Fundamentals - Preventive Biomechanics - page 127

In Chap. 7 optimization potentials and strategies regarding support material and
design optimization are identified. In this process, the topology of body supports is
altered to reduce internal tissue stress (and/or strain) in the region underneath the
ischial tuberosity of the seated body. To alter support topology, a similar approach
to that employed in parameter optimization is followed, Fig. 3.32 . This process is
further illustrated in Fig. 3.30 , exchanging the material parameters as unknown
causes with support contact surface topology (displacement) and tissue

displacement.
Mean tissue stress represents the scalar objective function value which is to be
minimized. Instead of stress, strain could equally well be used as an optimization
criterion. The approach is further discussed in detail in Chap. 7 .

3.4.7 The Least-Squares Method

Parameter identification can be carried out using simple procedures such as the
'hand-fitting method' or the 'trial and error method', see Abbott and Refsgaard
(1996). It can, however, also be approached more advantageously, considering the
process of parameter identification as an optimization problem. Automatic
parameter optimization is performed by employing a numerical algorithm to find
optima of a given objective function.
The objective function represents the quantity to be optimized, subject to the
parameters p T ¼½ p 1 p 2 ...p n used for input. In this regard, the least-square
method requires the sum of squared residuals, i.e. sum of deviations of simulated
and measured data, to be at a minimum. A detailed overview of the least-square
approach can be found in Ben-Israel and Greville (2003) or Grasselli and Peli-
novski (2007).
In the example of material parameter identification discussed previously, the
experimental output is given through force-displacement data F(u), where each
discrete displacement value u exp is assigned a measured force value F exp .In
addition, simulating the experiment and employing a given set of material
parameters p i , every simulated discrete displacement value u sim can be assigned a
simulated force value F sim . Each simulated set of material parameters will produce,
in the unique case, a different force-displacement output. Employing the least-
square approach, each individual output data set can be compared with the target
(the set of experimental data) and a scalar residual is assigned.

In Fig. 3.33 , various simulation outputs on the basis of different material
parameter sets P i are opposed to the target function of experimental data. The
depicted simulation outputs schematically represent different stages in the
parameter optimization process leading towards an approximate match of simu-
lation and experimental results.