# Seismic Qualification Testing for US Nuclear Power Generating Stations

## Part 1 (Random Vibration Testing)

The nuclear power industry in North America (USA, Canada & Mexico) requires seismic qualification testing for any equipment being installed in nuclear power generating stations. If it has a safety related function (Seismic Category I) then it must be qualified for its capability to perform satisfactorily in the event of an earthquake either by analysis or by testing. In the case of vibration testing, the requirements are defined in IEEE standards IEEE-Std-344, IEEE-Std-382 and IEEE-Std-323. These tests fall into one of two categories – either random multi-frequency (RMF) tests or sine-beat tests. This article discusses the former. The specific requirements of IEEE-Std-344 relating to random vibration qualification testing primarily use Shock Response Spectrum analysis as the fundamental measure of performance. Prosig has over 30 years’ experience in supplying seismic qualification testing systems.

The IEEE-344 standard makes numerous references to two categories of earthquake: an OBE or Operating Basis Earthquake, and an SSE or Safe Shutdown Earthquake. An SSE is postulated to be more severe than an OBE. The general requirement is that the equipment being qualified should be subjected to several OBE tests (typically five or less) followed by one SSE test. The severity of the motion is defined in terms of a Required Response Spectrum (RRS) which is a Shock Response Spectrum. (Note that the IEEE-344 standard somewhat ambiguously refers to the Shock Response Spectrum as “the Response Spectrum”, a term which could easily be confused with either the response Fourier Spectrum or the Spectral Density of the response)

### Earthquake Motion

Earthquakes produce three-dimensional random ground motions that are characterized by simultaneous, but statistically independent, horizontal and vertical components. A typical earthquake will usually begin with small vibrations that increase over a few seconds until it enters a period of strong motion lasting between 10 to 15 seconds. This is then followed by a period of decreasing vibration that decays over a few seconds. The ground motion is essentially broadband random vibration and can produce potentially damaging effects over a frequency range of 1Hz to 100Hz.

Figure 1: Example of simulated earthquake motion used for seismic qualification testing

The time history shown above is a typical example of a simulated earthquake motion. The corresponding Shock Response Spectrum (SRS) is shown as the blue curve in Figure 2 below. Whenever an SRS analysis is computed from measured test data it is usually referred to as a TRS or Test Response Spectrum. Also in Figure 2, the Required Response Spectrum (RRS) is the red curve overlaid on the TRS curve. Ideally all of the TRS curve should exceed the RRS, but the IEEE-344 standard does allow for up to five values to fall below the RRS provided that those values meet certain criteria related to their frequency spacing and the magnitudes of adjacent spectral values.

Figure 2: Example of a TRS enveloping an RRS

### Generation of Test Waveforms for Seismic Qualification Testing

There is more than one way of generating a suitable random waveform that meets the requirements of the RRS. The two most common ways are 1) replicating as closely as possible a known acceptable time history or 2) synthesizing a random multi-frequency waveform that produces a test response spectrum similar to the RRS. However, not only do the components of the excitation waveform in all three axes have to produce shock response spectra that exceed the levels of the required shock response spectra (RRS) but they also have to satisfy the additional requirements of Zero Period Acceleration (ZPA), Frequency Content, Stationarity and Statistical Independence, as specified in the relevant appendices of the IEEE-344 standard. In effect the excitation signal has to satisfy 5 separate conditions in order to meet the overall qualification criteria and thereby demonstrate that it is a good simulation of the desired seismic excitation.

### Qualification of Test Waveforms

Producing a waveform whose shock response spectrum in each axis marginally exceeds the levels of the corresponding RRS for each axis is just the first step – it’s the minimum requirement. Unfortunately it is quite possible to generate an excitation waveform that meets the RRS requirements but whose time history might not possess the correct spectral content in terms of frequency range, amplitude or consistency throughout its duration, or whose motions in all three axes are not independent of one another. The following tests (as detailed in the Appendices of IEEE-344) are intended to assess whether a seismic excitation waveform meets these criteria just described.

#### 1) Zero Period Acceleration (ZPA)

The Zero Period Acceleration is the value of the shock response spectrum evaluated at a frequency that is significantly higher than those contained in the motion time history. An Incorrect value for the ZPA can be caused by waveform distortion created by the excitation actuators or by looseness or rattling of the test item or the fixture. To minimise such errors the measured waveform should be low-pass filtered at the cut-off frequency of the RRS. The peak acceleration value of the filtered time history can then be used as the true ZPA value.

#### 2) Frequency Content Qualification

The objective of this requirement is to show that the input waveform to the equipment being tested contains the same range and amplitude levels of frequencies as those of the RRS. The IEEE-344 standard actually allows for three (or more) different ways of demonstrating that the frequency content is correct: either a Shock Response Spectrum (SRS), a Fourier Spectrum (FFT, DFT) or an Auto (Power) Spectral Density (ASD, PSD). The method used in the Prosig IEEE-344 software uses the SRS method since it relates directly to the RRS, whereas the other methods, although they are easier to compute, only relate indirectly to the RRS and therefore cannot be used for objective numerical comparison. Regrettably, the IEEE standard gives no guidance as to defining acceptable numerical limits for assessing the acceptability of the frequency content – probably because in the case of the Fourier and PSD methods it would be impossible to do so. The Prosig software calculates the ratio of TRS/RRS and compares that value against user-defined limits.

#### 3) Frequency Content Stationarity Qualification

The objective of this requirement is to show that the frequency content, as determined by the method described in the previous paragraph, is approximately the same throughout the strong portion of the excitation and doesn’t vary significantly from one time epoch to another – in other words it is statistically constant with time – within a “reasonable tolerance”. The IEEE-344 standard again allows various methods to determine if the content is statistically constant: either time-interval shock response spectra, time-interval spectral densities or 1/3 octave analyses of the time histories. In the case of the Prosig software, since it uses shock response analysis for the initial content, for consistency it uses the same type of analysis for determining the SRS variation from one epoch to another. Note that it is the shock response spectrum that is divided up into epochs not the seismic time history. For each SRS analysis frequency it compares the standard deviation of the time-interval SRS amplitudes against user-defined limits.

In the example below the strong part of the motion is clearly seen to lie between 5 secs and 35 secs.

Figure 3: Seismic Time History

The complete waveform is than analyzed over a range of frequencies and damping factors and the resultant peak absolute values for each epoch for all frequencies and all damping factors is calculated and stored for statistical analysis. A typical shock response time history for a 10Hz SDOF system with 5% damping is shown in Figure 4. The red lines depict the start and end of each 6 seconds epoch.

Figure 4: Shock Response Time History (@10Hz, 5% damping) showing epochs

Individual peak absolute values of the shock response time history are compared against the mean peak absolute value across the 5 epochs and if any of them diverge by more than a user specified amount from the mean then this indicates that the frequency content is not stationary and the test data has failed to meet the IEEE-344 standard. As in the previous qualification test the IEEE-344 standard gives no clear indication of what numerical limits should be used for determining statistical stationarity – it is down to the judgement of the user.

#### 4) Statistical Independence Qualification

The objective of this requirement is to verify that the resolved motions in all three (X,Y,Z) axes are independent of one another (real earthquakes are known to have this characteristic). The suggested methods for performing this test are better defined than the frequency content tests. In this case there are two possible methods: one based on coherence and another based on correlation. The Prosig IEEE-344 software supports both methods. In both cases only the strong motion portions of the three signals are processed.

a) Coherence Method
This method requires the calculation of the auto and cross spectral densities between all combinations of the three orthogonal signals and results in three ordinary coherence spectra. Taking just the (horizontal) X and Y motion, the respective time histories are x(t) and y(t). If the auto-spectral densities of each history are given by S(f)xx and S(f)yy and the cross-spectral density between the two directions is given by S(f)xy , then the coherence function is calculated as

$\gamma^2(f)=\frac{{|S(f)_{xy}|}^2}{S(f)_{xx}S(f)_{yy}}$

The coherence function can take any value in the range 0 to 1, where a value of 1 implies perfect coherence and a value of zero no coherence. To meet the statistical independence requirements the IEEE-344 requires the coherence to be less than 0.5 for all frequencies. An example of a coherence measurement is shown in Figure 5 below and which is found to be unacceptable because of a high value just below 100Hz.

Figure 5: Coherence between X and Y motions

b) Correlation Method
This method requires the calculation of the cross correlation between each pair of X,Y,Z combinations over a lag (time) range up to the duration of the strong motion. Taking the x(t) and y(t) signals only, the cross-correlation coefficient is calculated as:

$R_{xy}(\tau) = \frac{\frac{1}{N-\tau}\sum_{i=1}^{i=N-\tau}x_{i}y_{i+\tau}}{\sigma_{xx}\sigma_{yy}}$

Where N is the number of points in the strong section of the signals and $\sigma_{xx}$ and $\sigma_{yy}$ are the rms values of the two signals.

In order to meet the statistical requirements of IEEE-344, a correlation coefficient of 0.3 or less is acceptable. An example of a cross-correlation analysis for the same two X and Y signals is shown in Figure 6 below.

Figure 6: Correlation Coefficient for X and Y motions

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Sound & Vibration Signal Processing Analyst at Prosig
Adrian Lincoln is Signal Processing Technology Manager at Prosig Ltd and has responsibilities for signal processing applications, training and consultancy. He was formerly a Research Fellow at the Institute of Sound & Vibration Research (ISVR) at Southampton University. He is a Chartered Engineer and member of the British Computer Society and Institute of Mechanical Engineers.

## 3 thoughts on “Seismic Qualification Testing (Part 1)”

1. Luiz Eduardo T Ferreira