The objective of this presentation is to give a brief overview of the theory behind the Damage Based

Analysis (DBA) method including the derivation and practical application of the theory using the Python

computer language. The Theory and Derivation will use both Acceleration and Pseudo Velocity

methods to derive a series of equations for processing by Python. The results will compare both

Acceleration and Pseudo Velocity methods and discuss implementation of the Python functions. Also,

we will briefly discuss the efficiency of the methods and the amount of computer time required for the

solution. In conclusion, DBA offers a powerful method to evaluate the amount of energy imparted into

a system in the form of both Amplitude and Duration during flight and compare those results to the

ground test qualification environments. Many forms of steady state and transient non-stationary

vibratory motion can be characterized using this technique. DBA provides a more robust alternative to

traditional methods such as Power Spectral Density (PSD) using a maximax approach.

https://ntrs.nasa.gov/search.jsp?R=20170010183 2018-05-18T08:51:54+00:00Z

Damage Based Analysis (DBA):Theory, Derivation and Practical Application

using both an Acceleration and Pseudo-Velocityapproach

88th S&V Symposium Oct. 16-20, 2017

Jacksonville, FL

Vince GrilloDynamic Environments, KSC LSP Structural

Dynamics

Overview

Scope of the problem

Launch and Space Vehicles are subjected to complex, vibroacoustic non-stationary flight environments which vary in time during certain events ina mission profile.

Development, Qualification and Acceptance test specifications developedfrom historical data and analytical/empirical techniques dont always takeinto account the non-stationary aspect of some portion of the flight data.

Flight data is assessed after each mission by comparing the flight resultsto prior qualification testing using a Maximax approach which can bepotentially too conservative.

The need exists for a consistent, quantitative and accurate way tocharacterize and compare non-stationary flight data with stationary testenvironments.

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Historical Approach

Maximax Approach Vibroacoustic Data Typically, vibroacoustic flight data processed from instruments such as

accelerometers are treated as a series of overlapping stationary time segments.

Maximax is a technique used to capture the Power Spectral Density (PSD) duringeach time segment. The goal is to obtain the maximum value of the spectrum ateach frequency independently and loop through the total number of timesegments.

The Maximax results are then compared to the test specification.

Limitations to Maximax Method Peak responses in flight data can be considerably overestimated.

Maximax tends to result in excessive conservatism in the Qualification margin whichmay lead to more expensive designs and less reliability.

For a relatively immature design, component qualification may result in over-testswith excessive environments being applied which will impact cost and schedule.

Since Maximax is a purely mathematical transformation of the signal, results aredependent on the choice of processing parameters such as window size andoverlap.

The physical properties of the system such as damping and fatigue from stresscycles are not considered.

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4

Damage Potential

Absolute Acceleration and Pseudo-Velocity Approaches

Review of S.J.DiMaggio, B.H.Sako, S.Rubin , Absolute Acceleration and Scot I.McNeill Pseudo Velocity approaches.

Absolute Acceleration Method,Damage Indicators, G1 G12

G1 represents a =60sec equivalent PSD input that ensures the test response orSDOF base-drive response of a component, envelopes the maximum amplituderesponse of a component in flight.

Note that G1 or amplitude damage indicator is related to maximum amplituderesponse of a component in flight and does not take into account fatigue.

Fatigue will be represented by damage indicators such as G4, G8 & G12 which arefunctions of the slope b for stress cycles on the S-N curve and are derived inAppendix A. Each of these indicators have a fairly complex mathematical formand will need to be derived each time the slope b changes, see Appendix A.

In order to illustrate the meaning of and , figures (1 & 2) are shown in

Appendix A. 5

Using Equations (4 & 5) in Appendix A, we can solve for the power spectral density (PSD)by plugging in from eq(5) into eq(4) :

=

eq(6)

Eq(6) represents the power spectral density , which is a function of the max absoluteacceleration response at each natural frequency represented by a SDOF system. Eq(6) issolved by computing an SRS at each frequency for a series of SDOF systems, recoveringthe Accel-Time responses and finding the maximum amplitude at each frequency.

Pseudo-Velocity Method

From Appendix B, It can be shown that the maximum stress is proportional topseudo-velocity, = k where is the oscillator pseudo-velocity RMS.

From eq(21) appendix A, we have:

The resulting eq(21) represents the power spectral density (PSD), which is a function ofthe max pseudo-velocity amplitude response, at each natural frequencyrepresented by a SDOF system. This result is similar to eq(6).

From Appendix B eqs(23-25), the fatigue damage indicators G4 G12 are:

Where is the number of fatigue damage cycles from flight data, counted using rainflow methods in a seriesof Amplitude Bins similar to the method used in the acceleration approach.

Note that eqs(23-25) represent a much simpler form of the fatigue damage indicatorscompared to the acceleration method. Also, alternate fatigue damage indicators such asG6 or G10 could be easily derived for various values of slope b on the SN curve.

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=

]eq(21)

=

=

Practical Application - Python Implementation

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Fatigue Damage Equivalent fdepsd python code

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PSD Method Comparisons

Input Signal based on arbitrary PSD input spec, converted to Acceleration-Timehistory.

30-sec signal, sample rate=40kHz, 1.2M samples

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Fatigue Damage Equivalent mixed signal comparison

Fatigue Damage Equivalent (fdepsd) G1-G12 Acceleration, Velocity methodscompared to Maximax.

Synthetic stationary Accel-Time signal injected with multiple non-stationary transientevents approx. 200ms in length. fdepsd provides a better method to evaluate bothcombined steady-state and transient events in a composite signal.

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Performance considerations

For previous Fatigue Damage Equivalent processing which used Matlab like software,the average time to process the results for a signal > 300sec illustrated below was over45 minutes compared to 1.8 minutes for a Linux system. Note: Absolute Accelerationand Pseudo-Velocity methods for ASD computation correlate very closely.

Total CPU time spent processing fdepsd using Absolute Accel/Pseudo-Velocitymethods on both Linux_64 and Windows-x64. Both systems set to 8-cpus, parallelprocessing.

CPU time spent on Linux 64bit is very efficient and almost half that of Windows_x64.Most parallel CPU cycles on Linux consumed by user process with very little system/idletime.

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Conclusions

In summary, Damage Potential or Fatigue Damage Equivalent provides a powerfulmethod for characterizing both the Stationary and Non-Stationary nature of a randomvibration signal. Both the Amplitude and Fatigue characteristics of a signal arequantified based on characteristics of the system such as damping and stress cycles.Details for the damage indicators are summarized below:

G1: A 60 sec equivalent PSD input that ensures the test response of a componentenvelopes the maximum amplitude response of a component in flight

G4, G8 , G12 : A 60 sec equivalent PSD input that ensures the fatigue damage of acomponent in test envelopes the corresponding fatigue damage in flight for afatigue exponent of b=4,8,12.

Pseudo-Velocity approach provides a more efficient method to apply fatigue damageexponents.

The current Python implementation provides efficient Open Source software which isplatform independent and can compute the results in a reasonable amount of time.

Damage Potential Analysis provides a way to characterize the differences in energyimparted to a system during both Test and Flight and ensure that ground testing willenvelope both the Amplitude and Fatigue qualification requirements of a component inFlight.

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References

1. Analysis of Nonstationary Vibroacoustic Flight Data Using a Damage-Potential Basis,S.J.DiMaggio, B.H.Sako, S.Rubin, Journal of Spacecraft an Rockets, Vol. 40, No. 5,September - October 2003.

2. Implementing the Fatigue Damage Spectrum and Fatigue Damage EquivalentVibration Testing, Scot I. McNeill, Ph.D., Shock & Vibration Symposium, 10/26-10/30-2008, Orlando Fl.

3. International Standard, ISO 18431-4:2007(E), Mechanical Vibration and Shock SignalProcessing Part-4: Shock-response spectrum analysis, 1st edition 2007-02-01.

4. Standard practices for Cycle Counting in Fatigue Analysis, ASTM International E1049-85 (Reapproved 2005).

5. Random Vibration Data, Analysis and Measurement Procedures, Julius S. Bendat andAllan G. Piersol, 4th edition, John Wiley and Sons, Inc.

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Appendix A Absolute Acceleration Method

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Damage Potential Fatigue Damage Equivalent (FDE)

Fatigue Damage Equivalent FDE A