Artificial neural network analyses of AE data during long-term corrosion monitoring of a post-tensioned concrete beam.
Post-tensioning, as well as pre-stressing technology, is widely adopted in civil engineering, esp. in bridge engineering [1, 2], since it allows to obtain slender but high performing structures. Although this technology is effective from a structural standpoint, it is sensitive, depending on environmental conditions, in which the structure operates, to corrosion damages. In particular, several cases have been described in the literature of premature failures of structures due to localized attack such as corrosion fatigue, wear-corrosion, but mainly stress corrosion cracking (SCC) [3-5]. This SCC mechanism is more critical than others because it induces a premature and unexpected rupture of the steel cables, affecting the mechanical integrity of the structure .
The development of reliable and affordable technique for monitoring and for damage evaluation of reinforced concrete structures, and in particular of prestressed concrete structures, is therefore becoming a pressing demand since the increasing age of the structures, the progression of deterioration processes and the ever increasing demanded performance. Acoustic emission (AE) technique is very promising in this field since it is not invasive, allows a volume evaluation and at the same time offers the possibility to locate discrete defects.
AE was widely used in studying corrosion phenomena and in particular SCC since the early stage of the development of the technique . More recently AE technique was introduced in the civil engineering in evaluating SCC of reinforcing cables in prestressed concrete structure  as well as in the detection of corrosion of reinforcing bar, in the identification of corrosion processes  and for damage evaluation .
Concerning SCC phenomena it has to be underlined that in prestressing steel they evolve through complex and different mechanisms, where anodic metal dissolution and hydrogen embrittlement (HE) are not unique stages [11-12]. However, many mechanisms can be identified by AE [13-14]. AE signals are generated mainly by crack initiation and growth due to metal dissolution or HE. Furthermore the hydrogen evolution induced by cathodic reaction within the crack, the breakdown of thick surface-oxide films, the fracture or decohesion of phases (such as precipitates, second-phase particles and non-metallic inclusions), twin or slip deformation in the plastic zone at the crack tip are all mechanisms that can produce detectable AE signals .
By considering the above-mentioned aspects it is clear that traditional AE analysis techniques are not sufficient to discriminate the different stages of damage in a corroding structure. The adoption of new statistical methods of data analysis is necessary to find out the significant parameters capable of discriminating the different forms of damage. Pattern recognition techniques can be used with this aim , and signal processing is performed at the waveform level, either by applying digital filtering, Fourier transforms or other processing such as wavelet transform, or by extracting AE features as a mean to describe the shape and content of a detected AE waveform. However, waveform acquisition requires high data storage capacity and sophisticated equipment while feature analysis is based only on the evaluation of the main AE signal parameters such as energy, counts, amplitude, without the need of the waveform record and is carried out by mean of the cross evaluation of different "health indexes" related to AE signal intensity and to loading condition .
Aim of this work is to identify the different damage mechanisms in steel cables in a post-tensioned concrete beam due to hydrogen assisted cracking by means of AE technique. A self-organized map (SOM) procedure was applied in order to interpret the experimentally acquired data. It was possible to group events into sub-clusters, each being an identifier of a specific degradation condition. The topological neural map was implemented in identifying the temporal evolution of damage and its related structural risk.
2. Material and methods
2.1 Experimental set-up
AE monitoring was carried out on a post-tensioned concrete beam during long-term hydrogen assisted stress corrosion cracking test (HASCC). The beam had a length of 6.30 m and a cross section of 0.40 x 0.25 m (Fig. 1a). It was made by a concrete mix with 430 kg/[m.sup.3] of ordinary Portland cement (OPC) content having the characteristic compressive strength of [R.sub.ck] = 55 MPa. It was reinforced with four 18-mm steel bars and post-tensioned with four 7-wire 6/10" strands (Fig. 1b). Steel wire composition and mechanical properties are reported in Table 1.
Post-tensioning force induced a stress level on the strand of about 60% of the UTS, of about 52% UTS after deducing losses due to elastic shortening, creep and shrinkage in the concrete and relaxation in the steel. The tendon was completely grouted with the exception of a small corrosion cell of 25 cm in length in the middle of the beam  (Fig. 1c). The corrosive solution used was composed with 250 g/l of ammonium thiocyanate (N[H.sub.4]CNS) in accordance to ISO 15630 . The solution was kept at room temperature, and with constant liquid re-circulation from an external reservoir by a pump.
[FIGURE 1 OMITTED]
AE signals were recorded by a 10-channel Vallen AMSY-5 measurement system. It was used with 8 piezoelectric transducers for steel, VS150-M type that worked in 100-450 kHz frequency range with resonance at 150 kHz. The sensors were positioned on ends of steel wires (Figure 1c). The AE acquisition covered a period approximately of 7 months, with a daily 24h monitoring. Before analysis, raw data were de-noised as reported in a previous work . The neural network analysis has been proposed to provide meaningful information on the quality of acquired signals and their interpretation on the status of the structure and damage evolution. In particular a self-organizing map (SOM) was constructed. It allowed to homogenize the acquired data and to interpret them in explicit form with a topological map that exemplifies the damage evolution of the structure during the acquisition time.
All specific algorithms proposed to analyze AE data were written by using Matlab 7.5 software. The SOM analysis was carried out by using 6 uncorrelated variables (i.e. average frequency, amplitude, duration, energy, time and event frequency) extrapolated from the acquired AE signal, as resulted by correlation matrix analysis.
2.2 Self Organizing Map
Self-organizing map (SOM) or Kohonen's map is a neural network used in the classification of complex multi-dimensional data . The algorithm could be unsupervised, requiring no user intervention. The self-organizing map (SOM) is one of the most prominent artificial neural network models adhering to the unsupervised learning paradigm. The model consists of a number of neural processing elements, i.e. units. Each of the units i is assigned an n-dimensional weight vector [m.sub.i], [m.sub.i] [epsilon] [R.sub.m]. The training process of self-organizing map may be described in terms of input pattern presentation and weight vector adaptation. Each training iteration t starts with the random selection of one input pattern x(t). This input pattern is presented to the self-organizing map and each unit determines its activation. Euclidean distance between the weight vector and the input pattern was used to calculate a unit's activation. In this particular case, the unit with the lowest activation is referred to as the winner, c, of the training iteration, as given in equation 1.
c:[m.sub.c](t) = [min.sub.i] [parallel]x(t) - [m.sub.i](t)[parallel] (1)
Subsequently, the weight vector of the winner as well as the weight vectors of selected units in the vicinity of the winner are adapted. This adaptation is implemented as a gradual reduction of the difference between corresponding components of the input pattern and the weight vector, as shown in equation 2.
[m.sub.i](t + 1) = [m.sub.i](t) + [alpha](t) * [h.sub.ci](t) * [x(t) - [m.sub.i](t)] (2)
Geometrically speaking, the weight vectors of the adapted units are moved slightly towards the input pattern. The amount of weight vector movement is guided by a so-called learning rate, [alpha], decreasing in time. The number of units that are affected by adaptation as well as the strength of adaptation is determined by a so-called neighborhood function [h.sub.ci]. This number of units decreases in time. Typically, the neighborhood function is a unimodal function, which is symmetric around the location of the winner and monotonically decreasing with increasing distance from the winner. A Gaussian is used to model the neighborhood function. At the beginning of training a wide area of output space is subject to adaptation. The special width of units affected by adaptation is reduced gradually during the training process. Such a strategy allows the formation of large clusters at the beginning and a fine-grained input discrimination towards the end of training process. The training process of the self-organizing map leads to a spatial arrangement of the input pattern such that alike input are ordered in a topological map (U-matrix) [21, 22]. Training has enabled the convergence of the system towards a model clustering the internal nature of data (Fig. 2).
The default training algorithm in SOM script is this batch algorithm; this because it needs a much smaller number of iterations than the classic one, and each iteration uses a large number of input data points. The whole training set is gone through at once and only after this the map is updated with the net effect of all the samples. Actually, the updating is done by simply replacing the prototype vector with a weighted average over the samples where the weighting factors are the neighborhood function values.
[m.sub.i](t + 1) = [n.summation over (j=1)] [h.sub.ic(j)](t)[x.sub.j]/ [[n.summation over (j=1)] [h.sub.ic(j)](t)] (3)
where c(j) is the BMU of sample vector [x.sub.j], [h.sub.i,c(j)] is the neighborhood function (the weighting factor), and n is the number of sample vectors.
[FIGURE 2 OMITTED]
Additional information can be obtained by plotting the hit histogram U-matrix. This map shows the projection of data samples into map. The data are calculated by finding the BMU (Best Matching Unit) of each data sample from the map, and increasing a counter in the map unit each time it is the BMU. The colors are related to a specific level of a variable and hexagon size is related to the numbers of AE hits related to that cluster point.
3. Results and discussion
Figure 3 shows the cumulative hits plot against acquisition time, with the purpose to indicate the AE activity evolution with time. We can identify three relevant steps that could be related to specific damage evolution of the steel.
Region I: During the early stages of the test there was a significant AE activity due to initial electrochemical interaction between the steel wires and the electrolyte solution. This period of activity is characterized by several sub-steps due to the activation and stabilization of different corrosive phenomena. At first the AE activity is related to the homogenization and stabilization of reactions at the metal surface in the corrosive solution . Region I is characterized by events in a wide range of amplitude (in the range 40-70 dB) and usually medium-high rise-time (> 30 [micro]s). The low amplitude events could be attributed mainly to hydrogen formation at the steel surface [24,25]. As reported in literature, AE with amplitudes in the range of 40-50 dB with high rise-time can be induced by hydrogen evolution phenomenon . Besides, the presence of hydrogen favors the breakdown mechanism of a pseudo-passive layer at the metal surface of the strand and the beginning of hydrogen diffusion inside the metal, inducing a strong AE activity . During this incubation period, corrosion mechanisms are activated, as random pit formation on the surface of the metal . The localized corrosion is however not sufficiently energetic to be detected by AE, but it could also favor the energetically more relevant SCC . The SCC initiation phenomenon induces events with low duration, counts and rise-time and amplitude in the same range of hydrogen evolution events (30-50 dB) . The crack initiation is followed by short crack propagation, identified with AE at higher amplitude (in the range 60-70 dB) .
[FIGURE 3 OMITTED]
Region II: After 35 days a new swarm of significant events in a short period occurred (in about 15 days over 5000 hits were observed) and the cumulative AE hit curve increases significantly. Afterwards the structure has a new quiescent phase where the increase of AE hits is very low. At this stage, at the strand surface, micro-cracks gradually initiate, increase and coalesce [14,31,32]. This phase is the evolution stage concerning hydrogen embrittlement and propagation of cracks . This is confirmed by the relevant amount of events in the range amplitude of 40-50 dB with the rise-time about 100 [micro]s. The hydrogen diffusion through the metal lattice occurs. When the hydrogen uptake is sufficient for the steel to overcome its threshold stress intensity factor a new AE activity will take place, due to initiation and propagation of cracks . In region II the time period between two AE events increases significantly; this phenomenon could be related with the formation of plastic zone at the crack tip during the crack propagation stages . With increasing the crack length an increase of stress concentration occurs, which induces larger plastic zone ahead of the crack tips. This results in a greater blunting of the crack tip. Larger plastic zone implies that a longer time is needed for crack to resharpen by dissolution for further crack propagation. The period of time between two AE events corresponds to the period of material dissolution that induced the crack growth . This could explain the larger time gaps between two AE events during later stages of crack growth.
Region III: High-intensity AE events were recorded after four months. Some steel wires were approaching final rupture and the post-tensioned concrete beam was undergoing a stabilization phase due to a new redistribution state of stress levels. This phase of reassessment was the prelude to new damaging phases progressively much more destructive. After this period we acquired about 25,000 AE events for a total of about 800,000 cumulative counts. In this phase the AE were mainly generated by crack propagation. However, corresponding to wire failure, the intense AE activity was probably generated due to rapid reduction of the cross-section during its rupture . The large burst of activity characterized by very high energy and amplitude up to 90 dB is symptomatic of final ductile fracture of a strand .
These considerations are summarized in Fig. 4 that shows the rise time versus amplitude distribution of the data discriminated according to the three steps identified in Fig. 3. In Region I, it is possible to identify the AE phenomena related with corrosion activation and crack initiation (oxide breakdown, hydrogen evolution, SCC initiation). In Region II the acoustic events, characterized by low amplitude and medium risetime, were associated to hydrogen embrittlement mechanisms. Finally in Region III we have a large amount of data at medium amplitude related with crack propagation and few AE events with very high amplitude due to the final fracture of the strand.
[FIGURE 4 OMITTED]
The Kohonen's self-organizing map algorithm was applied to the uncorrelated variables resulting from the analysis of the correlation matrix, i.e. average frequency, amplitude, duration, energy, time and event frequency. In Fig. 5 the U-matrix map resulting from SOM analysis is reported. The U-matrix map shows distances from map units and their nearest neighborhood, evaluated by Euclidean method. High values of U-matrix map (red and yellow pixels) mean large distances between neighboring map units. Elements belonging to the same cluster are, therefore, identified by uniform areas of low value (blue pixels). In this specific case, we identified many homogeneous areas associated with cluster areas. It is interesting to note that using the topological maps of the variables (reported in Fig. 6) it should be possible, on the basis of variable magnitude distribution, to relate data cluster to local area of specific variables. In particular, according with the regions identified in Fig. 3 and on the basis of time variable maps we defined three regions on the U-matrix map. The definition of the area associated to the first region is heavy influenced by the event frequency distribution as can be observed in the topological map (Fig. 6).
[FIGURE 5 OMITTED]
In fact, the events characterized by high event frequency (red and yellow pixels in the event frequency topological map) are grouped in the right and central area of the map. The second region is a left bottom area in the U-matrix map. The events grouped there have a low event frequency and middle/average frequency and duration. The third region includes the top and right areas of the map. These events are characterized by energy and amplitude variables. In particular the AE events with highest energy are grouped in the top-right corner of the map. Furthermore, a large variation of duration and average frequency can be observed. In particular on the top of the map AE events with high duration and low average frequency are grouped; vice versa AE events with low duration and high average frequency are grouped in the right side of the U-matrix map.
Based on these considerations it is possible to say that the U-matrix identifies some clusters related to the damage evolution of the steel strand. But further investigation are necessary to better clarify the discrimination of that damage phenomena and its time evolution. With this purpose a so-called hits-U-matrix (Fig. 7) was performed using the data collected in the regions identified in Fig. 3. This graph shows the projection of data samples into the U-map. The projection is obtained by finding the BMU (best matching unit) of each data sample from the map, and increasing a counter in the map unit each time it is the BMU. The colors are related to a specific event group (activation or quiescence phase as defined in Fig. 3) and colored hexagon size is related to the numbers of AE hits related to that cluster point. Figure 7 shows that the interpretation of the U-matrix map could be much more complex than the previous analysis.
[FIGURE 6 OMITTED]
The clusters associated with the regions I, II and III are characterized by several events, which could create internal sub-cluster or interference regions where multiple families of events coexist.
Region I: About the data collected in region I, the activation AE are located mainly in the zone Ia (characterized by high energy and high duration) and Ib (characterized by low energy and low amplitude); in contrast, the quiescence data are not well identifiable in a specific area, although a group of hits of these events is identifiable in the zone Ic and Id. The area Ic includes AE events of the region I characterized by low energy, medium low amplitude and high average frequency. The area Id is related mainly with quiescence AE with high amplitude and relatively high average and event frequency.
Region II: Other considerations can be extrapolated analyzing the hits distribution for region II data. A large amount of activation AE are located in IIa and IIb region, with the former related with lower event frequency than the latter one. The zone IIc could be related with the quiescence phase of region II.
Region III: The analysis of the hits map for region III data confirms that the AEs of this region are located in the top of the map. In particular a large amount of activation data are located in the top corner. The AE with very high energy, generated during the activation of region III, are located on the top-right corner of the map (area IIIa). The quiescence phase is located in peripheral region of this section of the map. In particular in the quiescence phase two sub-cluster can be identified. Events with high duration and low average frequency are mainly grouped in area IIIb, while events with high amplitude and low duration are predominant in area IIIc.
With the purpose to verify the hits distribution and to better clarify the discriminating performances of the SOM analysis about the event evolution on SCC tests on post-tensioned strands, a hits validation map was analyzed by using a fuzzy response parameter to show the relative goodness of each map unit in representing the data. The fuzzy response was calculated by summing a function of quantization error as follow :
g(x, [u.sub.i]) = 1/[(1 + [q.sub.i]a).sup.2]) (4)
where [q.sub.i] = [absolute value of (x - [u.sub.i])] is the quantization error (i.e. the distance between the sample x and map unit [u.sub.i]). The scaling factor a is the average distance between each training data sample and its BMU. Consequently, a high value of the fuzzy response is related to high affordability of the previsioned hits.
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
Figure 8 confirm that the SOM analysis identified the damage phase of the SCC strand well as reported in Fig. 7. The activation and propagation data for each region are well clustered in local areas on the U-matrix map. All configurations showed a high fuzzy response index, related with high accuracy of the numerical analysis. A higher uncertainty was observed only for region II quiescence data, where we observe a low fuzzy response value (maximum value is only 480).
Consequently, only for this dataset, we believe that not enough information was available to discriminate with good affordability their location on the U-matrix map. Furthermore this investigation showed that in the middle of the U-matrix map an interference area generated by AE of region I and II was present.
[FIGURE 9 OMITTED]
On the basis of the above reported considerations it is possible to divide the U-matrix map into specific damage mechanism areas, according to the schematic representation shown in Fig. 9. Here, we can distinguish the activation, propagation and critical damage areas, respectively, related with areas Ia and Ib, IIa and IIb and finally IIIa. The peripheral regions, not directly related with a specific variable (and characterized by multiple sub-clusters) represent the quiescence areas. In particular, the peripheral area Ic includes quiescent events that occurred after the electrochemical activation of steel surface characterized by high level of average frequency. The so-called pre-critical damaging quiescent area (IIc) was instead characterized by low event frequency and middle duration events. Consequently, the lower peripheral region in the map is related with the quiescent phase events before the critical damaging of the structure, while the peripheral regions at the top and right of the map (IIIb and IIIc) are related to the quiescent phase following the critical damaging and characterized mainly by high amplitude values.
The changes in waveform patterns of AE hits during the above described damage evolution are well visualized in Fig. 10. Starting from the activation phase (Ia) where AE hits are characterized by low average frequency, medium amplitude and high duration, in region II (IIa) we can observe an AE hit population defined by medium-high average frequency, low amplitude and medium duration, while the final damage step (post critical quiescent phase in region III, i.e. IIIc) is characterized by very high average frequency, medium high amplitude and very low duration.
Globally, the authors believe that the self-organizing map algorithms and the related U-matrix maps are powerful instruments for analyzing multivariate data set. In the specific cases their application allowed not only to validate preliminary hypotheses formulated on the basis of the interpretation of cumulative hit curve but permitted to discriminate between different damage mechanisms occurring over time on steel strands on the basis of the correlation between specific AE wave attributes.
[FIGURE 10 OMITTED]
Acoustic emission (AE) technique was used to monitor hydrogen-assisted stress corrosion cracking of post-tensioned strands stimulated by using accelerated test with an ammonium thiocyanate solution. Three damage phases were clearly distinguished from the cumulative hit plot, but a more detailed interpretation of the damage mechanisms occurring on steel wires during aging time was obtained by using a self-organizing map (SOM) methodology. The numerical results show that it is possible to integrate in an effective and synergistic way by using SOM with the traditional univariate analysis. Moreover this methodology has proved particularly effective in identifying, using exemplified topological maps, the evolution and intensity of corrosion damage on steel wires in the monitored post-tensioned concrete beam. Initiation, propagation and critical rupture phases were clearly identified and associated to specific features of the AE events. Such results allow, also on the basis of further refining of the methodology, to hypothesize the use of such a procedure for in situ recognition of damage processes.
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Lucio Bonaccorsi (1), Luigi Calabrese (1), Giuseppe Campanella (2) and Edoardo Proverbio (1)
(1) University of Messina, Dept. Industrial Chemistry and Material Engineering, Viale F. Stagno d'Alcontres 31, S. Agata di Messina, 98166 Messina, Italy
(2) NDT consultant, Via San Giuseppe 7 is. 297, 98122 Messina, Italy
Table 1: Steel wire composition and mechanical properties Nominal chemical composition of eutectoid steel C Si S P Cr Ni Mn Cu Fe 0.81 0.24 0.002 0.008 0.12 0.04 0.65 0.1 Bal. Mean mechanical properties of cold drawn steel Steel type Yield stress UTS [f.sub.pk] Elongation (%) [f.sub.p 0.1k] (MPa) (MPa) Cold drawn 1670 1860 3.5
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|Author:||Bonaccorsi, Lucio; Calabrese, Luigi; Campanella, Giuseppe; Proverbio, Edoardo|
|Publication:||Journal of Acoustic Emission|
|Date:||Jan 1, 2012|
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