MODMAC algorithm

The maximum off-diagonal MAC (MODMAC) algorithm determines which additional degree-of-freedom (DOF) reduces the off-diagonal MAC values. It adds DOFs to a set of initial DOFs until the off-diagonal MAC values are below a given limit, or until the maximum number of DOFs is reached.

The solver adds either one DOF for a uniaxial sensor, or three DOFs for a triaxial sensor from the candidate DOF set to an optional, initial DOF set. The DOFs are added one at a time. The solver tracks a subset of the off-diagonal MAC values during the selection process. This subset starts with the current maximum off-diagonal element of the MAC matrix, or the element at position (0,1), when the initial set is empty. As other elements become the maximum off-diagonal element of the MAC matrix, they are added to the tracking list. In the absence of initial DOFs, the solver sets a maximum off-diagonal MAC value to 1.0.

The solver computes the algorithm as follows:

1. The solver computes the MAC matrix for the mode shapes partitioned to the required DOF set, NR. Each mode shape {Ψi} has NR terms.The solver saves the mode shapes {Ψi}T{Ψj} for further calculation and sets MACmax = maximum of all MAC(Ai, Aj), i ≠ j.

2. The solver repeatedly examines all other candidate DOFs to determine which DOF minimizes the number of tracked off-diagonal elements, p, of the MAC matrix that the solver is tracking.

3. The solver computes all the off-diagonal elements of the MAC matrix resulting from adding this DOF. The solver sets Nmax equal to the maximum off-diagonal element of this new MAC matrix and saves the mode shapes {Ψi}T{Ψj} for further calculation. The solver increments the number of tracked off-diagonal terms, p, and adds the new maximum off-diagonal element to the list of tracked elements.

4. If Nmax < MACmax, the solver adds this DOF to the sensor selection set and sets:Nk = Nk + 1, for uniaxial sensor or Nk = Nk +3, for triaxial sensorsMACmax = NmaxThe solver returns to step 2.

5. Otherwise, the solver returns to step 2 without adding this DOF to the sensor selection set.

6. The solver stops the computation when either Nk reaches the user specified number of DOFs or MACmax reaches the user specified MACthreshold.

Learn more

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

Normal Mode Indicator Function (NMIF) algorithm

Driving Point Residue algorithm

Scientific literature references for correlation

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MODMAC algorithm, Simcenter 3D 2021.1 Series

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