Crack monitoring on concrete structures with distributed fiber optic sensors—Toward automated data evaluation and assessment

The ability to measure strains quasi‐continuously with high spatial resolution makes distributed fiber optic sensing a promising technology for structural health monitoring as it allows to locate and measure damages in concrete structures, such as cracks. Depending on whether the distributed fiber optic sensor (DFOS) is embedded into the concrete matrix or bonded to the reinforcement, different approaches for crack width calculation exist. The high spatial resolution of DFOS quickly leads to a large amount of data, especially with time continuous monitoring. Scalable, automated analysis approaches are required to handle such big data and to derive a gain in knowledge from the measurements. Thus, in a first step, the Python framework fosanalysis is presented and made available to other researchers or monitoring specialists as free software. The most important input parameters for crack width calculation are discussed for concrete strain and steel strain DFOS. Accurate crack monitoring for a 4 m long reinforced concrete beam is demonstrated by using fosanalysis. The calculated crack widths are in good agreement with digital image correlation measurements.

Infrastructure in Germany is aging. 1,2Renewing and rebuilding has an enormous impact on scarce resources: environmental, financial, and manpower.Thus, the lifespan of existing structures such as tunnels, bridges, and Abbreviations: cOFDR, coherent optical frequency domain reflectometry; DFOS, distributed fiber optic sensor; DIC, digital image correlation; DSS, distributed strain sensing; ES, EpsilonSensor; GTM, geometric threshold method; NaN, not a number; ODiSI, optical distributed sensor interrogator; POL, polyimid; SHM, structural health monitoring; SSQ, spectral shift quality; TS, tension stiffening; SRA, strain reading anomaly.dams needs to be extended.Compensatory measures must be taken, as compromises neither in safety nor availability are acceptable.][9][10] Small in size, lightweight and cost-effective, distributed fiber optic sensors (DFOS) are a promising sensing technique for deployment on site. 3,11Great potential is offered by the quasi-continuous data for SHM, especially for monitoring from the beginning of a structure's existence, where it is not clear when and where damages will occur. 12,135][16] For crack monitoring, the DFOS must be robust to withstand the rough building site conditions (e.g., mechanical impact during concreting).At the same time, it must be sufficiently sensitive to reliably detect cracks and yet flexible to some extent so that DFOS breakage does not occur as a result of the emerging cracks.
For monitoring purposes, a timely and autonomous processing of the measured data is needed to generate upto-date information regarding the structure's condition. 17normous amounts of data are generated by continuous measurements, such as fiber optic measurements.For example, when measuring with a 10 m long DFOS with a gage pitch of 0.65 mm and a measuring frequency of 1 Hz, almost one million strain values are obtained per minute.The raw data alone are of no use, as the interest of inspection personnel is the exact location and characteristics of damages (such as cracks) and the owner's interest is the overall condition of the structure.Hence, it is necessary to aggregate data without manual interference and presenting the resulting information in a meaningful form, which is easily digestible even by people without deep technological understanding. 5Thus, widespread adoption of SHM requires fully autonomous, scalable data analysis solutions.

| Aim of this study
The current lack of automated evaluation for DFOS based DSS data hinders both research and industry.Hence, this study aims to contribute to the adoption of DFOS by attempting first steps toward an automated DFOS based SHM.Already existing crack width calculation approaches tailored for DFOS measuring reinforcement strains 8 and concrete strains 9 are contrasted.Supplementary to a related study, 10 which focuses on the influence of the DFOS type for successful crack monitoring, this study focuses on methodology of the data analysis of the experimentally gained data.
The presented workflow for crack monitoring is implemented in a PYTHON software framework fosanalysis which is made freely available to others on https://github.com/TUD-IMB/fosanalysis.git.The framework's usage is demonstrated and the methodology is verified experimentally.Based on the experiments conducted, 10 the performances of two DFOS, one measuring reinforcement strains and one concrete strains, are examined and compared; both embedded in the same reinforced concrete beam.The plausibility of results is provided by using digital image correlation (DIC) as a reference measurement.

| Crack width calculation using DFOS
Crack openings manifest as peaks in strain curves measured with DSS.The crack width w cr,i of the ith crack is estimated by integrating the strain curve over its transfer length: with the measured strain ε DFOS x ð Þ along the sensor coordinate x.The location of the crack x cr,i is determined by means of peak finding, see Section 2.5.The transfer lengths to the crack's left (l À t,i ) and right hand side (l þ t,i ) are discussed in Section 2.6.The procedure to compute the calculative tension stiffening (TS) component ε TS x ð Þ depends on the DFOS's application technique, see Section 2.7.Equation ( 1) is extensible with compensation for further influences (e.g., strains due to prestressing, shrinkage, creep, strain-induced fiber slippage, or temperature) by including another term in analogy to TS.
The numerical integration is computationally expensive in comparison to other approaches.It is slower than crack width estimation using a calibrated linear model based on the maximum strain within a strain peak. 18equiring calibration, those models are only valid for a specific combination of DFOS type, adhesive type, adhesive thickness, and installation method.Additionally, a calibrated model fails when the peak height changes due to fiber slippage, creep, or shrinkage of the materials.
Clear misinterpretations occur at the latest when slippage of the optical fiber within the DFOS cross section or delamination within the adhesive layer occurs.By integrating the strains along the DFOS length, the proposed approach does not have such restrictions and is usable for every DFOS-adhesive combination without prior investigation on the bonding behavior.Moreover, it works for all kinds of DSS, including DIC.
Equation (1) applies to both (1) reinforcement strain DFOS and (2) concrete strain DFOS.The approaches for calculating the crack widths differ in the way TS is compensated, see Section 2.7.
Reinforcement strain DFOS are bonded on the reinforcement.Concrete strain DFOS are subsequently glued to the concrete surface of existing structures or directly embedded into the concrete matrix during the construction process.It should be emphasized that DFOS attached to existing structures and DFOS embedded in the concrete matrix of newly built structures behave alike. 10owever, existing structures usually are in a cracked state, when installing DFOS.After the installation, crack width changes can be detected with the DFOS.Absolute crack widths are estimated by adding these changes to the pre-existing crack widths which need to be measured by a different method (e.g., with a crack ruler).

| Workflow
The workflow for crack monitoring consists of the following steps: further influences (not scope of this article).6. Obtain the cracks' widths w cr,i by integrating the strain for each crack over its transfer length using Equation (1).
Crack width calculation is predestined for automation, as the manual analysis (using e.g., spreadsheet software) is both error-prone and tied to an immense manual effort.Additionally, it requires insights into the principle procedure of the technique, but once understood, it is a monotonous task.The large amount of data are easily capable of bringing common spreadsheet software to its usability and technical limits.Hence, the mentioned steps are implemented in a PYTHON software framework, which is presented in Section 3.

| DFOS data acquisition
Up to eight DFOS can be measured at the same time with the Luna Inc. optical distributed sensor interrogator (ODiSI) 6100 series. 19The accompanying software is capable of exporting the strain data to a .tsvfile after measurement or providing it in real time during the measurement via a TCP/IP network socket. 19The exported data (a .tsvfile) contains metadata about the ODiSI system and the DFOS itself, measurement settings (gage pitch and measurement rate), gage positions, and the strain readings with their time stamp.Each reading contains a time stamp, a type and an array of strain data.

| Data preprocessing
Prior to the analysis, the data are preprocessed in order to enable further analysis.Three different types of disturbances are present in DFOS data: noise, strain reading anomalies (SRAs), and dropouts. 20oise is caused by the measuring technology itself. 19he first source of noise is the finite equipment accuracy and resolution.The second source is the random nature of photon scattering, causing variation of the response signal in-between different measurements.This variation is carried through the steps into the strain output.According to the law of large numbers, this variation gets smaller, the more scattering events occur.Thus, longer measurement intervals (sending more photons) and/or longer gage pitches (photons passing through more material) increases signalto-noise-ratio and resulting in a better signal quality. 20RAs are artifacts of incorrect cross-correlation findings, characterized by unpredictable, extreme (near infinite) positive or negative strain readings in single gages.The reliability and accuracy of the cross-correlation is associated to the similarity of the response spectrum to the fingerprint. 20ropouts occur if the cross-correlation fails because the dissimilarity of the signal to reference is too high.In this case, no spectral shift can be identified and the dropout is reported in form of not a number (NaN). 19As the backscattered spectrum changes with the deformation state of the fiber, the occurrence of dropouts is associated with the strain state.Hence, dropouts tend to accumulate in areas where the signal differs greatly from the reference (i.e., in the area of cracks, high strains, and steep strain variation occur).

| Signal quality
The signal quality is a central measure to assess the suitability of different DFOS for a specific measurement tasks.In the literature, several quality metrics are present.A common signal quality measurement is the signal-to-noiseratio, the ratio of the signal amplitude to the standard deviation of the noise. 21The spectral shift quality (SSQ) is also used, 9,22 which is the coefficient of cross-correlation between the current spectrum and the reference.SSQ ranges from no correlation (0.0) to full correlation (1.0) and is reported by some ODiSI systems along with the strain data. 20,22Some of the mentioned measures can be leveraged for anomaly detection and data preprocessing, when combined with anomaly criteria (i.e., thresholds).
The sensitivity of a DFOS can be assessed as well.One option is the ratio γ ¼ ε max w cr, max of the widest crack width w cr, max to the maximum strain of its peak ε max . 15Another one is the crack shape coefficient based on the variation variation in the transfer length of a crack. 124.2 | SRA removal SRA identification can be tackled by different approaches.22 One of those is the geometric threshold method (GTM).There, a gage reading is assumed a SRA if the absolute difference to the previous accepted gage reading exceeds a constant threshold.In another approach, a SRA is assumed when the associated SSQ for the gage falls short of a threshold.9,22 Identified SRAs are generally set to NaN. SR cancellation is best applied before smoothing, to prevent these outliers from influencing the smoothed signal.

| Dealing with dropouts
As numerical operations in PYTHON return NaN if the input contains NaN values, dropouts require special treatment.Two different option to deal with dropouts are eliminating or repairing.
For elimination, gages with NaN entries are simply removed from the data.As only gages with valid strain measurements remain, this is equivalent to using the integration algorithm's implicit interpolation.Elimination is viable for singular dropout entries, but fails for compact dropout areas.
The other option is to replace NaNs with virtual, reconstructed data.This data is derived from functions fitted to the surrounding intact data.Reconstruction of peaks heavily disturbed by SRAs and dropouts must resort to the second option.

| Noise reduction
Taking the mean of several measurements under identical conditions-called ensemble averaging-can improve the data quality (signal-to-noise-ratio). 21 This is possible by taking into account plausible strain readings only for the time average.For the noise, the effect is similar to longer measurements intervals.
Left-over noise is reduced by taking the symmetrical sliding mean along the DFOS length.A window, extending r s entries to both sides of its central entry (identified by the counting index j), is moved over the signal.The central entry ε j is assigned the mean of the values in this window: While the median is more stable against isolated outliers (such as SRAs), the mean has the advantage, that the strain integral is not changed.
Smoothing has some influence on the signal. 21First, the maxima are reduced and minima are increased, reducing the contrast of the signal.This contrast reduction can change the required prominence threshold, as discussed in Section 2.5.Second, coupled with the range reduction is a widening of peaks and dips.Third, smoothing might result in shifts in the peak's position. 21

| Detection and localization of cracks
As cracks cause peaks in the strain signal, the crack locations can be determined by means of peak finding algorithms.The most important peak parameter for the task of finding cracks is prominence.Prominence is a measure, how much a peak stands out from its surroundings.This parameter was originally established in topography to distinguish independent summits from sub-peaks.It is defined as the minimal drop in height, that must be descended in order to traverse from a local peak to any higher territory or the difference between a peaks height and the lowest contour line containing it and no higher point. 23,24The highest low-point among all possible paths from peak A to any higher territory is called key col.Thus, the prominence of the peak A is calculated by The prominence of the highest peak C is the difference between its height and the absolutely lowest point P C ¼ h C À h min,abs .In Figure 1, the concept of prominence is visualized.
The prominence threshold P min is utilized to distinguish signal peaks from the peaks introduced by noise or other further measuring anomalies.If the P min is set too high, minor legitimate peaks fall short of the prominence threshold and fuse with their "parent" into a single, wider crack.This can result in high overestimation of the crack width.However, if P min is set too low, many insignificant peaks will be identified as cracks and thus distort the result.Thus, this parameter is dependent on the quality of the data and might require manual adjustment.A stiff DFOS-adhesive combination leads to pronounced strain peaks, but can also lead to an irregular course between the cracks (e.g., especially when using filigree DFOS types due to high transverse pressure on the DFOS), which is why the prominence should be selected higher in this case. 10or crack detection, the absolute height of identified peaks h min is a second detection criterion.Since the concrete's ultimate tensile strain ε ctu of the concrete needs to be exceeded in order for a crack to form, peaks which do not exceed this measure are not identified as cracks.Keep in mind that in cases where the DFOS is installed subsequently, the absolute concrete strain is not known and only the relative strain changes (at a certain point in time) are measured.When the concrete member is prestressed, the strain changes up to the appearance of the first crack can be significantly greater than the concrete's ultimate tensile strain with ε ctu ≈ 100 μm=m.To refine the peak detection, further properties, such as the width of the peak can also be taken into account.

| Transfer length of a crack
Strains are measured in the core of the optical fiber only and transferred by means of bond from the surrounding material into the DFOS's core, exhibiting strain lag. 25,26ence, the (theoretically infinite) strain peak in a crack's location is smeared to both sides of the DFOS.The bond's stiffness is constituted by the materials' parameters, thicknesses and interface interactions of all layers inbetween the surrounding material and the DFOS's core. 10,25,26Stiffer bond results in less strain lag, shorter transfer length and higher strain peaks.
Influences of two adjacent cracks superimpose if the transfer length is longer than half the crack spacing. 27hat is, strains in the integration segment of a crack are partly due to the influence of the neighboring cracks.
Identifying the proportions of the strain contributions in the superposed strain signal is difficult. 28However, crack widths are accurately estimated without considering the overlapping influences, given that the adjacent cracks result in separate strain peaks. 10If the transfer length is too long, peaks of individual cracks merge into a single peak and the crack detection becomes unreliable.Hence, it is important to choose the appropriate DFOS type and application technique for the measuring task. 10he transfer length determines the integration limits in Equation (1).Therefore, the estimation of the transfer length is a crucial step for the width calculation.In the following, two approaches for transfer length estimation found in the literature are discussed.
The first approach is limiting the transfer length at the minimum strain in-between peaks. 8,9Here, x min,l,i and x min,r,i are the locations of the minimum strain ε DFOS between the ith peak at the position x cr,i and its left neighbor (at x cr,iÀ1 ) or its right neighbor (at x cr,iþ1 ).Consequently, the transfer lengths to left and right of the ith crack are The minimum is mechanically accurate for reinforcement strains under constant bending moments or pure tension and an acceptable initial estimation otherwise. 8he second approach is setting the transfer length to half of the distance to the neighboring cracks 10,12,29 : This approach is less prone to noise-induced minima.Hence, it is more stable on strain data with an irregular, erratic signal. 10A visual comparison is given in Figure 2 and the effect is discussed in Section 5.2.
Both approaches are only applicable in the stabilized cracking state, because they result in That means, every gage of the strain profile is assigned a crack integration segment and the measuring length is divided into integration segments without gaps between them.The crack formation state requires additional conditions for limiting the calculative transfer length (e.g., calibrated limits for a specific DFOSadhesive combination 18 ).

| Tension stiffening
The load bearing contribution of the concrete in-between cracks is called TS. 30 The strains measured with DFOS are influenced by TS.Compensation approaches for concrete strain DFOS 9,31 or reinforcement strain DFOS 3 are available in the literature.These are discussed in the following.

| TS for concrete strain DFOS
The total strains of DFOS embedded into the concrete is composed of the crack opening displacement and the elastic concrete strains. 31This elastic part due to TS does not contribute to the crack width opening and therefore must be compensated when calculating the crack width.
Away from the stress-free concrete in the direct vicinity of the crack, strains are reintroduced into the concrete by bond interactions with the reinforcement. 32Here, the calculative TS strains ε TS c for concrete strain DFOS are idealized to increase linearly 9 from the crack's position with the normalized distance to the crack and the limit strain which is the minimum of the concrete's ultimate tensile strain ε ctu and the measured strain at the transfer length end.The concrete's ultimate tensile strain ε ctu is calculated from the material properties 33 Illustration of the concept is given in Figure 3. Conventionally, a non-linear concrete strain increase toward the transfer length's end is assumed, 30,33,34 which is considered by the block coefficient.
This block coefficient is set to k t ¼ 0:6 for short-term loading, and to k t ¼ 0:4 for long-term or cyclic loading. 30,33The linear approach (Equation 6a-6c) is roughly equivalent to setting k t ¼ 0:5, resulting in a theoretical deviation to the norm by AE20%.However, the elongation due to TS is small in comparison to the crack opening displacement, keeping the error in the estimated crack width low (see Section 5.3).

| TS for reinforcement strain DFOS
An approach for crack width estimation for reinforcement strain DFOS, similar to the standards 33 is proposed. 8In a cracked specimen, the reinforcement strain curve oscillates around the theoretical mean reinforcement strain.The reinforcement's strain is limited by the upper limit in a cracked section and the lower limit at the end of the transfer length. 8,30,35The strain reduction in-between the cracks is caused by TS.
The TS component in the measured strains is The measured strains ε DFOS x ð Þ are assumed to be equal to the reinforcement strains due to the stiff bond between them. 8,10,36The hypothetical strain course in the reinforcement neglecting the bond interaction between reinforcement and concrete, denoted by b ε x ð Þ, is estimated by interpolating the strain peaks.The maximum strain is assumed to be the full tensile force in the cracked crosssection and the bending moment is assumed to change linearly between two cracks.The reinforcement ratio is denoted by ρ ¼ A s A c,ef and α ¼ E s E c is the ratio of YOUNG's moduli.The effect of TS is considered to be the area between b ε and ε DFOS within the integration boundaries multiplied by ρ and α.Compare Figure 4 for an illustration of the concept.
Finally, after all required components are gathered, the actual calculation according to Equation ( 1) is carried out for all identified peaks.

| THE FRAMEWORK FOSANALYSIS
The framework fosanalysis * was designed with regard to the needs outlined in Section 1.First and foremost goal is the automation of the DFOS data analysis process.Separating data from the algorithm improves both reproducibility and re-usability.Written in the PYTHON programming language and the back-end focus, the framework is cross-platform.The modular structure of the framework provides possibilities to extend and modify the functionalities as required.The extensive documentation directly interwoven with the code can be extracted by DOXYGEN for a full-fledged reference manual.
With modularity as its design principle, fosanalysis consists of several modules, each dedicated to a single specific functionality.The crack width calculation is put together by several exchangeable components in a plug and play manner.This workflow enables a fine grained access to algorithm settings in a flexible, yet easy to comprehend algorithm composition.
The framework available on PYPI and can be installed using the pip package manager: pip install -U fosanalysis.Assuming a successful installation, importing the necessary modules is the first step.After that, data can be imported from a demonstration file.This file contains artificial data in the format of a file, as it is exported by the Luna Inc. ODiSI software.To (re-)generate this file, the script generatedemofile needs to be run once.This script is available with the source of code of fosanalysis.The demofile is parsed and the interface to access the data is provided by a protocol object.sd = fa.protocols.ODiSI6100TSVFile("data/ demofile.tsv").
After loading the data, the position, the mean strain reading (using an ensemble average) as well as strain data of the first reading are obtained.Various functions provide flexible access to strain data using the PYTHON indexing or timestamps.Partitions in time and space of the data are retrievable as well.The complete content of the file is included in the ensemble average, if start and end parameters are omitted.Note, that taking the ensemble average across all (or several) measurement records smooths the data and reduces the number of NaN entries by discarding NaNs internally.However, the resulting array might still contain NaN entries.
F I G U R E 4 Crack width calculation for reinforcement strain DFOS according to Equation (9).*All source codes in this article are related to fosanalysis v0.3.0.The source code, documentation and getting started scripts for upcoming versions are available at https://github.com/TUD-IMB/fosanalysis.git.
Depending on the DFOS application method, either a Concrete or a Rebar objectimplementing the TS compensation according to Equation (6a)-(6c) and Equation ( 9), respectively-is used to calculate the crack widths.Beforehand, some of those exchangeable objects need to be generated.These are a Filter object for smoothing.The Crop object is used to restrict the data to the DFOS segment of interest (3 m to 5 m).The algorithm and its parameters for crack detection are held by the CrackFinder object.The transfer length estimation with its settings is provided by the CrackLengths object.All those objects, implementing a specific part of the workflow are passed to the Concrete object along with the retrieved data.During the instantiation of the object, the data is preprocessed: NaN entries are removed, the strain is run through the Filter object and finally cropped by the Crop object.Now, identifying crack locations, crack segments and calculating their respective widths follows.

sp.calculate_crack_widths()
Peak detection is not always successful, as it might miss valid cracks or identify peaks which are no cracks.To demonstrate how to correct those, we take a look at the position 3.7 m (cf. Figure 5).We observe, that the twin peaks are recognized as two separate cracks.From manual inspection of the specimen, however, we might know, that those could correspond to a single crack only.So, we first delete the wrong cracks by their index, the fourth and fifth crack (PYTHON's indexing is 0-based, e.g., the fourth crack has the index 3).After that, we add a single crack at the "correct" position 3.7 m.
sp.delete_cracks (3, 4)   sp.add_cracks (3.7)The cracks are recalculated by default after modifying the list of cracks.If the peak recognition is faulty in general, readjusting the parameters for pre-processing and peak finding might be necessary.
The lists of crack properties like the locations and widths can be obtained by.

| EXPERIMENTAL VALIDATION
Particularly relevant for monitoring existing structures in a critical condition is the subsequent bonding of DFOS to the concrete surface. 10However, for reasons of robustness and to reduce influence parameters on the bonding between concrete and DFOS (e.g., adhesive type), it is recommended to integrate the DFOS directly into the structure when monitoring from the beginning of a its existence.In the following, the suitability and reliability of DSS with a reinforcement strain DFOS and a concrete strain DFOS for crack monitoring using the previously presented procedures are investigated.The DFOS were directly embedded into the specimen before concreting.

| Experimental setup
In Figure 6, the geometry and applied instrumentation of the test specimen are shown.The specimen-a 4.0 m long reinforced concrete beam with a rectangular cross section of b Â h ¼ 30 cm Â 40 cm-was loaded in a 4point bending test under service load.In order not to F I G U E 5 Result of the getting started with strain data, tension stiffening, and crack properties.
influence the crack pattern, stirrups were omitted in the middle area, where no shear forces occur.More detailed information on the experimental setup and the determined material properties are available. 10

| Distributed fiber optic sensors
The cross-sections of used DFOS-best performing in a preliminary study 10 -are shown in Figure 7.
Reinforcement strains were measured with a polyimid (POL) coated DFOS.POL convinces with its stiff strain transfer, but bears the risk of a brittle fracture due to the high strains imposed by opening cracks. 9,14,37,38To avoid damage to the POL sensor during concreting and at the same time ensure a good strain transfer, the DFOS was laid in a groove cut along the rebar.Then, the DFOS was bonded with a cyanoacrylate adhesive and additionally protected against mechanical and chemical attack by a thin silicone layer.
The bonding technique has a significant impact on the quality of the strain data. 7The bond between the adhesive, coating, and glass core must have a sufficient stiffness so that the strain curve not too smeared and cracks can be reliably detected.It was shown that the used combination (groove, cyanoacrylate adhesive, and protective silicone layer) leads to the smallest amount of SRAs. 7he EpsilonSensor (ES) with its monolithic cross section was embedded directly in the concrete matrix and fixed at the level of the reinforcement with cable ties for securing its position during concreting.The robust monolithic design makes the ES fit to endure harsh building site conditions. 29Reliable bond to the concrete and precise strain measurement are reported for the ES. 10,12,29he strain curves and crack widths were measured directly after applying the target load of F ¼ 50 kN per press.The strain state of the DFOS showed already significant strains due to concreting and shrinkage prior to the experiment.Hence, the the strain measurements were tared before applying the load.For the fiber optic measurements, a Luna Inc. ODiSI 6100 series device was used as data acquisition unit.In order to be able to detect micro-cracks as well, the highest available spatial resolution-a gage pitch of 0.65 mm-was used.

| Digital image correlation
As a reference measurement, the central part of the beam's tensile zone (bottom of the beam) was observed with DIC over a length of 60 cm.Therefore, a stereo camera system with 12 Mpixels resolution (4000 Â 3000 pixels), was used.According to the calibration protocol, the deviation was 0.018 pixels, which corresponds to a theoretical accuracy of 2.7 μm with the existing measurement volume and the camera resolution.

| PARAMETER STUDY
In the following, the relevant parameters for crack width calculation are discussed.The analyses follow a workflow similar to the one presented in Section 2. The load was held constant during the measurements.Hence, taking an ensemble average is possible to improve the signal quality.The resulting data is shown in Figure 8.It is visible, that the strain signal of the ES shows pronounced peaks and returns to nearly zero in-between.The strain peaks of the reinforcement strain DFOS (POL) are less pronounced, having a smaller prominence.The maximum strains in the crack locations correspond to a stress in the reinforcement bars of approximately 400 N/mm 2 .Four cracks (C 1 through C 4 ) between 170 μm, 260 μm, 344 μm and 319 μm width and a micro-crack (M 1 ) of 31 μm surfaced in the area observed by DIC.The white background indicates the combined transfer lengths of those cracks.As the experiments in this paper were carried out in the upper serviceability limit state with moderate strains (with respect to the technical limitations of the interrogation unit), the treatment of dropouts is not a F I G U R E 7 Cross-section and application of the distributed fiber optic sensor (unscaled).
F I G U R E 6 Test setup and measurement layout.concern of this contribution.Due to the robust design of the monolithic DFOS and the installation technique of the POL, SRAs could be avoided.

| Crack detection
For the peak detection (and thus crack detection), prominence and smoothing strength are the most important parameters.With stronger smoothing, the amplitude-the prominence of peaks is tied to it-and the absolute height of peaks in the strain signal are decreasing.Thus, the number of identified cracks is reduced, as minor peaks fall below the prominence threshold.The crack width according to the missed cracks might be assigned to the cracks still identified, leading to an overestimation of the latter.
Seamlessly neighboring integration segments (as in Equation ( 5)) imply that the mean crack width w mean is roughly proportional to the number of cracks (neglecting compensation such as TS): In this case, the total elongation of the DFOS is equal to the sum all crack widths.Hence, fewer cracks result in higher mean crack width.
To study the interaction between prominence P min and smoothing strength determined by the radius off the sliding window r s , the data in the range of 2:0 m AE 0:8 m (area of constant bending moment) of both DFOS is analyzed using various values combinations for both parameters.Ten cracks, including a micro-crack were observed in this area.The resulting numbers of identified cracks for ES and POL are shown in Table 1.Comparing in-row, the loss in contrast due to smoothing out the noise is evident from left to right.Comparing in-column, the gradual dropping of identified cracks from falling short of the rising prominence threshold is visible.The general dropping in numbers from top-left to bottom-right shows the interdependence between these parameters.As is evident from Table 1, the ES does not require preprocessing, due to its good signal-to-noise-ratio, high peak prominence and naturally smooth signal.Neither smoothing nor the prominence are sensitive parameters for the peak detection for the ES.Thus, P min ¼ 100 μm=m and a smoothing radius of r s ¼ 0 is chosen for ES.Only when increasing the parameters to unreasonably high values, the micro-crack M 1 at first and secondly crack C 1 will be lost, compare Figure 11.
The signal-to-noise-ratio of POL is not as beneficial, thus the sensitivity of both smoothing and peak prominence is higher than for ES.The wide range of crack numbers in Table 1 for POL underlines this observation.The seemingly noisy signal oscillates with a period length of ≈ 1 cm (the rib spacing), which is attributed to local effects due to the reinforcement ribs. 36,39With the exception of micro-crack M 1 , all cracks are detected for the POL sensor at a prominence of P min ¼ 100 μm=m and a smoothing radius of r s ¼ 10.This specific configuration was chosen over the others resulting in the same crack count, because those would falsely identify a peak at m instead of C 1 , which is missed.
For both DFOS, the chosen parameter configuration and the resulting number of cracks is set in bold font in the tables.Consequences of wrong parameter choices are as follows.With insufficient data pre-processing, the peak detection has to deal with the left-over noise.Simultaneously setting the prominence too low gives many false positives, as noise spikes surpassing the threshold are identified as cracks.Thus, the number of cracks is overestimated, but the crack widths are underestimated, compare Equation (10).
However, if the prominence threshold set too high, small cracks with gentle strain peaks might not be detected.With insufficient smooth signal and too high prominence, spikes of the left-over noise dominate as peaks and are picked up as cracks, so identified crack locations are unreliable due to their randomness.Depending on the noisiness of the signal, both underand overestimation of crack widths, as well as wrong crack locations occur.Due to the lower strain amplitude, DFOS attached to reinforcement are more prone to this problem, than embedded in concrete ones.
With strong filtering comes the risk of serious signal distortion and feature loss, 21 similar to weak bond.If smoothing is set too strong, peaks in close vicinity tend to merge and form a single one, which accumulates the calculated crack width.Sharp, narrow peaks reshape to wide gentle hills and are lost as distinct features.Thus, choosing too strong smoothing will result in oversight of smaller cracks and a width overestimation of the too few identified cracks.If both smoothing and prominence are set too high, no crack might be identified at all.
Prominence and smoothing strength are inversely dependent.Both smoothing and peak prominence need to be chosen with regard to the mentioned influences.
It can be clearly seen that the required values for smoothing and prominence depend strongly on the DFOS type and its application technique.Generally, it is recommended to determine the relevant parameters for crack width calculation for a specific DFOS-adhesive combination in preliminary tests.The parameter choice is validated by checking the results for plausibility, for example, by comparing with DIC or manual crack maps.Thus, the iterative parameter estimation process is still semi-automatized.
The strain data and the identified cracks for the chosen parameters in the DIC section can be seen in Figure 11.

| Transfer length
Prior to crack width calculation by strain integration, the transfer lengths l À t and l þ t of each crack are determined.Two transfer length estimation approaches-"min" (see Equation (3a) and (3b)) and "middle" (see Equation (4a) and (4b))-are compared in Figure 9. Reference crack widths as observed by DIC are 170 μm, 260 μm, 344 μm, and 319 μm of the four cracks C 1 through C 4 and 31 μm for the micro-crack M 1 .The deviation between the DFOS and DIC crack width is for the ith crack is.
First, a tendency to underestimate the crack width is evident for both DFOS.Since the cracks close in the direction of the neutral axis, it is plausible that the cracks measured at the concrete surface with DIC are larger than those at the level of the reinforcement.No definitive preference of choice can be derived from the result, both approaches work well for the data at hand.Being the better estimation mechanically, the "min"-approach is preferred whenever possible and therefore used for the following investigations.
However, the "min"-approach is prone to random noise-induced dips, especially in erratic strain signal behavior (e.g., for very stiff DFOS 10 ).The "middle"approach might give better results in such cases, because of its predictability and immunity to those.Crack segments are more evenly distributed and the risk for randomly large integration segment fluctuation F I G U R E 9 Measurement deviation Δw cr according to Equation (11) depending on the transfer lengths (crack locations: cf. Figure 11). is reduced.However, narrow peaks (cracks with a short transfer length) neighboring wide peaks (cracks with a long transfer length), will gain width if the "middle"approach used.This is best observable at M 1 in the ES, which is assigned about 8.5 μm in width by the "middle"-approach.
Note, that both approaches are only appropriate in the stabilized cracking state.Due to the large distances between cracks in the crack formation state, both of the compared approaches will overestimate the crack width.Therefore, transfer lengths must be reasonably limited.

| Tension stiffening
Consideration of TS reduces the crack width of the four cracks by 3-15 μm, compare Figure 10.The amount is similar for both DFOS.Again, the lower crack widths compared to DIC are due to the DFOS's distance from the tensile surface.
For concrete strain DFOS, the crack width reduction due to TS compensation according to Equation (6a)-(6c) and Equation ( 8) has the upper bound: Assuming ε ctu ¼ 100 μm=m and l À t ¼ l þ t ¼ 10 cm results in a crack width reduction of w TS ¼ 10 μm.
With the non-linear behavior, the amount of TS for reinforcement attached DFOS is dependent on the signal amplitude, peak form, crack spacing, and strain maxima of neighboring peaks.In general holds, the wider the peak (in comparison to the valley), the less TS and the larger the amplitude, the more TS.If the total height of a peak is randomly increased by noise, TS is increased I G U R E 1 0 Measurement deviation Δw cr according to Equation (11) depending on TS compensation activation (crack locations: cf. Figure 11).
F I G U R E 1 1 Strain curves and crack widths in the reference area, calculation parameters as in Table 2.
for the neighboring cracks as well.By eliminating those spikes, makes TS more reliable.Beyond noise spike elimination, close to no influence is found on TS for the investigated smoothing rates with regard to the discussed amplitude reduction.
To achieve durable design, crack widths in reinforced and prestressed concrete structures are usually limited to 0.2-0.3mm.If the influence of TS is not taken into account, crack widths are-on the safe sidemarginally overestimated.

| Results
Appropriate parameter values according to the parameter studies in the previous sections, are displayed in Table 2.In Figure 11, the results of the crack width calculation using fosanalysis are shown.Both approaches yield good crack width estimates.The mean absolute difference to DIC are for the five cracks detected by ES Δw cr,mean,ES ¼ 24:3 μm and the four cracks detected by POL Δw cr,mean,POL ¼ 22:0 μm.The largest deviations are for ES Δw cr,mean,ES ¼ À44:6μm and for POL Δw cr, max,POL ¼ À43:1 μm.Crack widths calculated from strains measured by DFOS at height of the reinforcement are underestimated by tendency.This difference is due to crack closing toward the neutral axis of the specimen.
Prominent strain peaks combined with low signal disturbances and the unproblematic installation make ES well suited for crack monitoring.Embedding the ES directly into the concrete enables micro-crack detection with a surface opening width down to ≈ 30 μm, even when the DFOS is located in the tensile reinforcement plane.

| DISCUSSION
Cracks propagate irregularly through the concrete and have uneven surfaces.Additionally, a crack might be composed of several micro-cracks and the determination of the crack edges from a picture might be subjective to the investigator.Measuring the crack width only a small distance away results in a different value.These incertitudes can be described by means of epistemic uncertainty. 40,41Further sources of uncertainty due to limited knowledge are for example the transfer lengths of the DFOS, unreliable data due to SRAs and dropouts, and currently uncompensated influences (strains due to prestressing, temperature changes, creep and shrinkage, or unforeseen load).The accuracy of the presented method and influence of the following parameters is discussed with regard to this uncertainty.
The most crucial step in the presented workflow depends is the correct detection of cracks.The detection can be influenced by both pre-processing and the prominence threshold, which are interdependent.This dependency is the stronger, the poorer the signal-to-noise-ratio is.Hence, the prominence is one of the most important parameters.
Successful crack detection requires powerful preprocessing to deal with heavily disturbed strain signals.Smoothing alone is not a feasible approach for pre-processing signals featuring SRA, as moderate smoothing improves the peak detection consistency, but its beneficial is tightly limited. 21Instead, SRAs need to be detected (e.g., by GTM) and masked prior to replacing dropouts with interpolated values. 22o further pre-processing is necessary for the clear data of ES.The POL yields an overall worse signal with tight parameter tolerances for correct crack detection.
Observed differences in crack locations up to AE3 cm-most likely due to non-perpendicular crack propagation-fit well with other studies. 8,42The crack width errors are comparable with other studies. 8,29,43Herbers et al. 10 calculated crack widths with fosanalysis for subsequently installed DFOS and compared them with DIC measurements, where a tolerance of AE50 μm is defined as acceptable limit for practical purposes.
The estimation of transfer length is decisive for the accuracy and reliability of the resulting crack widths.Hence, it has the largest influence on the results after the most important step-crack detection.Accurate transfer length estimation is difficult especially for irregular strain signals.The parameter study showed the transfer length estimation causing comparably high variability in crack widths, but still within the specified tolerance.Hence, improving transfer length estimate's stability for irregular strain curves and irregular spacing would increase the method's reliability.
The reduction in crack width due to consideration of TS is well in the aforementioned uncertainty.Although, the linear TS model Equation (6a)-(6c) is a rough simplification, the error made in comparison to the standards is in single digit μm range.Because of its minor impact, TS is completely neglected by another study. 44n accordance with other studies, 10,29 concrete strain DFOS are, due to their pronounced strain peaks, better suited for crack monitoring than reinforcement strain DFOS.The good results of the ES due to its robust monolithic design is confirmed too. 16,29The strain curve of the reinforcement strain DFOS follows the distribution of the bending moment, which results in lower strain peaks and makes crack detection more difficult.

| CONCLUSIONS
DFOS have great potential for SHM, especially continuous and automated monitoring, enabling the observation of crack forming, even inside of structural members.Taking into account the large amount of data to be expected in continuous monitoring, automation is an urgent necessity for SHM.In this contribution, some steps toward an automated analysis for DSS data acquired with DFOS are achieved.general DSS data based crack width calculation workflow is presented, consisting of data acquisition, pre-processing, peak detection, transfer length estimation, TS compensation, and strain integration.The described workflow is implemented as a software framework fosanalysis, which is made available on https://github.com/TUD-IMB/fosanalysis.git.
Experiments on a 4 m long reinforced concrete beam were carried out.Parameter studies are conducted to identify appropriate input parameters for crack detection and crack width calculation for DFOS bonded to the reinforcement or directly embedded in the concrete.Noise reduction strength and the peak prominence are shown to be interdependent.The choice of these parameters depends strongly on the DFOS type and the application technique.Good signal-to-noise-ratio of the concrete strain DFOS simplifies crack detection and crack width estimation.Both transfer length estimation methods ("min", "middle") perform comparably well for the data at hand (stabilized cracking state, constant bending moment).Unless the data exhibits strong anomalous distortions, it is recommended to use the "min"-approach.Both investigated TS compensation approaches 8,9 have similar, minor influence on the estimated crack width.It is shown that there is a good agreement with the DIC measurements when TS is subtracted. 10However, neglecting the TS is quite legitimate for common crack widths in concrete structures.
Estimated crack widths of both DFOS types differ in an acceptable range from AE50 μm to the reference, DIC.Due to the higher sensitivity, concrete strain DFOS with monolithic cross-section are recommended for crack monitoring.For deployment on site, robust DFOS are required to withstand the rough construction conditions.
To conclude, several hurdles are yet to be taken on the way to fully autonomous DFOS based SHM.Among those are the reduction of manual intervention, improvement of stability to enable the use with data of worse signal quality, and consideration of various influences.Finally, the framework could be enhanced to detect further damages types, such as tendon damages.

F I G U R E 8
Averaged readings (polyimid: 41 and EpsilonSensor: 31); White background indicates the reference area.T A B L E 1 Number of identified cracks for EpsilonSensor (ES) and polyimid (POL).SensorP min (μm/m)