# Tech Tips

The following Tech Tips were previously published in the FEMtools News newsletter:

- Extracting Mass Properties from FRFs
- Orders-based Correlation and Model Updating
- Model Upgrading versus Model Updating
- Using Digital Twins for Structural Health Monitoring
- Exploratory Model Updating
- Full Field Modal Analysis using FEMtools MPE
- Scenario-based Damage Identification
- FRF-Based vs. Modal-Based Model Updating
- Modal Extraction for the FE Analyst
- Structural Health Monitoring of Piping Systems using Modal Analysis and Finite Element Model Updating
- Multi-Model Updating
- Bottom-Up Versus Top-Down Approach for Model Validation and Updating
- Automated Operational Modal Analysis
- Working with Abaqus Condensed Matrices
- Geometry Updating
- ODS-Based Model Updating
- Mapping Laser Scanning Measurements on a FE Mesh
- Estimating Rigid Body Properties from FRF Measurements: A New FEMtools Add-On Tool
- Ogden Material Identification using FEMtools Optimization
- Finding Optimal Master DOF for Guyan Reduction with FEMtools Pretest Analysis Tools

For technical papers, click here.

### Extracting Mass Properties from FRFs

Accurate values of the inertia properties are often unknown because an accurate CAD or finite element (FE) model of the full operational structure is seldom available due to the complex nature of the assembly components. This may be due to geometrical details or any parts like cabling that are missing in the model.

FEMtools RBPE uses the Inertia Restrain Method (IRM) to extract the rigid body response of the structure from FRF measurements, using the horizontal mass lines located between the low-frequency suspension modes and the elastic modes of the structure.

Because all ten inertia properties of a complex structure cannot be easily determined accurately using a model, several test-based methods have been developed. A weighing test may be possible to determine the mass of a structure, but the center of gravity and the moments of inertia are generally much more challenging to determine using a test. Direct measurements to find the center of gravity require specialized equipment like centrifuges or pendulum methods (using multiple suspensions). Besides requiring expensive equipment, these methods may be time-consuming or impractical for complex structures.they may be time consuming, or impractical for complex structures.

Indirect methods use structural responses from which the inertia properties can be extracted. Among the developed methods, the Inertia Restrain Method (IRM) is known to be practical and relatively insensitive to measurement noise. The IRM uses the Frequency response Function (FRF) mass line values to compute the inertia properties as presented by many researchers. From these rigid-body responses, the structure's mass properties are directly obtained by solving a set of rigid-body equations of motion. The advantage of this method is that the procedure is non-iterative and inertia properties are obtained through a direct solution of two linear problems.

Other than the FRF, the only additional input data required by the RBPE are the position coordinates and directions of excitation and response DOF. An optional wireframe mesh may also be provided for visualization purposes.

Accurate estimation of the inertia properties of a structure, and from there the rigid body modes, is necessary as input for simulation models that are used for multibody dynamics and modal-based substructuring. For example, the design of heavy engine supports that void large displacements at low frequencies requires the knowledge of the inertia properties and rigid body modes. The prediction of the response of an assembly using modal-based substructuring requires a modal base that includes elastic modes as well as the rigid body modes.

Another application is found in the validation and updating of finite element models. The experimentally obtained mass, COG and MMI values can be used as reference responses for comparison with the values obtained from simulation models, and used as targets for updating the mass parameters of the model. This updating process can be done using only the inertia properties but they can also be combined with other targets like static displacement or resonant frequencies. See FEMtools Model Updating for more information on this application.

References:

M. Afzal, K. Saine, C. Paro, E. Dascotte, **Experimental Evaluation of
the Inertia Properties of Large Diesel Engines**. Presented at the
38th International Modal Analysis Conference (IMAC), February 2020, Houston,
Texas, USA.

Download (PDF, 1.0 MB)

### Orders-based Correlation and Model Updating

Validation and updating of models for dynamic simulation can be
done using different types of validation testing to obtain reference
fingerprint data. Classic modal testing and operational modal
analysis are popular techniques but may not be suitable for rotating
machinery.

A new innovative 2-step methodology was presented
by Dynamic Design Solution, in collaboration with an industry
partner, to update finite element models of rotating machinery
that are dynamically excited by their moving parts.

In a first step, the modal parameters of the structure are estimated from a simulation model, and updated using test order responses as references. These are obtained from order tracking after run-up/down vibration testing or at a number of constant rotation speeds. The simulated order responses are computed from the initial modal parameters, obtained from the finite element model, and the loads acting on the machinery, obtained for each order, from postprocessing specific engine performance prediction software. The identification of the true modal parameters involves correlation analysis between simulated and test order responses, and an optimization process that uses the modal parameters as updating parameter to minimize the difference between the simulated and test order responses. This methodology provides an alternative to direct modal extraction from order response functions .

The second step consists of updating the physical parameters of the simulation model using the updated modal base, obtained in the first step, as the target. This is a standard modal-based updating task that can be performed by FEMtools Model Updating.

More information can be found in following presentation:

E. Dascotte, **Orders-based Validating and Updating of Rotating Machinery FE Models**, Presentation at 41st International Modal Analysis
Conference (IMAC), February 2023, Austin, Texas, USA.

### Model Upgrading versus Model Updating

Before starting a finite element model updating task, there are two questions that must be answered:

- Is the model verified? This check is needed to ensure that no errors will be introduced to mistakes (for example units, material selection) and complies to the specifications imposed by the solver. It also checks if the intentions of the model are met by the selected elements and mesh density.
- Is the model fit for purpose in terms of geometrical fidelity and refinement? Because every model is based on assumptions and simplification to some extent, it is necessary to understand the purpose of the simulation and the requirements that model has to satisfy in order to have a reasonable chance to produce relevant results with target accuracy.

Only when these questions are answered positively, model updating should be attempted. This is the process of determining the degree to which a model is an accurate representation to the real world, again from the perspective of the intended use of the model. Probably the most important and also challenging task in this process is to select the updating parameters. Obviously, only the parameters that are present in the model can be selected. Therefore, if the model is missing elementss that are important for an accurate simulation, then there are no parameters associated to those elements. It may be possible to compensate for missing refinement by updating other parameters but this will reduce the usefullness of the simulation results because the loss of physical reality.

The term model upgrading was introduced in literature to identify the phase during which the model must be assessed for its capability to predict the behavior for the intended use. Maybe features are missing due to oversimplification of the geometry leading to incorrect estimation of physics (like how to simulate joints).

For example, consider the following scenario and situation cases: a simulation model must correctly simulate mode shapes between 100 Hz and 1000 Hz. Tests reveals the existence of 10 modes.

Case 1: If there are zero modes predicted in the target range then there is probably something seriously wrong with the model. Turn to verification and check, for example, the units used and their consistency.

Case 2: Only 5 lowest modes are predicted in the target range. Probably the model not suitable for simulating the higher modes and global mesh refinement is needed.

Case 3: Modes 1,2 4, 6, 8,9 are predicted. Probably some types of modes are missing like torsional modes which are constrained by the model. Model upgrading may be needed and local refinement introduced in the model. Model upgrading involves changing the meshing, whereas model updating will leave the mesh fixed and focus solely on the physical properties assigned to elements.

An in-between situation is geometry updating which uses techniques for shape optimization to adjust the modelled geometry to the true measured geometry. See this Tech Tip for more information on this subject.

### Using Digital Twins for Structural Health Monitoring

The concept of Digital Twins has been presented by many companies recently. However, it can mean different things for different people. The definition of interest for people with an interest in Structural Health Monitoring (SHM), is that a Digital Twin is a simulation model that represents the true physical product to a sufficient extent, considering its purpose, during the entire service life of the product. In this context, test data is used to validate and update a simulation model so that structural responses can be predicted with confidence, even at locations that will not be instrumented. The simulation makes use of real-world loading and supports, also obtained from testing.

Depending on the monitored structure, a simulation model can be created with mature traditional codes (like Ansys, Abaqus, Nastran,...) that have the advantage of being well known, robust, and used by many companies worldwide. Data interfaces and driver add-ons are available in software like FEMtools.

Alternatively, specialist simulation codes may be available that are better suited for specific purposes, for example for modelling and simulation of oil&gas offshore platforms. The advantage of such specialist codes is that they are well adapted to the simulation and decision-making tasks at hand (e.g. material models, joints, nonlinearity, wave and wind load models, fatigue analysis according to industry standards,...). For this purposes, the scripting capability in FEMtools facilitates the development of customer interfaces and drivers.

The Digital Twin is created by reducing uncertainty on the input parameters (geometry, materials, joints, loading,...) based on validation test data (see FEMtools Model Updating). Such testing may be based on sensor data like accelerometers for operational modal analysis, strain gauges at selected locations, displacement transducers (e.g. GPS receivers) complemented by measurements of environmental conditions (e.g. wind, temperature, wave height).

In such Digital Twin, the stress at any location of the platform can be obtained, even if
there is no strain gauge in that location, and this at any moment in time (if the deformation measurement data is stored 24/7). This technology
was demonstrated by DDS on projects like Hong Kong Stonecutters bridge and Oil platforms in North Sea
[1-2].
There are other researchers who have demonstrated and confirmed the validity of similar techniques
to estimate the peak stresses at locations where there is no possibility for direct strain measurements, like for example at a
wind turbine tower base and foundation. Once peak stresses are known, and loading
(past and future) can be estimated, then fatigue analysis is used to estimate residual life expectancy.

Less uncertainty on stress evaluations means that lower safety factors can be used to demonstrate that the residual lifetime is sufficient. For example if an uncertain (non-validated) simulation model is used and a safety factor of 5 is needed, then 100 years lifetime must be demonstrated with the model if the requested remaining lifetime is 20 years. With a more reliable Digital Twin (validated and updated model), the safety factor may be reduced to 3 and only 60 years residual lifetime must be demonstrated. This may result is less critical spots to inspect or reinforce and thus saving time and money. This way, aging structures that may otherwise have to be decommissioned can be kept in operation for a longer time while respecting the safety standards.

**Bottom line:** the combination of a validated simulation model and load data from testing, results in a complete Digital Twin that can be used to compute peak stresses
at joints, welds or other critical locations even if these are not directly instrumented. From
there, it is possible to estimate residual life, decide on the need for reinforcements and better plan on-site inspections.

FEMtools is the perfect tool for developing Digital Twins, thanks to its interfaces with FE and test data, its unique blend of database and
analysis tools, framework architecture and scripting capabilities.

References:

[1] E. Dascotte, J. Strobbe, U.
Tygesen, **Continuous Stress Monitoring of Large Structures**. Presented
at the 5th International Operational Modal Analysis Conference
(IOMAC), May 2013, Guimaraes, Portugal.

Download (PDF, 1.2 MB)

[2] E. Dascotte, **Vibration Monitoring
of the Hong Kong Stonecutters Bridge**. Presented at the 4th
International Conference on Experimental Vibration Analysis for
Civil Engineering Structures (EVACES 2011), October 3-5, Varenna,
Italy.

Download (PDF, 1.0 MB)

See also
the webinar recording of "**The Combined Use of
Simulation and Test Data: From Test Planning to Response Estimation**" at
https://www.femtools.com/news/index.htm#20180501

*Digital Twin model of Hong Kong Stonecutters Bridge and an
aerial photograph shown side-by-side. The Digital Twin shows realtime deformation
of the bridge and stress build-up using input from GPS receivers at tower tops and on
the bridge deck.*

### Exploratory Model Updating

A major challenge in FE model updating is to decide about which updating parameters to use. In those cases that the updating parameters are well identified, for example because they have not been validated before or simply because there is much uncertainty about their value, then model updating is mainly a matter of running the automated procedure to iteratively update the selected parameter values. Depending on the sensitivity values, the choice of starting values, and number of selected parameters, there can still be difficulties to obtain satisfactory correlation with test results. However, many diagnostics and settings are available in FEMtools Model Updating to overcome these difficulties.

Many times updating parameters cannot be well identified, and then *exploratory model updating* can help.
This involves selecting parameters at the element level ("local parameters") and
updating them as independent parameters. With many local parameters selected, updating
results are presented as a color-coded plot that highlights the areas of the
model that need large modifications. This may provide insight about the type of
modification that is needed in the model.

Parameters like elastic modulus, mass density or
plate thickness are very useful parameters for this purpose. In the case of
exploratory model updating they
must be interpreted as indicators for mass and stiffness changes that may relate to
physical element properties (like material properties or joint stiffness) or can be used to pinpoint issues
with mesh density or lack of detail in the
model. In this latter case, upgrading the model or refining the mesh may be a necessary
first step before returning to updating of physical element properties

Eventhough exploratory model updating does not entirely solves the issue of parameter selection, it is a very powerful tool to assist in decision making. It helps to filter out parameters that do not matter, and focus on areas and parameters that are most likely to be in need of updating. Sensitivity analysis can also be used for this purpose but requires that the sensitivity pattern for each response is examined and compared. This can be unpractical in case there are many parameters and responses to examine. Model updating will condense the results in a single plot per parameter type. For example, the figure below shows the local updating of elastic modulus in an engine block, needed to match the first 10 modes shapes with test results. This may be due to a local stiffness issue or could be related to the choice of mesh density in this area. Further investigation is required to decide about how to interpret this result and what to do next.

Exploratory model updating is a unique capability of FEMtools Model Updating. It includes the tools to automatically generate and handle local updating parameters, and the possibility to efficiently compute a potentially very large number of sensitivity coefficients. The parameter estimator that is used for iterative model updating is a special-purpose gradient-based optimizer that is able to handle the big sensitivity matrix and large number of parameters. There is no more practical reason to not consider exploratory model updating for preliminary investigation and learning about the model at hand.

*Exploratory model updating of an engine block model to match 10 mode shapes. The areas colored in red requires further investigation.*

### Full Field Modal Analysis using FEMtools MPE

Researchers at Technical University Vienna (Austria) and University of Bologna (Italy) have used FEMtools MPE to process massive amounts of vibration data collected with modern full field measurement technologies.

In the framework of the EU-sponsored TEFFMA project (Towards Experimental Full Field Modal Analysis, FP7-PEOPLE-2011-IEF-298543), a comparison is made by means of challenging optical technologies (SLDV, Hi-Speed DIC, Dynamic ESPI) on the same broad band vibration measurement problem of a lightweight plate, with different spatial resolution and quality of the measured patterns. For each measurement, an experimental modal model is extracted and finite element model updating results are compared between different full field technologies. The results expected from this research will strengthen the path of full field technologies in mechanical engineering and other fields, ranging from aerospace to vehicle technologies, electronic components, and advanced material behaviour analysis.

The following figure shows an example of such high-resolution mode shape. Full field measurements were taken at 49042 points resulting in FRFs at 1285 frequency lines and occupying several GB of disk space per experiment. All FRFs of an experiment could be imported in FEMtools and efficiently processed by the Modal Parameter Extractor (MPE) add-on for extraction of mode shapes.

*Plate mode shape at around 246 Hz obtained using FEMtools MPE, from FRFs measured by ESPI using a 226x217 measurement grid.*

For more information, see the following resources:

- A. Zanarini,
**Full Field Optical Measurements in Experimental Modal Analysis and Model Updating**, Journal of Sound and Vibration 442 (2019) 817-842. - A. Zanarini,
**Broad Frequency Band Full Field Measurements for Advanced Applications: Point-Wise Comparisons between Optical Technologies**, Mechanical Systems and Signal Processing 98 (2018) 968-999. - TEFFMA project webpage (http://cordis.europa.eu/project/rcn/103580_it.html)
- Tthe researcher's web page (http://www.diem.ing.unibo.it/personale/zanarini/Zanarini_ricerca_EN.htm)

See also:

FEMtools Modal Parameter Extractor (MPE)

### Scenario-Based Damage Identification

Damage has a direct impact on the modal parameters of structures. However, finding the location and severity of the damage from the modal parameters is a challenging task. This is because damage identification problems are in general highly undetermined, i.e. the number of potential damage locations is much higher than the size of the experimental data set.

In a paper written by DDS engineers [1], the concept of a damage scenario-based framework was presented that tries to overcome this problem by both increasing the size of the experimental data set and reducing the number of investigated damage locations. Using a carefully validated FE model of the undamaged structure, the effects of a number of damage scenarios are simulated. Eventually, the identification routine detects the fingerprints of the damage scenarios in the frequency pattern of the damaged structure.

The scenario-based damage identification framework has been evaluated and showed promising results. It appears to be possible to decompose the measured frequency pattern into the signatures of a series of pre-defined damage scenarios. The scenario-based approach seems to be capable of not only identifying the location of the damage but also the degree of damage. It is a realistic assumption that only a limited number of damage scenarios with high probability can be expected most mechanical and civil structures. This situation can be enforced by introducing weak spots in a built structure and monitoring damage on these spots only, thus introducing manufactured damage scenarios.

In a follow-on paper by a Hansen et al [2], the same concept was further investigated with a focus on the practical considerations which are crucial to the applicability of a given vibration-based damage assessment configuration. The technique is demonstrated on a laboratory test case using automated OMA. to simulate the practical situation of ice accretion on wind turbine blades. Ice accretion on the rotor blades of a wind turbine leads, among other things, to added loads, safety issues and diminished aerodynamic performance of the airfoil. This type of perturbation constitute an added mass and occurs frequently in northern regions. The presented technique could be implemented directly to localize and quantify ice accretion.

References:

[1] T. Lauwagie, E. Dascotte, **A Scenario-based Damage Identification
Framework**. Presented at the 30th International Modal Analysis
Conference (IMAC), February 2012, Jacksonville, Florida, USA.

Download (PDF, 0.85 MB)

[2] J.B Hansen, R. Brincker, M. Lopez- Aenlle, C.F. Overgaard, K. Kloborg, **A
New Scenario-based Approach to Damage Detection using Operational Modal
Parameter Estimates**. Mechanical Systems and Signal Processing 94 (2017)
359-373.

For more information, contact support@femtools.com

### FRF-Based vs. Modal-Based Model Updating

For the purpose of finite element model validation, any test data that is reliable and relevant can be used. Some people give preference to using raw, unprocessed test data. In the field of structural dynamics, it can be discussed if it is better to use FRFs (Frequency Response Functions defined as response spectra divided by input force spectra) or the mode shapes that can be extracted from these FRFs.

Mode shapes are a powerful mathematical tool to represent the dynamics of a structure. Although limited to linear behavior and best used with lightly, proportionally damped structures, they allow a condensation of the often massive amount of FRF data. Working with a condensed set of data is more practical for FE-Test correlation and helpful to gain understanding of the gap between FE simulation and the true structural behaviour through the examination of modes shapes and resonant frequencies. For solving the FE model updating problem, requiring to minimize an objective function that describes the distance between FE and test, it is common to use a gradient-based optimization approach. The definition of the updating problem in terms of response residues (differences between comparable FE and test structural responses), computation of the gradients, and optimized parameter estimation all benefit from using the relatively compact set of modal data compared to the FRFs. The benefit comes from the ease of use and data handling, and computation speed.

The use of FRFs would be mandatory in case target modal parameters are not available or cannot extracted from the FRFs with confidence. For example, when the structure exhibits high non-proportional damping, high modal density, or nonlinear behaviour. Another benefit of FRFs is that amplitude levels are sensitive to damping. In the modal approach, the extracted modal damping, which is known to be highly unreliable, can only be used as input for the FE analysis. From FE computional point, modal superposition is still the industry standard tool for simulating FRFs. One can therefore state that if analytical mode shapes are used for simulating the FRFs, then these are the raw data and should be used for validating the FE model. On the other hand, test FRFs represent the true response of a structure under given test conditions, and therefore they reflect the true non-linear nature and real physical damping of a structure. If it is the objective of validating and updating an FE model to incorporate those properties in the model, then one cannot do with mode shapes. Vice versa, if the FE model is intended to be a linear and simplified representation of the real world behavior, then using FRF-based updating may result in residual discrepancies between the simulation and test FRFs that cannot be overcome by updating, due to missing refinement and necessary physical parameters in the FE model.

In summary, when extraction of modal parameters from FRFs is not recommended, when analytical FRFs are computed using a direct method, or when the updating parameters include damping, then FRF-based updating should be seriously considered. In all other cases, the modal approach is preferred. If only experimental FRFs are supplied, then the FEMtools MPE tool can be used for modal parameter extraction.

*An example of FRF-based (left) and modal-based correlation and model
updating using FEMtools Model Updating.*

For more information:

E. Dascotte, J. Strobbe, **Updating Finite Element Models
using FRF Correlation Function****s**, Proceedings
of the 17th International Modal Analysis Conference (IMAC),
February 1999, Kissimmee, Florida.
Download (PDF, 98 KB)

FEMtools Modal Parameter Extractor (MPE)

FEMtools Model Updating

### Modal Extraction for the FE Analyst

Testing and simulation are traditionally done by separate teams. Test engineers will hand test results over to FE analysts who use them for the FE model validation and updating process. Test data has an important role in the validation process and serves as the reference, representing the true physical behaviour of the structure during the specifically designed validation test. Considering the important role of test data in the validation process, it is mandatory to adopt the highest standards with respect to equipment, operator training, data processing and reporting. The quality of the test result must be guaranteed in order to make subsequent use of it for decision making during model validation and updating. Double checking of the test data by an independent expert may be required as part of a quality assurance standard.

In case validation testing is based on experimental modal analysis, the FE analysts working on model validation will usually be provided with only the modal parameters (resonant frequencies, mode shapes, modal damping). The data must be accompanied by a detailed report on the test conditions and processing that was done. However, it is recommended to also provide the analysts with the raw test data and the software tools to double-check modal extraction done by the test team. This provides them an opportunity to gain additional insight in the response of the structure under test and for making informed decisions during the updating process.

*Modal analysis of a satellite structure using the global MPE applet.*

The FEMtools Modal Parameter Extractor (MPE) add-on tool is a high performance tool that can be used by FE analysts with only minimal training to obtain modal parameters from Frequency Response Functions or output-only time histories. The polyreference method that is used produces very clean stabilization charts and reduces the often subjective separation between physical and mathematical poles. Complemented by validation tools and a local curvefit method for data that is affected by mass loading, this add-on tool provides a fast and easy way to increase confidence in the modal parameters by double-checking. In case different results are obtained, the FE analyst has good reasons to inquire with the test team and demand their confirmation of results.

See also:

Automated Operational Modal Analysis

FEMtools Modal Parameter Extractor (MPE)

### Structural Health Monitoring of Piping Systems using Modal Analysis and Finite Element Model Updating

Safe operation, availability and lifetime assessment of piping are of utmost concern for plant operators. The knowledge on how failures in piping and its support construction are reflected in changes of the dynamic behavior is a useful basis for system identification and Structural Health Monitoring (SHM).

Modal analysis of complex piping, the identification of system changes and the use of vibration dampers in piping still constitute challenges. Researchers at the MPA University of Stuttgart in Germany used Operational Modal Analysis (OMA), finite element modelling and model updating to study changes in the natural frequencies and corresponding mode shapes due to through-wall cracks or changing boundary conditions.

One part of their study involved the design of a new type of tuned mass damper (TMD) that was first tested in the laboratory of MPA. Using detailed FE modelling, updated by OMA, provided the information necessary to adapt these TMD for efficiently cancelling the resonances in a piping system of a chemical plant.

In another part of their research, the influence of local wall thinning on the eigenfrequencies and mode shapes of a laboratory piping system was evaluated. Using sensitivity analysis and FE model updating it was found that rotational spring stiffness of the supports were important parameters for successful model updating. FEMtools was also used to sort a large number of local mode shapes which led towards the detection of a high order mode that showed a collapse-like motion at the exact position of the local wall thinning.

*Comparison of the higher order mode shape of two FE models, without
(left) and with (right) local wall thinning in the elbow. Eventhough the change
in eigenfrequency was very small, an 8% change in Modal Assurance Criterion
(MAC) was observed, which was significantly higher than all other mode shapes.*

The correlation between FE analysis and modal testing for this particular mode shape was demonstrated to be most sensitive for local wall thinning at the elbow, compared to other (lower order) mode shapes. This finding suggests that it might be possible to design a structural health monitoring device that is capable to detect mode shape changes such as this, for example by using a laser doppler vibrometer and automated scanning robots which make it possible to get experimental modal data at a resolution close to that of the FE-model. Used on a regular basis in an operational plant, such device can be a cost-efficient tool to prevent structural failure.

More information can be found in the following paper:

G. Hinz, K. Kerkhof, **System Identification and Reduction of Vibrations of Piping in Different Conditions**, Proceedings of the ASME 2013 Pressure Vessels &
Piping Division (PVP2013), July 2013, Paris, France.

### Multi-Model Updating

Multi-Model Updating (MMU) is simultaneous updating of multiple finite models that each correspond with a different structural configuration, but that share common updating parameters. If for each configuration modal test data is available, then MMU is used to combine the sensitivity information from every configuration and in this way increase the number of updating targets. This will lead to an improved condition for model updating compared to using only a single test.

For example, solar panels for satellites can be tested during different stages of deployment. A finite element model and modal test data can be obtained that correspond with each stage of deployment. This provides a richer set of test data to serve as reference for updating element properties that are common in all configurations. Such properties can be, for example, joint stiffness or material properties. Using only a single stage of deployment would not provide sufficient information to identify all properties. Another example is composite material identification using tests on plates and coupons with different geometries. This will introduce more mode shape types and possibly also redundant test data for improved identification of material properties.

FEMtools Model Updating includes an MMU automation tool that collects the FE and test data for each configuration and automates the process of sensitivity analysis, sensitivity matrix assembly, parameter updating, and FE re-analysis. This makes MMU a straightforward and easy to use process.

For more information, contact support@femtools.com

### Bottom-Up Versus Top-Down Approach for Model Validation and Updating

Validating and updating a finite element model in a bottom-up procedure is in general more rewarding than a top down approach. The bottom-up approach naturally follows the validation pyramid with coupon and component testing a the base, building up to sub-assemblies and finally to full assemblies at the top. At each level the complexity is increased and joints are added. For updating purposes, this means that the updating parameters for each model to be validated are limited to the uncertain parameters introduced at the level under study. Components that have been validated previously can be frozen as superelements and added to an assembly at a higher level. In a top-down approach, the selection of relevant updating parameters would be a serious challenge given the large number of potential parameters in an assembly. It is also more difficult to conduct validation experiments if the assembly is a large structure, and in a top-down approach these would be the only validation experiments.

The bottom-up approach to model validation and updating is supported in a natural way by the dynamic substructuring methods that are available in FEMtools. Using substructuring, the different components that constitute an assembly are modeled, tested and updated separately. Updated components are frozen as Craig-Bampton superelements. Repeated tests at different phases of the assembly allow focusing on the modeling of joints. Component modes synthesis is used to obtain the responses of the assembly.

For more information, contact support@femtools.com

### Automated Operational Modal Analysis

A vibration monitoring system, combined with a structural health evaluation system, enhances safety by allowing better planning of inspections and maintenance work. Such a system may include an Operational Modal Analysis (OMA) tool to extract mode shape from acceleration, velocity, displacement or strain time histories in situations that the dynamic loads are unknown. This is typically the case for large structures like for example bridges, offshore platforms, or aircraft.

If the modal extraction process is automated then the modal parameters (resonant frequency, mode shapes and modal damping) can be monitored 24/7 over long periods of time, ideally covering the entire operational lifetime of the structure. They can be used for applications like FE model updating and damage identification. If the deformation of the structure is also monitored, then modal parameters, in combination with an updated finite element mode, are also used for dynamic stress recovery at all locations of the structures as an alternative to strain gauges. These stress are in turn used for accumulated fatigue monitoring.

The FEMtools Modal Parameter Extractor (MPE) add-on tool can be used for OMA. A high performance poly-reference Least Squares Complex Frequency (pLSCF) method is used that produces very clean stabilization charts and therefore lends itself for automated modes extractions. The MPE add-on also provides Digital Signal Processing (DSP) tools such as decimation, filtering, detrending, selecting reference channels and computing cross-power spectra. The integration within the FEMtools Framework allow for automation and combination with all the other FEMtools modules like FE-test correlation, model updating, and optimization. The availability of an extended function library for data manipulation, graphics display, interfacing with SQL databases and many other tasks, position FEMtools as an ideal platform for custom development of structural health monitoring and evaluation systems. A case study is described in the following conference paper:

E. Dascotte, **Vibration Monitoring of the Hong Kong Stonecutters
Bridge**. Presented at the 4th International Conference on Experimental
Vibration Analysis for Civil Engineering Structures (EVACES 2011), October 3-5,
Varenna, Italy.

Download (PDF, 1.0 MB)

For more information, contact support@femtools.com

For other papers, click here

### Working with Abaqus Condensed Matrices

ABAQUS can condense stiffness and mass matrices at external nodes and enriched by Craig-Bampton component modes synthesis. This is equivalent to the use of superelements in FEMtools and other finite element programs.

FEMtools 3.5.2 comes with a new interface to import
superelement matrices condensed with ABAQUS.

The superelement reduction can be used to speed-up pretest analysis, dynamic analysis, correlation analysis on large assemblies and even model updating of the residual part of the FE model. Using a wireframe connection between the external nodes, FEMtools allows the visualization of mode shapes using a ?test model? look and feel.

For more information, contact support@femtools.com

### Geometry Updating

The concept of geometry updating was explored in a recent study of the cast iron lantern housing of a gear box. The resonant frequencies and mode shapes of the test structure were measured using impact testing. Next, a set of digital pictures were taken from a number of different angles. By means of photogrammetry, these pictures were converted into a surface model that represented the actual geometry of the lantern housing. This surface model was then compared with an FE-model derived from a CAD-model of the lantern housing. In this way, the regions where there was a substantial difference between the actual geometry and CAD-model could be identified. Finally, the geometry of the FE-model was corrected based on the measured geometry using a mesh morphing technique. For the considered test case, the correction of the geometry provided a significant improvement of the quality of FEM-test correlation of the modal parameters.

The project demonstrated that only a limited number of geometry measurements are needed to update a CAD-based geometry using mesh morphing techniques. With geometry updating it is possible to eliminate most of the uncertainty on the geometry. As such, geometry updating eliminates, or at least reduces, the need for equivalent parameter changes to compensate the effects of geometrical inaccuracies. As the updating process provides parameter changes that are physically more relevant, the application range in which the updated FE-model can be used as a reliable predictive tool for design optimization can be increased.

Improving the accuracy of the FE model to predict a larger number of mode shapes covering a wider frequency range, increases chances to detect damages or manufacturing issues by monitoring the modal parameters. Combined with automated testing and metrology, this opens up the perspective of a modal-based quality inspection tool.

Two technical papers on this subject were presented at the international conferences and are now available for download from the FEMtools website:

T. Lauwagie, E. Dascotte,** Geometry-based Updating of 3D Solid Finite Element Models. ** Presented at the 29th International Modal Analysis Conference (IMAC), February
2011, Jacksonville, Florida, USA.

Download (PDF, 1.0 MB)

T. Lauwagie, F. Van Hollebeke, B. Pluymers, R. Zegels, P. Verschueren, E. Dascotte,
**The Impact of High-Fidelity Model Geometry on Test-Analysis Correlation and FE Model Updating Results. ** Presented at the International Seminar on
Modal Analysis 2010 (ISMA), September 20-22, 2010, Leuven, Belgium.

Download (PDF, 0.75 MB)

### ODS-Based Model Updating

Finite element model updating is a well established method for validating and improving simulation models in structural dynamics. The traditional approach consists of correlating simulation data with the results of an experimental modal analysis (EMA). Natural frequencies and mode shapes extracted from frequency response functions are preferred as references since they are independent of the applied loads.

However, the operational loads or boundary conditions can change the dynamic behavior of a structure, or make it impossible to perform an experimental modal analysis with measured or controllable dynamic loading. In such cases, only operational data can be used as reference data for model updating. Additionally, updating a model using operational data automatically guaranties the validity of the model under the considered operational conditions.

DDS recently introduced a new method in FEMtools for model updating based on Operational Deflection Shapes (ODS) that is able to update the mass, stiffness and damping properties of a structure simultaneously. A technical paper describing the method is available for download:

T. Lauwagie, J. Guggenberger, J. Strobbe, E. Dascotte, **Model Updating
using Operational Data. ** Presented at the International Seminar on Modal
Analysis 2010 (ISMA), September 20-22, 2010, Leuven, Belgium.

Download (PDF, 1.0 MB)

More technical papers on different subjects can be found here

### Mapping Laser Scanning Measurements on a FE Mesh

Laser vibrometry or electronic holography can be used to obtain vibration modes which in turn can be correlated with finite element results. Each experimental mode shape will typically be presented as a dense cloud of scanning points with each point moving in the direction of the laser or camera. Analyzing the correlation of these vibration modes with a finite element model poses some specific problems with respect to mapping the scanned surface onto FE model, identifying and extracting the corresponding translation degrees of freedom, averaging for measurement noise and computing numerical correlation criteria.

DDS has recently developed a custom solution for postprocessing a set of data files containing measured vibration modes with an ANSYS finite element model of a turbine blade. Written in FEMtools Script, this solution automates the entire work flow and reporting of results. It can be integrated into the FEMtools menus or operated in batch mode for processing large quantities of data or as part of an integrated quality inspection system.

For more information, contact support@femtools.com

### Estimating Rigid Body Properties from FRF Measurements: A New FEMtools Add-On Tool

Dynamic Design Solutions announces the upcoming release of *FEMtools Rigid
Body Properties Extractor*, a new tool to obtain the mass (M), center of
gravity (CoG) and mass moments of inertia (MoI) from the low-frequency
portion of measured accelerances (FRFs). These properties are useful to serve as
targets references in updating the finite element model of the tested structure,
or to reduce components to lumped masses for model reduction in structural
dynamics simulations or motion analysis.

Obtaining the rigid body properties is done in 2 steps. First, the rigid body responses (called "mass lines") must be extracted from the FRFs. The mass line corresponds to the value of the flat part of the response located between the low-frequency suspension modes and the elastic modes. These values are obtained by using a least squares fit of a low order polynomial (e.g. quadratic approximation). Once the mass line values are known, then the rigid body mass properties are obtained in the second step by solving a set of algebraic equations.

Experimental data are imported from a Universal File (UF) or other. The FRFs must satisfy some requirements with respect to the measurement configuration (acceleration/force obtained from a freely suspended structure), and the number and positioning of excitation and response locations. If these conditions can be satisfied, then the proposed method presents a low-cost and fast alternative to traditional pendulum techniques.

*FEMtools Rigid Body Properties Extractor Control Panel (click to enlarge). *

The FEMtools Rigid Body Properties Extractor comes as an add-on to any FEMtools configuration. It is an interactive tool that allows the user to display the FRFs, define a frequency band between the suspension modes and elastic modes, and analyze the mass line values. An inertia box visualizes the equivalent mass volume with animation of rigid body modes. The rigid body properties (M, CoG and MoI) are displayed in real-time using tabular format with several error estimates. They can be exported for use in other programs or be used as updating targets in FEMtools Model Updating.

This new exciting add-on is now available for beta evaluation. For more information and to request an evaluation copy, contact info@femtools.com

### Ogden Material Identification using FEMtools Optimization

The Ogden material model is frequently used in finite element programs to simulate the behavior of non-linear elastomers. The values of the material parameters of the Ogden model are highly material dependent. The main challenge in using the Ogden model in finite element simulations, is to find reliable estimates for the values of the Ogden material parameters. The relation between an imposed displacement and the resulting reaction force can be used to identify these material parameters using a mixed numerical-experimental approach. In this approach, the objective is to fit the simulated reaction force curve onto the measured reaction force curve. The computationally most efficient way of doing that is by using a gradient-based optimization strategy.

Such identification routine was implemented using FEMtools Script for the process identification part, FEMtools Optimization for the optimizer routines, and used MSC.Marc to compute the reaction force curves.

More information can be found in the following application note:

**Identification of Ogden Material Parameters using FEMtools**, Download (PDF, 433 KB)

### Finding Optimal Master DOF for Guyan Reduction with FEMtools Pretest Analysis Tools

The pretest analysis tools in FEMtools Correlation are primarily used to find the optimal number and location of transducers for modal testing. One of the methods that are available is the Iterative Guyan Reduction (IGR) method, which is an elimination method to optimize sensors using the modal cross-orthogonality as selection criterion. The method can as well be used for selecting master DOF for Guyan reduction. In an FEA-only context, there are no constraints on the number of master DOFs and their accessibility because they will not serve as test locations. Furthermore, master DOF can include rotational DOF.

Using the IGR tool in FEMtools is a fast and efficient way to select master DOFs for structural components that will be reduced using Guyan reduction.

For more information on this application, contact info@femtools.com