Usefulness of ambient-vibration measurements for seismic assessment of existing structures

Abstract

A large number of buildings in regions with low to medium seismic hazard have been designed without considering earthquake actions. Retrofitting of all buildings that fail to meet modern code requirements is economically, technically and environmentally unsustainable. Decision-making regarding retrofitting necessity and prioritization is complex. Ambient vibrations are non-destructive and easy to measure, and thus an attractive data source. However, ambient vibrations have very low amplitudes, which potentially lead to sensitivity to testing conditions and stiffness contributions from non-structural elements. Seismic assessment necessitates non-linear behavior extrapolation from linear measurements, which results in biased model predictions. Error-domain model falsification is a data-interpretation methodology that is robust to multi-source uncertainties with unknown and changing correlation values. In this contribution, static non-linear behavior predictions of an existing building in Lausanne, Switzerland, are presented. Ambient-vibration data has been gathered under changing conditions: from undamaged in-service to gradual removal of non-structural elements. Low sensitivity to non-structural elements are found. A numerical model based on the applied-element method is generated and shows potential utility of linear measurements for decision-making using non-linear models involving EDMF under uncertain conditions.

Full text

Originally published for SMAR 2017, fourth International Conference on Smart Monitoring,
Assessment and Rehabilitation of Civil Structures, Zurich, Switzerland, 2017.
Final publication is available in the related proceedings, Paper No. 162.
Usefulness of ambient-vibration measurements for seismic
assessment of existing structures
Yves Reuland1, Abdo Abi Radi Abou Jaoude1, Pierino Lestuzzi1, Ian F.C. Smith1
1 Swiss Federal Institute of Technology Lausanne (EPFL), Switzerland
ABSTRACT: A large number of buildings in regions with low to medium seismic hazard have
been designed without considering earthquake actions. Retrofitting of all buildings that fail to
meet modern code requirements is economically, technically and environmentally
unsustainable. Decision-making regarding retrofitting necessity and prioritization is complex.
Ambient vibrations are non-destructive and easy to measure, and thus an attractive data source.
However, ambient vibrations have very low amplitudes, which potentially lead to sensitivity to
testing conditions and stiffness contributions from non-structural elements. Seismic assessment
necessitates non-linear behavior extrapolation from linear measurements, which results in
biased model predictions. Error-domain model falsification is a data-interpretation methodology
that is robust to multi-source uncertainties with unknown and changing correlation values. In
this contribution, static non-linear behavior predictions of an existing building in Lausanne,
Switzerland, are presented. Ambient-vibration data has been gathered under changing
conditions: from undamaged in-service to gradual removal of non-structural elements. Low
sensitivity to non-structural elements are found. A numerical model based on the applied-
element method is generated and shows potential utility of linear measurements for decision-
making using non-linear models involving EDMF under uncertain conditions.
1 INTRODUCTION
A large part of the building stock in regions with low to moderate seismic hazard have been
built before thorough seismic considerations have been formulated in building codes. Replacing
all buildings that fail comparisons with modern design specifications is impossible from
economical, technical and environmental standpoints. Therefore, seismic vulnerability
assessment of existing buildings has an important role in prioritizing retrofitting actions.
However, assessing seismic vulnerability of existing structures is often complicated by the
absence of precise building information such as construction drawings and past structural
interventions, and by the large variability of material properties in existing buildings.
Although methodologies exist for rapid assessment at a city-scale level (Lestuzzi et al., 2016),
the evaluation of buildings with a high contribution to the resilience of a city, such as hospitals
and community centers, may require models with higher fidelity. Also, such physics-based
structural models are useful to design targeted and efficient rehabilitation and strengthening.

Model-based structural identification using measurement data is a widespread tool to reduce
uncertainty related to model parameter uncertainty. When buildings are analyzed, ambient
vibration measurements are a well-suited if not the only available non-destructive data source.
Development of economic, sensitive and transportable sensors has led to popularity of ambient-
vibration-based structural identification. However, ambient vibrations are strictly limited to
linear-elastic behavior. The low amplitudes of vibration, typically 10-6 to 10-3 m/s2, do not give
insights into non-linear behavior of buildings (Michel et al., 2011). Also, non-structural
elements, such as separation walls, doors, windows and heavy furniture, potentially contribute
to the building stiffness under very low amplitudes of excitation.
Capacity-based vulnerability estimation of buildings requires non-linear behavior predictions.
Therefore, model extrapolation is needed as non-linear behavior differs from exclusively linear
behavior under ambient vibrations. A structural identification methodology that explicitly
incorporates model uncertainties in a transparent way is used to perform such extrapolation:
Error-domain model falsification (EDMF) (Goulet and Smith, 2013; Pasquier and Smith,
2015b).
Through a full-scale case study the usefulness of structural identification using ambient
vibration data is assessed. Measurements have been taken on a typical Swiss masonry building
in Lausanne for three building states: initial state and after gradual removing of non-structural
elements such as windows and stair railings. A complex 3D structural model, using the Applied
Element Method (AEM), is used to predict modal properties and non-linear pushover curves of
the studied building.
This paper starts with a short description of the methodologies used to perform ambient-
vibration-based structural identification using an AEM model. Then, on a full-scale case-study,
the reduction in non-linear prediction uncertainty that can be obtained with exclusively linear
vibration measurement data is assessed. Finally, next steps and conclusions are discussed.
2 MODEL-BASED MEASUREMENT INTERPRETATION IN A SEISMIC CONTEXT
2.1 Error-Domain Model Falsification
Model-based structural identification is an inverse engineering task that involves ambiguities.
Even complex 3D models fail to provide an exact representation of full-scale structures under
in-service conditions. Therefore, discrepancies between model predictions and observed
behavior are inevitable. As engineering structures are systems, such model errors are spatially
correlated to an unknown extent (Goulet and Smith, 2013). Also, for approximate engineering
models, uncertainties are rarely zero-mean normal distributions and a limited number of
uncertainty sources undermines the applicability of the Central Limit theorem (Pasquier and
Smith, 2015a).
EDMF is based on the principle of using measurements to falsify inappropriate model instances
instead of optimizing single models. Therefore, measurement and model uncertainties are
combined to calculate thresholds T that bound the domain of acceptance for residuals between
model predictions g(θ) and measured values y for all Nm measured quantities, according to Eq.
(1).
∀𝑖=1,…,𝑁!: 𝑇
!"#,!≤𝑔!𝜽−𝑦!≤𝑇
!!"!,! (1)
Through the transparent incorporation of uncertainties and the threshold-based reasoning, the
applicability of EDMF to tens of full-scale structures and the intuitive understanding by
practicing engineers has been shown (Smith, 2016). Also, through avoiding the definition of
exact uncertainty distributions and by being insensitive to unknown and changing uncertainty
correlations, EDMF results in robust identification and prediction ranges (Pasquier and Smith,
2015b).

In this application to existing buildings, fundamental frequencies derived from ambient
vibrations are proposed as a measurement source. Ambient vibrations are a time-efficient and
non-destructive measurement source. Measured accelerations are transformed to the frequency
domain and analyzed using the Frequency Domain Decomposition technique (Brincker et al.,
2001), a popular output-only modal identification technique in civil engineering applications.
EDMF has been used in the past with ambient vibration-based modal properties for linear model
identification on bridges (Goulet et al., 2013).
2.2 Applied Element Method
In Switzerland unreinforced masonry buildings make up for the major part of the building stock.
Predictions related to the non-linear behavior of masonry, an orthotropic material composed of
bricks and mortar joints, remain challenging. In this paper, the AEM is used to predict non-
linear pushover curves of a masonry building. AEM is suitable to predict post-yield structural
behavior of masonry structures that are defined by a particularly large range of potential failure
modes (Garofano and Lestuzzi, 2016; Guragain et al., 2012; Karbassi and Nollet, 2013).
In order to capture failure modes that govern masonry structures, such as rocking, joint de-
bonding, sliding or shear diagonal cracking, AEM divides structural components into elements
that are connected with springs at element contact points (around the edge). Pairs of normal and
shear springs localize stresses, strains and deformations (Meguro and Tagel-Din, 2002). Two
types of springs represent masonry behavior: the first type of springs characterizes brick
behavior while the second type of springs merges brick-mortar interface and mortar behavior.
The behavior of bricks and mortar is assumed to be similar to concrete-type behavior models
(Extreme loading® for Structures, 2013). The defined springs are able to capture joint de-
bonding, shear sliding, direct tension and partial connectivity between elements. However,
shear-compression failure due to high axial loads is not taken into consideration.
3 CASE STUDY: VILLA MARGUERITE, LAUSANNE (SWITZERLAND)
Usefulness of ambient vibration measurements for structural identification is investigated
through application to a full-scale masonry building. The Villa Marguerite in Lausanne is a
typical Swiss masonry building with 4 floors that has been built in the early 20th century.
Ambient vibrations have been measured on three days, prior to the demolition of the building,
using six tri-axial acceleration sensors. The first set of measurements is representative of the
initial building state under in-service conditions. The second measurement set has been taken
after removal of windows and doors and provisional replacement by wooden panels. The third
set of measurements has been taken after all secondary elements, except non-structural walls
have been removed. Also, changing atmospheric conditions (temperature and humidity) and
solar radiation conditions (changing daytimes) influence the measurement sets (see Table 1).
Results from Frequency Domain Decomposition (FDD) of measurements from the third
measurement set are reported in Figure 2. Two fundamental bending modes and one torsional
mode can be detected.
The evolution of the fundamental bending frequencies in the two directions is reported in Table
1. Only small changes that do not exceed the levels of measurement uncertainties (sensor
sensitivity, cable losses, digitizer-losses and time-domain to frequency-domain transformation
are estimated to result in a zero-mean normal distribution with a standard deviation of 0.2 Hz)
are observed. Modal characteristics from ambient-vibration measurements are thus insensitive
to small changes in atmospheric conditions and non-structural elements such as windows and
furniture. As a consequence, ambient vibrations can be measured under in-service conditions.

A physics-based model of the structure is developed using AEM (see Figure 1) with
approximatively 26’000 elements connected using 1’900’000 non-linear springs. Although
AEM allows high-fidelity representation of the structural system, some assumptions are
inevitable at the modelling stage: soil-structure interaction is ignored as the base is modelled to
have fixed supports; non-bearing separation walls are omitted; and the slab and roof structure
are idealized to be isotropic elements with an equivalent stiffness and an equivalent density that
include non-structural covering.
Figure 1. Figure of the Villa Marguerite, Lausanne (Photo Credit IMAC EPFL) and view of the AEM
model of the Building.
Figure 2. Spectral analysis of vibration measurement on the building. Singular values are calculated from
the Correlation Power Spectral Density (CPSD) matrix to identify global structural modes.
Nine parameters are estimated to have an influence on the linear and non-linear model
predictions (see Table 2). Slab parameters (density and stiffness), equivalent roof stiffness and
brick parameters are assumed to have an influence on linear and non-linear behaviour
predictions of the structure, while mortar properties (compressive and tensile strength, friction
coefficient and separation strain) mainly govern the predicted non-linear behavior range. Initial
parameter ranges are derived using engineering judgement and existing literature.
In order to bypass important simulation time and guided by the needs of a preliminary model
class evaluation, a Box-Behnken sampling scheme is used. Thus, a total of 121 parameter
combinations sampled from initial parameter ranges shown in Table 2 are simulated. The Box-
Behnken design divides the initial parameter ranges by picking extreme points of the range as
well as the center point. In cases where a thorough structural identification of all the parameters
is useful, the 121 parameter combinations can be used to derive a surrogate model.

Table 1. Natural frequency derived from ambient vibration measurements for changing building states
defined by gradual removal of non-structural elements. Changing environmental conditions and non-
structural elements have little influence on observed natural frequencies.
Building state
Date of
measurement
Longitudinal
fundamental
frequency [Hz]
Transversal
fundamental
frequency [Hz]
Initial
26th June, 2015
(midday)
5.7
5.8
After removal of some
secondary elements
14th July, 2015
(evening)
5.7 (-)
5.7 (-2%)
After removal of all
secondary elements (except
separation walls)
15th July, 2015
(morning)
5.5 (-3.5%)
5.8 (-)
Table 2. Initial and identified parameter ranges for chosen material properties of the structural model.
Parameter identification reduces the range of linear parameters only.
Material property
Units
Initial range
Identified values
Young’s modulus of bricks
kN/mm2
50 – 1000
50
Poisson’s coefficient of bricks
-
0.1 – 0.3
0.1– 0.3
Young’s modulus slab
kN/mm2
750 – 2500
750 – 1625
Density slab
t/m3
2.0 – 4.5
3.25 – 4.5
Tensile Strength of Mortar
N/mm2
0.5 – 2.5
0.5 – 2.5
Compressive Strength of Mortar
N/mm2
5.0 – 20.0
5.0 – 20.0
Friction Coefficient of Mortar
-
0.55 – 0.95
0.55 – 0.95
Separation Strain of Mortar
-
0.05 – 0.15
0.05 – 0.15
Young’s modulus roof
kN/mm2
500 – 1500
1000 – 1500
In addition to the measurement error N(0,0.2Hz), three sources of model uncertainties are
identified: model error due to element size and secondary parameters (uniform between -7.5%
and +7.5%); omission of non-structural walls (with a thickness below 10 cm) and irregular
boundary conditions as well as simplification of the roof structure (between -10% and 10%);
and omission of soil-structure interaction by idealizing fixed boundary conditions (-15% to 0%).
According to Eq. (2), a negative model error, εmodel, corresponds to a model that results in
overestimating structural responses. Given boundary conditions cannot be stiffer than fixed, the
uncertainty is biased towards overestimated frequencies. EDMF allows engineers to define such
biased uncertainties.
𝑇𝑟𝑢𝑡ℎ=𝑔𝜽+𝜀!"#$% (2)
Frequencies that are predicted using the AEM model (see Fig. 1) are reported in Figure 3 for the
bending modes alongside measured frequencies and EDMF thresholds. Compared to the
measured frequency, the frequency predictions are shown to be overestimated. This observation
is in agreement with the biased model uncertainty estimation.

Unsurprisingly, the reduction in parametric uncertainty that is achieved using linear
measurements is restricted to linear material properties. As can be seen in Table 1, the highest
reduction in parametric uncertainty is achieved for Young’s modulus of masonry bricks. As a
Box Behnken design is used to sample the parameter space, an upper limit of potential
parameter identification using EDMF is obtained.
Based on the AEM model (see Fig. 1), which has been employed to predict natural frequencies,
non-linear transversal push-over curves are predicted. A linearly increasing displacement
distribution along the building elevation is used to derive pushover curves. Predicted base shear
as a function of displacement of the upper slab is reported in Figure 4.
Through a reduction in the parametric uncertainty related to linear material properties (see Table
1), non-linear prediction uncertainty is reduced. Although predictions of the maximum force
that the building can sustain remain scattered, the displacement capacity of the building is
predicted with higher precision. This is an encouraging finding for structural identification of
non-linear structures with linear measurement data.
Figure 3. Predicted frequencies related to the fundamental bending modes in the longitudinal and
transversal direction. Predictions are biased with regard to the measured frequencies.
Figure 4. Predicted push-over curves in the transversal direction. Prediction uncertainty can be reduced,
however the prediction range resulting from candidate models remains large.

4 DISCUSSION AND OUTLOOK
Comparison between model predictions and measured behavior shows a systematic
overestimation of natural frequencies. Model assumptions such as fixed boundary conditions
lead to overestimated results. Future work includes estimating the influence of non-fixed
boundary conditions (soil-structure interaction) on the predicted natural frequencies in order to
reduce the combined uncertainty. EDMF allows the engineer to gradually include knowledge
and increase model fidelity by adapting uncertainties in a transparent way.
In such a perspective of gradual knowledge acquisition, tensile strength of mortar has the
highest influence on candidate pushover curve predictions. Therefore, further reduction in the
prediction of maximum base shear necessitates knowledge acquisition regarding mortar tensile
strength. However, current technology requires laboratory tests to deduce material strength.
Surrogate models are needed to perform a thorough identification of parameter values, which is
an important step if, for instance, retrofitting is to be designed. A low number of samples has
been used for the Latin Hypercube Sampling in order to get a first evaluation of the model class
and the capacity to reduce parametric prediction uncertainty in the non-linear range.
If predictions that involve extrapolation are performed, the prediction uncertainty differs from
the identification uncertainty. An exact quantification of prediction uncertainty is needed to
provide the decision-maker with robust prediction ranges.
The non-linear predictions that are used to verify the usefulness of linear measurements for non-
linear parameter identification are static non-linear pushover curves. In case dynamic non-linear
time histories are predicted, the uncertainty reduction might be more important, given the
influence of the fundamental modes on dynamic building behavior.
5 CONCLUSIONS
Structural identification of non-linear behavior models using linear measurements is presented.
The following conclusions are drawn from the application of vulnerability predictions using a
non-linear AEM model and linear vibration measurements:
- Although ambient vibration measurements are characterized by low amplitudes, low
sensitivity to non-structural elements such as windows and furniture is observed. This is
an essential feature for robust model identification using physics-based models.
- Reducing the parametric uncertainty of linear properties can reduce the behavior
uncertainty in the non-linear range. Additional case studies are needed to confirm this
finding. In addition, the costs of measurement acquisition and especially of complex
non-linear structural models may not justify the application of the methodology in cases
for which the reduction in prediction uncertainty is low.
- EDMF allows the engineer to combine various uncertainty sources in a transparent and
intuitive way. In addition, in presence of scarce numbers of measurements and model
predictions, EDMF helps to indicate subsequent steps to take.
6 ACKNOLEDGMENTS
This work was funded by the Swiss National Science Foundation under Contract No. 200020-
169026. Costs of the measurement system were partially covered by the Swiss National Science
Foundation under grant No. 150785. The authors thank the Real Estate and Infrastructures
Department of EPFL for the access to the building and A. Herzog for documenting the tests.

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