A New Cloud-based software for automated SHM of Civil Structures

Abstract

The principle of the Cloud based Flamenco software is that operating vibration response data is uploaded by the owner of the structure, then modal parameters are automatically extracted, and the results are visualized by the owners on a web browser (like Google Chrome, Firefox, etc.). The software consists of a cloud-based web application with front and backend, meaning that the clients will always have access to its latest version, regardless of the operating system installed on their computers. Since it is essential for the owner of the structure to non-disclose his operational data and the extracted information, only the owner has access to these data. In the paper the principles for implementing the OMA extraction features are outlined, it is explained how to check the operating data for sensor errors, and how to remove influence from time varying operating conditions. The software is illustrated on a simple case where operating data from a wind loaded structure is analyzed.

Full text

A New Cloud-based software for automated SHM of Civil Structures
Rune Brincker1, Sandro Amador2, Emmanouil Lydakis2
1 Brincker Monitoring ApS
2 Department of Civil and Mechanical Engineering
Technical University of Denmark
ABSTRACT
The principle of the Cloud based Flamenco software is that operating vibration response data is uploaded by the owner of the
structure, then modal parameters are automatically extracted, and the results are visualized by the owners on a web browser
(like Google Chrome, Firefox, etc.). The software consists of a cloud-based web application with front and backend, meaning
that the clients will always have access to its latest version, regardless of the operating system installed on their computers.
Since it is essential for the owner of the structure to non-disclose his operational data and the extracted information, only the
owner has access to these data. In the paper the principles for implementing the OMA extraction features are outlined, it is
explained how to check the operating data for sensor errors, and how to remove influence from time varying operating
conditions. The software is illustrated on a simple case where operating data from a wind loaded structure is analyzed.
Keywords: Automated OMA, Cloud based, sensor errors, condensation, operating conditions
INTRODUCTION
Here we will give a short introduction to both classical OMA and to Structural Health Monitoring (SHM) as the broad
scientific areas they are, and then give a short review of some important papers about automated OMA.
OMA overview
OMA is the technology of obtaining modal information from the operating responses. That is, we perform no test, we just put
sensors on the structures as it is operating, and we use these data to obtain the modal properties of the structure.
OMA is today a well-established technology, and therefore it is easy to give the reader the right advice, that is, he should take
a look at the two reference/textbooks that has been published few years ago, that is Rainieri and Fabbrocino from 2014, [1],
and Brincker and Ventura from 2015, [2]. The reader should also get himself acquainted with the broad literature and the
many applications published in the IOMAC proceedings from 2005 up until now, [3].
SHM overview
The Wikipedia definition of SHM is, quote:
SHM involves the observation and analysis of a system over time using periodically sampled response
measurements to monitor changes to the material and geometric properties of engineering structures such as
bridges and buildings.
Therefore, it involves sensors and sensor systems, data acquisition and storage, feature extraction, data compression and
statistical model estimation. Historically, bridges and the last years also wind turbines and to some extend offshore structures
in general have been in focus.
In general, in SHM the focus on modal parameters is small. In most SHM applications signals from specific locations are
being used, mainly just to describe the operating responses in the observation points.
Our reference to the reader is here just the famous paper by Farrar and Worden, 2007, [4]

Auto OMA overview
In this paper however, we will focus on one of the most important problems that this whole SHM technology is suffering
from – the very limited use of the SHM data. The tradition is that data go down in large data repositories, and is then taken
out for further analysis if and when there might be a reason for doing so. As a result, a lot of the information in the SHM data
is never used.
One of the main reasons why OMA has been developed is actually due to the potential of using the OMA as a main source of
information in SHM applications, see for instance Rainieri 2009, [6]. The development of the OMA in this direction has been
going on over the last decade, and we shall here mention a few important contributions.
In Brincker 2007, [5] the principles of the well-known frequency domain decomposition (FDD) is used to describe where in
the frequency band we have physical information, and which peaks that should be discarded because they are not modal
peaks but harmonics. The paper focus on theoretical considerations, and no real data is being used. A similar approach is
used In Rainieri 2009, [6], where the auto OMA is also based on the FDD, and the technique is illustrated on SHM data from
the engineering main building at University of Naples where the first three modes are automatically identified over a period
of 10 days. No information about the success rate is reported.
In Tcherniak et al 2011, [7], 3000 data sets from a wind turbine was studied, but only a smaller amount was analyzed using
an automated approach based on the SSI OMA algorithm. A clustering technique was used to pick physical modes. The paper
confirms the ability of OMA to provide modal parameters of the entire wind turbine structure under real operational loads,
but no information is given about success rate of the applied automated OMA.
In Reynders et al 2012, [8] the work aims at a general interpretation tool for stabilization diagrams that work for both EMA,
OMA and OMAX. The paper has a good review of earlier approaches to auto OMA, especially to clustering techniques using
stabilization diagrams. The automated OMA is illustrated on the Z24 bridge case, but only 14 data sets was analyzed. The
paper reports that automated and manual identification ended up with similar results.
In Devriendt et al 2014, [9] the Polymax and the SSI OMA techniques were used to analyze data continuously collected for 2
weeks resulting in 2016 data sets of 10 min duration while the wind turbine was idling or parked. It was concluded that
operating data was too far from being a result of white and stationary input. Data was measurement in 4 tower locations and
SCADA data like rotor rotational speed, rotor pitch angle, nacelle yaw angle and wind speed was included in the analysis. No
success or failure rate was reported, but high success rate was defined as being bigger than 80 %. The methodology has been
able to successfully identify the closely spaced fore-aft and side-side modes of the tower, even when the frequencies cross
each other.
In Lorenzo et al 2014, [10] simulation data from a reference operating wind turbine was used to investigate the Polymax
OMA identification using response data from both tower and blades. It was concluded that a straight forward application of
the OMA technique is only possible if the turbine is in parked conditions with the brake engaged. If the blades are rotating,
several pre-processing steps are needed in order to apply the conventional OMA technique. No automated identification was
reported.
In Neu et al 2017, [11], a data driven SSI based OMA technique and a clustering technique was used to distinguish between
physical modes and noise modes on 1000 data sets from only 2 sensors. Stabilization diagram with subsequent clustering was
used to find the physical modes. The experimental case was a wind tunnel test where a glass fiber reinforced polymer plate
(500mm × 90 mm × 4 mm) was subjected to different flow conditions. It is reported that the four lowest modes were
successfully identified from nearly every dataset, but no success rate was reported.
In Juul et al 2018, [12], a short introduction is given to an automated time domain poly reference OMA technique using a
sliding filter on simulated data. Two different methods were used to find the physical modes in the sliding filter stabilization
diagram, and it was concluded that the so-called Shortest Path Algorithm (SPA) had the highest success rate. No success
rates were reported.

SOFTWARE SOLUTION
In an OMA based SHM solution priorities are on other things than when we are doing OMA on a limited amount of data,
where we have to get maximum information out of the limited data, so we spend time on minimizing both random and bias
errors.
In the SHM solution we have enormous amounts of data, so that reducing random errors might not be essential, and bias
errors are not that important either, because we are not so concerned about hitting the right frequency, but more concerned
about changes over time.
Further, man power most be reduced to a minimum, otherwise we will remain in the unlucky situation that we have had until
now, where only a microscopic part of the total amount of monitoring data is being used.
What is really important is robustness, so that for each and every data set that arrives for identification, the probability of
failure to detect the natural frequency of any mode is minimal. This means that all algorithms must be robust to a degree that
has not been seen before, because if there has been a storm, it would be unacceptable if nearly all identifications of data sets
during the storm failed due to the un-expected environmental conditions.
Furthermore, let us say that we do SHM for earth quake damages, then it would be un-acceptable, that because the power
supply failed to work, the server that had the software installed, also lost power and failed to work during the earth quake. If
we want a system that always works, we have to install the solution in the Cloud. This is the safest place for both data and
software.
That might be a challenge for some users, that they have to send their data up in the Cloud – somewhere outside of their well
protected territory. This problem can only be solved by securing a strong non-disclosure policy about all user data.
Let us in following section try to explain how the Flamenco software has been planned to deal with the above-mentioned
challenges.
Typical OMA
Let us illustrate how the so-called poly reference technique has been planned for implementation in both time domain and
frequency domain. For more information, see Brincker and Ventura [2].
Using an AR model based identification approach first step is to find the AR matrices in the homogenous free decay part of
an ARMA model
(1)
12
( ) ( 1) ( 2) ( ) 0
na
n n n n na− − − − − − − =y A y A y A y
given the free decay
()ny
in discrete time with
np
number of samples. To estimate the AR matrices we form a block
Hankel matrix with block rows
(2)












−+
−−
−
=
)1()1()(
))1(()3()2(
)()2()1(
1
npnana
nanp
nanp
yyy
yyy
yyy
H

and one block Hankel matrix with only a single block row
(3)
 
)()2()1(
2npnana yyyH ++=
Eq. (1) can then for all the possible values of be formulated as
(4)
12
=AH H

where
A
is a side-by-side collection of the AR matrices, and the solution is then found by regression
(5)
21
ˆ+
=A H H
where
1
+
H
is the pseudo inverse of
1
H
.
In time domain we can exclude the initial conditions, and only deal with the free response after the structure has been excited
like we are doing in a free response formulation like Eq. (1). In the frequency domain every point depends on the whole time
domain, so going to the frequency domain we have somehow to include the impulse that created the free decay in the time
domain. Thus, we have to add a right hand side to Eq. (1). Using the Z-transform and adding the simplest possible right hand
side to Eq. (2) it can be shown that we end up with the following equation
(6)
0
1
)( ))(( YYAI =







−
=
−kfe
na
n
kinw
n
Where
0
Y
is a constant matrix added to represent the right hand side of Eq. (1),
)(kw
is the dimensionless frequency from
zero to

, and
( ( ))fkY
is the frequency domain free decay where
()fk
goes from DC to Nyquist or defines a smaller
band. It is normal practice to use the so-called half spectral density as a free decay in the frequency domain, so imagining
this, we can re-write Eq. (6) by using an alternative definition of the AR matrices we end up exactly the same equation like
Eq. (4).
If the response has
nc
number of channels, thus the response vector is
1nc
, then the problem is over determined as long as
ncnananp −
, however since there is always some noise present, the procedure will only work satisfactory if the
problem is well over determined, thus we must require that
ncnananp −
.
For both the time and the frequency domain formulations, the modal parameters are found by forming the well-known
companion matrix and the modal model has in this case eigenvalues corresponding to modes. The number of modes to be
determined can be adjusted by adjusting the frequency band.
Condensation and expansion
The smallest AR model one can use is based on one single AR matrix. This provides us with
/2nc
modes, which might be
useful in many cases. However, if a large channel count is being used, we might end up with too many noise modes that
might cause troubles in finding the physical modes. In such a case we might to reduce the channel count. For this purpose,
condensation can be used
If our random response
()ty
has the covariance matrix
C
, then we perform the SVD that for the symmetric and real matrix
has the form
(7)
T
=C USU
And we then simply take the most principal vectors by reducing the number of columns in the matrix
U
to obtain to
r
U
so
that the condensed responses are, see Olsen et al [13]
(8)
( ) ( )
T
r
tt=z U y

If on the other hand we have very low channel counts, then we can of course increase the number of AR matrices in the
model, but we can also add in more channels to expand the number of measurements. This can be done by stacking the
random response
()ty
with its differentiated or integrated signals or stacking the sampled signal of one or more time-shifted
responses.
As mentioned above, the most important is to assure robustness. Thus, the aim of condensation and expansion (of channels
and model order) is to find the optimum number of modes in the model so that the number of noise modes optimize both
accuracy and robustness.
Modal participation
Normally we would be happy to obtain the classical modal parameters like mode shapes, natural frequencies and damping
ratios. However, if we want to judge what is noise modes and what is physical modes, it is useful to obtain the modal
participation vector. It is also useful to have the modal participation vector for plotting how well our modal model fits the
empirical spectral densities.
In Brincker et al [14] it is shown that if the random response has the covariance matrix
C
, and the real valued mode shape
matrix is
B
, then the real valued modal participation matrix
Γ
can be estimated as
(9)
1
ˆ4
T

+
=Γ CB
where
T+
B
is the transpose of the pseudo inverse of the mode shape matrix. The length of each modal participation vector
defines a scalar measure of the modal participation for each mode.
Sensor fault detection
In a real measurement system, sensors will sooner or later fail to work as assumed. So, without sensor fault detection, we do
not have a chance to make OMA based SHM work reliably. Here we are lucky to be able to make use of the most central
equation in dynamics, the equation that defines the modal coordinates
(10)
( ) ( )tt=y Bq
The idea is now to estimate the modal coordinates from the measured responses
(11)
ˆ( ) ( )tt
+
=q B y
to form the synthesized response
(12)
ˆ
ˆ( ) ( )tt=y Bq
If we have a failing sensor, we will see a large deviation between the measured and synthesized signal for that sensor, so that
the faulty sensor can be excluded from the OMA.
Operating conditions
The influence from operating conditions like temperature, or power production for a wind turbine, or traffic for a bridge, have
a major influence on the modal parameters. In order to see if the structure has changed, we need to remove the main part of
this influence.

We could of course measure the temperature, measure the power production of the wind turbine, or the traffic on the bridge
and try to establish the model for how the natural frequencies depend on the environmental conditions.
But we might not have this information available, or even though we have it available, it might be difficult use, simply
because a temperature reading is very dependent upon where we measure it. Again, luckily enough, we have tools available
to deal with this without any information about the environment. We will use the idea of the OMA once again.
Now we will consider a vector
()tu
of natural frequencies as a function of time. In a certain time interval
T
we will have a
mean value
0
u
that is considered to represent the physics, and a noise contribution
()te
from the changes of the environment
that we like to model. We then need to model the zero-mean signal
(13)
0
( ) ( )tt=e u -u
as a random response just like doing any other OMA. We need to follow good practice once gain, like looking for a low
number of modes in a limited frequency band to obtain the solution like in Eq (12) where we model the signal , and we can
then can obtain the synthesized random response where the influence the influence from environmental conditions is
removed
(14)
0
ˆˆ
ˆ( ) ( ) ( )
ee
t t t= − +u Bq B q u
Here
e
B
and
()
etq
are mode shapes and modal coordinates of the signal
()te
.
SHM case
The considered case is data from a monitoring campaign with a wind loaded wooden mast with a steel topside. The vibration
response is acquired by a measurement system with four 3D sensors placed at strategic locations on the topside so that the
rigid body motions of the top side can be determined. In the present case we are demonstrating auto OMA on the first 500
data sets of the first week of the monitoring campaign where no damage was introduced.
The case is further described in Lydakis et al 2023, [15], where a longer period is considered and damage is introduced and
identified from the change of the modal parameters.
The mast structure is shown to the left of Figure 1, and the five natural frequencies over time is shown to the right of Figure
1. In Figure 2 is shown the typical validation plot for the user to check that the identified modes fit the empirical spectral
density. In this case we can see that the fits are good. The identified modal parameters for the same plot are given in Table 1.
In All 500 data sets all five modes were all identified well. Success rate of 100 %.
Table 1. Modal parameters for the 5 modes of random data set shown in Figure 2. Mode shapes much like a wind turbine because the
dominating mass is at the top, and the direction with the dominant moment of inertia defines fore-aft (FA) movement, and the
perpendicular the side-side (SS) movement.
Mode
Natural frequency
[Hz]
Damping ratio [%]
Type of mode
1
1.188
1.829
First bending FA
2
1.194
1.098
First bending SS
3
1.984
1.013
Torsion
4
9.794
0.606
Second bending FA
5
12.465
0,744
Second bending SS

Figure 1. Left: The wind loaded mast. Right: Results of auto OMA of the first 500 data sets showing first 5 natural frequencies of the
structure. Button line include the first two closely spaced modes. No damage introduced.
Figure 2. The users validation plot for a random middle data set of the 500 uploaded data sets. Frequency band from DC to 14 Hz.
Conclusion
A Cloud based SHM software solution has been presented and the basic principles of implementing well-known
identification technique into the software solution has been explained.
The solution has been tested on 500 data sets from a monitoring campaign with a wind loaded wooden mast, and in all 500
data sets all 5 modes were successfully identified.

References
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