Recommended Operations

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Violet Little
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1 Category LMS Test.Lab Access Level End User Topic Rotating Machinery Publish Date 1-Aug-2016 Question: How to 'correctly' integrate time data within Time Domain Integration? Answer: While the most accurate velocity or displacement measurements are made directly, in many cases, it may be too late or impractical. In these situations, you may wish to integrate your acceleration data. With that said, to correctly integrate (or double integrate) time data, a few steps must be taken to ensure the results are as expected. This document explains the recommended operations and gives related formulas. Recommended Operations 1. Detrend AC Fit a low degree polynomial (up to 6 th order) through the data and subtract it. This removes any low frequency components which ultimately lead to an explosion of the time data when integrating. 2. Resample Up-sample the data by at least four times the original sampling frequency (f s ) before integrating. This removes linearization errors caused by the integration algorithms themselves (Simpson, Four-point, Bode, etc.), which are particularly sensitive at frequencies greater than one-quarter the sampling rate. 3. Integrate If using the Simpson, Four-point, or Bode methods as historically done, the resampling steps are most likely necessary. If using the Trapezium method, the results may be okay without resampling, reducing this process from 5 to 3 steps. 4. Resample After the integration (single or double) was performed on the up-sampled time domain curve, it is down-sampled to the original sampling frequency. 5. Filter Use a high pass filter to remove the mathematical integration constant. Historically, two filters were used for double integrations, though in more recent versions of LMS Test.Lab, no real improvements are gained using repeated filters

If using Time Animation: Using filters on time data can introduce phase shifts and lead different frequency components to be shifted with different time delays.

For this reason, it is advised to set the Filter Mode option to Zero Phase Filtering when defining the time domain filters.

2 If using Time Animation: Using filters on time data can introduce phase shifts and lead different frequency components to be shifted with different time delays. This may distort the amplitude of the resulting time signal, causing inaccurate Time Animations. For this reason, it is advised to set the Filter Mode option to Zero Phase Filtering when defining the time domain filters. While this introduces no phase distortion in most of the trace, there are significant transition effects due to the integration and filter at the beginning and the end of the signal, which is why they should not be used in Time Animation. Corresponding Formulas In short, the following formulas are recommended when integrating time data in the LMS Time Signal Calculator. Note all formulas may be saved and recalled as a Throughput FormulaSet (.TFS). When attempting to integrate more than one channel at a time, it is recommended to utilize nested formulas which take advantage of the Repeat for and Increment options. These are created by manually copying one formula and pasting it into the channel field of another. A. Un-nested formula Easy to follow, but difficult to manipulate for multiple channels Note: The intermediate steps are noted as variables, denoted as VAR#, and are not shown (or saved) in the Time Data Selection Data Set after being calculated in the Time Signal Calculator

01;50;15);2.5;2;IIR(1)) Polynomial degree 4x f s Filter cutoff freq* f s 2. Integration using Trapezium method: Formula: Polynomial degree FILTER_HP(DOUBLEINTEGRATE(DETREND_AC(CHx;2);2);2.

3 B. Nested formula Difficult to follow, but easy to repeat for multiple channels 1. Integration using Simpson s rule: Integration method (Simpson) Formula: Zero phase filtering FILTER_HP(RESAMPLING(DOUBLEINTEGRATE(RESAMPLING(DETREND_AC(CHx;2);65536;80;0.01;50;15);1 );16384;80;0.01;50;15);2.5;2;IIR(1)) Polynomial degree 4x f s Filter cutoff freq* f s 2. Integration using Trapezium method: Formula: Polynomial degree FILTER_HP(DOUBLEINTEGRATE(DETREND_AC(CHx;2);2);2.5;2;IIR(1)) Integration method (Trapezium) Zero phase filtering Filter cutoff freq* Comment The *2.5 Hz high pass filter cutoff frequency and the 2 nd degree polynomial chosen for the de-trend function in the cases above are simply generic examples. These values may change depending on the application as well as other factors including the usable frequency range of the transducer and the amount of drift present in the measurement. Please note that while the examples above were formulated to perform a double integration, a single integration may be performed by simply changing DOUBLEINTEGRATE to INTEGRATE in the formula line

Appendix: Common Time Integration Mistakes Below are common, double integration (acceleration to displacement) mistakes in the time domain, when using the Time Signal Calculator.

4 Appendix: Common Time Integration Mistakes Below are common, double integration (acceleration to displacement) mistakes in the time domain, when using the Time Signal Calculator. Comparing these examples to the corrected trace serves as a general indicator of why each step/parameter is necessary, as explained in the previous section. No Detrend AC If you do not complete an AC de-trend operation (to the appropriate degree), some drift may be present in the result. No Up-sample If you do not up-sample before the integration using the Simpson s rule, significant errors may be present related to frequency content greater than one-quarter the sampling frequency

5 No Down-sample If you do not down-sample to the original sampling frequency after integrating using the Simpson s rule, the amplitude may change. This is related to an over or underestimation of the integration algorithm, which is sensitive at frequencies greater than a quarter the sampling frequency. By down-sampling, you remove those frequencies. No High Pass Filter If you do not use a high pass filter, the integration constant, seen as a low frequency or DC component, may dominate the result. Too High of a HP Filter Cutoff Frequency By forgetting to change the default cutoff frequency for the high pass filter from 500 Hz, there may be little to no displacement in the resulting trace. This occurs because the lower frequency components, which account for most of the displacement, were filtered out

Pole Zero Correction using OBSPY and PSN Data

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