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## 3.1Topology correlation and test preparation

Topology correlation is the phase where one correlates test and model geometrical and sensor/shaker configurations. Most of this effort is handled by fe_sens with some use of femesh.

Starting with SDT 6.0, FEM sensors (see section 4.3) can be associated with wire frame model, the strategy where the two models where merged is thus obsolete.

As described in the following sections the three important phases of topology correlation are

• combining test and FEM model including coordinate system definition for the test nodes if there is a coordinate system mismatch,
• building of an observation matrix allowing the prediction of measurements based on FEM deformations,
• sensor and shaker placement.

### 3.1.1  Defining sensors in the FEM model

Prior steps are to declare

• a FEM model (see section 4.2). For this simple example, the FEM model must describe nodes, elements and DOFs.
• a test wire-frame model (stored in TEST in the demo) with sensors in the .tdof field, as detailed in section 2.2.1 for the geometry and  section 2.2.2 for sensors

One then declares the wire frame (with sensors) as SensDof case entry as done below (see also the gartte demo). The objective of this declaration is to allow observation of the FEM response at sensors (see sensor Sens).

``` cf=demosdt('demo gartfeplot'); % load FEM
TEST=demosdt('demo garttewire');  % see sdtweb('pre#presen')
cf.mdl=fe_case(cf.mdl,'sensdof','outputs',TEST)

% View the Case entry in the properties figure
fecom(cf,'curtabCase','outputs');fecom('ProViewOn')
fecom('TextStack') % display sensor text
% now display FEM shape on sensors
fe_case(cf.mdl,'sensmatch')
cf.sel(2)='-outputs';
cf.o(1)={'sel 2 def 1 ch 7 ty2 scc .25','edgecolor','r'};
```

Section 4.3 gives many more details the sensor GUI, the available sensors (sensor trans, sensor triax, laser, ...). Section 4.3.4 discusses topology correlation variants in more details.

### 3.1.2  Test and FEM coordinate systems

In many practical applications, the coordinate systems for test and FEM differ. fe_sens supports the use of a local coordinate system for test nodes with the basis command. A three step process is considered. Phase 1 is used get the two meshes oriented and coarsely alligned. The guess is more precise is a list of paired nodes on the FEM and TEST meshes can be provided. In phase 2, the values displayed by fe_sens, in phase 1 are fine tuned to obtain the accurate alignement. In phase 3, the local basis definition is eliminated thus giving a cf.CStack{'sensors'} entry with both .Node and .tdof fields in FEM coordinates which makes checks easier.

``` cf=demosdt('demo garttebasis'); % Load the demo data
cf.CStack{'sensors'} % contains a SensDof entry with sensors and wireframe

% Phase 1: initial adjustments done once
% if the sensors are well distributed over the whole structure
fe_sens('basis estimate',cf,'sensors');

% Phase 1: initial adjustments done once, when node pairs are given
% if a list of paired nodes on the TEST and FEM can be provided
% For help on 3DLinePick see sdtweb('3DLinePick')
cf.sel='reset';    % Use 3DLinePick to select FEM ref nodes
cf.sel='-sensors'; % Use 3DLinePick to select TEST ref
i1=[62 47 33 39;          % Reference FEM NodeId
2112 2012 2301 2303]';% Reference TEST NodeId
cf.sel='reset'; % show the FEM part you seek
fe_sens('basis estimate',cf,'sensors',i1);

%Phase 2 save the commands in an executable form
% The 'BasisEstimate' command displays these lines, you can
% perform slight adjustments to improve the estimate
fe_sens('basis',cf,'sensors', ...
'x',     [0 1 0], ... % x_test in FEM coordinates
'y',     [0 0 1], ... % y_test in FEM coordinates
'origin',[-1 0 -0.005],... % test origin in FEM coordinates
'scale', [0.01]); % test/FEM length unit change

%Phase 3 : Force change of TEST.Node and TEST.tdof to FEM coordinates
fe_sens('basisToFEM',cf.mdl,'sensors')
fe_case(cf.mdl,'sensmatch')
```

Note that FEM that use local coordinates for displacement are discussed in sensor trans.

### 3.1.3  Sensor/shaker placement

In cases where an analytical model of a structure is available before the modal test, it is good practice to use the model to design the sensor/shaker configuration.

Typical objectives for sensor placement are

• Wire frame representations resulting from the placement should allow a good visualization of test results without expansion. Achieving this objective, enhances the ability of people doing the test to diagnose problems with the test, which is obviously very desirable.
• seen at sensors, it is desirable that modes look different. This is measured by the condition number of [cφ]T[cφ] (modeshape independence, see [14]) or by the magnitude of off-diagonal terms in the auto-MAC matrix (this measures orthogonality). Both independence and orthogonality are strongly related.
• sensitivity of measured modeshape to a particular physical parameter (parameter visibility)

Sensor placement capabilities are accessed using the fe_sens function as illustrated in the gartsens demo. This function supports the effective independence [14] and maximum sequence algorithms which seek to provide good placement in terms of modeshape independence.

It is always good practice to verify the orthogonality of FEM modes at sensors using the auto-MAC (whose off-diagonal terms should typically be below 0.1)

``` cphi = fe_c(mdof,sdof)*mode; ii_mac('cpa',cphi,'mac auto plot')
```

For shaker placement, you typically want to make sure that

• you excite a set of target modes,
• or will have a combination of simultaneous loads that excites a particular mode and not other nearby modes.

The placement based on the first objective is easily achieved looking at the minimum controllability, the second uses the Multivariate Mode Indicator function (see ii_mmif). Appropriate calls are illustrated in the gartsens demo.