Simcenter Testing Solutions Vibration Control: System Identification and Verification
Summary
Details
Direct YouTube link: https://youtu.be/mh_kRtmtb6E
With Simcenter Testlab Revision 2206 and higher, the SelfCheck feature of Vibration Control was replaced with System Identification and Verification (Figure 1).
The System Identification and Verification is a complete holistic health and integrity check of the closed-loop control system. It also helps to ensure the safety of the Device Under Test (DUT) so that excitation levels don’t induce the predicted responses which can exceed prescribed safe levels.
This article has the following content:
1. Introduction and Background
2. The System Transfer Function (TF) Measurement Timeline
2.1 Background Noise and DC Offsets
2.2 Broadband Noise Buildup
2.3 Measure SysID
2.4 Verify Openloop & Response S/N
2.5 Extrapolation to Full Level
2.6 Report Results
3. System Identification Worksheet
3.1 Single-Axis Case
3.1.1 Acquisition Tab
3.1.2 Settings Tab
3.2 Multi-Exciter Case
4. System Verification
4.1 Single-Axis Case
4.2 Multi-Exciter Case
4.2.1 MIMO Random Control
4.2.2 Acoustics
4.2.3 Time Waveform Replication (TWR)
5. Conclusion
1. Introduction and Background
This SI/SV is new as of Simcenter Testlab Revision 2206, which was released in June of 2022. The term “Selfcheck” is more familiar since it has been around since the first release of software. The one-step selfcheck in the test process has been expanded to a 2-step SI/SV process. The first step is the “System Identification” (SI) and the second step is the “System Verification” (SV):
- System Identification (SI): The SI, (very similar to the previous “Selfcheck”) will first measure the System Transfer Function (TF) of the entire control and instrumentation loop.
- System Verification (SV): The SV uses the results and SI information to derive the Inverse Transfer Function (ITF) which is used to calculate the drive voltage signals that are sent to the amplifier/shaker. The tools that are available in the SV interface can also be used to investigate in more detail, information about the system and the instrumentation in case there are problems detected either directly with the SI results or when predicting the responses which will occur after the test has begun with the Device Under Test (DUT) in place on the shaker.
As before, the SI/SV is a pre-test check of the control system. There are many components and electrical connections in the system that need to be checked for potential issues (Figure 2).
There is a lot that can go wrong! This check is becoming more important since there is a trend in industry to extend from single axis to multi-axis testing, or more generally, multi-exciter testing. This makes the system checkout more complicated, so a more thorough procedure is required to fully verify the system, but still be efficient to avoid over-burdening the operator.
For more information regarding multi-input multi-output (MIMO) testing see the community article: Multi Input Multi Output MIMO Testing
In general, the same SI/SV process is the same for all Simcenter Testlab environmental applications and control modes, some of which are shown in Figure 3.
Figure 3: System Identification (SI) and System Verification (SV) are common to all Simcenter Testlab Environmental test modes.
There are some slight differences in the options and results when using SI/SV for the different applications, and these will be described through the article.
2. The System Transfer Function Measurement Timeline
The system transfer function (TF) is a complete end-to-end check of the entire control and instrumentation chain. This TF is also referred to as the “SysID”. The TF defines the response spectrum measured due to the outgoing voltage spectrum produced by the control system. The TF is the basis from which all other results of the system check are determined, so it is important that an accurate measurement is made. The quality of the TF is indicated by the Coherence function. If there are bad coherence results then that is the first flag that will be raised alerting a problem. The SI uses a low-level random signal to measure the TF. The SI procedure is described in the following segments and the timeline is described schematically in Figure 4.
Figure 4: Timeline for System Identification (SI) procedure steps.
The following provides a description of the sequence of steps which are depicted in the System Identification (SI) measurement procedure:
2.1 Background Noise and DC Offsets
With no signal from the Simcenter SCADAS DAC (Digital to Analog Converter) driving the shaker system, the background noise level on all channels is measured (Step 1). This is also where DC offsets and DC variations are checked. This is the first check that evaluates any unwanted noise in the system, either AC or DC related, that will contaminate the measured signals. Sometimes there are issues with electrical noise due to ground loops. A scope mode is available to look at the noise in the time or frequency domain to help assess the sources of the noise.
2.2 Broadband Noise Buildup
The measurement starts by sending out a low level, broadband vibration signal from the DAC output (Step 2). Mainly for safety’s sake, this is sent out at a very low level, but also so as not to induce fatigue in the structure.
The output is built up in a number of levels determined by the setup parameters until the minimum RMS level is achieved. The first level is determined by the Maximum voltage divided by the number of steps, and each subsequent steps use the same step size. After the minimum level has been reached, then at each step the signal-to-noise ratio is checked, (“Minimum signal to noise ratio” parameter in the SI Settings). If this is not achieved at each step, then an “Open Channel” message appears.
2.3 Measure SysID
After the minimum level is reached, the control channels are used to calculate their signal to noise ratio (S/N) and coherence. All these criteria are checked for the appropriate minimum or maximum acceptable levels. If these criteria are met, the drive output is then gradually reduced to zero (Step 3). This is also where the initial TF is measured. The default minimum (5mV) and maximum (20mV) levels are sometimes too conservative and need to be increased to get good S/N results. This is especially true if the lab has inherent noise issues, which can be introduced from the amplifier, shaker, or from instrumentation wires running from the controller to the shaker and coming in the vicinity of power cables. If a minimum coherence defined by the random control safety parameter “Min. system coherence” has not been achieved across the test spectrum, then a warning is given to check the coherence. The Minimum System Coherence parameter is set in the Advanced Control Setup parameters menu under the "Safety" tab.
2.4 Verify Openloop & Response S/N
The next step (Step 4) is where quality checks are made for all control and response channels such as S/N, open channels, and overloads. In addition to calculating levels on all channels, transfer functions between all control and response channels using the DAC Voltage spectrum as the reference are also computed.
2.5 Extrapolation to Full-Level
These transfer functions are checked for consistency via a coherence function and used in the prediction of levels for the full-scale test (Step 5) using a linear transformation and the full-level target profile to project the DAC voltage levels required for the full-level test.
2.6 Report Results
The results from all of the prior steps are then summarized in a report to the operator (Step 6). In addition, a summary report can also be saved in the System Identification folder for the test section, if the option to save the “SI & SV report” is checked on in the settings.
3. System Identification Worksheet
The System Identification worksheet is very similar with the traditional “Selfcheck” of previous versions. All terminology is the same and the data that is presented from the acquisition is also the same, although in a reconfigured interface. With the expansion of applications to include multi-axis excitation, this is reflected in an expansion of the presentation of the SysID acquisition and results. There are slight differences between the 2 cases for SIMO and MIMO as will be described next.
3.1 Single-Axis Case
For a uniaxial shaker setup:
3.1.1 Acquisition Tab
In the System Identification worksheet, there are two tabs at the top, “Acquisition” and “Settings”. First, in the Acquisition tab, there are two selections with radio buttons, “Acquisition” and “Prediction”. With the acquisition radio button selected, a real-time update of the tabulated and graphical data is available and will be presented to the operator in the “Responses” area of the display. An example is shown in Figure 5.
Figure 5: During the measurement of the system transfer function (TF), there is a real-time update of the results and data as it is acquired in the Acquisition tab (top) of the System Identification workbook.
Key Points of the Acquisition Tab:
- A global status is given with the color-coded indicator which can be green (all ok), orange (warning but test may continue), or red (test may not proceed).
- In the Overview of the SysID Results at the top, the “Loop Gain” gives the ratio of control response level to the voltage level output from the DAC. This should be consistent between different tests when the amplifier level is set in the same position. There should be a balance between the amplifier setting and how much DAC output is required to take advantage of the dynamic range of both.
- During the acquisition and drive build up, there is a live update of the tabulated data for each channel over the entire spectrum.
- There is also a live graphical display for each channel. The pull-down allows to choose a number of graphs and a choice of time or spectral results.
- A very convenient means for evaluating noise issues in the system is available as an option using the digital scope prior to the drive build-up. This is also very useful when having sensors that need time to settle, for example charge accelerometers.
- There is an option to customize the name of the System Identification results and all data will be saved into the data folder in the Navigator worksheet. The stored results can later be recalled in the SV interface.
After the acquisition is completed, the “Prediction” radio button is automatically selected. This can also be selected manually. The results of Step 5 in the timeline are used for full level predicted responses for all control and response channels (Figure 6).
Figure 6: The results from the measurements are used to predict full test levels.
If levels are not expected to exceed any limits then an “OK” is given for each channel.
3.1.2 Settings Tab
In the System Identification worksheet, the other tab called "Settings" at the top is used to set up the parameters for the System Identification testing.(Figure 7).
Figure 7: The "Settings" tab (top) of the System Identification workbook is used to tailor the test.
Key Points of the Settings Tab:
- Depending on the situation, there may be reasons to use sources other than the traditional periodic random type. There is also the pseudo, shaped and the user defined arbitrary source types available.
- The drive spectrum can be used which is predicted from a measured ITF in the System Verification.
- There is a possibility to manually increase the voltage output to the amp/shaker for the sake of safety. This would also be useful in case the amplifier settings were changed and you want to be sure with a manual buildup of voltages.
- The same settings as were available in the previous selfcheck setup sheet are still available. By default, the settings of the SysID are inherited from the test setup, but these can be manually overridden.
3.2 Multi-Exciter Case
In the System Identification worksheet, compared with the single-axis case, there are a few slight differences for the multi-exciter case regarding the setup information:
- A minimum requirement in the MIMO test instrumentation is that there are at least as many control sensors as there are exciters. When the number of controls equals the number of exciters, this is what’s called “Square Control”.
- There can also be more control sensors than there are exciters, and this is called “Rectangular Control”.
In all cases, there is typically going to be some level of coupling in the excitation responses. This means that each individual control sensor can potentially have response energy coming from each individual exciter. It is the job of the controller software to distinguish the response energy due to each individual exciter. The fundamental requirement for this is to have independent complex source signals sent to the exciters. This is depicted in matrix form in Figure 8.
Figure 8: The objective of the System Identification for MIMO testing is to generate the transfer function matrix [H]] between each control and each excitation source.
For more clarification and information about these concepts please see the community article: Multi Input Multi Output MIMO Testing.
To accommodate the independent sources by decorrelating the energy, an extra option is available in the Settings Tab to set the relative phases of each excitation source, as shown in Figure 9.
Figure 9: To accommodate the requirement for independent sources for MIMO testing, there is an extra tab to set the phase strategy of random sources.
More about random and Schroeder phase strategies in the knowledge article: Using Pseudo-Random for high quality FRF measurements
4. System Verification
The System Verification worksheet allows for a deeper insight of what to expect when the actual test is run at full level. Based on accurate measurements during the System Identification, the low-level drives and responses are used in a linear extrapolation of the system transfer functions to predict what can be expected. This worksheet is very useful for more complicated tests including multi-axis testing, however for more basic testing the SV is not necessary and can revert to the same number of steps as was standard with the Selfcheck. This is a selection in the Advanced tab with the “Autocalculate” radio button selected. In this case a test can be started after the SysID is measured.
The SysID can also be bypassed if there is a valid SysID folder of data available by selecting a System Identification folder and by selecting the “Last System Identification Acquisition” or assigning a valid SysID to the Input Basket, as shown in Figure 10.
Figure 10: The System Verification workbook can be bypassed after the System Identification measurement by using the "Autocalculate" button in the "Advanced Parameters" menu of the System Verification worksheet.
Care should be taken in this case to ensure it is indeed a valid transfer function.
4.1 Single-Axis Case
System and Summary: In the System Identification worksheet, it was shown in the prior section 3.1.1 that the full test level predictions are already summarized and presented. The System Verification worksheet allows to dig deeper into these predictions and display the results in a graphical form and allows to investigate more thoroughly the measured SI data and full-level predictions. In case there are issues predicted, this is also a nice environment to efficiently investigate the source of the problem which may be used to suggest actions to overcome them. A good example of this is when overloads or open channels are predicted, then the ranges and thresholds are available to change from the default settings.'
The graphical displays in the upper portion of the interface can be used to display the transfer function data. The selections are presented with an efficient matrix-based data selection, as shown in Figure 11.
Figure 11: The System Verification provides and efficient matrix-based means for quickly displaying the results from the System Identification measurements and predictions.
As mentioned earlier, the “Autocalculate” can be used to skip the System Verification step, which is selected in the Advanced tab. The overload, range, and openloop threshold levels are also determined by the Advanced settings as shown in Figure 12.
Figure 12: The "Advanced" button can be used to set the Autocalculate option of the predictions to full level. There are also options to set the range and Openloop threshold levels.
The results of these are available for viewing in the lower right and some can be overridden by the operator to overcome the errors which may stop a test from proceeding.
When using the Shock Control application, there is an added option to show the predicted Shock Response Spectrum (SRS) as shown in Figure 13.
Figure 13: The lower right area of the System Verification workbook allows the predicted SRS Spectrum when in the Shock Control Application.
The alarm and abort levels are also included with the selected data.
Pre-Test Analysis: There is a Pre-Test Analysis minor worksheet, Figure 14, which allows to present the predicted responses and drive signals if there are response limits set.
Figure 14: The Pretest Analysis minor worksheet is available to show the predicted response limiting and notching.
This also produces an average control spectrum. If there is limiting predicted, then it is convenient to use this control spectrum as the target in the test setup. This can allow the controller to have this limiting information built into the control prior to the start, which can alleviate some of the burden of the controller.
4.2 Multi-exciter Case
System and Summary – In the MIMO case, the complexity of the test can increase quite significantly due to the number of excitation sources and control channels which can all have influence on each other simultaneously. The quality of the matrix of transfer functions acquired in the SysID step becomes much more important and must be assessed thoroughly in the System Verification step to ensure a quality and successful control test.
Verifying the quality starts with visualizing the results, as shown in Figure 15.
Figure 15: The results of the System Identification can be efficiently displayed in the System Verification workbook.
Compared with the Single-axis case, there are some added options available in the Advanced tab, as shown in Figure 16.
Figure 16: The "Advanced" tab has added options for the MIMO case.
Using these advanced options will depend on the application and MIMO Random Control “Mode”, which will be explained in the next sections.
4.2.1 MIMO Random Control
In the MIMO Random Control Test Setup worksheet, there are options in Random Control mode which will have some influence on the test setup parameter selections. The options in random control modes are shown in Figure 17 with a brief description to follow:
Figure 17: Control mode options in the "MIMO Random Control" application software.
- Matrix Mode – This is the most traditional method where the full target spectral density matrix is the full matrix between all control sensors where coupling is accounted for in the control. It requires to explicitly define all target Power Spectral Density (PSD) and Cross-power Spectral Density (CSD) terms using the corresponding profile editors.
- PSD Mode – The target spectral density matrix only consists of the diagonal Auto-power PSD targets. Typically, profiles from single-axis test specifications for x, y and z axes can be used. The cross coupling between control sensors is not part of the control and are computed automatically as a suitable positive semi-definite target matrix that:
- minimizes as much as possible the power needed for driving the actuators.
- tries to cope with the physical constraints of the test set-up in terms of coherence and phases.
- This completion of the target matrix is performed automatically when the initial estimate of the system transfer function matrix is known (i.e. after system identification), but will be allowed to change during the control test. (in PSD mode).
- Acoustic – This enables to input test references as Sound Pressure Level (SPL) in 1/1 or 1/3 octave bands. The workbook then generates line spectra from these reference profiles and further combines with the information provided by the initial estimate of the system transfer function matrix from the SysID to produce the full target spectral density reference matrix.
- Acoustic Spatial Averaging – This mode is similar to Acoustic mode but only requires one single target Sound Pressure Level (SPL) profile which applies to every control microphone in the field. This option reduces the number of clicks for the end-user in the common case where a homogeneous SPL is intended.
Having selected the appropriate mode in the MIMO Random Control Setup sheet, we will discuss the extra options in the SV Advanced tab and how they can be used:
Enhance reference profiles (ERP) – This option is available for both Structures and Acoustics modes. Enhancing the reference profile is done through a so-called projection algorithm. It will optimize the SDM by adjusting the CSD’s to achieve an optimized Spectral Density Matrix, (SDM).
General points regarding the ERP:
- The ERP only applies for the case of rectangular control where the number of control responses are greater than the number of exciters.
- The same algorithm is used in both structures and acoustics cases.
- Diagonal PSD’s are the target in all cases and should not vary.
- ERP allows to alter the CSD’s iteratively in the Pretest calculation to achieve the target PSD’s. The maximum number of iterations can be specified.
- One should always use the Enhance Reference Profiles (ERP)! It cannot make a good SDM worse and can only make a bad SDM better.
- There is an option to specify the number of iterations for the algorithm to evaluate. The calculations are done in the Pretest to generate the optimal Target SDM. This is done automatically when ‘Autocalculate’ option is on, or manually with the ‘Calculate’ button.
- More in this paper: "Experimental verification of projection algorithms and optimization routines for acoustic field uniformity enhancement in MIMO direct field acoustic control (isma-isaac.be)"
Points regarding ERP specifically for Matrix Mode:
- The entire SDM is the target response for control.
- Using the ERP allows to manipulate the CSD’s (only) in a Pretest analysis but maintains the SDM during the test.
- Matrix mode without ERP may not be physically realizable and more likely to have abort conditions on the PSD’s and CSD’s.
- Without the ERP on, the full SDM is the target and is maintained as close as possible by manipulating the complex drives, (Amp/Phase).
- Alarms and aborts are checked on entire SDM, PSD’s and CSD’s
- Maintain physical realizability, (positive semi-definite matrix)
Points regarding ERP specifically for PSD Mode:
- Only the diagonal PSD’s are maintained as targets for control
- Only PSDs are defined by user. The SDM (CSD’s only) originates from the SYSID
- When applying ERP, the CSD’s can vary during the test, but not PSD’s.
- Alarms and aborts are checked only on PSD’s.
- Minimizing of Drives is standard and is always applied automatically in Pretest. Based on paper: “A minimum drives automatic target definition procedure for multi-axis random control testing”.
Pre-Test Analysis – The goal of the system Identification is to determine the Inverse Transfer Function which allows to compute a drive signal that will adhere to a given reference response. This can be displayed in the Pretest Analysis as shown in Figure 18.
Figure 18: The complex data which makes up the "Inverse Transfer Function" between each Drive Signal and Control Sensor is shown.
For MIMO testing this involves input from multiple sources and a number of control responses that equals or is greater than the number of sources. The pseudo-matrix inversion that is used to compute these drive signals needs to have uncorrelated sources to distinguish one drive signal from any other.
With “Coupling”, or Coherent Sources it is difficult to discern the uniqueness of the input drives from one another in order to have an accurate matrix inversion. The difficulty is indicated in the so-called “Singular Values”, and the closer to zero these values are, the more difficult it is to find a unique and accurate solution. This is called an “ill-conditioned” matrix, and the control will be difficult at frequencies where the singular values are close to zero. In that case a threshold can be given and below which the values in the matrix solution will be determined in a “least-squares” sense as an estimation. It is always a good idea to evaluate the Singular Values as part of the System Verification for MIMO testing. An example of a Singular Values display is shown in Figure 19.
Figure 19: Evaluating the Singular Values functions (blue and magenta curves) gives an indication of controllability.
One of the singular values is set to a value of one at every frequency. The others (there is one singular value per control channel) are scaled relative to the first. The higher the values, the easier the Multi-Input Multi-Output (MIMO) system is to control.
4.2.2 Acoustics
Optimize Control Selection: The discussions in the previous section for MIMO Random Control also applies for the Acoustic case, but the “Optimize Control Selection” is only available in MIMO Random Control for Acoustic Control Modes for both the Acoustic and Spatial Averaging methods. This is a feature that is typically targeted for Direct Field Acoustic Testing (DFAT) applications. The algorithm identifies an optimal set of L control channels out of T number of channels, where L<T. The purpose is to reduce the number of control channels as low as possible but still maintaining the reference PSD’s. This can significantly reduce the burden of the controller while still achieving the desired control. The minimum number of control microphones required is equal to the number of Drives. Using the options available, optimization of control selections, along with ERP, and coupled with the Minimization of the Drives, will render the control SDM as the most optimized in terms of efficiency of the setup and controllability.
Pre-Test Analysis: Implementing the optimal control microphone selections is done in the “Pre-Test Analysis” sub-worksheet of System Verification, as shown in Figure 20.
Figure 20: The optimal control microphones are chosen out of the number of channels deemed as "Control" in the channel setup.
The input parameters which the algorithm will work on are determined in the “Processing” panel. This will allow evaluating the minimum number, and location of control channels needed to properly control the acoustic volume based on the reference profiles for both acoustic modes. During the System Identification, the total number of control channels can be a combination of control and response monitoring microphones, and this declaration of control channels is defined in the channel setup.
Using all of the microphones available as candidate control choices, the algorithm will pick and choose out of these, the optimal set of control microphones, leaving the rest as response monitoring microphones. The results of this are shown in Figure 21.
Figure 21: The predicted octave response of the three chosen control microphones is shown along with the corresponding alarm and abort spectrums. The locations are also graphically shown in the geometry display.
The example shown is for three control microphones chosen out of six candidates.
4.2.3 Time Waveform Replication (TWR)
The System Identification worksheet is the same as the other applications, however there are some slight differences in the Time Waveform Replication (TWR) workbook related to the System Verification worksheet. In this application, the “System Model” is introduced. This is a group of spectral data which consists of 3 components: the System Transfer Functions (g/V), the Coherences, and the Singular Values resulting from the ITF calculations. Viewing of the model is accommodated in the System Verification interface as shown in Figure 22.
Figure 22: The TWR “System Model” consists of three components which can be viewed in the displays.
A model comes automatically after the SysID is completed. By default, this is then deemed the “New Model”. The details of this worksheet are beyond the scope of this document and are left to the online help. There are however a couple of important points regarding the worksheet which are applicable. There are 3 sub-tabs in the worksheet which allow to inspect the components of the model which will be used in the control. The first tab is the “FRF” tab which was shown and described previously. The next tab is the “Inverse FRF” tab which allows inspecting the ITF or the Singular values. The choice that is shown is selected by the radio buttons as shown in Figure 23.
Figure 23: Inspection of the model components Inverse Transfer Function (ITF) and Singular Values are available for viewing within the "Inverse FRF" tab.
The next tab available is for using the model to calculate the predicted drive signals and corresponding responses. This is shown in Figure 24.
Figure 24: Using the "Prediction" tab, the predicted drive signals can be calculated with the "Calculate" button.
The predicted data can be displayed in either the time or frequency domains.
Note: The predicted results can be calculated only if the “Activate Recording” radio button is turned on in the System ID Settings tab.
5. Conclusion
The System Identification/Verification process (formerly referred to as “Selfcheck”) is important to verify the integrity of the entire control system, including all software settings, mechanical, and electrical components. It also serves to ensure the safety of the unit under test, which can sometimes be very expensive hardware, such as spacecraft or other.
The capabilities and purpose of the selfcheck have been retained with the System Identification (SI) worksheet, but an extension to this is warranted in the analysis of the results due to the increased complexity from the trend in multi-exciter testing. The System Verification (SV) worksheet allows a more extensive but efficient means for assessing the results and diagnosing any issues that may be uncovered for both single and multi-axis testing.
The System Identification and System Verification process is common to all environmental control modes, including structural and acoustical applications, but the nuances of each are addressed in the article.
Hope this helps with using System Identification and System Verification!
Questions? Email william.flynn@siemens.com.
Related Vibration Control links
- Index of Testing Knowledge Articles
- What is Vibration Control Testing?
- Vibration Control FAQs
- Power Spectral Density
- Fatigue Damage Spectrum
- Breakpoint Table Generator
- Getting Started with Random Control
- Random Control: Weighting, Frequency Resolution, and DOFs
- Random Control: Measurement Channels
- Sine Control: Estimation Methods
- Sine Control: Closed Loop Control Parameters
- Sine Data Reduction
- Sine Control: Notching
- Simcenter Testlab: Tracked Sine Dwell
- Vibration Control: Multi-Point Control Averaging
- Single Axis Waveform Replication (SAWR)
- Vibration Control: Test Sequencing
- Direct Field Acoustic Noise Testing
- Shock Response Spectrum
- Classical Shock Pulses
- Shock Response Analysis and Synthesis
- Kurtosis
- "Excessive DC Level" message
- Inverse Transfer Function (ITF) in Random Vibration Control
- Vibration Control Seminar
- Vibration Control YouTube Playlist