (t ), ν ∼ D for all t, and where ν follows the distribution D. A model, M, is defined by the specific choice of the functions f and g, i. e. by the model structure, and some parameters, θ.
Entirely based on this model, a feedback linearization control law is designed by using the model structure, model parameters and model states and then applied to control the model and the plant.
The rescoring method computes new model scores by comparing the model structure with native template structures via VOROLIGN.
