An Assessment of Spacecraft Target Mode Selection Methods

J.F. Mercera,I,*, Prof G.S. Agliettia,II, Dr M. Remediaa,III, A. Kileyb,IV

aSurrey Space Centre, University of Surrey, Guildford, Surrey, UK, GU2 7XH*Corresponding author Ij.mercer@surrey.ac.uk, IIg.aglietti@surrey.ac.uk, IIIm.remedia@surrey.ac.uk

bAirbus Defence and Space, Gunnels Wood Rd, Stevenage, UK, SG1 2AS, IVandy.kiley@airbus.com

AbstractCoupled Loads Analyses (CLAs), using finite element models (FEMs) of the spacecraft and launch vehicle to simulate critical flight events, are performed in order to determine the dynamic loadings that will be experienced by spacecraft during launch. A validation process is carried out on the spacecraft FEM beforehand to ensure that the dynamics of the analytical model sufficiently represent the behavior of the physical hardware. One aspect of concern is the containment of the FEM correlation and update effort to focus on the vibration modes which are most likely to be excited under test and CLA conditions. This study therefore provides new insight into the prioritization of spacecraft FEM modes for correlation to base-shake vibration test data. The work involved example application to large, unique, scientific spacecraft, with modern FEMs comprising over a million degrees of freedom. This comprehensive investigation explores: the modes inherently important to the spacecraft structures, irrespective of excitation; the particular ‘critical modes’ which produce peak responses to CLA level excitation; an assessment of several traditional target mode selection methods in terms of ability to predict these ‘critical modes’; and an indication of the level of correlation these FEM modes achieve compared to corresponding test data. Findings indicate that, although the traditional methods of target mode selection have merit and are able to identify many of the modes of significance to the spacecraft, there are ‘critical modes’ which may be missed by conventional application of these methods. The use of different thresholds to select potential target modes from these parameters would enable identification of many of these missed modes. Ultimately, some consideration of the expected excitations is required to predict all modes likely to contribute to the response of the spacecraft in operation.

KeywordsTarget mode selection, Coupled loads analysis, modal analysis, finite element analysis.

Acronyms and AbbreviationsADM Atmospheric Dynamics MissionCLA Coupled Loads Analysis COC Cross-Orthogonality CheckDOF Degree of freedomECSS European Cooperation for Space StandardisationESI Equivalent Sine Input

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FEA Finite Element AnalysisFEM Finite Element ModelFRAC Frequency Reponses Assurance CriteriaFRF Frequency Response FunctionJAXA Japan Aerospace Exploration AgencyKEF Kinetic Energy FractionsMAC Modal Assurance CriteriaMKE Modal Kinetic EnergyMP Modal ParticipationMPP Measurement Point PlanNASA National Aeronautics and Space AdministrationRSS Root-Sum-SquareSEF Strain Energy FractionsSEREP System Equivalent Reduction Expansion ProcessSRB Solid Rocket Booster SRS Shock Response SpectrumTAM Test Analysis Model

1 IntroductionThis work explores the issue of identifying the vibration modes which should be considered as potential targets to correlate in spacecraft finite element model (FEM) validation activities. The studies presented herein aim to clarify the extent to which the modes of significance are inherent to the particular spacecraft structure or are dependent on the excitation being applied and coupling with the launch vehicle. Additionally, several traditional methods for target mode selection have been assessed based on ability to identify those modes which contribute most to the peak displacement and acceleration responses in the structure under loading which replicates typical qualification testing scenarios. Finally, comparisons are made to test data in order to highlight the potential to improve correlation of local modes in the structure through more focused correlation effort resulting from improved critical mode identification.

Having good correlation practices, such as target mode selection, is particularly crucial for spacecraft applications as it is not possible to conduct physical testing which truly represents the operational conditions, meaning that there is heavy reliance on the FEM to accurately simulate the spacecraft dynamic response to critical loading scenarios. In order to determine the loading levels and dynamic responses arising from significant flight events, Coupled Loads Analyses (CLAs) are carried out which couple a mathematical model of the spacecraft with a model, often multiple models for different load cases, of the launch vehicle. The spacecraft FEM is first evaluated against data gathered from vibration tests to ensure that it correctly reproduces the dynamic responses characteristic of the actual spacecraft hardware. Subsequently, a considerable amount of time and effort may be spent on FEM correlation and update; however, it is not uncommon for the final FEM to display minimal improvement over the original. As such, there is a need to ensure that correlation metrics and targets are physically meaningful, and that the procedures applied are as effective and efficient as possible.

There are many different approaches which may be applied to the issue of spacecraft FEM-test correlation. One common approach involves the correlation through modal analysis and the application of Modal Assurance Criteria (MAC) [1] and Cross-Orthogonality Checks (COC) [2]. With this approach, FEM normal mode shapes from eigen-analyses are evaluated against

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corresponding experimental mode shapes extracted from frequency response functions (FRFs) captured during vibration tests. For large, intricate structures, such as scientific spacecraft, the modes within the frequency range of interest are typically too numerous for all modes to be dealt with in-depth during correlation and update. This requires the application of target mode selection methods to identify modes to prioritize in correlation and update activities.

Another approach is the direct comparison of test and analysis results obtained in the frequency domain; such as using the Frequency Response Assurance Criteria (FRAC) [3]. FRF based methods have the advantage that the FRFs from the test can be used directly in the correlation, without requiring the extraction of modal parameters and identification of target modes [4]. This is a benefit in that it not only circumvents the effort required to extract the modal parameters, but also avoids the uncertainty introduced to the test data as a potential consequence of modal parameter estimation issues. Conversely, it should be noted that there are also drawbacks to the frequency based approach. For example, while FRF based comparisons may somewhat negate the issue of target mode selection, more care must be taken in deciding which responses are considered most critical, as testing can include hundreds of accelerometers therefore generating a large amount of data to use as potential correlation targets. Additionally, in normal modal analysis, damping may be neglected, whereas when comparing responses in the frequency domain it is necessary to introduce a damping model to the FEM [5]. The inclusion of damping is an added level of complexity and uncertainty not present in purely modal comparisons. Consequently, modal based correlation is a common approach and is mandated by the European Cooperation for Space Standardisation (ECSS) modal survey assessment [6] and corresponding NASA documentation [7]. Due to the frequent application of modal techniques, the results of modal correlation checks are arguably more widely understood and values indicating good correlation are well established. The required level of correlation in terms of FRF based methods on the other hand is currently less clear [8]. As such, modal correlation remains an industry standard, making target mode selection a topic of continued relevance.

Over the years, not only has the intricacy of spacecraft structures increased, but the analytical representation of the structure in the FEM has become more detailed and meshes more refined. With ever increasing numbers of degrees of freedom, the numbers of modes represented in these models are also increasing. In many cases, there is also a high modal density within the frequency range of interest. Additionally, the increased complexity of FEMs raises the number of parameters which have potential to become variables during FEM update. As such, more than ever, an emphasis on containment of the problem, and focus on the most important aspects, is crucial to effective correlation activities. Thus there is a need: to assess whether traditional methods, even with considerable heritage, are still suitable with respect to state-of-the-art applications; to ensure that these methods are being implemented appropriately; and to consider newer alternative approaches which present potential benefits.

This study has therefore been conducted in order to: determine the extent to which the structure itself dictates the modes of significance, versus the influence of the applied excitation; to assess several commonly applied methods used to select target modes for correlation; and to explore potential for improvement in the levels of correlation of these critical modes to test data. Primarily, modal characterization from normal modes analysis is to be evaluated against an alternative measure of mode significance which accounts for excitation levels derived from CLA loading scenarios [9]. This provides a means to assess the ability of the more standard

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target mode selection criteria to identify the modes which are ultimately the most significant to the spacecraft during qualification testing, and eventually in launch/flight.

Among the most commonly used target mode selection criteria is modal effective mass [10]. It is referenced as an indicator of mode importance in both the ECSS Modal Survey Assessment documents [6] and corresponding NASA documentation [7]. Modal effective mass is a measure which is used to identify modes typically associated with notable loads through the base of the spacecraft, and which are therefore expected to have an influence in the interaction with the launch vehicle during the CLA. These modes are therefore often considered as the most important to correlate as they contribute not only to responses within the spacecraft, but also to the dynamics of the coupled system when mounted in the launch vehicle. Nevertheless, modes with relatively low effective mass may also be extremely significant in terms of excitation of the equipment on the spacecraft itself. Local modes, only affecting particular components or sub-systems in the structure, can have serious consequences for the operation of the spacecraft and its ability to successfully complete its mission. Identifying locally, as well as globally, significant modes is therefore a key consideration when developing target mode selection procedures. [11, 12]

Parameters which are able to highlight modes demonstrating prominent dynamic activity in a particular region of the structure must therefore also be examined. A common method to identify these local modes is the examination of energy fractions. For each mode, the energy fractions are essentially an indication of the amount of energy of the total system which is contained in any given component/sub-system. This can take the form of kinetic energy or strain energy fractions (KEF and SEF, respectively). These energy fractions are often calculated in order to identify local modes ,which may be missed by modal effective mass identification due to their minimal impact on the response of the overall load levels [11], but which are nonetheless critical when attempting to ensure the successful operation of the spacecraft. As such, Chung and Sernaker [11] proposed that both the modal effective mass and the energy fractions should be considered in conjunction in order to include both global and local modes of note as targets.

It is important to note that there has been no consideration of excitation/loading scenarios in the aforementioned target mode selection methods, which typically utilize values calculated directly from normal modes analysis. Mode participation (MP) analysis [12], sometimes referred to as mode contribution analysis [13], is a means of quantifying the relative importance of modes, in the considered frequency range, for given excitations [14]. MP analysis therefore provides means to determine which modes are most significant with respect to the final loading conditions the structure is expected to encounter. The CLAs of various flight events are the most relevant dynamic loading scenarios to examine when considering spacecraft applications. Barnett et al [15] therefore drew the conclusion that the MP analysis of responses to CLA input levels would be an appropriate method to determine ‘critical modes’ of the spacecraft structure. The work presented herein aims to explore this more fully, for multiple modern spacecraft, and draw comparisons between MP analysis and multiple traditional target mode selection methods.

In practice, it is typical for testing and target mode selection for correlation to take place before any CLA has been conducted for the spacecraft in question. An objective of this study is therefore to improve the selection of target modes for future spacecraft FEM correlation by using information available for spacecraft which have already been subjected to CLA. As the investigations presented herein focus on spacecraft for which some CLAs have already been

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conducted, the excitation and damping levels used in these CLAs are known. The use of MP analysis here is to apply this knowledge to establish the most ‘critical’ modes under CLA level excitation. This provides a set of significant ‘target’ modes. Comparisons are then made between these ‘target’ modes and those prioritized by the more conventional mode selection methods, not requiring prior knowledge of the CLA (as this may not be available in practical target mode selection scenarios). As a result, an examination is presented of the ability of different traditional methods to select these modes, which are most likely to contribute significantly to the spacecraft dynamic response in qualification testing and CLA. Thereafter, a brief comparison is made between the selected target FEM modes and mode shape data extracted from vibration tests of the corresponding spacecraft. This allows some insight into possible correlation levels for the modes identified as significant, emphasizing any poor correlation which highlights the need to identify these critical modes for focused update effort.

The following sections briefly provide some of the theory behind the target mode selection methods included in this investigation, followed by a description of the analyses conducted. The results are then presented fully for one spacecraft, and discussed with reference made to noteworthy similarities and differences to the second example spacecraft used in the study (the full results of which are presented in the appendix), before final conclusions are drawn.

2 TheoryThe spacecraft correlation and update process exists to ensure that the FEM and test dynamic responses match adequately for subsequent use of the FEM in the CLA to be reliable. To conduct FEM-test correlation in the modal domain, it is necessary to select the target modes of interest which are to be the priority when allocating resources to the correlation and update efforts. These target modes should therefore be those which are most likely to be significant to the structural dynamics and should support the flight ‘certification’ process.

2.1 Spacecraft Experimental Modal AnalysisAssuming appropriate thermal control and design, spacecraft such as those considered herein will typically encounter the most severe structural loading during launch. Vibration experiments are conducted at different stages in the spacecraft development process to both: provide data for the correlation of the FEM to be used in CLAs; and to test that the structure is able to withstand excitations enveloping the predicted launch levels. Large spacecraft, such as those examined in this study, will eventually be mounted vertically in the launch vehicle and constrained at the base. An effort is therefore made to replicate these conditions in the test setup and to use this ‘fixed base’ (sine) test as a commercial compromise to dynamically correlate the FEM. An adaptor is used to attach the spacecraft to the electrodynamic shaker, allowing the excitations to be applied through the base of the structure in a similar manner to the transmission of loads at the spacecraft-launcher interface during launch. A sinusoidal input excitation is applied to the structure, gradually sweeping through the frequency range of interest (usually ≈5-100Hz). The sine sweep is implemented on a single axis at a time, and is typically performed separately in the lateral directions, as well as along the longitudinal direction. Throughout these tests, typically a few hundred accelerometers capture the response throughout the structure, while force measurement devices monitor the loads, particularly at the shaker/adapter interface. [16]

While this study considers FEMs secured rigidly at the base, with perfect sinusoidal excitation, it should be noted that this approach has drawbacks when comparing to the actual test data,

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where there are inevitable flexibilities and imperfections. As such the use of virtual testing (mathematical models simulating the shaker control system and dynamics, as well as the actual spacecraft structure) , to more accurately represent the test set-up and excitation of the physical hardware in the FEM, is a current area of some research focus for spacecraft applications such as those considered herein. [17, 18]

Fig.1. Electromagnetic exciters on the multi-shaker during BepiColombo lateral base shake test [19]

2.2 Modal Correlation MetricsTwo of the most commonly applied modal metrics used to compare FEM and test dynamics are the modal assurance criteria, most commonly referred to as MAC, and the use of orthogonality checks.

With the MAC, the test mode shapes and FEM eigenvectors are compared directly, using the FEM degrees of freedom (DOFs) corresponding to the test accelerometer measurement points plan (MPP). The experimental and analytical mode shapes are given here by ψ and Φ respectively:

MAC=(ψT ϕ)2

(ψTψ )∙ (ϕT ϕ ) (1)

Once the MAC has been performed for a given mode pair, a value between 0 and 1 is obtained which indicates how closely matched the vectors are, with a perfect match yielding a value of 1. It is generally considered, and indicated in ECSS-E-ST-32-11C [6], that target modes achieving a MAC of at least 0.9 indicates a good correlation and is the minimum required value for the fundamental lateral bending modes of a spacecraft. It is, however, also clear from ECSS-E-ST-32-11C [6] that the required degree of correlation is dependent on the perceived relative importance of the mode under consideration.

The COC is also an ECSS [6] and NASA [7] required check, and works similarly to MAC, but with the reduced mass matrix (MTAM) employed to weight the relative importance of the DOFs being considered. This approach takes advantage of the orthogonal relationship between normal modes and the system mass matrix.

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COC=(ψT M TAM ϕ)

√(ψT M TAMψ )√(ϕT MTAM ϕ ) (2)

An ideal result of perfectly matched mode shapes, which are orthogonal to the mass matrix, will yield a diagonal matrix, and for mass normalized modes this becomes an identity matrix. Again, in ECSS-E-ST-32-11C [6] it is specified that off-diagonal values <0.1 and leading diagonal terms >0.9 are deemed to indicate a good correlation, but specific target values are a function of the perceived significance of each mode.

It should be noted that although several different methods [20-25] exist for performing the reduction to obtain MTAM, the System Equivalent Reduction Expansion Process (SEREP) [24] has been shown [26-29] to be suitable for its ability to provide an accurate representation of structures such as the spacecraft considered in this study .

In order to carry out these modal checks, it is therefore necessary to prioritize modes and select appropriate correlation targets reflecting the perceived relative importance of the modes in question.

Correlation of the natural frequency of the modes of interest is assessed separately to the correlation of the mode shape vectors (which are correlated based on MAC and COC values as described previously). The natural/eigen- frequency correlation metric typically applied is the frequency difference method. This quantifies the percentage difference between the FEM and test modal frequencies. In ECSS-E-ST-32-11C [6] it is stated that a frequency difference between 3-10% may be acceptable depending on the relative perceived significance of the mode in question. Fundamental bending modes require ≤3% frequency difference whereas for other modes of interest, with modal effective mass <10%, a frequency difference of anything ≤10% may be considered acceptable.

Most target mode selection methods relate to modal parameters but are otherwise independent of the mode frequency (i.e. a mode may be selected as a target, based on parameters such as modal effective mass, regardless of the natural frequency of the mode). When the ultimate excitation to be applied to the structure is considered as part of the target mode selection process, such as with the CLA level inputs applied in this study, the frequency of excitation becomes more significant. A mode occurring at a frequency associated with high excitation will be deemed more critical than modes at frequencies not likely to be excited. As such, good correlation with respect to frequency is more important than for typical methods. One means to address this is to apply a frequency shift to the excitation, in a similar manner as is applied in frequency domain correlation techniques such as the Frequency Domain Assurance Criteria, commonly known as FRAC. For example, peaks in excitation level could be applied to span +/- 15% of their predicted frequency, thus providing an envelope to excite modes which may occur at a frequency slightly removed from their true natural frequency; the more exact excitation profile could be applied later in the correlation process once the frequency errors were known and reduced.

2.3 Coupled Loads AnalysesCLAs are employed to determine the loads (internal forces, displacements and accelerations) that the spacecraft will experience through interaction with the launch vehicle, by coupling FEMs of the spacecraft and launcher and performing analyses on the combined system. CLAs are vital to predict the loads the spacecraft will be subjected to by the launch vehicle throughout

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the various critical flight events. Subsequently, this information can be used to ensure that the spacecraft design is such that it will withstand the predicted mechanical environment and be capable of carrying out its mission. [16]

2.3.1. Flight EventsThe 5 main flight events typically of concern for Ariane 5 are: Solid Rocket Booster (SRB) ignition/Lift-off, Transonic, SRB 3rd acoustic mode, SRB end of flight and SRB jettisoning [30]. Similarly for the Vega launcher, some of the key flight events include: Lift-off phase, Flight with maximum dynamic pressure, 1st stage flight with maximal acceleration and tail off, 2nd stage ignition and flight, 3rd stage ignition, 3rd stage maximal acceleration and Attitude & Vernier Upper Module flight [31]. For each of the flight events it is necessary to perform multiple CLA load cases and often even sub-load cases to capture the entire spectrum of loading which could be experienced by the spacecraft-launch vehicle system.

2.3.2. Equivalent Sine InputIn physical testing of large spacecraft, it is not generally feasible to exactly replicate the transient inputs of the CLA (especially with multi DOF based excitation), as such the equivalent sine input (ESI) is typically used to aid in informing minimum excitation levels in a sine test when notching of the input spectrum is performed. The ESI is a means of applying a frequency dependent sinusoidal base excitation which envelopes the loading during the key CLA flight events. Despite its limitations, such as the application separately in each translational axis direction, rather than more representative 6-DOF transient, ESI is nevertheless commonly accepted practice for such applications. [16]

Typically shock response spectra (SRS) are generated from the CLA interface base motion accelerations for different values of damping factor Q. The actual ESI envelope is then calculated from the SRS using the following equation:

ESI= SRS√Q2+1

→ SRSQ

(asQ≫1) (3)

Where the Q factor is related to the modal damping coefficient, , by the following relation:ζ

Q= 12 ζ (4)

In practical spacecraft vibration verification testing, a pre-defined excitation spectrum is generally defined by the launch authority (e.g. [30, 31]). In many instances, notching may be applied to reduce the magnitude of excitation at particular frequencies in order to prevent overly severe and unrepresentative loading. Over testing is a potential issue due to the difference in boundary conditions between fixed base test and the reality where the spacecraft is coupled to a flexible launch vehicle. In such cases, the ESI from the CLA may be used to inform appropriate notched excitation levels. [16]

2.4 Analytical Identification of Significant ModesThe following sub-sections give details of the various different target mode selection methods which have been applied to the spacecraft FEMs in this study. These include methods intended to identify both local and global modes of significance from modal analysis, as well as methods to determine which modes contribute most towards the peak responses of the structures when subjected to base shake excitations.

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2.4.1. Modal Effective MassThe modal effective mass, Meff, provides an indication of the contribution of each vibration mode, i, towards the resulting loads in the structure when subjected to base excitation [32]. It can be evaluated from the following [33]:

M eff i=εi2mii (5)

Where mii is the element of the generalized mass matrix and is a scaling factor such that the εrigid body mass of the structure may be given as:

M r=εTmii ε (6)

The summation of modal effective masses across all modes is equal to the rigid body mass. The Meff values for each mode are therefore typically expressed in the form of a fraction or percentage of the structure rigid body properties in each axes direction (3 translational and 3 rotational). Besides its use as a target mode indicator, the modal effective masses can also be employed as an additional correlation criterion, as the Meff values for modes from the FEM may be compared to those measured from the corresponding test data. [32]

2.4.2. Kinetic and Strain Energy FractionsThe SEF and KEF may be computed by means of the equations [33]:

SE=12

( {ϕ }T [K ] {ϕ }) (7)

KE=12

( {ϕ }T [M ] {ϕ }) (8)

SEF=SEc

SEs (9)

KEF=KEc

KE s (10)

where is the modal eigenvector; K and M represent the stiffness and mass matrices; while Φsubscripts c and s signify the component or full system respectively. Hence, for the modes considered, SEF and KEF quantify the distribution of energy within the structure. Modes with a sizeable fraction of energy confined to a single vital component or substructure should be considered as potentially meriting inclusion on the list of modes to be prioritized for in-depth correlation and update of the FEM.

It has been suggested, such as by Chung and Sernaker [11], that, in order to identify all significant global and local modes, both the modal effective mass and the energy fractions should be considered concurrently.

2.4.3. Mode Kinetic Energy by Generalized MassWhile for spacecraft the modal effective mass and kinetic energy fractions are possibly the most widely used target mode selection methods, alternative techniques have been proposed. One such approach is to use a measure of the overall mode kinetic energy (MKE) to rank modes [34]. This assessment of MKE can be achieved through calculation of the generalized mass of modes.

MKEi=mii=diag [ϕT Mϕ ] (11)

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M denotes the full system mass matrix and Φ is the matrix of modes. It should be noted that for the results to be meaningful the modes are scaled/normalized with respect to the maximum displacement in the mode shape displacement vector.

Bedrossian et al [34] found this approach to be effective in identifying the modes of interest in an investigation of the experimental X-33 rocket plane vehicle. However, while that study was conducted under free-free conditions, this work is concerned with fixed-base modes which better represent the test and flight conditions of the spacecraft under consideration.

2.4.4. Root-Sum-Square Displacement MethodThe root-sum-square (RSS) displacement method, as introduced by Hidalgo [35], is an approach to target mode selection based on assessing the mode shape displacement magnitudes, summed across the DOFs of interest. In this case the modal displacements at the test MPP DOFs have been considered, meaning the RSS for each mode (i) becomes:

RSS Resultant Valuei=∑n=1

MPP

[ϕx2+ϕ y

2+ϕz2]1 /2 (12)

It is important to note that, as for MKE, it has been suggested [34] that this method be applied using mode shape vectors scaled for values of unity in the maximum displacement.

In a study of target mode selection, Bedrossian et al [34] concluded that the use of the RSS displacement method in conjunction with modal kinetic energy by generalized mass was the ideal combination. The investigations found that generalized mass was extremely effective at identifying target modes, but would also result in the inclusion of ultimately “un-interesting” modes. It was concluded that RSS was an appropriate method of filtering out these extra modes. On the other hand, it is possible with RSS that important modes could be missed if the locations being excited have not been sufficiently captured by the considered measurement points. The parallel consideration of the generalized mass method provides a safeguard against the possibility of such modes being discarded imprudently, as could be the unintentional consequence of selection on the basis of RSS alone.

2.4.5. Modal Participation FractionsIt is important to note that all of the afore-described target mode selection methods are based on parameters which may be calculated directly from normal modes analysis of the structure. With these approaches, no consideration is given to the excitation the structure will ultimately encounter. The excitation is often unknown at the time of correlation, such as for spacecraft FEMs which have not yet undergone CLA, and so these methods are still necessary. It has nevertheless been noted that a more comprehensive indication of mode significance must consider the excitations expected during operation. As such methods exist to assess the extent to which a given mode participates in response to a known excitation. [12, 15]

In linear structural analysis, for any given input excitation, the response at a given location/DOF is the sum of individual contributions made by each mode of the system. For large structural analysis problems, it is common to execute finite element analysis (FEA) in the modal domain; first determining modal parameters, then subsequently constructing the response to an input based on the contributions of those modes. Any deviation from a direct, non-modal, calculation arises from truncation to the finite number of modes. As such the modes included in such analyses should include, and exceed, all modes in the expected frequency range of excitation. [12, 33]

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The summation of the responses of each considered mode, i, combine to determine the overall response to the given input excitation. Mode Participation is a means to investigate the relative contribution each mode adds to the final responses at the output DOFs considered. The fraction of the overall response, R, at a given DOF for a given input, which is attributed to the mode being considered is known as the modal participation fractions, modal participation factors or modal contribution fraction:

MP fraction=Ri

R (13)

For small problems, it is possible to calculate all of the MP fractions for all response DOFs and to therefore assess the relative contributions of all modes within the considered frequency range. For larger problems the number of modes and DOFs may be prohibitive making it infeasible to consider the MP fractions of every mode across the entire excitation environment. In such cases, the MP fractions may be used to analyze only the highest magnitude responses and thus identify the modes of most importance to the structure for the applied excitations being investigated. [15, 33]

2.4.6. Modal Kinetic Energy FractionsMP fractions provide insight into the local contribution of a given mode towards the response at a given DOF. In a similar, but more global manner, the kinetic energy contribution of a given mode can be used as a measure of the level of involvement of a mode resulting from a given input. The overall kinetic energy in the system resulting from a given input will be a summation of the kinetic energy contribution of the modes of the structure. The fraction of the overall kinetic energy, KE, for a given input excitation, which is attributed to the mode (i) being considered, is defined here as the modal kinetic energy fraction [33]:

Modal KEfraction=KEi

KE (14)

Therefore, along with the MP fraction, the modal KE fraction may also be considered when establishing how much of a contribution a given mode makes in the response of the system to input excitations.

It should be noted that MKE described previously (in section 2.4.3) is a target mode selection parameter calculated directly through normal modes analysis (performed using appropriate scaling). It therefore provides a single value of MKE (or generalized mass) for each mode in the system, without consideration of any applied input excitation. Conversely, the Modal KE fraction method introduced here instead provides a measure of how active, in terms of kinetic energy, each mode is in response to an applied input excitation. Therefore, at each frequency step in the analysis the Modal KE fractions are calculated for all contributing modes in the considered frequency range, and it is the maximum contribution for each mode which is considered for ultimate comparisons.

3 MethodsMost of the results presented herein are based on purely analytical results from finite element analysis of the considered spacecraft structures using MSC-NASTRAN FEA software [36]. These analyses allow for a comparison between conventionally selected target modes, and modes with high participation in peak responses to CLA-ESI levels of excitation.

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Some additional comparisons with test derived mode shapes have also been made in order to give some insight into the potential benefits of applying effective target mode selection methods in actual test-FEM comparisons.

3.1 Analyses PerformedVarious methods have been proposed to assist in the selection of top priority modes for correlation. The more common target mode selection methods have been applied and then assessed on the basis of ability to identify the modes found to contribute significantly to peak responses in the spacecraft.

3.1.1. Normal Modes AnalysisSome of the conventional target mode selection methods from normal modal analysis of spacecraft which have been applied include:

Modal Effective Mass

Strain and Kinetic Energy fractions

Generalized Mass

Root-Sum-Squared Displacement

3.1.2. Mode Contribution AnalysisTo identify the modes which contribute most to peak responses in the spacecraft structure, an un-notched, constant, nominal 1g magnitude of input excitation has been applied to the spacecraft FEMs at the base interface. The resulting modal participations have been analyzed in order to assess the relative significance of modes in the spacecraft, as an inherent consequence of the nature of the structure itself.

The ultimate goal is to develop a method to identify the modes which are most likely to provide substantial contributions to peak responses in key flight events. Therefore, for spacecraft applications, it is those modes excited by CLA level input which must be ascertained. In order to achieve this, in addition to the nominal sine-sweep, a mode participation analysis has been carried out on the spacecraft when subjected to ESI applied at the base of the spacecraft. The ESI excitation levels across the frequency range of interest have been determined from data generated during CLAs. The ESIs envelope the loading levels experienced across the considered frequency range for the main flight events of concern for the considered launch vehicles.

By comparing the mode participation from nominal input with that from CLA-ESI it has been possible to establish which modes are likely to be significant to the structure regardless of the excitation and those modes which may seem non-critical, but which are in fact likely to be excited during CLA.

It should be noted that, in this work, scaling has been applied such that the mode with largest contribution to the peak (acceleration and displacement) response in a given translational direction is given a value of unity. This allows the modes to be compared, and their significance assessed, relative to this highest contribution modes.

3.1.3. Summary of AnalysesThe analytical investigations performed in this work are summarized in Table 1. Most target mode selection methods are performed using simple calculations based on normal modes

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analysis. In addition to those more conventional methods, modal participation analyses are also applied. The MP analyses are performed for base-shake sine-sweeps of the spacecraft. In one case a nominal, constant input excitation magnitude is applied, in order to provide a baseline for modal contribution based only on structural characteristics. Subsequently, CLA-ESI level input is applied and the modal participations calculated. This allows for an assessment of which modes are: important to the spacecraft regardless of input; significant as they are excited by CLA; insignificant as they are not excited by CLA; or insignificant regardless of input.

Analysis Type Modal Analyses Sine-Sweeps (1g and CLA-ESI)

Method Details Method Global/LocalAcceleration

ScaledDisplacement

Scaled

Target Mode Selection Method

Meff GlobalMPfraction MPfraction

KEF LocalSEF Local

Modal KEfraction Modal KEfractionGen. Mass GlobalRSS Both

Table 1. Summary of analyses performed.

3.2 Experimental Comparisons PerformedThe modes of significance have been determined based on peak responses resulting from CLA-ESI levels of input to the FEM. These modes are to be compared to the mode shapes extracted from initial base-shake sine-sweep test campaigns conducted on the corresponding physical spacecraft structures.

The test data used herein have been gathered from base-shake sine-sweep testing, as described previously. Appropriate local and global modal parameter extraction methods have been applied to the test FRFs in order to obtain modal data for correlation [37]. This extraction has been carried out with the aid of FEMtools software [38], which makes use of global poly-reference Least Squares Complex Frequency [39] and local curve-fit methods [40].

Modal metrics, most notably the popular MAC assessment, are to be applied to quantify the level of correlation which has been achieved. In this manner it is possible to assess whether current procedures have resulted in good correlation for these modes of significance. Where there is poor correlation, this shows the potential to improve procedures to identify critical modes earlier and provide improved focus for FEM correlation and update efforts.

3.3 Example SpacecraftThe studies presented herein focus on large, unique, scientific ESA spacecraft; Aeolus and BepiColombo. Most of the results are analytical, making use of FEMs which have been subjected to some preliminary CLAs, from which excitation levels have been determined and re-applied for MP analysis.

3.3.1. Atmospheric Dynamics Mission AeolusThe spacecraft Aeolus is shown in Fig.2 both in the form of physical test set-up, left, and corresponding FEM, right. This Aeolus spacecraft is intended for global wind-component-profile observation, and aims to improve weather forecasting. The spacecraft has a mass of approximately1800kg and the FEM consist of over 500,000 DOFs.

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During base-shake sine-sweep vibration tests carried out on the structural thermal model of Aeolus, data were collected using accelerometers which captured the responses at a MPP of approximately 300 DOFs. The locations on the FEM corresponding to this MPP are considered in these investigations; with the responses examined in the modal contribution analyses being selected from these locations.

Fig.2. Aeolus set up for base-shake vibration test [19] (left) and finite element model (right)

3.3.2. BepiColomboThe ESA/JAXA collaboration spacecraft BepiColombo, shown in Fig.3, has also been considered as an example for use in this study. BepiColombo, a Mercury magnetospheric and planet surface mapping mission, has a stacked configuration comprising of two planetary orbiters and a propulsion module. The spacecraft has a mass of approximately 6500kg and the FEM consist of over 1,500,000 DOFs.

During base-shake sine-sweep vibration tests carried out on the structural thermal model of BepiColombo, data were collected using accelerometers capturing the response at approximately 400 DOFs. As for Aeolus, the points on the FEM corresponding to the test MPP will be used for the generation of the responses examined in the modal contribution analyses.

14

Fig.3. BepiColombo set up for base-shake vibration test [19] (left) and finite element model (right)

4 Results and Discussion

4.1 Analytical ResultsIn this section, results for the Aeolus spacecraft are presented and discussed, with reference made to any notable similarities and differences to the BepiColombo results, which are reported fully in the appendix.

MP and modal KE fractions have been determined and scaled with respect to the acceleration and displacement responses at the MPP locations on the structure, as described previously. This gives the relative significance of the modes of the structure under each considered excitation. In this case, the excitations considered are base-shake sine-sweeps conducted separately in the X, Y and Z directions. Both 1g level excitations and CLA-ESI level excitations have been applied. The MP (circles) and modal KE fractions (crosses) with respect to acceleration and displacement responses are presented in Fig.4 and Fig.5 respectively, where the size of the markers is an indication of the modal effective mass.

It should be noted, and observed from Fig.4 and Fig.5, that no significant modes of the spacecraft appear to be present in the frequency ranges of below 15Hz and between 45 and 60Hz; which are the frequencies of known significant lateral and longitudinal Vega launch vehicle excitation [31]. As such differences in the relative participation of modes between the 1g level sine-sweep and the CLA-ESI are not as pronounced as would be expected if the spacecraft were not designed to avoid the presence of critical modes in these frequency ranges. Nevertheless, some noteworthy differences are observed between the two cases, such as the lateral X-direction fundamental bending mode rising in significance relative to modes just over 60Hz, as the X-direction CLA-ESI excitation magnitude at 17Hz is higher than that at 60Hz.

It should be noted that, for BepiColombo, the higher frequency modes are found to be less significant under CLA-ESI loading levels. This may be partly due to the ESI envelope covering Ariane V CLA load cases which predominantly excite the lower frequency range, under 35Hz. It should be noted that, for Ariane V, it is common for experience, as well as CLA analyses, to

15

provide guidance for expected excitation levels. This is particularly of note at frequencies over 60Hz.

Fig.4. Aeolus acceleration results. Modal participation fractions (circles) and modal kinetic energy fractions (crosses) against mode natural frequency [Hz]. 1g level sine sweep (above)

and CLA-ESI (below).

16

Fig.5. Aeolus displacement results. Modal participation fractions (circles) and modal kinetic energy fractions (crosses) against mode natural frequency [Hz]. 1g level sine sweep (above)

and CLA-ESI (below).

Fig.4 and Fig.5 provide an indication of the relative significance of the modes of the spacecraft, with respect to their contribution to displacement and acceleration responses in the structure. In order to make some assessment of the ability of other target mode selection criteria to

17

identify the modes of most significance, it had been necessary to select the target ‘critical modes’. In the following discussions and figures, the target modes are those associated with values exceeding 0.5 for at least one of the 4 criteria (acceleration scaled MP fractions, acceleration scaled modal KE fractions, displacement spaced MP fractions, and displacement scaled modal KE fractions) displayed in Fig.4 and Fig.5. For the sake of these comparisons, the target modes have been classified into tiers; modes giving values over 0.5 for all 4 criteria are assigned as tier 1, if only 3 criteria exceed 0.5 the mode is tier 2, and so on.

Based on these selection criteria, for Aeolus there is good correspondence between the modes selected as targets based on the 1g level analysis and those selected based on the response to CLA-ESI conditions. However, the change of excitation did influence the relative participation fractions of the modes, as outlined previously. For BepiColombo the change of excitation had an even more notable impact, significantly influencing which modes met the criteria to be included as targets.

As discussed previously, modal effective mass and strain and/or kinetic energy fractions are often considered in conjunction when identifying target modes. As such, strain and kinetic energy fractions have been plotted against modal effective mass in Fig.6 and Fig.7 respectively. The target modes, selected from the results given the plots in Fig.4 and Fig.5, are shown in Fig.6 and Fig.7 by crosses and/or plus signs, while non-target modes are dots. From observation of the target mode markers, it can be seen that that the majority of target modes fall into a definite trend in relation to SEF against modal effective mass. A straight (linear-logarithmic) line has been added to the plot to highlight this relationship.

The main outlying point on Fig.6 and Fig.7 is a mode around 80Hz which has been identified as potentially significant under CLA-ESI input despite having low effective mass and relatively low strain and kinetic energy fractions. This mode has a high participation response during CLA-ESI input, which was not observed in 1g level input. The relative significance of this mode was higher in the CLA-ESI as the input excitation levels for the Y-direction ESI peak under 10Hz, where no significant modes are observed, and the next highest magnitude of excitation occurs around 80Hz. Under CLA-ESI, this mode is therefore made more significant, relative to the other modes, due to the applied excitation.

It is important to note that several approaches exist for applying effective mass and energy fractions as target mode indicators, including; considering target modes with >2% or >5% modal effective mass regardless of energy fraction, and/or modes with >1% if energy fraction >0.5. The findings presented here confirm that these approaches have merit, but may not identify all of the modes of interest for structures such as the example spacecraft. For example, here modes of Aeolus with effective mass <1% have been identified as having potential to contribute significantly to peak acceleration and/or displacement responses in the spacecraft. Similarly, for BepiColombo modes with effective mass <2% and energy fractions <0.5 have been identified as potentially significant. The results given here appear to indicate that, particularly for strain energy fraction, the target modes could be identified through relationship displayed by the diagonal line in Fig.6.

Table 2 and Table 3 provide a summary of the use of different ‘threshold’/’cut-off’ criteria to select modes from modal effective mass and strain or kinetic energy fractions respectively. The different combinations of threshold values for modal effective mass and strain or kinetic energy fractions define different regions/areas of the graphs given in Fig.6 and Fig.7. In each region, the ration of ‘target’ to ‘non-target’ modes (as selected from figures Fig.4 and Fig.5) is

18

determined, and the number of target modes which fall outside the considered region is given. In this manner it is possible to compare approaches. Depending on available time and resources, a trade-off must be reached between the number of potentially less significant modes included as correlation targets and the risk of not including a mode which has the potential to contribute to large accelerations and/or displacements in the spacecraft during CLA and/or qualification testing.

It can be seen it Table 2 that for Aeolus only 1 ‘target’ mode falls below the diagonal line shown on Fig.6, and this mode is only tier 4 becoming significant due to CLA level excitation, and would not be possible to identify as a target through observation of only effective mass and energy fractions. The same is true for the 1 target mode outside this range for BepiColombo, as it would not be identified for any of the threshold values typically applied when considering effective mass and energy fractions as identification criteria for identifying potential target modes.

Fig.6. Aeolus modes plotted with strain energy fraction against modal effective mass. Target modes from CLA-ESI are crosses, from 1g excitation are plus signs, and non-target modes are

dots.

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Fig.7. Aeolus modes plotted with kinetic energy fraction against modal effective mass. Target modes from CLA-ESI are crosses, from 1g excitation are plus signs, and non-target modes are

dots.

In Region(s) Outside Region(s) In Region(s) Outside Region(s) In Region(s) Outside Region(s)targets modes/

total modestargets modes targets modes/

total modestargets modes

missedtargets modes/

total modestargets modes

missed10 0 - - 0.80 9 1.00 13 0.88 2210 0 5 0.5 0.80 9 1.00 13 0.88 2210 0 2 0.5 0.71 8 0.75 13 0.73 2110 0 1 0.5 0.50 8 0.36 12 0.43 205 0 - - 0.64 6 0.78 9 0.70 155 0 2 0.5 0.62 5 0.70 9 0.65 145 0 1 0.5 0.50 5 0.47 8 0.48 132 0 - - 0.50 4 0.65 5 0.57 92 0 1 0.5 0.43 4 0.50 4 0.47 81 0 - - 0.36 3 0.39 3 0.38 6

0.41 1 0.28 1 0.33 2

Region(s) of the Graph Aeolus BepiColombo Both Spacecraft

Meff [%] >

SEF >Meff [%]

> SEF >

above line

Table 2. Summary of effective mass and strain energy fraction criteria to select target modes

In Region(s) Outside Region(s) In Region(s) Outside Region(s) In Region(s) Outside Region(s)targets modes/

total modestargets modes targets modes/

total modestargets modes

missedtargets modes/

total modestargets modes

missed10 0 - - 0.80 9 1.00 13 0.88 2210 0 5 0.5 0.67 9 1.00 13 0.78 2210 0 2 0.5 0.57 9 0.80 12 0.67 2110 0 1 0.5 0.50 8 0.56 11 0.53 195 0 - - 0.64 6 0.78 9 0.70 155 0 2 0.5 0.58 6 0.73 8 0.65 145 0 1 0.5 0.53 5 0.60 7 0.57 122 0 - - 0.50 4 0.65 5 0.57 92 0 1 0.5 0.48 3 0.57 4 0.52 71 0 - - 0.36 3 0.39 3 0.38 6

0.42 2 0.30 3 0.34 5

Both SpacecraftRegion(s) of the Graph

Meff [%] >

KEF >Meff [%]

> KEF >

above line

Aeolus BepiColombo

Table 3. Summary of effective mass and kinetic energy fraction criteria to select target modes

20

Fig.8. Aeolus modes plotted with root-sum-square against generalized mass. Target modes from CLA-ESI are crosses, from 1g excitation are plus signs, and non-target modes are dots.

Another combination of parameters which have been suggested as combining to indicate target modes of interest is using generalized mass and RSS (for the case where modes as scaled to a maximum displacement of 1). Again, these parameters have been plotted against each other, and the target (X or +) and non-target (dot) modes indicated, in Fig.8. Unlike with modal effective mass, it does not appear that high values of generalized mass or RSS are necessarily indicators of mode significance. It does, however, appear that there is value in considering both parameters together as a trend is seen in the target modes, which appear along the front/leading edge of the data set. It should be noted that even the target mode which appeared to be an outlier in Fig.6 and Fig.7, does follow the trend seen in Fig.8. Nevertheless, it is a less well defined relationship and the trend observed in Fig.8 for Aeolus is less distinct in the results for the BepiColombo spacecraft, which demonstrates more outliers where target modes are set back from the front of the data set.

4.2 Experimental Comparison ResultsSome comparisons to test gathered data have been made in order to give some insight into the levels of correlation which may be observed for the modes identified as having potential significance during the CLA. It should be noted that these comparisons are made using the same FEMs which have been used throughout the analytical analyses forming the main part of the study. These are not necessarily the current best-correlated versions of the FEM for the spacecraft and therefore do not represent the levels of correlation achieved by the final FEM. Nevertheless, the following results should give some indication of which modes are likely to correlate well or poorly to test data.

The target modes have been identified based on likelihood to contribute towards large acceleration and/or displacement responses in the spacecraft to CLA-ESI level input (as shown

21

in the lower plots in Fig.4 and Fig.5). A summary of the target modes matched based on MAC to the corresponding test mode, is given in Table 4, which also indicates the associated frequency differences between the FEM and test.

MP and Modal KE Fraction

Criteria > 0.5Tier FEM Freq [Hz] Freq Diff. (%)

16.98 4.1017.25 1.4777.88 9.61

3 of 4 2 60.88 21.0826.49 3.0441.05 16.6742.86 1.4861.43 3.9477.18 10.0085.46 8.3263.73 4.8365.18 17.7680.89 34.60

1

3

4

All 4

2 of 4

1 of 4

Table 4. Aeolus FEM target modes compared to best MAC matched test mode

MAC and COC for the target FEM modes and associated best matched test modes are given in Fig.9, which gives correlation level against natural frequency and Fig.10 which shows the correlation level against the modal effective mass.

Fig.9 reveals that the correlation of the target modes, particularly with regard to the MAC criteria, is best at the relatively low frequency tier 1 fundamental lateral bending modes, and generally decreases with increasing frequency. There are tier 1, 3 and 4 target modes at around 77-80Hz which are not well correlated. The tier 1 mode at 77.88Hz is considerably better matched in COC than MAC, which indicates that the local behavior of the mode at some lower mass DOFs may be poorly correlated. Although some of these more localized modes may not have been considered as correlation targets by traditional target mode selection, using the MP and modal KE methods described previously, these modes could be identified as correlation targets. Once identified as target modes, appropriate focused effort could be made to assess the test-FEM differences and make updates if/where appropriate. It could be the case that the DOFs in question are not considered particularly significant, or the differences may be the result of some known and understood inherent difference between the test and FEM set-up. If, however, the FEM is genuinely displaying behavior not observed in the test, then updates may be required to resolve the issue and develop a more representative FEM.

The results given here are for the Aeolus spacecraft; however similar trends are seen for BepiColombo. As expected, the level of correlation tends to decrease with increasing natural frequency of the modes, highlighting the need for effective identification of target modes at higher frequencies.

It is evident from Fig.10 that the target modes with high effective mass are well correlated in terms of cross-orthogonality. This is important as it indicates that the bulk of the mass of the spacecraft is behaving in a manner which is representative of the test measured response. This

22

is beneficial as the high effective mass modes are likely to be most influential on the launch vehicle. Nevertheless, the criteria applied here have shown the low effective mass modes included in this comparison may be significant to the discrete displacement and/or acceleration responses in the spacecraft. Therefore a better correlation for these modes would be desirable and could possibly be achieved if the correlation and update efforts are properly focused through effective application of appropriate target mode selection methods.

Fig.9. Aeolus target FEM modes compared to closest matched test modes using modal assurance criteria (MAC) and cross orthogonality check (COC) against natural frequency.

Fig.10. Aeolus target FEM modes compared to closest matched test modes using modal assurance criteria (MAC) and cross orthogonality check (COC) against modal effective mass.

It has been noted from correlation activities conducted on the spacecraft considered herein that some level of ‘modelling error’ in FEMs as complicated as these is inevitable. Such ‘errors’ often take the form of assumptions made in the modeling of internal boundary conditions. The use of NASTRAN RBE2 (rigid body) elements to replicate joints connecting different parts of the structure is a common practice, but one associated with high levels of uncertainty and potential to give poor representation of the real structure behavior. Although good practices can mitigate true ‘poor modelling assumptions’, the uncertainty associated with the modelling of internal boundaries and joints such as these mean that some reliance on the correlation process is required in order to highlight all such issues. By providing a means to focus on the truly significant local modes, the associated local areas of the model in need of update should also be highlighted. Thus there is correlation/update focus not only in the modal sense, but also in

23

terms of the physical location on the FEM. Small changes, for example to RBE2 connections, in the right part of the model can have a notable influence on the MAC values of the affected modes. Further details of specific modelling issues addressed in the update for BepiColombo are presented in this work from Mercer et al [29].

5 ConclusionsAn important part of spacecraft FEM validation is the selection of the target modes which are to be the focus of the correlation and update of the FEM to base-shake vibration test data. This is a topic of growing importance given the ever increasing size and complexity of spacecraft FEM. However, this runs parallel with the, largely unquestioned, continued application of traditional target mode selection methods. These are the issues which motivated this exploration of alternative approaches, including consideration of the impact of predicted operational excitation levels. This study has applied a variety of target mode selection methods to large, unique, scientific spacecraft FEMs. Globally significant modes were identified by calculation of modal effective masses, while noteworthy local modes were discerned through close inspection of the energy distribution among the spacecraft sub-systems/components. Aside from the conventional target mode selection criteria, alternative methods have also been applied which are intended to quantify modal participation in response to CLA flight event level ESI; thus providing an indication of ‘critical modes’ against which to assess the more traditional approaches.

Several traditional target mode selection approaches have been evaluated. Although the comparisons confirm that, as expected, there is value in currently popular methods, particularly when applied in conjunction with each other to account for both global and local behavior; crucially, not all of the ‘critical modes’ would be identified by conventional means. Particularly, it is indicated that a new approach to selecting the threshold values applied when combining the modal effective mass and strain energy fraction criteria has potential to improve the likelihood of identifying significant local modes. These modes would have been missed if current, accepted and widely applied, threshold values had been used. Even with the application of the newly suggested thresholds, at least one potentially ‘critical mode’ would not have been identified for each of the spacecraft considered. This suggests a limitation in the methods based solely in modal analysis, which could be overcome by some form of modal participation/contribution analysis under appropriate excitation as advocated in this work.

Although there was some overlap in the modes with high contribution in response to 1g level excitation and those with significant involvement in CLA-ESI analyses, the different excitations cases were found to have a notable influence over the relative contribution of certain modes. In particular, BepiColombo showed a marked change in the relative contribution of modes under CLA-ESI level conditions. This suggests that expected excitations, from knowledge based on past CLA and launch experience, should ideally be taken into consideration during target mode selection. This would be aided further by some preliminary CLA type analyses, giving as close a representation as possible to the CLA environment, at/before the target mode selection stage. Including consideration of the CLA amplitude levels (as was done in this study) would provide some benefit, while details from a full coupled analysis with a suitable launcher model would provide even more insight into the modal behaviour in the coupled system.

It is possible that poor representation of certain modes in uncorrelated spacecraft FEMs may influence the results of any preliminary CLAs and subsequent mode selection. However, although more local modes are significant in terms of responses in the spacecraft, the overall

24

loads and interactions with the launch vehicle are likely to be dominated by the high modal effective mass modes which are typically relatively well correlated before update. Thus, although not necessarily a good representation of the spacecraft local responses, such an exercise would still provide potentially valuable information about the most likely CLA excitation levels, and would be a useful component in the target mode selection process.

It is also noted, however, that the existence of some overlap in 1g and CLA-ESI target modes does suggest that some of the modes of significance are driven predominantly by the inherent nature of the structure, irrespective of the applied excitation.

The final comparisons made to test data, for the ‘critical modes’ identified from CLA-ESI analysis of the FEMs, confirm the expectation that more local, low effective mass, modes and those at higher frequencies are generally more likely to be poorly correlated. This serves as an example to highlight the importance of effective isolation of the potentially significant local high frequency modes. Otherwise, there is potential for key modes to remain overlooked due to being wrongly considered as low priority when allocating resources for focus of correlation and update efforts.

AcknowledgementsThis work was supported by funding from Airbus Defence and Space.

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Appendix

Full results are given here for the BepiColombo spacecraft corresponding to the plots presented for the Aeolus spacecraft in the main results section.

A.1Analytical Results for BepiColomboThe MP fractions (circles) and modal KE fractions (crosses) with respect to acceleration and displacement responses are presented in Fig. A.1 and Fig. A.2 respectively (with the size of the markers is an indication of the modal effective mass). Results for both 1g level and CLA-ESI sine-sweep analyses are given.

It should be noted, and observed from Fig. A.1 and Fig. A.2, that no significant modes of the spacecraft appear to be present in the frequency ranges of below 8Hz for predominate lateral modes and below 31Hz for longitudinal modes; the frequencies corresponding to known significant lateral and longitudinal Ariane V launch vehicle excitation [30]. As such differences in the relative participation of modes between the 1g level sine-sweep and the CLA-ESI are not as pronounced as would be expected if the spacecraft were not designed to avoid the presence of critical modes in these frequency ranges. Nevertheless, some differences are observed, such as the lateral Y-direction fundamental bending mode lowering in significance relative to modes around 18Hz and 26Hz, as the Y-direction CLA-ESI excitation magnitude at 18Hz and 26Hz is significantly higher than that around 13Hz. Likewise, in the X-direction with 1g level excitation, there are modes round 60Hz which have the potential to contribute significantly to local acceleration responses. When the CLA-ESI level of input in the X-direction is applied, the magnitude of excitation at this frequency is relatively low, therefore leading these modes to have a low level of significance. This may be due to the ESI envelope covering Ariane V CLA load cases which predominantly excite the frequency range under 35Hz.

SEF and KEF plotted against modal effective masses largely follows the same trend as was present for Aeolus, and are presented for BepiColombo in Fig. A.3 and Fig. A.4. The main outlier is a tier 4 mode indicated by the 1g level analysis as having potential to have a large participation fraction locally to the excited DOF.

27

Fig. A.1. BepiColombo acceleration results. Modal participation fractions (circles) and modal kinetic energy fractions (crosses) against mode natural frequency [Hz]. 1g level sine sweep

(above) and CLA-ESI (below).

28

Fig. A.2. BepiColombo displacement results. Modal participation fractions (circles) and modal kinetic energy fractions (crosses) against mode natural frequency [Hz]. 1g level sine sweep

(above) and CLA-ESI (below).

29

Fig. A.3. BepiColombo modes plotted with strain energy fraction against modal effective mass. Target modes from CLA-ESI are crosses, from 1g excitation are plus signs, and non-target modes

are dots.

Fig. A.4. BepiColombo modes plotted with kinetic energy fraction against modal effective mass. Target modes from CLA-ESI are crosses, from 1g excitation are plus signs, and non-target modes

are dots.

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Fig. A.5. BepiColombo modes plotted with root-sum-square against generalized mass. Target modes from CLA-ESI are crosses, from 1g excitation are plus signs, and non-target modes are

dots.

Generalized mass and RSS have been plotted against each other, and the target (X or +) and non-target (dot) modes indicated, in Fig. A.5. A rough trend is seen in many of the target modes, lying along the upper edge of the data set. Nevertheless, there are a few outliers, most notably the tier 1 mode found as being significant to responses to longitudinal excitation.

A.2 Experimental Comparison Results for BepiColomboThe data from sine-sweep testing of the BepiComombo spacecraft have been processed to extract experimental mode shapes. These have been compared with the target modes, as selected from the results (shown in Fig. A.1 and Fig. A.2) of ESI-CLA analysis. As for Aeolus, must be emphasized that this FEM is not the final, best correlated version matching this test data. Nevertheless, comparisons give an indication of possible correlation levels for these modes deemed to have potential significance to the structure. The test-FEM MAC and COC for BepiColombo are presented against frequency and modal effective mass in Fig. A.6 and Fig. A.7 respectively.

Again, the level of correlation appears to decrease with increasing frequency. There also appears to be decreasing correlation with decreasing modal effective mass, with notable exceptions. The more local target modes, with effective mass under 1%, appear to be relatively well correlated.

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Fig. A.6. BepiColombo target FEM modes compared to closest matched test modes using modal assurance criteria (MAC) and cross orthogonality check (COC) against natural frequency.

Fig. A.7. BepiColombo target FEM modes compared to closest matched test modes using modal assurance criteria (MAC) and cross orthogonality check (COC) against modal effective mass.

Vitae

J.F. Mercer (PhD Student) obtained a master’s degree in aeronautical engineering from the University of Glasgow in 2013. At time of publication she is a PhD student at Surrey Space Centre in the University of Surrey, conducting research into the topic of spacecraft finite element model correlation.

Prof G.S. Aglietti (Director of Surrey Space Centre)

Dr M. Remedia (Post-Doctoral Researcher)

A. Kiley (title)

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