Prediction of long-term strain in concrete structure using convolutional neural networks, air temperature and time stamp of measurements

https://doi.org/10.1016/j.autcon.2021.103665Get rights and content

Highlights

  • A method for predicting long-term strain in concrete structures is proposed.

  • A CNN is employed to define the correlation between strain and air temperature.

  • Time-dependent inelastic behavior of concrete structure is reflected in CNN training.

  • The performance is evaluated using strain data measured from a concrete footbridge.

Abstract

A data prediction method for long-term strain measurements from concrete structures based on the strong correlation between air temperature and structural response is proposed. A convolutional neural network (CNN) is employed to capture and define the relationship between the structural response and air temperature. The CNN is trained using measurements of air temperature and strain collected before the data interruption. To reflect the time-dependent long-term behavior of a concrete structure, the air temperature and corresponding time information are simultaneously utilized in the input layer of the proposed CNN. The trained CNN is then used to estimate the strain in the structure using only the air temperature data from the weather station in the event of a data loss from the structure's sensors. The presented method is validated using long-term data from fiber optic sensors embedded in a concrete footbridge at Princeton University and air temperature data from a nearby weather station.

Introduction

The performance of structures degrades throughout their service lives due to natural or man-made effects. For example, repeated, unexpected, or excessive loading can damage the structure or its structural members, reducing the structure's life span, and additional loads can inflict further damage that may even collapse the structure. To better manage structures and prevent disasters, techniques for structural health monitoring (SHM) have been developed [1,2]. SHM involves the installation of various types of sensors in the structure and measuring structural responses to identify the structure's state and evaluate its safety. Strain is a structural parameter that directly corresponds to various external loads and can be used for stress evaluation; Therefore, information about strain in the structure can be effectively used for structural safety evaluations [3]. Consequently, relevant SHM techniques have indeed been developed using strain measured in structures or structural members within structures [4,5]. In particular, the strain-based SHM approaches have been actively conducted for structures such as bridges, which can be regarded as beam-like structures [6,7].

Structures are influenced by various external agents such as temperature, wind, vehicles, and people. Structures are particularly affected by ambient temperature because most structural components are exposed to the external environment. They undergo continuous temperature changes due to solar radiation and air temperature variations, and these changes cause dimensional changes in structures that can result in generation of thermal strain and thermally induced mechanical strain and stress [8]. The temperature-induced structural behavior can be observed from structural responses such as strain and displacement [[8], [9], [10], [11]]. Bridge monitoring studies [10,12] have actually shown that temperature-induced strain can be larger than service load-induced strain such as that imposed by vehicles. Therefore, long-term monitoring aimed at investigating the relationship between temperature variations and temperature-induced responses has become an important research topic. Xu et al. [8] monitored the temperature of a long suspension bridge and its structural responses for approximately eight years. They confirmed a strong linear relationship between temperature and the displacement of the bridge tower and deck in the longitudinal direction. They found that the vertical displacement of the bridge deck was also correlated with the temperature of the structure. Yarnold and Moon [9] used long-term monitoring data to analyze the relationship between the temperature variations in a long-span steel tied arch bridge and its structural responses. They found a nonlinear relationship between temperature, displacement, and strain in 3D space. Using temperature and strain data measured from fiber Bragg grating (FBG) sensors installed in a long-span suspension bridge, Xia et al. [10] suggested a structural transfer function by establishing the temperature-strain relationship as an input-output relationship. Moreover, they defined a damage index using temperature variations and temperature-induced strain, and used the index for damage detection. The above studies clearly demonstrated that the temperature and temperature-induced responses of bridges were correlated with each other.

Long-term monitoring can be made more challenging by defects in the sensors installed in structures (e.g., long-term drift), temporary interruptions due to unstable power supplies, errors in the measurements, and data loss during transmission [13,14]. To address these problems, structural response reconstruction and recovery methods have been developed [15,16]. Based on the correlations of responses measured by sensors, methods for restoring the stress or strain responses used to evaluate the safety of structures have been proposed [[17], [18], [19]]. A method of recovering the long-term vibrational structural responses of structures [20] and a method of predicting the wind-induced strain of structural members [21] have recently been proposed based on deep learning techniques.

In addition to the studies on the data reconstruction, recovery, and prediction methods described above, studies have been conducted to estimate structural responses using temperatures measured in structures based on the strong relationship between the temperature and temperature-induced responses of bridges or beam-like structures [[22], [23], [24]]. Kromanis and Kripakaran [22] proposed a regression model to capture the relationship between the temperature and temperature-induced responses of bridge structures. Using temperature and structural responses obtained from a bridge, a model trained by a support vector machine (SVM) was employed to estimate temperature-induced strain. These researchers also studied the estimation of temperature-induced responses such as strain and tilt by applying various regression algorithms, such as multiple linear regression and robust regression, as well as the support vector machine to temperature data measured from small truss bridge specimens and a 10-m footbridge [23]. Wang et al. [24] established the relationship between the temperature and strain of a long-span cable-stayed bridge using the Bayesian dynamic linear model, and developed a method for estimating strain using this relationship, validating the proposed method using one and a half months of data in summer and winter.

The above long-term monitoring data prediction methods defined the relationship between temperature and temperature-induced strain measured in the bridge structures, and then estimated strain using this relationship. The temperature data used were measured by temperature sensors installed in the structures. However, temperature sensors may also be subjected to the real-life problems of missing data [14]. When measured temperature data is missing, any temperature-induced strain estimation method based on such data is invalid. Abdel-Jaber and Glisic [14] compared the temperature measured by sensors installed in a footbridge on the Princeton University campus, USA, with the temperatures measured at a local weather station (Trenton Airport Weather Tower), approximately 10 miles (16 km) away from Princeton University. This comparison confirmed a strong correlation between the temperature of the footbridge and the temperature of the weather tower. Because the periodic (hourly) temperature measurement at the weather station is managed by the federal government (the National Oceanic and Atmospheric Administration), these measurements are highly reliable and have a relatively low probability of data loss, indicating that temperature data measured at a weather station can be used to estimate temperature in nearby structures.

In addition to thermal behavior, a time-dependent (rheological) inelastic comportment is observed in concrete structures in the long-term [[25], [26], [27], [28]]. Hedegaard et al. [25] investigated the long-term monitoring structural responses of a concrete bridge over five years. Their monitoring data showed inelastic behavior such that the strain of the bridge continuously decreased over time because of creep and shrinkage effects. Hu et al. [26] investigated long-term monitoring data of 14 years for a curved prestressed concrete box girder bridge. Strain data measured from the sensors installed in the concrete web in the bridge confirmed that the strain tended to gradually decrease over time. Webb et al. [27] studied long-term strain monitoring of a prestressed bridge using fiber-optic sensors. In the measurements, a gradual reduction of strain data by creep and shrinkage was observed. Furthermore, they compared measured strains with predictions by models for inelastic behavior of concrete structures. Abdel-Jaber and Glisic [28] analyzed the characteristics of strain responses monitored for approximately seven years in a concrete footbridge. They classified post-tensioning, temperature-induced seasonal variations, and creep and shrinkage components from the long-term strain responses. They also suggested a long-term strain response approximating function in which the seasonal variation of thermally generated elastic strain was represented as a sine function, and the long-term rheological strain caused by creep and shrinkage was represented as an exponential function. Besides, many studies focused on long-term monitoring of vertical deflection for concrete structures considering time-dependent effects. Robertson [29] monitored long-term structural responses of a long-span prestressed concrete bridge. A time-dependent step-wise finite element analysis program was employed to predict long-term defection of the bridge. By considering time-dependent effects due to creep and shrinkage in the analysis, the prediction performance of the program was improved. In a research [30] on long-term defection monitoring of a concrete bridge, a method for directly identifying shrinkage and creep in the structure was presented. The method based on the time-dependent responses to be monitored identified the creep and shrinkage and accurately predicted long-term vertical deflections of the structure. Hence, in the long-term monitoring of concrete bridges, we cannot ignore time-dependent inelastic long-term behavior which can be associated with creep and shrinkage. To predict the inelastic behaviors of concrete structures such as creep and shrinkage, several physical models such as ACI209 [31], CEB90 [32], and B3 [33,34] were developed. In these models, rheological effects such as relative humidity as well as curing conditions such as drying time and water-to-cement (w/c) ratio, and material properties such as compressive strength, sizes of aggregates, and cement types were considered. However, in real projects, calibration of sophisticated numerical models can be difficult to achieve, as it would require expensive long-term experiments. Another long-term studies, this time on columns of high-rise buildings [35,36], showed that simplified physics-based models might be effective, with relative error compared with SHM data of about 20–25%. However, loading and environmental conditions in these cases were very simple: columns were under uniaxial loading and temperature and humidity around the buildings were almost constant over the year (buildings are situated in Singapore). Such favorable environmental conditions are not present in the majority of locations around the world, and uniaxial loading conditions are not present in structural elements exposed to bending. Hence, in the majority of real projects, such a good performance of simplified models cannot be expected. The improvement that data-driven approach can offer to physics-based modelling is to use the SHM data from real-life structures in order to calibrate sophisticated physics based models, so they can take into account complex stress states of structures and avoid the need for calibration experiments. This paper deals with creation of data-driven models, while merging these models with physics-based models is considered out of the scope of this paper, and will be addressed in future research.

While the physical models considered above are in general different, they are concordant in identifying four main strain constituents: mechanical strain, thermal strain, and two constituents of rheologic strain, creep and shrinkage. Besides, some other strain constituents can also be present, such as endogenous, carbonation and plastic strain in concrete at early age, swelling induced by alkali-silica reaction, etc. In general, the strain constituents (mechanical, thermal, creep, shrinkage, etc.) develop simultaneously, and strain sensors measure their combination. Eq. (1) represents a simplified expression of strain evolution at observed point, as measured by sensor, assuming uniaxial state of stress at that point. The purpose of this equation is to illustrate physics behind the strain evolution, rather than to propose an accurate, sophisticated model.εnτ=εn,στ+εn,Tτ+εn,cτ+εn,shτ+εn,otherτwhere: n is direction of normal strain component, εn,σ is mechanical strain, εn,T is thermal strain, εn,c is creep, εn,sh is shrinkage, εn,other is combination of all other strain constituents, and τ is the time at which the strain is observed. Eq. (1) can be rewritten as follows [35].εnτ=σnτE+αT,nΔTτ+KcσnτEfcτ+εsh,final,nfshτ+εn,otherτwhere: σn is stress (in direction n), E is modulus of elasticity, αT,n is thermal expansion coefficient (in direction n), ΔT is change in temperature (with respect to some reference temperature), Kc is creep coefficient, fc is creep function ranged between 0 and 1 fc(0) = 0, fc(∞) = 1), εsh,final,n is final shrinkage (in direction n), and fsh is shrinkage function ranged between 0 and 1 fsh(0) = 0, fsh(∞) = 1).

In Eq. (2), estimating creep and shrinkage parameters (Kc, fc(τ), εsh,final,n, and fsh(τ)) is particularly challenging in real-life settings. Various above-mentioned physical models use different input parameters to determine them, and consequently they result in different estimations of rheologic strain for the same concrete [35,36]. Thus, there are epistemic errors in these models that cannot be minimized by tuning them to only the initial set of measurements. The use of data-driven methods, such as the one proposed here, has potential to inform and harmonize these physics-based models in the future, by providing better estimates of creep and shrinkage functions, learned from the field data.

Rheological effects result in twofold challenges for accurate predictions of long-term strain: in one hand, they are non-linear and dependent on several factors such as position in the structure, relative humidity, concrete mixture, etc., thus, difficult to predict based on physical models; in the other hand, potential drift in sensor data is difficult to distinguish from rheological strain. In addition, in the previous prediction models [[31], [32], [33], [34]] for creep and shrinkage, the ranges of concrete properties and external conditions were limited. In other words, if some properties such as compressive strength and w/c ratio are not within defined ranges in the models, the evaluation of creep and shrinkage parameters would involve extrapolation, and the prediction results might be incorrect. Furthermore, as the application of additives and mix conditions of modern concrete such as high strength concrete were not defined in the models, they may result in inaccurate predictions in some conditions. While several studies addressed the relationship between the temperature and strain in real-life settings, to the best of the authors' knowledge, no study attempted to include rheological inelastic behaviors in the machine learning methods employed to define the relationship between temperature and strain in long-term.

Therefore, in this study, we propose for the first time a data-driven method for predicting long-term strain data of concrete bridges using air temperature, which accounts for rheological effects by including time-stamp of measurements in the input dataset. These predictions can be used to estimate structural behavior in the event the SHM system is partially or fully non-functional. In addition, these predictions can be used to evaluate whether the sensors are subjected to drift, i.e., to validate reliability of long-term data. We assume, in our method, that at the time of sensor installation onto structure, and during the initial period of measurements, the sensors are new and do not experience failure or drift. This assumption is justified by the fact that sensors designed to monitor strain and temperature in the long term (e.g., based on vibrating wire principle or fiber-optics) do not experience failure or drift in the first several years (e.g., see [37]). However, we acknowledge that failure or drift can occur in the long-term due to deterioration processes (mechanical and thermal cycling, humidity, corrosion, etc.). Failure of a sensor will interrupt collection of data at the location of the sensor, which can impair data analysis used for evaluation of structural performance and condition. To enable data analysis, it would be beneficial to predict the data for failed sensors, and hence the need for our long-term predictive model. Drift creates systematic error in measurements, which cannot be detected by statistical analysis of measurements performed by the sensor which experiences the drift alone [38]. Thus, drift evaluation process must include measurements performed by additional sensors, preferably performed by an independent calibrated measuring system, if available [38]. In typical applications, this is frequently not possible: two different independent sensors are almost never installed at the same location in a structure due to costs; thus, inclusion of measurements performed by sensors installed at other locations in the structure is frequently the only available option. However, in the case of temperature, independent measurements could be provided by an external calibrated weather station [14]. Our predictive model can be used to detect the drift, as in the case of drift an unusually high difference between predicted and measured (drifted) data will be observed. The threshold for detection of the difference can be set by using the root mean square error of the model (see Section 4). Thus, besides the strain and temperature data measured by the monitoring system on the structure, temperature data measured at a weather station nearby the structure is introduced in the proposed method. A convolutional neural network (CNN) is employed to capture the relationship between air temperature and the strain responses of the structure, based on the correlations between air temperature at the weather station and temperature in the structure, as well as the correlation between temperature and strain responses of structure. The CNN is trained by setting the air temperature data measured reliably from the weather station as input information and the strain data acquired from the bridge structure as output information (prior to the occurrence of sensor defects). The trained CNN is then used to estimate the strain in cases when the strain in the structure could not be measured. To reflect the time-dependent behavior of the long-term monitoring of concrete bridges in the proposed prediction method, the time of air temperature measurement is additionally set as the input information of the CNN. We tested the proposed method by using the structural response measured from fiber-optic strain sensors installed in Streicker Bridge, in conjunction with air temperature measured at a weather station near the bridge. The performance of strain estimation by the CNN, trained with data measured from Streicker Bridge over four years, was examined. In addition, to validate the capacity of the input configuration of the proposed method to reflect the time-dependent behavior of concrete bridges, we compared the strain estimation performance of the CNN considering the time information as well as air temperature data in the input layer with that of the CNN using only air temperature data without time information in the input layer. Furthermore, we also compared the strain estimation performances of the CNNs trained with structural responses measured at the top and bottom of cross-section in the bridge by taking into consideration the difference in temperature sensitivity of structural responses at these two locations in cross-sections of the bridge. Finally, we investigated how the performance of the proposed method depends on the measurement period of the structural response data used for CNN training.

Section snippets

Strain and temperature measurements

To create and explore the method proposed in this study, we used a sensor network on the Streicker Bridge at Princeton University. The bridge, shown in Fig. 1(a), is a pedestrian bridge with a total length of 104 m. Construction began in 2009, and the bridge opened for use in 2010. The bridge has one main span and a total of four ramps, two on each end of the span. The deck of the main span is supported by an arch. The ramps are curved continuous prestressed concrete girders, and each girder is

CNN training data generation from measured data

The proposed method is aiming at predicting static strain data of structures in the event of a data loss from a structure's sensors. The relationship between the two types of measured information is described by Eq. (6), based on the air temperature measured at the nearby weather station and the strain data measured from the structure before the data loss. Because many variables are involved and uncertainty is inherent in the mathematical definition of this relationship, the proposed method

Evaluation of method

To evaluate performance of the proposed method, we used the air temperature data recorded at a local weather station (Trenton Airport) during an approximately four-year period and the strain data measured at the Streicker Bridge, during the same time, i.e., from June 2010 to July 2014. Of these measurement data, we trained the CNN using the data from June 2010 to July 2013 and examined the strain estimation performance of the trained CNN using the data from July 2013 to July 2014, which were

Conclusions

In this study, we proposed a data prediction method based on a CNN for the long-term strain responses of concrete structures. Based on the strong relationship between air temperature and the strain in structures, we presented a CNN that set the air temperature data recorded at a weather station near the structure as input information and strain data measured from the structure as output information. To consider the time-dependent non-elastic long-term strain effects in the structure (e.g.,

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science, ICT & Future Planning, MSIP) (No. 2021R1A2C3008989). We would like to thank Steve Hancock and Turner Construction Company; Ryan Woodward and Ted Zoli, HNTB Corporation; Dong Lee and A.G. Construction Corporation; Steven Mancini and Timothy R. Wintermute, Vollers Excavating & Construction, Inc.; SMARTEC SA, Switzerland; Micron Optics, Inc., Atlanta, GA. In addition

References (41)

  • B.K. Oh et al.

    Real-time structural health monitoring of a supertall building under construction based on visual modal identification strategy

    Autom. Constr.

    (2018)
  • H.M. Lee et al.

    A wireless vibrating wire sensor node for continuous structural health monitoring

    Smart Mater. Struct.

    (2010)
  • H. Abdel-Jaber et al.

    A method for the on-site determination of prestressing forces using long-gauge fiber optic strain sensors

    Smart Mater. Struct.

    (2014)
  • D.H. Sigurdardottir et al.

    On-site validation of fiber-optic methods for structural health monitoring: Streicker bridge

    J. Civ. Struct.

    (2015)
  • W. Hong et al.

    Strain-based damage-assessment methods for bridges under moving vehicular loads using long-gauge strain sensing

    J. Bridg. Eng.

    (2016)
  • Y.L. Xu et al.

    Monitoring temperature effect on a long suspension bridge

    Struct. Control. Health Monit.

    (2010)
  • Q. Xia et al.

    In-service condition assessment of a long-span suspension bridge using temperature-induced strain data

    J. Bridg. Eng.

    (2017)
  • J. Reilly et al.

    Identifying time periods of minimal thermal gradient for temperature-driven structural health monitoring

    Sensors

    (2018)
  • F.N. Catbas et al.

    Condition and damage assessment: issues and some promising indices

    J. Struct. Eng.

    (2002)
  • H. Abdel-Jaber et al.

    Systematic method for the validation of long-term temperature measurements

    Smart Mater. Struct.

    (2016)
  • Cited by (28)

    View all citing articles on Scopus
    View full text