Damage detection is an important area with growing interest in mechanical and structural engineering. One of the critical issues in damage detection is how to determine indices sensitive to the structural damage and insensitive to the surrounding environmental variations. Current damage identification indices commonly focus on structural dynamic characteristics such as natural frequencies, mode shapes, and frequency responses. This study aimed at developing a technique based on energy Curvature Difference, power spectrum density, correlation-based index, load distribution factor, and neutral axis shift to assess the bridge deck condition. In addition to tracking energy and frequency over time using wavelet packet transform, in order to further demonstrate the feasibility and validity of the proposed technique for bridge condition assessment, experimental strain data measured from two stages of a bridge in the different intervals were used. The comparative analysis results of the bridge in first and second stage show changes in the proposed feature values. It is concluded, these changes in the values of the proposed features can be used to assess the bridge deck performance.

Continuous awareness of the evolution process of the structural condition in civil structures over time is of great value, as it supports to make informed decisions about infrastructure assets, maintenance and management [

Structural condition assessment by monitoring has gained popularity in recent years because it can provide engineers with abundant information about a structure’s health through various sensors [

The use of monitoring-based indicators to assess the bridge deck condition, their sensitivity to damage and resistance to random traffic patterns are the main factors [

Thus, dynamic damage identification methods are based on changes in dynamic parameters, typically decreasing stiffness and increasing damping [

According to 1977 FHWA report, bridge decks are deteriorating at an ever-increasing number and pace. Therefore, extensive studies have been developed to detect early damage based on variations of modal parameter estimates, despite the unsettling effect of environmental and operational factors [

Some of the modal parameter limitations can be overcome by using the changes of modal displacements [

Moreover, curvatures are less sensitive to environmental factors than natural frequencies [

In the frequency domain, the power spectral densities have been widely used for damage identification [

Erazo et al. [

Although wavelet transform is widely used, the frequency resolution in the higher frequency domain is not high in the wavelet transform. Thus, it may be challenging to differentiate a signal containing high-frequency components that are very close to each other. Therefore, the wavelet packet transform (WPT) technique has been developed to address this issue [

This study aims at developing a systematic approach to extract damage indicators for deck bridge assessment of in-service bridge structures using strain measurement acquired by an SHM system. The method is based on damage features from the time, frequency, and time-frequency domains by monitoring the structural vibration. The remainder of this paper is organized as follows. In

An intelligent structural health monitoring (SHM) mainly aims to provide an early warning for damage and reduce the possibility of a potential major collapse, leading to a loss in life and economy [

To draw out a clear procedure for the proposed methodology for bridge deck condition assessment, this section explains the detailed procedure. First, strain measurements at different web and flange sections are collected and then preprocessed. Second, load distribution factors and the location of the neural axis are determined to provide information on bridge performance and potential damage to the bridge deck. Third, the correlation coefficients between various measurements are introduced and transformed. Fourth, wavelet packet transform is conducted on the signal of two various conditions. Finally, the sensitive damage features are extracted using a wavelet packet transform based on energy curvature difference and frequency fluctuations over time.

A bridge’s live load girder distribution factor (GDF) is a ratio of the live load applied to each beam girder when a vehicle crosses the bridge [

As

The neutral axis is an axis in the beam’s cross-section with no longitudinal stresses or strains (axis of zero stress). It is a key parameter in most structural design theories. Also, it serves as a potential indicator of the safety status of the structure [^{th} to the j^{th} node, the gauge length _{m}. The

As illustrated in

where

Where

where

From

In this study, the neutral-axis position ratio (

The correlation index has been widely used as a damage-sensitive feature for detecting damage [^{th} girder, where _{i}

where ^{th} girder strain of l^{th} observation, ^{st} and j^{th} girder becomes [

where _{i}_{j}_{i}_{j}^{T} means the transpose of ^{th} and j^{th} girders.

Curvature difference can reflect the changes in the analyzed signal, so it is a viable measure for damage identification [

where

Then this can be simplified as:

The WPT can be accomplished through the level-by-level decomposition of the signals. Wavelet packets can be defined as follows [

where

where

where

where _{0,0} as shown in _{1,0}) and a detail (in the subspace W_{1,1}). Each approximation or detail acquired from the top-level, supposedly in the subspace W_{j,k}, can be further decomposed into a new approximation and detail, located in two subspaces W_{j+1,2k} and W_{j+1,2k+1}, respectively. This process can be repeatedly up to a given depth ^{j−1}. Therefore, the WPT generates a binary tree of subspaces spanned by a set of bases onto which a signal can be mapped for analysis with multiple resolutions. This characteristic allows WPT to be successfully used for feature extraction in the pattern recognition fields [

The data was collected from a multi-span concrete box Girder Bridge, located across the Lieshi River, Rugao city, Jiangsu Province. The bridge has 27 piers, 26 spans, and five prestressed concrete box girders in each highway direction as shown in

Common measurements in structural monitoring are acceleration and strain responses [

Since strain gauge readings are deviated due to the surrounding condition variations, each event was reset by subtracting the average ambient strain before the traffic event from each reading recorded at the time of the event to guarantee that only strain readings due to living load were captured.

Based on the analysis of a bridge’s strain responses (outputs only) under vehicle load, various damage indicators were calculated using strains collected by various strain gauges during traffic accidents. Data measured under states #1 and #2 at various interval are considered to assess the reliability and performance of the proposed features for bridge condition assessment over time.

According to [_{n}/h) for state #1 and state #2. It is noticed that there is variation from girder #1 to girder #2 and from one point to another in one beam. The results show that neutral-axis position ratios are reliable and robust on-site, applicable to typical bridges, and can be considered a universal parameter in beam-like structures besides the deformed shape. Based on the strain responses relationship at the top and bottom of the girder cross-section, the neutral-axis position shift can be considered an indicator of defaults or abnormality to evaluate flexural curvature and neutral axis position.

On the other hand, the estimated correlation index values are plotted against the number of load events, as shown in

For validation, the correlation measures at two points in the flange (G1, G2) and one in the web (G1) are transformed to the time-frequency domain using wavelet transform.

Besides, Power Spectral Density (PSD) is computed using Welch’s method.

Data from state #1 and state #2 of bridge states are decomposed by WPT wavelet packet coefficients (WPCs). The decomposition idea is to start from a scale-oriented decomposition and then analyze the obtained signals on frequency sub-bands. Thus, the signal is filtered into equal-width sub-bands at each level, and the signal energy is portioned among the sub-bands. The wavelet function db3 and decomposition level 4 are chosen from our previous studies [

For graphical illustration, the WPCs corresponding to the 16th node of state #1 and state #2 of knots (4,0), (4,1), (3,0), (3,1) are presented in

Since the Parseval’s theorem also applies to the wavelet packet transform, the power of a wavelet packet node m (or frequency node) was computed as the squared values divided by the number of frequency band nodes. The averaged sum of the scale-averaged wavelet spectrum over all scales is normalized.

To show the energy contents resolved with both frequency and time, contour representation in time frequency is represented.

The ECD index is the sum of the content of energy curvature differences after a signal is split by WPT and considers the signals’ spatial distribution.

Besides, the change of energy components over time for states #1 and #2 is investigated.

This paper proposed a new method to assess the bridge deck condition during operation. In the proposed method, we use various damage indices represented in load factor distribution, neutral axis shifts, correlation factor, power spectral density distortion, energy curvature difference, energy components evolution over time, and frequency components evolution over time. Wavelet packet transform is used for signal decomposition using db3 and depth 4. Furthermore, the signal is filtered into equal-width sub-bands at each level and partitions the signal’s energy among the various sub-bands. Real experimental strain data from two bridge statuses of a bridge are used to show further the feasibility and validity of the proposed technique for damage identification. The change in the proposed features is observed. The variation in the correlation values, neural axis shifts, and power spectral density can be used as potential parameters for early abnormalities and bridge deck assessments.

In addition, the wavelet power spectral can be used to reduce the signal’s noise effect and trace the damage through the curvature of the power spectrum energy. Also, the ECD index curve mutation can be employed to assess the bridge deck performance. The absolute difference between the energy curvatures of the intact and the damaged structure increase with the damage. The change in the proposed features is observed. The variation in the correlation values, neural axis shifts, and power spectral density can be used as potential parameters for early abnormalities and for bridge deck assessments. At the same time, the wavelet packet spectrum varies with time and fluctuates with an increasing trend. We concluded that the proposed approach could effectively assess the bridge deck condition. Also, the wavelet packet transform’s ability to provide nonlinear and non-stationary features makes it an effective tool for structural response analysis. In addition, these features can be used as input to an artificial neural network classifier for damage classification. However, more research needs to be performed to confirm the given method’s robustness and show the effectiveness of the proposed features for damage detection and condition assessment.

The authors received no specific funding for this study.

The authors declare that they have no conflicts of interest to report regarding the present study.