Effects of Environmental Conditions on Historic Buildings:

Interpretable Versus Accurate Exploratory Data Analysis

Marco Parola

1 a

, Hajar Dirrhami

2 b

, Mario G. C. A. Cimino

1 c

and Nunziante Squeglia

2 d

Dept. of Information Engineering, University of Pisa, 56122 Pisa, Italy

Dept. of Civil and Industrial Engineering, University of Pisa, 56122 Pisa, Italy

Keywords:

Structural Health Monitoring, Leaning Tower of Pisa, Regression Analysis, Deep Learning, Interpretability.

Abstract:

The goal of structural health monitoring is to continuously assess the structural integrity and performance of a

building or structure over time. This is achieved by collecting data on various structural parameters and using

this data to identify potential areas of concern or damage. A critical challenge involves some properties being

severely damaged by recurrent variations of external factors. These variations in environmental and opera-

tional conditions (such as humidity, temperature, and trafﬁc) can deﬂect the variability in structural behavior

caused by structural damage and make it difﬁcult to identify the damage of interest. In this paper, we present

a study on how regression analysis and deep learning can be used to measure the inﬂuence of environmental

factors on the structural behavior of the Leaning Tower of Pisa. Transparent linear regressors offer the beneﬁt

of being simple to understand and interpret. They can provide insights about the relationship between input

and target variables, as well as the relative importance of each input in forecasting the outcome. On the other

hand, deep learning models are capable of learning nonlinear relationships between input and target variables.

Deﬁnitively, in this work the accuracy-interpretability trade-off for structural health monitoring is discussed.

1 INTRODUCTION

In order to diagnose and assess the stability condi-

tion of historic monuments, Structural Health Moni-

toring (SHM) is crucial. Indeed, such structures are

constantly exposed to the action of environmental ef-

fects, such as sun’s radiation, temperature variations

or wind motion, that eventually have a tendency to

lose their structural integrity. It is therefore essen-

tial to ensure precautions and perform proper analy-

ses to prevent any deterioration of these monuments

and preserve culture.

One of the most common analysis consists of

detecting whether the structure under examination

is affected by damage. This information is funda-

mental and useful for structural engineers to under-

take restoration measures and avoid unintended con-

sequences. However, in SHM, this information is of-

ten not enough and other tasks are available to pro-

vide more speciﬁc additional information, such as the

https://orcid.org/0000-0003-4871-4902

https://orcid.org/0000-0000-0000-0000

https://orcid.org/0000-0002-1031-1959

https://orcid.org/0000-0001-8104-503X

region of the structure where the damage is present

by addressing a damage location task, or measuring

damage degree by performing a damage quantiﬁca-

tion task (Parola. et al., 2022).

All of these tasks enable for the information col-

lecting needed to evaluate the scenario severity to

which a structure may be subjected, attempting to as-

sess any changes in the sensitive features indicative of

damage. Unfortunately, there are additional variation

sources, such as variations brought on by environ-

mental factors. If these impacts are not considered,

they can result in incorrect damage diagnosis or less

accurate injury detection. Differentiating between the

two sources of variance in static or dynamic charac-

teristics is crucial (Kullaa., 2014).

Effective monument maintenance, which distin-

guishes symptomatic changes of damage from envi-

ronmental ones, relies on a framework composed of

two main aspects: (i) the gathering of data and (ii)

the processing of them to obtain useful information

about the structure. The collection of data describ-

ing the structure exploits an SHM system involving

the use of sensors installed directly at the building

to measure its properties. SHM systems are divided

into two groups based on the kind of parameters they

Parola, M., Dirrhami, H., Cimino, M. and Squeglia, N.

Effects of Environmental Conditions on Historic Buildings: Interpretable Versus Accurate Exploratory Data Analysis.

DOI: 10.5220/0012119700003541

In Proceedings of the 12th International Conference on Data Science, Technology and Applications (DATA 2023), pages 429-435

ISBN: 978-989-758-664-4; ISSN: 2184-285X

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

429

acquire: (i) Static systems, which track the temporal

development of variables that change gradually over

time (such as wall slopes or crack widths) by period-

ically sampling sensor devices; (ii) dynamic systems,

which track vibrational variables like speeds or ac-

celerations in order to collect information on broader

dynamic features like natural frequencies intrinsic to

the structure or modal forms (Zonzini et al., 2020).

About how the data are processed, Machine

Learning (ML) and later Deep Learning (DL) were

progressively introduced to enhance the analysis in-

struments adopted to solve these problems (Sujith

et al., 2022), as they exploit a data-driven approach.

These data-driven methods can be relied upon a su-

pervised or unsupervised learning. The former makes

use of labelled input-output pairs, where the input

is structural response, while the value of the target

structural parameters are the corresponding outputs.

On the other side, instead of requiring an associated

output label, unsupervised algorithms are frequently

used to ﬁnd damage-sensitive patterns or similarities

in initial data (Cimino. et al., 2022). Speciﬁcally,

transparent machine learning models have the advan-

tage of being simple to understand. As an exam-

ple, modular neural architectures refer to a design ap-

proach based on a collection of small neural (Cimino

et al., 2009). However, such constrained architec-

tures are limited in capturing input-output complex

patterns.

Regression analysis is considered a supervised

learning problem in the ﬁeld of machine learning be-

cause it involves training a model on labeled data,

where the true values of the output variable are

known. In the SHM domain, regression analysis can

be adopted to model the problem of measuring the in-

ﬂuence of environmental conditions on the health and

the structural behavior of a building (Farreras-Alcover

et al., 2015) (Dervilis et al., 2015).

The case study investigated in this paper is the

Leaning Tower of Pisa located in the Miracle Square

in Tuscany. The SHM system installed on the Lean-

ing Tower operates as a static system whereby, upon

activation, it records a single value for each sensor.

The system is programmed to activate on an hourly

basis. However, since the monitoring system has been

installed in 1993, the sampling frequency has varied

by the service staff. To overcome this problem, time

series resampling techniques can be adopted. The lo-

cations where the sensors have been installed on the

tower are illustrated in Figure 1 and Table 1.

The novel contribution of this work is to explore

the inﬂuence of the environmental conditions on a

speciﬁc historical monument: the Leaning Tower of

Pisa. Such analysis is performed through two dif-

ferent regressive methods; more speciﬁcally, we go

deeper by measuring the impact of these conditions

on the individual sensors.

The paper is organized as follows: Section 2 out-

lines the methods and methodologies we used to an-

alyze the sensor data, while Section 3 provides an

overview of the data discovery process. Section 4 de-

scribes the conducted experiments and displays the

results achieved by the two compared models. Fi-

nally, Section 6 summarizes the work and addresses

the conclusions.

Figure 1: Sensor locations on the tower, as indicated by the

color legend in Table 1.

Table 1: Sensor system installed on the leaning tower.

Sensor # Leg Thresholds

Deformometer (D) 10 [-0.5,0.5] mm

Telecoordinom. (T) 4 [-2.1,1.8]

∗

”

Termometer (TM) 1 [-10,42] °C

Wind speed (WS) 1 [0,45] m/s

Wind dir (WD) 1 [0,360] deg

Pressure (P) 1 [1, 1.04]

∗

hPa

Solar radiation (SR) 1 [0,1]

W/m

2 METHODS

Our methodology is structured in two main parts: data

discovery and regression analysis. In the data dis-

covery phase, we explore the data identifying aspects.

·10

DATA 2023 - 12th International Conference on Data Science, Technology and Applications

430

This includes study the linear dependencies between

environmental and operational factors through a cor-

relation analysis. Indeed, by introducing the correla-

tion matrix, correlation degree between pairs of vari-

ables in a dataset can be computed, allowing the iden-

tiﬁcation of which ones are positively or negatively

correlated, and how strongly they are related to each

other.

During the regression analysis phase, we use re-

gressive techniques to model the relationship between

the dependent variable and one or more independent

variables. This enables to identify key factors inﬂu-

encing the dependent variable and make predictions

about future outcomes. Combining these two strate-

gies provides a comprehensive and rigorous approach

to investigating our research purpose and generating

interesting insights.

A linear regression problem aims to ﬁnd the line

that best ﬁts the data, which is expressed through the

equation.:

y = β

+ β

+ ... + β

(1)

Where x1, x2, ..., xn are the independent variables

and the goal is to ﬁnd the best coefﬁcients values

(beta1, beta2, ..., beta n) that minimize the sum of the

squared differences between the predicted values of y

and the actual values of y.

In non-linear regression, the relationship between

the independent and dependent variables is modeled

using a non-linear function, such as a polynomial or

exponential function.

Overall, regression analysis is a powerful tool

for understanding and predicting the relationship be-

tween variables. It can be used for a wide range

of applications, such as the measurement of the in-

ﬂuence of environmental factors on a structure’s be-

havior (Farreras-Alcover et al., 2015) (Dervilis et al.,

2015).

The goal of this strategy is to understand how en-

vironmental factors, such as temperature, humidity,

wind, and precipitation, can affect the structural in-

tegrity of a building over time.

Gathering information on the environmental vari-

ables and the structural behavior of a building, such

as displacement, strain, or vibration measurements, is

one technique to employ regression analysis in this

context. The operational quantities can then be pre-

dicted using a regression model built using this data

and the environmental parameters.

Against the traditional statistical models, Neu-

ral Networks (NNs) have proven to be an effective

solution for regression problems in many contexts.

They offer several advantages for regression prob-

lems, such as the ability to learn complex non-linear

relationships and the ability to handle large and noisy

datasets.

The methodology entails resolving a regression

problem and subsequently evaluating the performance

of two distinct models using a chosen metric.

We introduce performance metrics to evaluate the

performance of our regression model: mean squared

error mse and coefﬁcient of determination R

. The

mse measures the average squared difference between

the predicted and actual values of the response vari-

able as shown in Equation 2.

mse =

∑

i=1

− ˆy

)

(2)

where n is the number of observations, y

is the

actual value of the response variable for the ith obser-

vation, and ˆy

is the predicted value of the response

variable for the ith observation.

On the other hand, the R

value measures the pro-

portion of variation in the response variable explained

by the regression model. The equation for R

is shown

below:

= 1 −

res

tot

(3)

where SS

res

is the residual sum of squares, which

is the sum of the squared differences between the ac-

tual and predicted values of the response variable, and

tot

is the total sum of squares, which is the sum of

the squared differences between the actual values of

the response variable and the mean value of the re-

sponse variable.

3 DATA PREPROCESSING AND

MINING

In this section, we present the data preprocessing

and mining techniques we applied to a sensor device

dataset. The goal of this process is to extract valu-

able insights and knowledge from the raw data, which

would then be used for further analysis in the next sec-

tion.

3.1 Data Preprocessing

This section presents the dataset collected from a

static monitoring system. It hourly records samples

by enabling continuous monitoring and tracking of

environmental changes. The dataset covers a period

of two months, from May to June 2020, during which

the monitoring system captured the 19 parameters

Effects of Environmental Conditions on Historic Buildings: Interpretable Versus Accurate Exploratory Data Analysis

431

listed in Table 1. The collected data underwent a se-

ries of preprocessing steps to ensure its quality and

consistency. The data preprocessing pipeline is com-

posed of the following steps:

• detection of out-of-scale samples, based on upper

and lower thresholds;

• normalization, to mitigate the phenomena of the

curse of dimensionality by applying the z-score

scaling;

• statistical anomalies detection, where observa-

tions with an actual value farther than ±2.5 from

the data distribution of the current moving average

are dropped;

• missing samples recovery, short sequences of suc-

cessive missing samples are reconstructed for iso-

lated missing samples, by using a linear interpo-

lation between the closest neighbors for the out-

liers that have already been identiﬁed (at most 4

samples). Long missing value sequences, such as

those caused by device failure, are not recreated.

• temporal data resampling, since the sampling rate

was changed over time during the entire monitor-

ing period, the entire time series was resampled to

1-hour frequency.

3.2 Data Mning

In order to avoid redundancy and be more concise,

we present a subset of deformometers given the com-

mon trends among them. Figure 2 displays the partial

correlation matrix between deformometers 4, 5, 11,

12, the four telecoordinometers with the ﬁve envi-

ronmental factors; for space reasons we have not in-

cluded the full matrix.

The highest correlation (absolute) values are re-

lated to the temperature, exept for north-south direc-

tion of both the telecoordinometers (T1 and T3).

We can observe a reduction in the value measured

by all the deformometers and the two east-west di-

rection telecoordinometers, when the temperature in-

creases. For the deformometer, an increase in temper-

ature causes an expansion of the Tower, which will

then tend to solicit the man-made cracks in which the

sensors are installed, so the measured value decreases.

Regarding the telecoordinometer, the correlation

is due to the fact that temperature causes not only an

horizontal expansion, but also in the vertical direc-

tion; this expansion-contraction cycles causes move-

ment in the Tower, which is then perceived by the

sensor that measures the inclination in the east-west

direction. The correlation related to solar radiation is

also negative and strongly linked to the previous ob-

servations, considering the relationship between radi-

ation and temperature.

For wind speed and direction, the correlation val-

ues are extremely close to zero, suggesting a low im-

pact of the wind condition on the structure.

Finally, pressure is the only factor showing a pos-

itive correlation with the operational factors; in this

case, as the pressure increases, the values measured

by the deformometer and telecoordinometer sensors

increase, although with a low correlation value.

Figure 2: Partial correlation matrix - environmental sensors

against operational sensors.

To further explore the data discovery phase, we

conduct a regression analysis over the entire monitor-

ing period considered in this work. Equations 5, 6, 7

and 8 describe linear models of the relationship be-

tween environmental factors and deformometers D4,

D5, D11 and D12, respectively; while equations 9,

10, 11 and 12 similarly describe the dependence of

telecoordinometers T1, T2, T3 and T4, respectively.

This analysis provides valuable insights into our

data, allowing to better understand how different sen-

sors interact with each other and how they are affected

by environmental factors. By examining these rela-

tionships, we can identify patterns and correlations in

the data that may not be obvious from the visual in-

spection.

Correlation and linear regression analyses per-

formed previously show a relevant dependence of op-

erational sensors on environmental factors. However,

several studies show that the relationship between en-

vironmental conditions and structural parameters can

DATA 2023 - 12th International Conference on Data Science, Technology and Applications

432

D1 = (4.43e−4) W S − (1.39e−6) W D − (2.81e−3)T M + (2.54e−6) SR + (2.40e−4) P (4)

D4 = (4.43e−4) W S − (1.39e−6) W D − (2.81e−3)T M + (2.54e−6) SR + (2.40e−4) P (5)

D5 = (3.43e−4) W S − (9.45e−7) W D − (1.39e−5)T M + (1.25e−5) SR + (7.46e−5) P (6)

D11 = (7.67e−4) W S + (9.7e−7) W D − (1.23e−3)T M − (9.51e−6) SR + (1.49e−4) P (7)

D12 = (2.75e−4) W S − (3.91e−6) W D − (1.01e−3)T M − (1.09e−5) SR + (3.39e−5) P (8)

T 1 = (4.10e−2) W S − (1.19e−3) W D − (3.17e−2)T M − (8.59e−4) SR − (4.37e−2) P (9)

T 2 = −(2.74e−2) W S − (3.83e−5) W D − (1.30e−1)T M − (2.17e−3) SR + (1.46e−2) P (10)

T 3 = (5.80e−3) W S − (4.27e−4) W D + (3.09e−2)T M − (2.18e−3) SR − (2.36e−2) P (11)

T 4 = −(2.88e−2) W S + (6.03e−4) W D − (2.18e−1)T M − (9.92e−4) SR + (6.59e−3) P (12)

introduce some nonlinear components (Hsu and Loh,

2010) (Shi et al., 2016). Therefore, in the experiments

section we also explore a DL regression architecture

to model the nonlinear components of the relationship

between environmental and operational sensors.

4 EXPERIMENTS AND RESULTS

The whole machine learning pipeline has been im-

plemented on Google Colaboratory (Colab)(Bisong,

2019), an open web platform design on top of the

open-source Jupyter project. The virtual machines on

which Colab is run are powered by a NVIDIA Tesla

K80 GPU cards. The source code has been publicly

released and can be accessed at (Parola, 2023).

This section shows the results achieved by the two

regressive models previously described by presenting

the value of evaluation metrics.

A single neuron with a linear activation function

implemented the linear regressor (Jolivet et al., 2008),

while the second model is a deep NN with a hidden

layer containing 16 neurons. Both models have ﬁve

neurons in the input layer, as the number of environ-

mental sensors. The training phase has been run for

150 epochs where the Adam algorithm has been used

as the optimizer and an early stopping condition was

set to prevent overﬁtting with a patience value equal

to 10.

Tables 2 and 3 show the evaluation metrics val-

ues of mse and R

obtained from the linear regressor

model and NN model for the deformometer and tele-

coordinometer sensors, respectively.

Table 2: Deformometer mse and R

LR NN

sensor mse R

mse R

D1 .277 .719 .206 .791

D2 .242 .754 .188 .809

D3 .258 .737 .186 .810

D4 .202 .794 .168 .829

D5 .303 .551 .222 .774

D6 .241 .754 .190 .806

D8 .201 .797 .152 .847

D9 .431 .549 .237 .752

D11 .509 .482 .374 .619

D12 .299 .694 .239 .761

Mean .287 .679 .208 .838

Table 3: Telecoordinometer mse and R

LR NN

sensor mse R

mse R

T1 .705 .290 .489 .507

T2 .568 .424 .479 .514

T3 .721 .280 .436 .565

T4 .716 .281 .542 .455

Mean .677 .318 .486 .510

From above tables it is evident how the deep learning

based strategy is more effective in estimating the in-

ﬂuence of environmental effects on the structural be-

havior of the tower of Pisa; indeed, we can observe for

each table row the mse value is higher for the linear

regressor column compared with the DL model.

Speciﬁcally, both models are able to accurately

forecast the deformometer sensor group behave, with

a R

mean values for the linear regression being

Effects of Environmental Conditions on Historic Buildings: Interpretable Versus Accurate Exploratory Data Analysis

433

67.9% and the NNs being 83.8%. The mse mean

value of the deformometers is 28.7% using linear re-

gressor and 20.8% using NN. As a result, we ﬁnd that

the deep learning architecture outperforms the linear

models by a factor of 27%, computed as the error of

the ﬁrst method minus the error of the second one over

the error committed by the ﬁrst.

Telecoordinometer sensor modeling does not ex-

hibit the same effectiveness, as the NN R

has a low

value of 51.0%; while the performance of the linear

regression is signiﬁcantly poorer with an R

value of

31.8%.

5 DISCUSSION

Empirical results clearly denote how NNs outperform

a linear regression approach in modeling operational

sensors depending on environmental factors. How-

ever, the linear regression strategy may be preferred

to NNs due to the lack of explainability of DL, which

is considered a black-box approach (Guidotti et al.,

2018).

By analyzing the linear regression coefﬁcients,

we can identify the environmental factors having the

most signiﬁcant impact on sensor measurements can

be identify and a quantitative indication of them can

be measured. This information can then be used to

develop correction factors that take environmental in-

ﬂuence into account and improve the accuracy of the

monitoring system by calculating the corrected fea-

tures adjusted from environmental effects (Roberts

et al., 2023).

6 CONCLUSIONS

In this work, two regressive techniques to estimate the

inﬂuence of environmental condition on structural be-

havior have been designed and compared, after a data

mining phase to explore the time series data. The sen-

sor network data of the leaning Tower of Pisa have

been chosen as case study to implement the method-

ology.

In conclusion, transparent regression models may

not be able to detect complex patterns in the data but

have the beneﬁt of being easy to understand and re-

quiring less computing capabilities. Although deep

learning models may capture complicated patterns,

they can be challenging to interpret and need a lot

of computational resources and training data. The

choice between transparent regression models and

deep learning models ultimately depends on vari-

ous speciﬁc challenges of the problem and histori-

cal building to monitor: ranging from logical mod-

els to scoring systems. In any exploratory data anal-

ysis different models co-exist. Future research ef-

forts aimed at establishing interconnections between

different models could be founded on model-centric

explanations derived from ontologies, which serve

as standardized representations. This approach has

the potential to help both system designers and users

make systematic connections between explanations

and their respective data sets and models.

ACKNOWLEDGEMENTS

This work has been partially carried out in the frame-

work of the PRA 2022 101 project “Decision Sup-

port Systems for territorial networks for managing

ecosystem services”, funded by the University of

Pisa. This work has been partially supported by

the Tuscany Region in the framework of the ”Se-

cureB2C” project, POR FESR 2014-2020, Law De-

cree 7429 31.05.2017. Work partially supported

by the Italian Ministry of Education and Research

(MIUR) in the framework of the FoReLab project

(Departments of Excellence).

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