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## fe_sens

Purpose

Utilities for sensor/shaker placement and sensor/DOF correlation.

Syntax

Command dependent syntax. See sections on placement and correlation below.

Placement

In cases where an analytical model of the structure is available before a modal test, you can use it for test preparation, see section 3.1.3 and the associated gartsens demo. fe_sens provides sensor/shaker placement methods.

### indep

sdof = fe_sens('indep',cphi,cdof)

For a given set of modes mode (associated to the DOF definition vector mdof) and possible sensor locations (DOFs described by the DOF definition vector cdof), the modal output matrix cphi is constructed using

cphi = fe_c(mdof,cdof)*mode

sdof=fe_sens('indep',cphi,cdof) uses the effective independence algorithm [14] to sort the selected sensors in terms of their ability to distinguish the shapes of the considered modes. The output sdof is the DOF definition vector cdof sorted according to this algorithm (the first elements give the best locations). See example in the gartsens demo.

### mseq

sdof = fe_sens('mseq Nsens target',DEF,sdof0) places Nsens sensors, with an optional initial set sdof0. The maximum response sequence algorithm used here can only place meaningfully NM (number of modes in DEF) sensors, for additional sensors, the algorithm tries to minimize the off-diagonal auto-MAC terms in modes in DEF.def whose indices are selected by target.

[FEM,def]=demosdt('demo gartfe');
def=fe_def('subdef',def,1:15); % Keep ten modes
def=fe_def('subdof',def,feutil('findnode group 4:6',FEM));
sdof= fe_sens('mseq 15',def);
FEM=fe_case(FEM,'sensdof','Test',sdof);
feplot(FEM);fecom('curtabCase:Test');fecom('proviewOn');

### [ma,mmif]

Shaker placement based on most important components for force appropriation of a mode. The input arguments are poles po, modal output shape matrix cphi, indices IndB of sensor positions where a collocated force could be applied, IndPo tells which mode is to be appropriated with the selected force pattern. Ind0 can optionally be used to specify shakers that must be included.

sdof(:,1) sorts the indices IndB of positions where a force can be applied by order of importance. sdof(:,2) gives the associated MMIF. load gives the positions and forces needed to have a MMIF below the value val (default 0.01). The value is used as a threshold to stop the algorithm early.

ma uses a sequential building algorithm (add one position a time) while mmif uses a decimation strategy (remove one position at a time).

Correlation

fe_sens provides a user interface that helps obtaining test/analysis correlation for industrial models. To get started you can refer to the following sections

• defining a wire-frame with translation sensors in section 2.2.1 and section 2.2.2
• adding sensors to a FEM as a SensDof entry is illustrated in the topology correlation tutorial section 3.1.

Commands supported by fe_sens are

### basis

These commands are used to handle cases where the test geometry is defined in a different frame than the FEM. An example is detailed in section 3.1.2.

BasisEstimate guesses a local coordinate system for test nodes that matches the FEM model reasonably and displays the result in a fashion that lets you edit the estimated basis. Arguments are the model, and the name of the SensDof entry containing a test frame.

model = fe_sens('basisEstimate',model,'Test');

A list of node pairs in the FEM and test frames can be provided as an additional argument to improve results. The list is a two columns matrix containing FEM (resp. test) NodeId in the first (resp. second) column. If four nodes are provided, the estimation is an exact triplet positioning, the first node being the origin and the 3 other being directions (must be non colinear). For shorter or longer node lists, the positioning is based on global distance minimization between paired nodes.

Basis is used to set the local test basis in a script (see example in section 3.1.2).

BasisToFEM is used to transform the SensDof entry to FEM coordinates. This transformation is done after basis adjustment and makes verification easier by clarifying the fact that the sens.tdof uses the 5 column format with measurement directions given in the FEM format. The only reference to test is the identifier in sens.tdof(:,1) which is kept unchanged and thus where a 1.01 will refer to test direction x which may be another direction in the FEM.

### SensMatch, sens, ...

The building of observation matrices for SensDof entries is now described under sensor SensMatch (building topology correlation to locate test nodes in the FEM model) and sensor Sens (building of the observation matrix after matching). Please read section 4.3.4 for more details.

The obsolete near,rigid,arigid commands are supported through SensMatch calls.

### tdof

tdof = fe_sens('tdof',sens.tdof) returns the 5 column form of tdof if sens.tdof is defined as a DOF definition vector. For more details see sens.tdof and section 4.3 for general sensor definitions.

fecom('ShowLinks Sensors') generates a plot with the mode wire-mesh associated with the SensDof entry Sensors.

For older models where the wire frame is included in the model with a negative EGID, fecom('ShowLinks') still generates a standard plot showing the FEM as a gray mesh, the test wire-frame as a red mesh, test/FEM node links as green lines with end circles, and rotation interpolation links as blue lines with cross markers.

### stick

The stick command can be used to find an orthonormal projection of the test nodes onto the nearest FEM surface. The projected nodes are found in the match.StickNode field.

[sens,def]=demosdt('demo gartte cor');
match=fe_sens('stick sensors',sens,'selface');

### WireExp

def = fe_sens('wireexp',sens) uses the wire-frame topology define in sens to create an interpolation for un-measured directions. For a tutorial on this issue see section 3.3.2.

The following example applies this method for the GARTEUR example. You can note that the in-plane bending mode (mode 8) is clearly interpolated with this approach (the drums of the green deformation have global motion rather than just one point moving horizontally).

[TEST,test_mode]=demosdt('demo gartte wire');
TR=fe_sens('wireexp',TEST);
cf=feplot;cf.model=TEST;fe_sens('WireExpShow',cf,TR)
pause %Use +/- to scan trough deformations as a verification

cf.def(1)=test_mode;
cf.def(2)={test_mode,TR};
fecom(';show2def;ScaleEqual;ch8;view2');
legend(cf.o(1:2),'Nominal','Wire-exp')

The command builds default properties associated with the wire frame (beams properties for segments, shells properties for surfaces, elastic properties for volumes). In some cases you may get better properties by defining properties yourself (see section 7.4 and section 7.3).

Section 4.3, femesh, fe_exp, fe_c,ii_mac, ii_comac