SDT provides advanced solutions to perform Experimental Modal Analysis in MATLAB.
The standard EMA procedure provides a complete methodology to solve the frequency domain output error problem.
The strategy includes single pole MIMO estimation or stabilization diagrams to initialize the analysis, followed by model tuning strategies which enhance traditional procedures.
This iterative approach is both intuitive and very often more accurate than methods found in other modal analysis packages.
The parametric EMA procedure adds tools to semi-automatically identify parametric transfers and navigate into the parametric identification result.
Standard EMA
The procedure is integrated in the “dock Id” providing an interactive interface to perform this task.
The video demonstrates its use for standard cases.
⚙️ Define pole/residue model options
- Real and Complex modes
- Residual terms
- Data Type: Displacement, velocity or acceleration over force
- Collocated sensors and reciprocity strategy
🌱 Initialize poles (mode frequencies and dampings)
- Single poles MIMO estimator (Peak picking)
- LSCF stabilization diagram with automatic pole selection capability for simple test cases
- Mode Indicator Functions (MMIF, CMIF, AMIF, Sum, SumI,…)
💡 Estimate residues (shapes)
- Full Band (model containing all poles at once)
- Local Pole (sequential estimation of single pole models around resonances)
- Local Band (sequential estimation of poles gathered in frequency bands)
🔎 Check identification quality
- Local mode criteria (Error, contribution, NOS,…)
- Error criteria associated to model constraints: multiple modes, minimal MIMO model, reciprocity constraints for modal scaling
⏯️ Animate mode shapes
- Navigate between identified shapes to animate them if a test geometry is available
- Rotate, pan and zoom with the camera
🔄 Optimize modes (poles + residues)
- Ad-hoc optimization algorithm (IDRC)
- Gradient optimization algorithm
➡️ Post-process the identification result to suit your needs
- Pole/residue model transformation to
- state-space
- second-order mass, damping, stiffness
- polynomial forms
- Transformation of complex modes to normal modes through the identification of diagonal by block damping matrix (non-proportional damping models)
📄 Generate automated report
Many refinements can be needed in the process.
The tool is thus meant to be versatile in the options, visualization choices, and tuning for expert users if needed.
It retains a default configuration that should suit most needs, devised from our numerous application cases throughout the years.
Parametric EMA
Parametric EMA aims to identify parametric transfers obtained from the measurement of a dynamic system in different configurations.
Typical examples of analysis are
👉 Modal property dispersion in batches of similar components
👉 Mode tracking with temperature
👉 Mode tracking with excitation amplitude level
💡We have converged toward a standardized strategy that tackles all these analyses using the same framework.
This framework relies on two steps:
1 – Transfers corresponding to the first system configuration are loaded and EMA is performed manually.
2 – Automatic optimizations of poles from current configuration to the next are sequentially performed.
⏯️ The following video illustrates its implementation where the varying parameter is the temperature.
The data is part of our tutorials for parametric experimental modal analysis on the GARTEUR test case with temperature dependency.
The test being MIMO, the transfers span a frequency band, outputs, inputs, and several temperatures, making it a 4D database.
⚙️ Data are split into MIMO transfer blocks corresponding to each temperature value.
The two-step algorithm is then performed:
1️⃣Transfers corresponding to the first temperature are loaded and EMA is performed (here using the automatic interpretation of LSCF stabilization diagram).
2️⃣Automatic optimizations of poles from current temperature to the next are sequentially performed.
🔎 The evolution of the identified modes with the temperature is finally analyzed.