(Pro version only)
When a specific test setup has been selected in the channel selector in the Main Toolbar the Estimate tab window is available in the SSI editor.
The Estimate tab window of the Stochastic Subspace Identification editor is presented below in the case of the Plate 4 Datasets example:
In the example, it is the Unweighted Principal Component (UPC) technique that has been chosen. However, it could just as well be the Canonical Variate Analysis (CVA) algorithm or the Principal Component (PC) algorithm.
The window is divided vertically in two. On the left a stabilization diagram is shown and on the right some information relating to the stabilization diagram is presented.
The validation of the time domain estimation of the state space models is actually performed in frequency domain. The reason for this is that it is very easy in frequency domain to see the repeated trend of structural modes when estimating multiple state space models. But you should remember that the actual estimation behind the screen is performed on the raw time series data of the currently selected test setup in time domain.
The stabilization diagram presents the natural frequencies of all the estimated eigenvalues as well as a background wall-paper of the Singular Value Decomposition of the spectral density matrices of the currently selected test setup. This wall-paper has nothing directly to do with the estimation. However, it is a valuable help in the search of structural modes since these will be located at the spectral density peaks.
The horizontal axis is a frequency axis ranging from zero to the Nyquist frequency. The vertical axis lists the dimensions of the available state space models. This range goes from 1 to the maximum state space dimension specified in the Signal Processing configuration.
The problem of parametric model estimation is that you do not know the true model order. In our case it means that the exact state space dimension is unknown. The way to overcome this is to estimate a range of candidate state space models. The important issue here is that the information of the structural (physical) system will be contained in all the estimated models if the state space dimension is high enough. This is revealed as a repeated trend across the state space models of some of the estimated eigenvalues (the vertical line of red crosses in the above figure). If such a repeated trend is located at a resonance frequency it is a strong indication that a structural modes has been estimated.
The problem is that there can be a lot of candidate models and in order to minimize this number you should make use of the so-called modal indicators. You set up a series of requirements that the repeated modes must fulfill in order to be called stable.
A stable mode of a model is one that compared with one of the estimated modes of the previous model fulfill the union of the following requirements:
A user-specified maximum allowed deviation of the natural frequency of the mode when compared with one of the modes of the previous model.
A user-specified maximum allowed deviation of the damping ratio of the mode when compared with one of the modes of the previous model.
A user-specified maximum allowed deviation of the Modal Assurance Criterion (MAC) of the mode shape vector of the mode when compared with one of the modes of the previous model.
A user-specified maximum allowed deviation of the Modal Assurance Criterion of the initial modal amplitude vector of the mode when compared with one of the modes of the previous model.
If the deviations of all the above requirements of a mode is less than the specified maximum allowed deviations then a mode is characterized as stable and will be marked with a red cross. If one or more of the above requirements are not fulfilled then the mode is characterized as unstable and will be marked with a green diagonal cross. So by decreasing the maximum allowed deviation the number of candidate models will also decrease. The setting of the requirements are performed in the Modal Indicator tab. The modal indicators used are documented in the Modal Indicators tab of the Stochastic Subspace Identification editor.
When a state space model is estimated from measured data not only structural modes will be estimated but also so called noise (computational) modes. These noise modes are used by the algorithms to account for non-fulfilled assumptions. Noise modes appear e.g. in the following situations:
Limited data records (Accounts for the violation of the infinite amount of data assumption).
Non-linearities (Accounts for the violation of the linear system assumption).
Colored noise caused e.g. by non-white excitation and / or filtering (Accounts for the violation of the assumption of having white noise disturbance only).
Typically, noise modes are spreaded in a non-systematic and non-repeated way. Because they usually are very heavily damped and because structural modes usually are lightly damped we can exclude large parts of the noise modes from the analysis by looking at the damping of a mode. If the damping ratio is larger than some predefined value, say e.g. 5%, then the mode is probably a noise mode. The setting of the range of the damping ratio of a structural mode is performed in the Modal Indicator tab. Modes having damping ratios outside this range are characterized as noise modes and marked in the stabilization diagram with yellow diagonal crosses. Besides being marked they are also excluded completely from the evaluation of stable/unstable modes.
Estimating models can be done using the Signal Processing Control configuration editor available from the Project, Signal Processing, Signal Processing Control menu item or from the Signal Processing Control pane in the task bar. Alternatively, models can be estimated directly from the SSI editor when no models have been estimated using the Signal Processing Control. Please note that before this option is available the Maximum state space dimension must be enabled in the Signal Processing Control editor before the loaded data is processed.
In the following image it is assumed that no models have been estimated using the Signal Processing configuration editor. When you start the Stochastic Subspace Identification editor the first time after having processed the loaded data you will see a window like below:
As it can be seen, no state space models have been estimated yet. Now, in order to find a sensible range of models to estimate you should firstly inspect the singular values of the weighted common SSI input matrix. These values can be inspected in the stabilization diagram window (marked with yellow in this example).
The singular values (the yellow horizontal bars) indicate the rank of the weighted common SSI input matrix. What you are doing when you estimate a state space model is to specify what subspace of singular values of this matrix to include in the estimation. This subspace should at least include all singular values significantly different from zero.
Let us estimate models with state space dimensions from 30 to 50. We select the desired range by pointing at the dimension 30 with the mouse and pressing the left mouse button. Keeping the mouse button down drag the mouse to the dimension 50 as shown below (this procedure can also be done in reverse order):
In the information window to the right we see the actual position of the mouse. No models have been estimated so far. To estimate these the user must click the right mouse button somewhere in the Estimate tab window. This will open the following context-sensitive menu:
Alternatively the user can click the Estimate Selected Models button 
in the SSI toolbar.
Selecting the Estimate Selected Model(s) will open the following Estimate Models dialog:
In the appearing dialog options for the State Space Dimensions are available. Clicking the Estimate multiple models will activate the Start, Stop and Increment selectors to the right in the dialog. Use the three boxes to setup the estimation range and increment as wanted.
The settings can be transferred to the remaining test setups (if present in the project) by clicking the Update all Test Setups field.
In the dialog are also options for Crystal Clear SSI ® . This algorithm can be Disabled, enabled in Automatic mode or enabled in Manual mode. For now, select the Disable option. Later on this page the effect of enabling Crystal Clear SSI ® will be shown.
When all settings have been selected, click the Estimate button to estimate the selected models. The estimation status will be shown in the status bar as shown in the picture below:
When the Estimation process has finished, click the Close button. Now the modes in the selected range will be shown in the Estimate tab window. When finished estimating, a result as below will appear:
As seen in the picture above a lot of details are shown in the stabilization diagram. It might be convenient for the user to get a closer look at the range of interest. This can be done by marking the range that the user wants to zoom to with the left mouse button followed by a click on the right mouse button. The context-sensitive menu will appear again. This time the user should choose Show Models in Selected Range.
The estimated models are shown as below. Please note the dimension axis that now corresponds to the selected range.
The next task is then to verify if one of the estimated state space models is adequate. First you narrow the range by decreasing the maximum allowed deviation of the modal indicators. Then you inspect the modal result of the candidate models by pointing the green cursor rectangle at the models and looking in the Modal Results window. If you are unsure about the result try to extend the range of estimated models. If a state space model seems to be appropriate, then you select it for Mode Selection and Linkage (see below).
If you have more than one test setup in the project you open the Data Organizer window or go to the channel selector in the Main Toolbar to change to the next test setup. You can then go back to the Stochastic Subspace Identification editor and estimate an adequate state space model for this next test setup.
Note: If the modes do not seem to stabilize properly, or if a presumably adequate model is close to the maximum state space dimension, or if the singular values of the weighted common SSI matrix does not drop close to zero at say half of the maximum state space dimension, you should definitely try to increase the maximum state space dimension in the Signal Processing configuration. This is done in the Signal Processing configuration wizard. An example of a bad situation is shown below for the same building model test setup and with the same choice of modal indicators. The problem is that the maximum state space dimension only is 16 instead of 80 as before.
When you have found an adequate state space model you must select it for Mode Selection and Linkage. This means that you select which of the modes of the state space model that are structural and you link the mode shapes of these modes together across the test setups.
First you move the green cursor rectangle to the adequate model, then secondly you select the menu item Project, Modal Analysis, Stochastic Subspace Identification, Select Cursor Model for Mode Selection and Linkage or click Select Cursor Model for Mode Selection and Linkage from the context sensitive menu as shown below:
Alternatively you can click the Select Model for.... button 
in the SSI toolbar.
Any previous selected and linked modes will now be overwritten by this action, and when you remove the cursor rectangle from the model you will then see a cyan rectangle that is locked to this model to indicate the selection.
In the Estimate Models dialog shown above, there are 3 options for Crystal Clear SSI ® : Disable, enable in Automatic mode or enable in Manual mode. If the Model Estimation is repeated with Crystal Clear SSI ® turned on, then the Stabilization Diagram is likely to change substantially. Open the Estimate Models dialog again and check the Automatic option in Crystal Clear SSI ® :
Press the Estimate button again. The Stabilization Diagram now looks like this (after selecting the Show Models in Selected Range option):
Due to the application of the Crystal Clear SSI ® algorithm, both the Stable modes and the Noise modes are now well defined, and the unstable modes have practically speaking disappeared.
You can modify the appearance of the wall-paper with the Singular Value Decomposition of the spectral density matrices as well as the color of the eigenvalue markers. This is done by activating the Properties dialog from either the context-sensitive menu or the View menu. In both cases, select the menu item Properties ....
As explained above, the horizontal axis is a frequency axis ranging from zero to the Nyquist frequency. This frequency range can be adjusted using the zoom bar located below the stabilization diagram window.
You can export the estimated state space models to a file in ASCII format. To export either the Cursor Model or the Model Selected for Mode Selection and Linkage, right-click the mouse to activate the context-sensitive menu. From the Export menu item select the model you want to export.
Note: You can use the General 2D Display Options and 2D Display Properties with this display.