Need to calculate sound levels in an identical manner as a sound level meter?
Simcenter Testlab and Simcenter Testlab Neo can calculate sound levels with the same precision as a dedicated sound level meter.
This article explains all sound level functions that can be calculated in both Simcenter Testlab and Simcenter Testlab Neo:
1. Background 1.1 Standard Sound Levels: LAF, LAS, Limpulse, Luser 1.2 Average Sound Levels: RMS, LAeq 1.3 Sound Exposure Levels: SEL, LAE 2. Calculating Sound Levels in Simcenter Testlab Neo 2.1 Online Time Data Acquisition 2.2 Process Designer 3. Calculating Sound Levels in Simcenter Testlab "Classic" 3.1 Online Signature Acquisition 3.2 Signature Throughput Processing
1. Background Section
Sound Level Meters (sometimes referred to with the acronym SLMs) are used to measure the amplitude of sound in various environments for ensuring compliance with safety standards and to manage noise pollution. Sound Level Meters have been in use for many years (Figure 1).
Figure 1: Older analog sound level meters (left) indicated noise levels with an analog needle (bottom middle). More modern sound level meters have digital readouts (right).
Sound level meters quantify sound in decibels (dBs). In older sound level meters, the dB level was indicated by a needle. In more modern sound level meters, the needle was replaced by a digital readout.
Settings on the sound level meter affect how the decibel level shown on the meter is calculated:
Time Integration Constant: The time integration constant (or time averaging frame) determines how quickly the decibel readout responds to changes in sound levels. Setting options include fast (0.125 seconds), slow (1 second), and impulsive (0.035 seconds or 1.5 seconds).
Weighting: The sound level is affected by the weighting filter applied to the data. Possible weightings include Linear, A, B, C, etc. For example, the A-weighting setting is used to approximate the frequency response of human hearing.
Averaging: The decibel level can be a peak hold average or an RMS average.
When performing a sound measurement, there are often standards which specify the settings to be used.
1.1 Standard Sound Levels: LAF, LAS, Limpulse
The sound level metrics LAF, LAS, and Limpulse characterize the sound level by applying different time weightings (Fast, Slow, and Impulse, respectively). These weightings determine how quickly the measured level responds to fluctuations in the sound signal.
How quickly the sound level metric changes due to fluctuations in the sound signal depends on the Time Averaging Frame (also called the Time Integration Constant):
LAF (Level A-weighted Fast): LAF uses an exponential time averaging method with a time averaging frame of 0.125 seconds (1/8 second). It is designed for quickly changing, transient signals. The level ramps up relatively quickly (< 0.5 seconds to reach full amplitude) and decays at a rate of 34.7 dB per second.
LAS (Level A-weighted Slow): LAS uses an exponential time averaging method with a time averaging frame of 1 second. It is better suited for more stationary noise levels. The level takes almost 5 seconds to ramp up to full amplitude and decays more slowly compared to L>sub>AF.
Limpulse (Level Impulse): Limpulse employs a peak detector. It has a time constant of 0.035 seconds on the rising edge of a signal and a 1.5 second time constant on the falling edge. Limpulse captures the maximum sound pressure level peak rise value more quickly than LAF (rising edge) but has a slower decay rate (falling edge) than LAS.
The response levels of LAF (red), LAS (yellow), and Limpulse (purple) to the same sound (black) are shown in Figure 2 below.
Figure 2: Overlay of level responses to the same sound signal (black): LAF (red), LAS (yellow), and Limpulse (purple).
In the graph above:
LAF responds quickly to changes in the signal compared to LAS due to the exponential time averaging method setting. LAS is suitable for slowly changing signals, while LAF is used for constantly varying transient types of signals. In older Sound Level Meters, the needle moved more quickly in response to sound with the fast setting than the slow setting.
Limpulse has the quickest response to the upward sloping fluctuation in the sound signal and slowest response to the downward fluctuation. This is because of the peak detector nature of the Limpulse calculations. Limpulse is often used for single impulsive events like gunshots or impacts. In older Sound Level Meters, the slow decay on the falling edge gave the user time to write down the peak value.
The formula for LAS and LAF is shown in Equation 1 below:
Equation 1: Formula for Level A-weighted Slow (LAS) and Level A-weighted Fast (LAF) expressed in decibels
Where
pA(ξ) is the instantaneous A-weighted sound pressure
pref is the reference sound pressure (20 μPa)
t is current instance in time
ξ is an instance of time within the integration interval (integration interval is from -infinity to t in this case)
dξ is time integration step
τ is the time constant (1 second for slow, 0.125 seconds for fast)
The function e−(t−ξ)/τ acts as a weighting factor that decreases exponentially as you go back in time from the present moment (t) to past times (ξ). The weighting effect:
Sound that occurs at the current time (when ξ = t) have maximum weight (100% of current sound)
Sounds from τf seconds ago have a weight of e-1 which is approximately 0.368 (37% of current sound)
Sounds from 2τf seconds ago have a weight of e-2 which is approximately 0.135 (14% of current sound)
Sounds from 3τf seconds ago have a weight of e-3 which is approximately 0.05 (5% of current sound)
The Simcenter Testlab LAF, LAS, and Limpulse output for a sound signal is shown in Figure 3 below:
Figure 3: Top – Sound recording (red trace), Bottom – LAF (blue), LAS (green), and Limpulse (black).
In this article, the sound level calculation results will all be calculated and shown for the same signal (red in the graph above).
1.2 Average Sound Levels: RMS, LAeq
Some sound level metrics try and represent the average level of sound over the measurement time:
RMS (Root Mean Square): The RMS method uses linear averaging (all samples equally weighted) within the time averaging frame.
LAeq (Level A-weighted Equivalent): LAeq also uses linear averaging with a 0.1 second time averaging frame and any time increment. It provides the constant sound pressure level that would contain the same amount of sound energy as the original time-varying sound over the same period.
Given the same amount of time, RMS of an A-weighted signal equals LAeq when averaged over the full measurement time.
The formula for LAeq is given in Equation 2 below:
Equation 2: Formula for Level A-weighted Equivalent (LAeq) expressed in decibels (dB)
Where:
pA(ξ) is the instantaneous A-weighted sound pressure
pref is the reference sound pressure (20 μPa)
t is current time instance
ξ is an instance of time within the integration interval (integration interval is from beginning of measurement signal to current time in this case)
dξ is time integration step
T is the measurement time interval in seconds.
Simcenter Testlab can produce two results based on the measurement time interval setting used: “LAeqT” (choose “Cumulative” option) and “LAeqt” (choose “Instantaneous” option):
“LAeqT” is based on the total accumulated time from the beginning of the measurement.
“LAeqt” is based on the time interval between two consecutive time data points.
LAeq calculation results from Simcenter Testlab are shown in Figure 4 below:
Figure 4: Top – Sound recording (red trace), Bottom – LAeq cumulative results (LAeqT, blue trace) and LAeq instantaneous results (LAeqt, red trace).
1.3 Sound Exposure Levels: SEL, LAE
Sound Exposure Level (SEL) and Level A-weighted Exposure (LAE) try to indicate the amount of sound that a listener is exposed to over time.
SEL (Sound Exposure Level) and LAE (Level A-weighted Exposure) both normalize the sound exposure to a reference time of 1 second. This allows comparison of sound events with different durations.
The formula for LAE (which is A-weighted) is in Equation 3 below. The formula for SEL is the same but has Linear weighting instead of A-weighting.
Equation 3: Formula for Level A-weighted Exposure expressed in decibels (dB)
Where:
pA(ξ) is the instantaneous A-weighted sound pressure
pref is the reference sound pressure (20 μPa)
t is current time instance
ξ is an instance of time within the integration interval (from beginning of measurement signal to current time)
dξ is time integration step
T0 is a reference time of 1 second used to normailize the measurement
T is the measurement time interval (in seconds) (can be from beginning of measurement or between samples)
Simcenter Testlab software can produce two results labelled “LAET” (choose “Cumulative” option) and “LAEt” (choose “Instantaneous” option):
“LAET” is based on the total accumulated time from the beginning of the measurement.
“LAEt” is based on the time interval between two consecutive tracking data points.
The result is scaled to represent the equivalent sound energy normalized to one second.
The Simcenter Testlab LAE output for a sound signal is shown in Figure 5 below:
Figure 5: Top – Sound recording (red trace), Bottom – LAET cumulative results (LAET, blue trace) and LAE instantaneous results (LAEt, red trace).
SEL uses linear weighting while LAE is A-weighted. Both use a time averaging frame of 0.1 seconds.
Notice that the LAET and SELT values only increase or accumulate over time.
2. Calculating Sound Levels in Simcenter Testlab Neo
In Simcenter Testlab Neo, the SPL (Sound Pressure Level) method provides options to calculate all the standard sound levels (LAF, LAS, Limpulse), average levels (RMS, LAeq), and exposure levels (SEL, LAE). This can be done both live during acquisition and in postprocessing.
2.1 Online Time Data Acquisition
To monitor the sound level while acquiring data, go to the Measure worksheet of Simcenter Testlab Neo Time Data Acquisition as shown in Figure 6.
Figure 6: Sound level metrics can be monitored live in Simcenter Testlab Neo Time Data Acquisition.
With the SCADAS system not armed, highlight the data sampling rate in the upper right that contains the microphones to be used for the sound level monitoring. After highlighting the sample rate, the icons just above become sensitive.
Click on the icon with the word "dB" and a needle showing. An entry “SPL” should appear under the sampling rate. Highlight the word “SPL” (Sound Pressure Level) and define the level calculation to be performed under the “…” button. Choose SEL, LAeq, etc as desired.
Once the SPL is defined, arm the system and choose the appropriate data to show in the Active Run pivot table.
In the method library, find the method “SPL”. It has a symbol that represents the needle found on an analog sound level meter (Figure 7).
Figure 7: Sound level metric options available in the SPL method of Simcenter Testlab Neo Process Designer.
The method properties allow selection of the sound pressure level type, which determines the time averaging method, frame, and increment. Some settings are fixed based on standards while others can be adjusted:
LAF: Is calculated every 0.025 seconds. Each 0.025 step in the result trace is based on a 0.125 second time averaging frame.
LAS: Is calculated every 0.02 seconds. Each 0.02 step in the result trace is based on a 1 second time averaging frame.
Limpulse: Is calculated every 0.2 seconds by default but can be changed by user. Uses 0.035 second time averaging frame on rising edge and 1.5 second time averaging frame on falling edge.
LAE and SEL: Calculated every 0.1 seconds by default, but can be changed by user. Time averaging frame is 0.1 seconds.
LAeq and RMS: Calculated every 0.1 seconds by default, but can be changed by user. Time averaging frame is 0.1 seconds.
The default settings of the Simcenter Testlab Neo methods ensure as much of the sound recording data is used as possible. The intention is to have no gaps and try to use all samples in the calculation of the sound levels.
For exposure metrics like LAE and SEL, the time increment can make a difference on the accumulated total and "end time". For example, with a 9.862 second recording and with 0.1 second increment, the last data output point will only reach up to 9.8 seconds. With an increment of 0.005 seconds, the last data output point will reach 9.860 seconds.
The "Maximum hold" setting will report the peak value even if it falls between output samples. It will report the maximum on the next sample.
3. Calculating Sound Levels in Simcenter Testlab "Classic"
Sound Level Meter functionality is also available in Simcenter Testlab "classic" in both online and postprocessing.
3.1 Online Signature Acquisition
In Simcenter Testlab Signature “classic”, after defining some microphone channels, go to the “Online Processing” workbook. In the middle there is a tab called “Level Calculation” (Figure 8) that is used to define sound metrics (LAF, LAS, etc) to be calculated.
Figure 8: In the “Online Processing” worksheet of Simcenter Testlab Signature, add sound level metrics to be calculated in the “Level Calculation” tab.
The time between sound levels is determined by the tracking parameters in Simcenter Testlab. For example, in the Tracking Setup worksheet, the increment can be set by the user (Figure 9):
Figure 9: Tracking settings in Simcenter Testlab "classic".
Based on the tracking (time between rpm steps, etc) not all data samples may be used in the calculation of the sound levels. There might be gaps in the output sound level data.
The tracking points should not be confused with the time averaging frame (ie, time constant). The time averaging frames (0.125 seconds for fast, 1 second for slow, etc) are the same between Simcenter Testlab Neo and Simcenter Testlab classic, but the tracking interval can be set differently.
More information about setting up a measurement in Simcenter Testlab Signature can be found in the knowledge article: Simcenter Testlab Signature.
3.2 Signature Throughput Processing
To calculate sound levels from an already recorded sound signal, turn on “Signature Throughput Processing” from the main menu of Simcenter Testlab.
In the “Navigator” worksheet, right click on the time history to be processed and choose “Replace in Input Basket”. In “Time Data Selection” add the input basket contents to the dataset.
Then go to “Time Data Processing”. Choose “Change Settings” under Section as shown in Figure 10.
Figure 10: Define sound level metrics (LAF, LAS, etc) under the “Level Calculation” tab of the “Change Settings” button of Section.
From the “Level Calculation” tab, select the sound level to be calculated from the pulldown and click “Add”. Multiple functions can be calculated from the same recording.
The tracking increment can be set with the "Change Settings" button under "Acquisition Parameters".
