Consequence parameters

Square nodes in the ANFIS structure denote parameter sets of the membership functions of the TSK fuzzy system. Circular nodes are static/non-modifiable and perform operations such as product or max/min calculations. A hybrid learning rule is used to accelerate parameter adaption. This uses sequential least squares in the forward pass to identify consequent parameters, and back-propagation in the backward pass to establish the premise parameters. 

Hooke s Law, which states that a proportional relationship exists between stress and strain, usually holds for a viscoelastic material at a small strain. This phenomenon is called linear viscoelasticity (LVE). Within the LVE region, the viscoelastic parameters G and G" remain constant when the amplitude of the applied deformation is changed. Consequently, parameters measured within the LVE region are considered material characteristics at the observation time (frequency). 

Within a molecule, a nucleus is characterized by its magnetic properties and electronic environment and by the following consequent parameters associated with the corresponding NMR signals chemical shift, coupling constants, relaxation rates,15 and nuclear Overhauser enhancement (NOE).1617 All these values may be used to extract qualitative or quantitative information about the structure, the conformation, and the behavior of molecules in solution. 

C is a set of consequence parameters (evaluated e.g. as a number of injuries or deaths) and F is a set of frequency parameters (probability per time unit) both associated with some accident scenario. They can be described as... 

Adding a number to one of the antecedent parameters or the consequent parameters. This value is related to the maximum and minimum value for each input space and is equal to = maximwnminimum/50 for the first iteration. 

We now turn to the influence of the ordinary diffusion coefficient D in polymer separation. We noted earlier that D is related to the hydrodynamic radius of a polymer molecule by the Stokes-Einstein equation. Consequently, parameter D reflects the dimensions of the polymer chain or, for a given polymer class, the molecular mass. Thus we have a situation in which the two parameters controlling retention in thermal FFF, D and Dj, depend upon two entirely distinct polymer characteristics D depends upon the physical dimensions of the polymer chain and thus on its molecular mass while Dj depends only upon the chemical composition of the polymeric material. 

The inverse frequency factor is then divided by the consequence parameter to arrive at a dimensioifless inverse risk parameter. Thus, a higher value of the resultant parameter indicates higher safety of a pipeline segment. 

C = Consequence parameter F = Frequency and exposure time parameter P = Possibility of avoiding hazard W - Demand rate assuming no protection... 

The clustering software computes the fuzzy. K -partition matrix U (a matrix with membership values of each feature to each cluster), and the consequence parameters / , for each rule i. 

The membership functions can easily be fitted into a sigmoidal shape, this would lead to a slightly different model, and the consequence parameters might have to be optimized in order to assure optimal model performance. 

It can easily be seen that the consequence parameters can be computed from a least-squares approach. The outputy in Fig. 29.1 andEqns. (27.6) and (27.5) can be written as ... 

The number of parameters in the fuzzy sub-models is quite large. One rule of the fuzzy model for the net growth rate, for example, contains about 10 parameters, depending on the type of membership function that is used. Owing to the curse of dimensionahty the number of parameters increases exponentially for systems with higher dimensions. Therefore, only the consequence parameters have been optimized. 

The respective factors are to be considered in the process of determining the probability and consequence parameters, which makes their value more precise. The factors are represented by the functions ... 

The final relation for risk estimation is defined as a sum of the probability and consequence parameters as follows ... 

Gait analysis deals with different kinds of data such as kinematics, kinetics, and EMG data. However, acquired data were always in form of temporal curves which are difficult to be interpreted clinically. Consequently, parameter extraction is necessary in order to select significant characters of temporal curves of kinematics, kinetics, and EMG data. 

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