Long-term Structural Health Monitoring System Research Articles

Simulation and prediction of vortex-induced vibration of a long suspension bridge using SHM-based digital twin technology

Although wind tunnel tests have already become a design basis for improving the stability of long-span bridges under the action of wind loads, vortex-induced vibration (VIV) events of in-service long-span bridges have still been frequently reported in recent years. The reasons behind this could be attributed to the limitations and uncertainties involved in wind tunnel tests as well as the changes and degradations of in-service bridges. In consideration that most long-span bridges have now been equipped with long-term structural health monitoring (SHM) systems and that digital twins could provide a new solution for simulating and predicting the reality, this study aims at developing a digital twin for VIV of a long suspension bridge to simulate and predict its VIV. The design document-based finite element (FE) model of the bridge is first updated using the measured dynamic characteristics. The numerical model for VIV of the bridge is then established using the vortex-induced force (VIF) model established based on wind tunnel test results. The numerical model together with the VIF model are finally updated against the measured vortex-induced responses (VIR) to produce a digital twin for VIV of the bridge. The relationships between the parameters in the VIF model and wind characteristics are further investigated to enable the digital twin to predict future VIV events. The accuracy of the digital twin for predicting the future VIV and the influence of the VIF parameters obtained from wind tunnel tests on the prediction accuracy both are confirmed through comparisons between the predicted and measured results.

Statistical Analyses of the Non-Uniform Longitudinal Temperature Distribution in Steel Box Girder Bridge

The frequently conventional assumption that bridge temperature is uniformly distributed on long-span bridges could lead to uncertainty when analyzing temperature effects. This study investigated the surface temperature of steel box girders on a long-span suspension bridge, emphasizing the distribution characteristics in the longitudinal (spanwise) direction. The girder surface temperature distribution was monitored using the long-term structural health monitoring system (SHMS). First, the probability density functions (PDF) of the girder surface temperature were analyzed. The results showed that the PDFs had bimodal characteristics and could be well-fitted using the weighted superposition of two normal distributions. Meanwhile, there was an obvious difference between the PDFs of the measuring points at different longitudinal sections of the bridge, which is inconsistent with the assumption that the temperature was uniformly distributed in the longitudinal direction. Subsequently, the longitudinal distributions of the girder surface temperature were statistically analyzed, and polynomial functions were introduced to fit the distribution curves along the left and right sides of the mid-span. A correlation analysis was then performed, highlighting the variability in temperature in the longitudinal direction. Additionally, the longitudinal temperature distribution pattern could be summarized as (i) the highest in the mid-span, the lowest in the tower, and increasing along the side span; (ii) there were also significant differences between the left and right sides of the mid-span. Finally, the time- and space- distributions of the temperature were studied, and a contour map was displayed. The results showed that the girder surface temperature had significant three-dimensional spatial characteristics and was not only non-uniformly distributed in space but also in time. This work is useful for a more accurate analysis of temperature effects on long-span bridges.

A data-driven sensor placement strategy for reconstruction of mode shapes by using recurrent Gaussian process regression

Current Optimal Sensor Placement (OSP) strategies for bridges mostly rely on data from a finite element model rather than from the real structure due to high cost in placing massive sensors for data collection. For large-scale bridges, however, it is difficult to formulate a precise model and thus the OSP strategies building upon a finite element model inevitably suffer from modelling errors. Besides, the finite element model cannot account for real measurement noise. Premised on the fact that it is not expensive to make in-situ trial measurements with a few sensors on a target bridge before deploying a structural health monitoring (SHM) system on it, a data-driven OSP strategy is proposed in this study which aims at accurately reconstructing mode shapes (to facilitate vibration-based structural damage detection) by using only a few vibration sensors to be included in the SHM system. The proposed OSP strategy is also applicable for the upgrade of a long-term SHM system currently deployed on a bridge, by using historical data collected from the current SHM system. To precisely reconstruct mode shapes, a two-stage OSP strategy in terms of Recurrent Gaussian Process Regression (RGPR) is developed, and its performance is validated on a simulation model and a real bridge. In the first stage, the greedy algorithm is leveraged to temporarily deploy sensors on the structure and train accurate RGPR models using the collected data, which are used to afford spatially complete mode shape data for optimization later. Starting from a few sensors temporarily deployed on the bridge, a one-by-one sensor adding procedure is performed to configure increasing sensors until the target is achieved. In the second stage, Cuckoo Search (CS) algorithm is pursued to obtain the globally optimal sensor placement solution, from which the temporarily deployed sensors can be re-configured to the optimum positions. Both the best sensor quantity and positions are obtained by the proposed OSP strategy.

Meta-Model Assisted Continuous Vibration-Based Damage Identification of a Historical Rammed Earth Tower in the Alhambra Complex

ABSTRACT This work presents the development of a model-based online damage identification system for a 13th century rammed earth (RE) tower in the Alhambra, the Muhammad Tower. The system is fed with continuous data from an ambient vibration-based monitoring system and a meteorological station. Ambient vibrations are continuously processed through Operational Modal Analysis (OMA), and environmental effects are minimised via statistical pattern recognition. The normalized modal signatures are used to update the stiffness properties of certain parts of the tower through inverse model calibration. To do so, a high-fidelity three-dimensional finite element model (FEM) of the tower is developed. Since its computational burden precludes conducting online calibration, the FEM is bypassed by a light Kriging surrogate model (SM). In this light, the developed SM-assisted system identification constitutes a long-term Structural Health Monitoring (SHM) system outputting quasi-real-time series of modal properties and local stiffness parameters, so providing full damage assessment (detection, localization and quantification). The presented results refer to a time period of three months since January until March 2022. Numerical results and discussion are reported concerning the characterization and removal of environmental effects, and synthetic damage scenarios through non-linear simulations are used to validate the developed damage identification system.

Advances in intelligent long-term vibration-based structural health-monitoring systems for bridges

The true realization of the benefits of vibration based structural health monitoring (VBSHM) in real-world applications is acquired through long-term continuous monitoring so that one can attain a detailed grasp of the behavior of the monitored structure. The challenges in long-term continuous VBSHM include: the large volume of accumulated monitoring data; the effective extraction of engineering information amid the influences of noise and uncertainties embedded in the monitoring data; maintaining continuity and consistency in the long-term monitoring data considering that the system and instrumentation may change due to sensor failure or renewal due to advances in sensing technologies. To meet these challenges, this paper presents recent research that has resulted in the development of a framework and specialized signal processing and data analytic tools for long-term continuous VBSHM suitable for real-world monitoring applications of structures in the field. These include efficient tools for large scale intelligent data processing and analysis, management of monitoring database and extracted information relevant to the structural health of the monitored structure. The novel Automated In-Line Full Space Identification (AI-FSI) method is presented to address the needs and challenges associated with long-term continuous VBSHM, such as the automation of all data processing and analysis operations including modal parameter estimations and mode tracking, and the need of minimizing the measurement and computational uncertainties and variability in the operational modal analysis results. A smart self-diagnostic system for the monitoring of the health of the data collection sensors and monitoring system has also been developed that will allow the consistent use of the monitoring data of different sensor configurations and era in the monitoring project. Examples on the efficiency of analyzing the monitoring data collected over 20 years from the Confederation Bridge monitoring project in Atlantic Canada by using the developed novel framework and data analytic tools are presented.

An automated structural health monitoring system developed for Ekaterinburg Arena

Introduction. The paper presents those essential Structural Health Monitoring (SHM) implementation details that have not been sufficiently documented in Russian national guides or regulations. The study aims to systematize and share the experience of applying the previously developed SHM theoretical principles to the existing large-span unique sports facility Ekaterinburg Arena. The paper provides information about determining monitored structural elements, instrumentation alignment, and monitoring parameters’ threshold value.
 Materials and methods. The long-term SHM system of the large-span structure of the Arena is organized around hardware and software for processing the data constantly incoming from tiltmeters, strain gauges, accelerometers, a motorized total station, and a weather station.
 Results. A unified information system for automated SHM of the Arena has been created. It comprised modules for data acquisition, high-performance databases for storing metrics, metadata, and the project information, services for evaluating and visualizing structural parameters, components for the instrumentation self-diagnosis, an application development interface for sophisticated data analysis, and a 3D model of the structure. Engineering methods for evaluating the initial values of the controlled parameters and their thresholds acceptable for regular operation are proposed. The technique of calculating internal forces based on the strain gauge data with a redundant measurement pattern has been tested.
 Conclusions. The obtained monitoring results have become a valuable source of initial data for developing automated methods for detecting and locating damages in structures, improving structural analysis and design methods, predictive maintenance, surveys, and solving other knowledge-intensive tasks. Applying the SHM theoretical principles to the real structure can significantly contribute to developing the current immature scientific and regulatory framework for implementing similar monitoring systems at complicated construction facilities.

A web‐based and design‐oriented structural health evaluation system for long‐span bridges with structural health monitoring system

This paper presents a web-based and design-oriented structural health evaluation system (SHES) for long-span bridges equipped with long-term structural health monitoring system (SHMS). The key parameters of a long-span bridge, used in its limit state design, are recollected. The key design parameters cover not only bridge acceleration, displacement, internal force and stress but also wind loading, temperature loading, traffic loading, earthquake excitation, and corrosion. Data analysis methods are applied to the measurement data recorded by SHMS installed in the bridge to obtain its measured/predicted key parameters. Because most design parameters are reliability-based, data analysis methods therefore include not only statistical analysis, fatigue analysis, corrosion analysis but also extreme value analysis. The design key parameters and the measured/predicted key parameters are then used to evaluate the health status of the bridge in terms of loading, serviceability, safety, and durability. The three statuses of structural health monitoring, that is, normal monitoring, critical monitoring, and inspection initialization, are correspondingly defined as a reference for maintenance and management decision. All of the above are implemented with a series of web-based software. The feasibility and advantage of the proposed SHES are finally demonstrated through a case study using a real long-span butterfly arch bridge.

Full-scale monitoring of wind effects on a supertall structure during six tropical cyclones

Full-scale measurements under real wind conditions are viewed as the most reliable approach to investigating the wind effects on supertall structures. However, long-term monitoring on wind characteristics at the maximum atmospheric boundary layer height and the corresponding wind-induced responses of structures are very limited, especially under strong tropical cyclones. In this study, field monitoring of wind effects on a 600 m high supertall structure is obtained during 6 tropical cyclones by means of a sophisticated long-term structural health monitoring (SHM) system deployed on the structure. Wind characteristics (wind speed, direction, turbulence intensity, gust factor, power spectral density) of these tropical cyclones above 450 m height are presented and analyzed. The dynamic properties of the supertall structure are determined from the field measurements and compared with those stipulated in design. The damping ratios of the supertall structure are estimated by the virtual dynamic shaker (VDS) and the enhanced virtual dynamic shaker (EVDS) methods. In addition, the response amplitude-dependence of the structural natural frequencies and damping ratios is investigated. Finally, the comfort performance of the supertall structure during different tropical cyclones is assessed against four comfort criteria. The findings of this study would be beneficial to professionals and researchers engaged in wind-resistant design and practice of skyscrapers.

The use of receiver operating characteristic curves and precision-versus-recall curves as performance metrics in unsupervised structural damage classification under changing environment

The development of long-term structural health monitoring systems is recently receiving a growing scientific interest in the field of Civil Engineering. In the context of unsupervised learning processes, deviations of dynamic parameters from their normal conditions can allow damage detection. However, due to the fact that modal properties are highly sensitive to environmental and operational factors, it is extremely important to remove such effects in order to obtain suitable damage sensitive features. In this regard, the selection of a proper multivariate statistical data analysis method for removing environmental effects is a key issue, heavily affecting the distribution of the residuals, the control chart and therefore the damage detection. However, specific criteria guiding the optimal definition of such statistical methods are yet to be established. In order to bridge this research gap, an original methodology is proposed in the present paper, based on Receiver Operating Characteristic (ROC) curves in combination with Precision-versus-Recall (PR) curves. Specifically, ROC and PR curves are computed and compared for a variety of statistical methods for data normalization and different damage scenarios and the model selection strategy is formulated as an optimization problem. The proposed approach is exemplified by application in two case studies of continuously monitored structures: the Z24 Bridge in Switzerland and the Consoli Palace, a mediaeval masonry building in Italy. The results highlight that the combined use of both ROC and PR curves represents a suitable tool for defining the most effective statistical data analysis method and the optimal damage threshold, in order to minimize the occurrence of false alarms and missing alarms.

Analytical calculation of temperature‐induced strain of supertall structures

Estimating temperature-induced strain is of critical importance for structural safety assessment. Most previous studies estimated the temperature-induced strain by statistical analysis, resulting in the unexplainable physical meaning of the obtained model coefficients. In this paper, an analytical formula for the temperature-induced strain of supertall structures is derived based on the simulated temperature field. First, a supertall structure is simplified as a cantilever column, and the theoretical relationship between the sectional two-dimensional temperature field and strain is derived. Afterwards, the structure is extended to a generalised cantilever column bounded by springs at the top end, and the theoretical relationship of temperature and strain is derived as well. The formula shows that the sectional strain is composed of the sectional average temperature-induced strain and the gradient temperature-induced strain along two horizontal directions. A finite element (FE) model is established to verify the derived strain formula. Finally, the formula is applied to a real supertall structure, the Wuhan Yangtze River Navigation Centre, on which a long-term structural health monitoring system has been installed. The temperature field of the whole structure is obtained by the FE heat transfer analysis, and the temperature-induced strain is calculated according to the derived formula. The average difference between the theoretically derived and measured strains is less than 7 με. This study provides a simple theoretical formula for calculating the temperature-induced strain of supertall structures, avoiding the complicated FE structural analysis.

Probabilistic principal component analysis‐based anomaly detection for structures with missing data

Structures are subjected to various kinds of structural deterioration and damage with use over long periods of service life. For the safety assurance of structures, it is very important to have a long-term monitoring system and continuous assessments of structural integrity using the measured data. The objective of this paper is to develop an anomaly detection algorithm for a long-term structural health monitoring (SHM) system based on probabilistic principal component analysis (PPCA). Static stress data were measured and used in this monitoring system. A baseline PPCA model is built under various environmental loading conditions. Then, newly monitored data are projected onto the principal vectors. Anomaly indices and their probability distributions are evaluated to determine the presence of structural damage indicated by outliers. This method is also capable of dealing with incomplete data and recovering the missing data. First, numerical simulation studies of a revolving auditorium are carried out to validate the proposed PPCA-based method. Then, real monitoring data collected from the SHM system are used to detect the presence and locations of anomalies in the revolving auditorium.

From TLS data to FE model: a workflow for studying the dynamic behavior of the Pulpit by Giovanni Pisano in Pistoia (Italy)

This paper discusses the first results of an ongoing two-year research activity aimed to identify the actual dynamic behavior of the Pulpit of Giovanni Pisano in Pistoia in order to design a long-term structural health monitoring system. First steps of the research have foreseen a Photogrammetric and Terrestrial Laser Scanner (TLS) survey of the structure in order to build a refined digital three-dimensional geometric model of the Pulpit to be employed for both documentation and structural assessment. The paper reports the main outcomes of the TLS survey together with the procedure employed to obtain a reliable finite element model of the Pulpit. An original workflow for direct transfer of high accuracy TLS-based three-dimensional model to a finite element model is proposed and discussed.

Temperature effects on static and dynamic behavior of Consoli Palace in Gubbio, Italy

Abstract In recent years, the development of long-term structural health monitoring systems for preventive conservation of historic monumental buildings is receiving a growing trend of scientific interest. Nevertheless, the damage detection effectiveness of these systems is still debated, especially in respect to complex masonry palaces where both local and global failure mechanisms can be activated, whereby the majority of the documented successful applications are limited to masonry towers. In particular, one major issue that needs to be solved in order to derive damage sensitive features is associated to the removal of the effects of changes in environmental conditions and, primarily, of ambient temperature, from static and dynamic signatures. This paper aims to contribute to improving knowledge in this field, by investigating temperature effects on static and dynamic response of an iconic Italian monumental palace: the Consoli Palace in Gubbio. With the purpose of early detecting earthquake-induced damages, as well as damages caused by material degradation associated to awkward environmental conditions, a simple low-cost mixed static and dynamic long-term structural health monitoring system has been installed on the Palace by the authors in July 2017. After discussing surveys, ambient vibration tests, diagnostic investigations, numerical modeling and model calibration of the Palace, the analysis of the first year of monitoring data is presented. This analysis shows that, differently from what observed in other literature works on historic masonry towers, the natural frequencies of the Palace show a marked and sometimes non-linear decreasing trend with increasing ambient temperature, that can be effectively removed through linear statistical filtering provided that dynamic regression models, using past values of predictors, are used. On the other side, the evolution of the amplitudes of two major cracks monitored within the building also shows a marked linear decreasing trend with increasing ambient temperature. These results are meaningful towards the use of monitoring data for assessing the initial health conditions of a structure, as well as in a damage detection perspective.

Deterioration assessment of buildings using an improved hybrid model updating approach and long-term health monitoring data

In recent years, it has become increasingly important to develop methodologies for reliable deterioration assessment of civil structures over their life cycle to facilitate maintenance and/or rehabilitation planning processes. Several approaches have been established to address this issue mainly using Bayesian probabilistic model updating techniques with some capability to incorporate uncertainties in the updating process. However, Bayesian model updating techniques are often found to be complex and computationally inefficient as opposed to their deterministic counterparts such as conventional or hybrid techniques of sensitivity-based model updating. Nevertheless, the deterministic model updating techniques have not been well developed for sophisticated assessment applications such as deterioration evaluation. To address these issues, this article presents a novel methodology for deterioration assessment of building structures under serviceability loading conditions, based upon an improved hybrid model updating approach incorporating the use of long-term monitoring data. This is first realized by a simple but effective scheme to simulate the deterioration mechanism in serviceability loading conditions before enhanced with innovative solutions to classify structural elements as well as to handle measurement and updating uncertainties in a meaningful way. The effectiveness of the established methodology is illustrated through a benchmark 10-story reinforced concrete building which is equipped with a long-term structural health monitoring system.

A multi-sensor sub-Nyquist power spectrum blind sampling approach for low-power wireless sensors in operational modal analysis applications

A novel multi-sensor power spectrum blind sampling (PSBS) approach is proposed supporting low-power wireless sensor networks (WSN) for Operational Modal Analysis (OMA) applications. The developed approach relies on arrays of wireless sensors, employing deterministic non-uniform in time multi-coset sampling to acquire structural response acceleration signals at sub-Nyquist sampling rates, treated as realizations of stationary random processes without making any assumption about the average signal frequency content and spectral support. The acquired compressed measurements are transmitted to a central server and collectively processed via a PSBS technique, herein extended to the multi-sensor case, to estimate the power spectral density matrix of an underlying spatially correlated stationary response acceleration random process directly from the compressed measurements. Structural modal properties are then extracted through standard frequency domain decomposition (FDD). The efficacy of the proposed approach to resolve closely-spaced modes is numerically tested for various data compression levels using noisy response acceleration signals of a white-noise excited finite element model of a space truss as well as field-recorded acceleration time-histories of an instrumented bridge under operational loading. It is shown that accurate mode shapes based on the modal assurance criterion can be obtained from as low as 89% less measurements compared to conventional non-compressive FDD at Nyquist sampling rate. Further, significant gains in energy consumption and battery lifetime prolongation of the order of years are estimated, assuming wireless sensors operating on multi-coset sampling at different data compression levels. It is, therefore, concluded that the proposed PSBS approach could provide long-term structural health monitoring systems with low-maintenance cost once wireless sensors with multi-coset sampling capabilities become commercially available.

Making good use of structural health monitoring systems of long-span cable-supported bridges

Many long-span cable-supported bridges have emerged in recent years, but are exposed to harsh environment conditions. The installation of long-term structural health monitoring (SHM) systems to the bridges has become a trend to monitor their loading conditions, assess their performance, detect their damage, and guide their maintenance with the utmost goals of ensuring their functionality, safety and sustainability. Nevertheless, it is not very clear how to make good use of SHM systems toward these goals. This paper takes the Tsing Ma suspension bridge in Hong Kong as an example and recapitulates the relevant works done by the author and his colleagues and students in the past 20 years to manifest how the SHM system installed in the bridge has been utilized since 1997. The SHM system installed in the bridge is briefly introduced first. How to use the SHM system for investigating highway loading, railway loading, wind characteristics, and temperature effects is then presented. Identification of time-varying natural frequencies and modal damping ratio of the bridge under strong winds using the data recorded by the SHM system is also demonstrated. Toward the performance assessment and damage detection of the bridge, SHM system-based computer simulation and damage assessment are targeted and some typical examples are given. The establishment of SHM system-based bridge rating system for bridge maintenance is also briefly introduced.

Threshold selection for extreme value estimation of vehicle load effect on bridges

In the design and condition assessment of bridges, the extreme vehicle load effects are necessary to be taken into consideration, which may occur during the service period of bridges. In order to obtain an accurate extrapolation of the extreme value based on limited duration, threshold selection is a critical step in the peak-over-threshold method. Overly high threshold results in little information to be used and excessively low threshold leads to large bias in parameters estimation of generalized Pareto distribution. To investigate this issue, 417 days of strain data acquired from the long-term structural health monitoring system of Taiping Lake Bridge in China are employed in this article. According to the tail distribution of the strain data induced by vehicle loads, four homothetic distributions are chosen as its parent distribution, from which lots of random samples are generated by the Monte Carlo method. For each parent distribution, the 100-yearly extreme values at different thresholds are estimated and compared with the theoretical value based on those samples. Then a simple and empirical threshold selection method is proposed and applied to estimate the weekly extreme strain due to vehicle loads on the Taiping Lake Bridge. Results show that the estimate on the basis of the threshold obtained by the proposed method is closer to the measured result than the commonly used methods. The proposed method can be an effective threshold selection tool for the extreme value estimation of vehicle load effect in future engineering practice.

Probabilistic corrosion fatigue life assessment of a suspension bridge instrumented with long-term structural health monitoring system

The long-term performance of engineering structures in a corrosive environment will be significantly affected by the coupled action of corrosion and fatigue. In this article, a probabilistic corrosion fatigue analytical model is proposed by taking into account the effects of corrosion-induced reduction of the cross-sectional area and deterioration of the fatigue strength of structural components. The proposed model is exemplified to evaluate the probabilistic corrosion fatigue life of a typical welded joint in the suspension Tsing Ma Bridge instrumented with a long-term structural health monitoring system. A genetic algorithm–based mixture parameter estimation method is developed to facilitate the multimodal modeling of stress spectrum derived from the long-term monitoring data of dynamic strain. The achieved results demonstrate that with the increase in the service life, the reliability index of the investigated typical welded joint is dramatically reduced under the combined effect of corrosion and fatigue.

Techno-economical and practical considerations for SHM systems

Nowadays, the increasing demand of Structural Health Monitoring (SHM) systems, either for research or specific monitoring applications, is posing several questions on their technical and economical sustainability. In general, the initial cost of a full scope and long-term SHM system is significant, but also, the operational and maintenance costs have an important role. In practice, it has been found that there is a correlation between the cost of the SHM system and its main monitoring scope, including the size and complexity of the structure to be monitored. Additional considerations must include peripheral systems (hardware and software) to process, analyze and to store data efficiently for long-term evaluations. Even though, most SHM systems are designed assuming that the benefits overweight the costs. In practice, the payback from technical knowledge, maintenance reduction costs, safety or reliability, are not easy (if not impossible) to quantify. While most engineers and researchers are thinking on sophisticated techniques and more efficient or accurate sensors, the users concerns are on practical and economic issues to justify the initial investment and the cost to operate the monitoring system. Cost-benefit or cost-efficiency analysis is not an ordinary practice for researchers, but is becoming a standard requirement for infrastructure investment projects. In this document, the guidelines for the preparation and presentation of cost and benefit analysis of investment programs and projects required by the Mexican Government, are used to evaluate some specific SHM systems of highway bridges. In general, it is found that the main challenge for these analyses is the availability of conclusive information to justify the sustainability of the monitoring projects, especially those which are related to the benefits.

Threshold selection for extreme strain extrapolation due to vehicles on bridges

In the design and condition assessment of bridges, the extreme vehicle load effects are necessary to be taken into consideration which may occur during the service period of bridges. In order to obtain an accurate extrapolation of the extreme value based on limited duration, threshold selection is a critical step in the peak-over-threshold method. Overly high threshold results in little information to be used and excessively low threshold leads to large bias in parameters estimation of generalized Pareto distribution. To investigate this issue, 417 days of strain data acquired from the long-term structural health monitoring system of Taiping Lake Bridge in China are employed in this paper. According to the tail distribution of the strain data induced by vehicle loads, four homothetic distributions are chosen as the parent distributions, from which lots of random samples are generated by the Monte Carlo method. For each parent distribution, the 100-yearly extreme values at different thresholds are estimated and compared with the theoretical value based on those samples. Then a simple and empirical threshold selection method is proposed, which can be an effective threshold selection tool for the extreme value estimation of vehicle load effect in future engineering practice.