Min-MAC algorithm

The Min-MAC sensor selection algorithm searches for the best locations in which to place the sensors by minimizing the off-diagonal terms of the MAC matrix.

The solver starts with the required set of degrees-of-freedom and adds either one DOF for uniaxial sensor or three DOFs for triaxial sensor. The DOFs are added one at a time from the candidate DOF set. The solver monitors a subset of the off-diagonal MAC terms during the selection process. This subset starts with the current largest off-diagonal element of the MAC matrix. As other elements become the largest off-diagonal element of the MAC matrix, they are added to the tracking list.

The algorithm proceeds in the following stages NOTE:

1. The solver calculates the MAC matrix for the mode shapes partitioned to the required DOF set, NR. So each mode shape {Ψi} has NR terms. There are LA mode shapes in the data set.The solver keeps the inner products for further calculation: {Ψi}T{Ψj}. It sets:The number of tracked off-diagonal terms: p = 1The current number of DOFs for the sensor selection set: Nk = NR**MACmax = maximum of all MAC(Ai, Aj), i ≠ j

2. The solver loops over all other candidate DOFs to determine which DOF minimizes the p off-diagonal elements of the MAC matrix that the solver is tracking.

3. The solver calculates all off-diagonal elements of the MAC matrix resulting from adding this DOF. The solver sets Nmax equal to the largest off-diagonal element of this new MAC matrix and keeps the inner products for further calculation.

4. If Nmax < MACmax, the solver adds this DOF to the sensor selection set and sets:Nk = Nk + 1MACmax = NmaxThe solver returns to step 2.

5. If Nmax > MACmax, the solver increments p and adds the new largest off-diagonal element to the list of tracked elements.The solver returns to step 2 without adding this DOF to the sensor selection set.

6. The solver stops when Nk reaches the user specified number of DOFs.

Mode weighting is optionally incorporated into this algorithm by modifying the original off-diagonal MAC values as follows:

MACweighted(Ai, Aj) = (wi + wj) / 2 * MAC(Ai, Aj)

where wi and wj are ith and jth mode weights with values between 0 and 1.

Because the mode weighting generates a MAC matrix that has lower off-diagonal values for modes with lower weight, these modes have reduced importance for the Min-MAC based sensor selection.

Learn more

Sensor 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)

MODMAC algorithm

Normal Mode Indicator Function (NMIF) 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

Min-MAC algorithm, Simcenter 3D 2021.1 Series

© 2020 Siemens

Came, T.G. and Dohrmann, C. R., “A modal test design strategy for model correlation”, International Modal Analysis Conference, Nashville, TN, 13-16 February 1995.

window.mainLanguage="en_US"

window.delivId=""

window.projectId=""

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