Normal Mode Indicator Function (NMIF) algorithm

The NMIF exciter selection algorithm searches for the optimum number of exciters and the optimum location for these exciters. These exciters must excite all normal modes.

The normal mode indicator function (NMIF) is evaluated at each analysis mode frequency. For each exciter input, the algorithm defines multiple mode indicators, one for each sensor location NOTE.

For each candidate exciter p and analysis normal mode j, the normal mode indicator function NMIFjp is calculated as follows:

NIMF_{jp} = \frac{\sum_{q=1}^M |\Re{{H_{pq}(i\omega_j)}}| |H_{pq}(i\omega_j)|}{\sum_{q=1}^M |H_{pq}(i\omega_j)|^2}

where:

• M is the number of sensor DOFs.

• \Re{{x}} is the real part of the complex number x.

• ωj is the natural frequency of the jth mode.

• Hpq(iωj) is the transfer function for the jth mode from qth sensor DOF to the exciter p. The transfer function Hpq(iωj) is calculated for each possible direction as follows:

H_{pq}(i\omega_j) = e_x H_{pxq}(i\omega_j) + e_y H_{pyq}(i\omega_j) + e_z H_{pzq}(i\omega_j)

where:

• ex, ey, and ez are the direction cosines that depend on the specified off-axis angles. If you choose 45°, there are thirteen possible combinations of direction cosines, thus thirteen different transfer functions for a given exciter p. If you choose 30°, there are thirty one possible combinations of direction cosines, thus thirty one different transfer functions for a given exciter p.

• Hpxq(iωj), Hpyq(iωj), and Hpzq(iωj) are the transfer functions for each orthogonal directions, X, Y, and Z, respectively. The transfer function equation for the X-direction is as follows:

H_{pxq}(i\omega_j)=\sum_{k=1}^N \frac{{\psi_{Ak}}{px}{\psi{Ak}}_q}{\left(\omega^2_k - \omega^2_j\right)+2i \varsigma_k \omega_k \omega_j}

where:

• N is the number of analysis normal modes.

• {ΨAk}px is the pxth element of the kth analysis mode shape matrix.

• {ΨAk}q is the qth element of the kth analysis mode shape matrix.

• ζk is the critical damping ratio of the kth mode. The critical damping ratio for all modes is the same. It is the value that you specify in the Damping Ratio (%) box of the Exciter Selection Configuration dialog box.

Similar transfer function equations are used for the Y and Z directions where you replace x by y or z.

After calculating the NMIF values for every direction and every analysis mode at all candidate exciter location, the software finds the optimal exciter number, location, and direction as follows:

1. For each exciter direction, the software counts the number of modes with NMIF values below the threshold value. These modes are considered excited.

2. The software finds the exciter locations and directions that excite the maximum number of modes. If more than one exciter location and direction excite the same maximum number of modes, the software selects the exciter with the minimum value of these maximum NMIF values to be the optimal exciter.

3. To find the next optimal exciter location and direction, the software removes all NMIF values that are below the threshold value for all modes excited by the previously found exciters and repeats all steps until enough exciters are selected to excite all analysis normal modes.

The software issues a warning if there are modes that are not excited.

It also calculates the weighted average NMIF values for the optimal exciters as follows:

NIMF_p^{\omega a}=\frac{\sum_{j=1}^{n_p}\omega_j NIMF_{jp}}{\sum_{j=1}^{n_p}\omega_j}

where:

• np is the number of excited modes for exciter p.

• wj is the weight of the jth excited mode.

Learn more

Exciter selection configuration

Pre-test solution process

Correlation solution process

Look up more details

Modal Analysis

Converting complex modes to real modes

Accounting for repeated modes

Modal Scale Factor (MSF)

Modal Assurance Criteria (MAC)

Coordinate MAC (COMAC)

Cross-orthogonality (X-Ortho)

Frequency Response Assurance Criterion (FRAC)

Min-MAC algorithm

MODMAC algorithm

Driving Point Residue algorithm

Scientific literature references for correlation

Quick links

Command reference

Pre/Post video examples

Bulk Entry Descriptions

Simcenter 3D tutorials

Browse Simcenter 3D help by product area

Normal Mode Indicator Function (NMIF) algorithm, Simcenter 3D 2021.1 Series

© 2020 Siemens

Napolitano, K.L., and Blelloch, P.A., “Automated Selection of Shaker Locations for Modal Tests”, International Modal Analysis Conference on Structural Dynamics, Kissimmee, FL, February 2003.

window.mainLanguage="en_US"

window.delivId=""

window.projectId=""

MathJax.Hub.Config({ TeX: { extensions: ["autoload-all.js"] }, tex2jax: { displayMath: [ ] }, "SVG": { scale: 125 } });