Firstly, the identifiability of three piezoviscosity models (Barus, Roelands and WLF) is analyzed by minimizing a least squares distance between pressure viscosity responses.
The identification is carried out by minimizing a least squares functional comparing inhomogeneous displacement fields from experiments and FEM simulations at given (measured) force loads.
The PEM algorithm estimates the system parameters by minimizing a least square cost function as follows: {min},J_{N} = {min} frac{1}{N}sumlimits_{k = 0}^{N - 1} {|{y_{k} - hat{y}_{k} }|_{2}^{2}} (21).
Therefore, we propose to obtain the spread parameters by minimizing a least square criterion between the signal model proposed in Equation 8, and the signal generated from the image on the circular antenna.
Then, we estimate the spread values by minimizing a least squares criterion between generated and model signals.
The parameter vector estimate is the result of minimizing a least-squares (LSs) criterion, which can be expressed in the time domain as well as in the frequency domain, following the Parceval theorem: (9).
This multilinearity property is exploited for parameter estimation using the standard alternating least squares (ALS) algorithm[4, 5] that consists in alternately estimating each matrix factor by minimizing a least squares error criterion conditionally to the knowledge of the other matrix factors that are fixed with their previously estimated values.
Given (mathbf {x}_{i}in mathbb {R}^{d}), a set of training inputs, and (y_{i}in mathbb {R}), the corresponding outputs, with i=1,...,n, the algorithm finds the hyperplane in the non-linearly transformed kernel space, f(x), that better fits a given set of training data, minimizing a least squares criteria.
The optimization model minimizes a least squares criterion between intended indoor temperatures and a direct response model.
The solver minimizes a least-squares function: the square of the difference between the solution at each of the three percentiles and the elicited values for the percentiles.
