Efstathiades - Application of Neural Networks for the Structural Health Monitoring in Curtain-wall Systems
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Engineering Structures 29 (2007) 3475–3484 www.elsevier.com/locate/engstruct
Application of neural networks for the structural health monitoring in curtain-wall systems
Ch. Efstathiades a , C.C. Baniotopoulos a , P. Nazarko b,∗ , L. Ziemianski b , G.E. Stavroulakis c,d
a Institute of Steel Structures, Faculty of Engineering, Aristotle University of Thessaloniki, GR-54124, Greece b Department of Structural Mechanic, Rzeszow University of Technology, W. Pola 2, 35-959 Rzeszow, Poland c Department of Production Engineering and Management, Technical University of Crete, GR-73132 Chania, Greece d Department of Civil Engineering, Carolo Wilhelmina Technical University, D–38106 Braunschweig, Germany
Received 3 August 2006; received in revised form 21 August 2007; accepted 21 August 2007 Available online 25 September 2007
Abstract In a curtain-wall system, the main and the most possible cause of failures, is the total or partial destruction of its connections with the bearing structure. The present paper deals with the respective health monitoring problem and proposes an Artificial Neural Network (ANN) in order to identify possible imperfections in a typical curtain-wall system. Several Finite Element (FE) models of the curtain-wall system were developed and a parametric analysis was carried out dealing with the loss of rigidity in the aforementioned connections. During the numerical investigations, datasets containing the deflections of the columns of the curtain-wall structure were computed. The obtained results were used to create the Patterns Database, which, in turn, was used as the input for the training of the ANNs. Due to the relatively small number of training patterns, the regularization technique was also employed in order to improve the network generalization. The number of sensors and their optimal placement for appropriate network training were investigated. A wide variety of network architectures was studied and their influence on the network training was analyzed. The obtained results showed that ANNs can be an efficient method for the identification and localization of imperfections in curtain-wall systems. c 2007 Elsevier Ltd. All rights reserved.
Keywords: Curtain-wall system; Structural health monitoring; Artificial neural networks; Finite elements method; Damage detection; Regularization techniques
1. Introduction Curtain-wall systems are becoming one of the most important parts of modern structures, since they greatly improve both their serviceability and their appearance. This is due to the fact that curtain-wall systems recently began to be designed as a part of the principal load-bearing structure. In consequence, a wide research effort on the structural behavior of such facades is nowadays in progress having as final target ¸ the improvement of the response of such systems and the optimum design (from the financial and safety point of view) since in certain cases the cost of the facade exceeds the fifteen ¸ percent of the total cost of a structure [1]. Currently the curtain-wall systems are being used in various shapes and types, not only in new buildings but also during the
∗ Corresponding author. Tel.: +48 17 865 1535; fax: +48 17 865 1173.
E-mail address: [email protected] (P. Nazarko). 0141-0296/$ - see front matter c 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2007.08.017
renovation of existing structures, mainly in order to improve the physical properties of buildings (Fig. 1(a)). The early detection of damages in a curtain-wall system, by means of Structural Health Monitoring (SHM), is an important factor since it supports early decisions about necessary repair and helps the engineers to avoid unfortunate accidents. One of the most possible positions for a fault in a curtain-wall system is the connection of the facade with its bearing structure. In ¸ most cases, these connections are easily accessible during the construction of the facade (Fig. 1(b)), but they are not accessible ¸ during the operation life of the building. The curtain-wall system is suspended from the main structure through point connections in certain distances over the whole area. The bolted connections used in curtain-walls cannot be assumed to be either completely rigid or pinned, but in most cases they are semi-rigid. For the generation of the Patterns Database (PD), damage in these connections can be represented by introducing a different (much lower) stiffness
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Fig. 1. Curtain-walls used: (a) In the renovation of an existing building. (b) During the construction.
value to some of the degrees of freedom (different for each type of partial destruction) in the finite element (FE) model. The identification of such faults by means of locating their position and severity may prevent failures and the respective detrimental consequences. 2. SHM and artificial intelligence methods An employment of SHM systems may be very useful to improve the reliability of modern structures and study their behavior under various effects. In recent years, the development of Nondestructive Damage Testing and Assessment (NDT&E) techniques became an interesting topic of research, not only for civil infrastructure [2], but also for mechanical systems, aircrafts and aerospace structures [3]. As a matter of fact the integrity of the structure is a very important aspect, since it may reduce maintenance costs and, in extreme events, avoid the collapse (e.g. after infrequent but high forces like earthquakes, wind gusts, accidental impacts). Ideally, health monitoring of civil infrastructure consists of determining by measured parameters the location and severity of damage in structure in real time, as they happen. Currently, these methods can only determine whether or not damage is present [4], whereas information about the extent of damage is not sufficiently accurate. However, the preliminary results related to the failure of the supports in the curtain-wall system will be presented in this paper and only the position of the partial destruction of a single support will be predicted. Further work will be extended to damage severity assessment and recognition of failure in several locations at the same time (multiple damage sources). During the past decade, the concept of Artificial Intelligence (AI) has offered some useful methods, especially for the solution of the so-called inverse problems. In this area, Artificial Neural Networks (ANNs) are mostly in use for damage identification [5–10]. Employment of such novel techniques allows us to predict the structural health during the service, without the need to interrupt or terminate the usage of the structure.
The correct selection of the structural parameters susceptible to damage is a very important issue for the success of the task. Network training is usually carried out based on values like modal shapes, natural frequencies, displacements, acceleration spectra, strains, etc. [11]. The optimal positioning of the sensors is an additional critical factor for the effectiveness of monitoring techniques. Taking into account the cost of sensors, the installation of strain-gauges on every part of a structure is, from both the financial and the technological point of view, impractical. Due to this fact a simple analysis of sensor placement will be provided in order to focus regularities in damaged structure deflections. 3. Formulation of the problem In the present section the damage detection problem of a curtain-wall system is formulated. Exploration of partial destruction in supports (connections with the supporting structure) is the main objective of this study. Firstly, the FE model of the curtain-wall system was created and data was generated, defining the relationship between changes in boundary conditions and the different values of the deflections at the midpoints of the mullions in the curtain-wall system. Control points were located at midpoints of each part of the columns and displacements related to different damage patterns were computed. Only the horizontal displacements under static wind load are going to be measured. In addition we considered that each time only one connection will have partial destruction. The results from the above parametric analysis lead (together with related target vectors) to the formulation of the Patterns Database (PD). Based on the changes of the structural response due to the occurrence of a fault, NNs were trained to assess the position of damage. The following issues will be addressed in the following sections: • • • • • FE models of curtain-wall system Creation of the PD and data preprocessing Selection and optimal placement of control points Tuning the ANNs for damage detection Application of a regularization technique (jitter).
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Fig. 2. Details of the connection: (a) Cross-section of a typical bracket. (b) A bolt in the bracket with the slotted holes.
4. Numerical computations 4.1. Model description The FE model of the curtain-wall system is used to compute the required data for the ANNs training. It is composed of a typical grid of 1 m height and 1 m width, respectively, and comprises vertical aluminium members (mullions) interconnected by discontinuous horizontal aluminium members (transoms) [12]. The glass panels are continuously supported over all sides of the grid. For mullions and transoms beam elements are used, whereas glass panels are considered to be shell elements. The whole system of the curtain-wall is supported on the bearing structure (a building) with connections (in our model the supports), where it is assumed that the mid supports are partially, whereas the end supports are fully restrained. The main loads that are acting in the model are wind loads (acting perpendicular at the X –Z plane of the structure) along with the dead load of the elements of the curtain-wall system. Eurocode1 gives provisions for the calculation of the wind load, which is generally dependent on the location and the height of the structure. For the present study the value of the wind load was taken as equal to 1 kN/m2 . 4.2. Connections The connections of the curtain-wall system with its bearing structure consist of the brackets and the fixings (bolts) as it is shown on the simple cross-section through a typical support point (Fig. 2(a)). Brackets may be made of aluminum, steel or stainless steel and are required to: – transfer to the bearing structure vertical loads due to selfweight, – transfer to the bearing structure horizontal loads due to live loads (wind pressure), – help for the adjustment of the curtain-wall system and overcome dimensional variations (slotted holes for fixing) (Fig. 2(b)),
– allow to avoid imposed loads on the curtain-wall due to relative movement of the system and the structure. Moreover, they have to both resist the corrosion and be simple to construct since curtain-wall systems are mainly erected at a height. The type and the size of the fixings (bolts) depend on a number of requirements like load values, load nature, thickness of members etc. Concerning the adjustment of the curtain-wall systems to their bearing structure, brackets have slotted holes, that is “bolt 1” has a freedom to move slightly in the direction of the Y Y axis and “bolts 2” have a freedom to move slightly in the direction of the X X axis (Fig. 2(a)). When a fault is introduced to the structure (e.g. a bolt is partially slacked), the boundary conditions of the supports (Fig. 3(a)) in the FE model are changed. For instance, in an end support, when the bolt1 (Fig. 2(a)) is slacked out we have a reduction in the translational stiffness coefficients Rx, Rz and the rotational stiffness coefficient Rx x. On the other hand, when the bolt2 (Fig. 2(a)) is slacked out we have a reduction in Rz and Ryy. Considering that both bolts have been slacked out, we generate the data defining the relationship between changes in boundary conditions, i.e. due to the faults in the connections with the supporting structure, and the different structural responses, i.e. the deflections at the midpoints of the mullions of the curtain-wall system (exactly 117 control points, as showed on the Fig. 3(b)). 4.3. Results of the analysis A parametric analysis is performed by calculating each time the displacements in all 117 midpoints of the mullions (Figs. 3(b) and 4) by taking into consideration the changes of the boundary conditions and obtaining finally the displacements for all 53 cases: namely the 52 different possible faults in the connections (Fig. 3(a)) together with the case of the intact (healthy) structure. In such a way the table with 53x117 deflection values was developed, on the assumption that the severity of damage is the same and that the magnitude of
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Fig. 3. The finite element model of the curtain-wall system: (a) The numbering of the supports. (b) The numbering of the midpoints of the mullions.
loading is the same (see Table 1). An exemplary deflection value due to existing damage in one of the supports (marked as 3-3 on Fig. 3(a)) was presented in the Fig. 4. All data obtained from the analysis using the FEM were subsequently used for the ANN training. 5. Applications of ANNs The fault location problem in the proposed approach will be solved based on the prediction of ANNs. The basic and most important issue is the training of the networks which should lead to a sufficient approximation of the transformation between inputs and outputs. First of all, the learning and testing datasets are defined by selecting patterns (e.g. randomly) from the available PD. The learning process iteratively calculates the free parameters of the network by minimizing the computed error between the target and obtained network outputs. The testing is carried out based on data that the network has never seen before. The ability of such a prediction for the training set was named the “network generalization”. Feed-forward networks consisted of one or two hidden layers and trained by the backpropagation algorithm are proposed and tested in this paper. A constant, equivalent static wind loading is used. For each damage case, a number of 12 to 20 units, related with selected control points on the structure, were allocated in the input layer. The output layer consisted of the damaged support position (two units related with damaged support coordinates). The ANN simulations were implemented using the Neural Networks Toolbox of Matlab R . The logsigmoid transfer function, written as f (N ) = 1/(1+exp(−N )), was used to activate the neurons in both the hidden and the output layer. The functions trainrp and trainlm according to the resilient backpropagation algorithm (RPROP) were used for the training of the networks in this preliminary study. The evaluation of the accuracy of the neural approximation was done based on the most popular Mean Square Error (MSE) defined as: MSE = 1 V
V
Table 1 Some results of the parametric analysis of the glass–aluminium curtain-wall system Mullion midpoint deflection (mm) 1 2 3 ... 117 Deflections in certain control points due to a fault in a single support (coordinates) None 0–0 1–0 0–3 1–0 ... 3.920 5.735 6.238 3.922 3.921 5.735 6.238 3.922 3.921 5.736 6.239 3.922 3.893 5.725 6.239 3.922 3.897 5.705 6.216 3.922 ...
12–9 3.920 5.735 6.238 3.923
Fig. 4. The disturbance of the curtain-wall system deflections due to the existence of a fault in one support.
A second auxiliary factor, called the Success Ratio (SR), that follows the formula: SR = N Bep · 100% V (2)
[ti − oi ]2
i=1
(1)
has been introduced. Here N Bep is the number of patterns within the Bep area (where a relative error ep is not greater than the assumed level) and V is the number of patterns in the considered sets. For the estimation of the neural prediction the following relative error was used [8]: ep = 1 − yi /ti · 100%
p p p p
(3)
where ti and oi are the target and output vectors for every iteration respectively, and V = L , T denotes the number of elements in the target vectors (learn and test, respectively).
where, ti , yi are, respectively, the target and neurally computed ith outputs for the pth pattern.
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Fig. 5. Damage identification error (MSE) for the networks (16-H-2) trained with different input vectors (1, 2, 3) and various sizes of the hidden layer H ; manual selection of testing set.
5.1. Data preprocessing From a parametric numerical investigation the PD has been created. The displacements for all considered cases of partial defect at single supports were computed in 117 control points (Fig. 3(b)). The total number of achieved patterns consisted of 53 cases, from which 52 were related with damage in the single support and 1 with the undamaged structure. The input and output data for the network were first normalized to the range [0.1, 0.9] for all cases. Then, they were divided into learning and testing vectors with ratio of 70% and 30% respectively. In the early studies the selection of testing data was carried out randomly, during each time of simulation. That leads to multifold validation [8]. On the other hand, due to the relatively small number of damage patterns, it easily causes nonuniform distribution of testing patterns and produces high randomness. Due to this fact a manual selection (covering the whole dataset) was carried out in parallel, in order to avoid the above mentioned effects. It was assumed that every third support will be included in the testing set. In this study better precision was obtained for training with a pre-selected constant training vector. For a network with 16 inputs, 2 outputs and one hidden layer with 3 nodes, i.e. a 16-3-2 network, the MSE results for the case with the random test data selection, have values higher than 0.009 and 0.027, for the prediction of the x and z coordinates, respectively. For the subsequent sections of this paper, only manual selection of test data will be done. First, the network’s input vector xi was defined in three different ways, in order to find the most efficient data form: xi = di xi = d0 − di xi = (d0 − di ) /di (4) (5) (6)
these simulations (Fig. 5) showed that slightly lower level of error values were achieved for the first input vector, while the introduction of the information from the undamaged structure (inputs no. 2 and 3) led to worse precision in the prediction of the damaged support coordinates. It may be easily seen, especially for the learning rate (marked by circle), where for the same conditions (network architecture, activation functions, etc) the error level is significantly higher. Several tests related with various sizes of the hidden layer showed that the best results were achieved for the smallest networks (herein 16-3-2). It is a consequence of the small number of training patterns, because networks with large number of neurons in the hidden layer may easily overfit the learning dataset and give worse results for the testing set (the network generalization is impossible in this case). The validity of a neural network-based damage detection approach also depends on the initial weights and biases, the order in which the inputs are presented to the network, the choice of transfer functions, the training algorithm, etc. [10]. Thus, to achieve sufficient efficiency, the training procedure was repeated at least 50 times and the respective average error results are shown in this paper. 5.2. Brief analysis of PD Apparently, there are deflections in the PD that can vary more than the others. It is also possible that some control points occur more often in the set of the highest values. The effort in this section is to find the set of control points from the range of 117 values that are the most sensitive to the position of damage. All 52 damage cases were compared with the deflection for the undamaged structure and the number of 50 maximum values for each case was taken into consideration. Next, the number of control points that was included in this matrix was considered. The most frequent indices with 20 maximum and 20 minimum values were shown on Fig. 6 by squares and diamonds respectively. From this dataset the index 57 appears
where di , d0 are the displacements of the ith damage case and the undamaged structure, respectively. It was supposed that by including the information of the undamaged structure the accuracy of prediction will be improved. The results of
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Fig. 6. Position of the control points with the greatest and the most frequent variations of deflections due to the failure of one support.
36 times while some of the 2600 analyzed values appear merely 13 times. A first conclusion could be that the deflection at the center of the structure is more frequent and relatively high, while on the border of the structure it is smaller and less frequent. The second hint is that we should add to the input vector, values computed for the middle points of the columns. 5.3. Various sizes of the input vector An objective of the test presented here was the optimal selection of control points, their numbers and their position on the curtain-wall system. It has been already assumed at the beginning that the set of input data will be only consisting of the deflections at the middle point of each column. The studied input combinations are collected in Table 2. The size of network input vectors leads to different ANNs architectures. Moreover, the influence of the number of neurons in the hidden layer was evaluated in relation with the accuracy of the prediction. Our investigations started from networks with only one hidden layer and a small number (three units) of neurons in this layer. Next, the number of neurons and hidden layers was increased. The learning algorithms trianrp and trainlm were used for two independent networks. The obtained identification accuracy was better for the trainrp and only this case will be discussed in this paper. The results of this study for the input vector consisted of 12, 16 and 20 displacement values as shown in the following graphs (Fig. 7). As before, the output of the networks consisted of the two coordinates of the damaged support. In order to have better results for our case, since we have a poor number of patterns (here 52), a small number of neurons in the hidden layer have to be employed. Furthermore, it seems that the optimal input vector size is equal to 16 units and that a higher value of this number does not lead to significant improvement in the prediction accuracy (compare the graphs in the Fig. 7). Another conclusion is that the “x” coordinate was predicted with better precision than the “z” coordinate. Neural Networks with two hidden layers were also tested. There were no significant differences in the group of
Table 2 Assumed sets of control points Number of points 12 16 20 Combinations of control points 15 18 22 25 55 58 60 63 93 96 100 103 15 17 20 23 25 54 56 58 60 62 64 93 95 98 101 103 14 16 18 20 22 24 26 54 56 58 60 62 64 92 94 96 98 100 102 104
Table 3 Average MSE values of damaged support location Network 16-3-2 16-4-3-2 16-5-3-2 16-3-2 MSE-learning x 0.0060 0.0034 0.0046 0.0040 (*) z 0.0125 0.0053 0.0067 0.0093 (*) MSE-testing x 0.0243 0.0271 0.0228 0.0146 (*) z 0.0530 0.0515 0.0518 0.0492 (*)
trained architectures. The MSE values of damaged support identification for several networks are collected in the Table 3. It may be assessed that the lowest value of error was achieved for the network 16-4-3-2, but the loss of the network 16-3-2 is very small, especially in the testing results. As it was mentioned above, small architectures are privileged for this case of the PD. Based on exemplary results provided by the network 163-2 (adequate error values were distinguished by brackets with star in the Table 3), a graph with the predicted failure position was created (Fig. 8). On the graph, the location of the supports (target coordinates used to train the neural networks) was marked by circles (empty circles) and the position of the control points was marked by stars. Furthermore, the position of supports that were included in the testing set was marked by squares. Learn results after 2000 training epochs were shown by “+” while the testing set was presented by “X”. It may be seen that the precision for some damaged support locations is not sufficient enough and the accuracy of network prediction should be improved further. The results obtained in this section are shown also on the SR plot (Fig. 9), which in fact correspond to the cumulative probability function. For instance when the relative error is not
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Fig. 7. MSE of fault location for various inputs and number of neurons in hidden layer: (a) Networks trained with 12 control points. (b) Networks trained with 16 control points. (c) Networks trained with 20 control points.
Fig. 8. Identification of fault location by the network 16-3-2.
Fig. 9. Success ratio plot for learn and test datasets provided by the network 16-3-2.
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Fig. 10. MSE of neural fault location with various standard deviations of the artificial noise.
greater than i.e. Bep = 10% the identification is approximately on the level of SR = 30% and SR = 60% for testing and learning sets respectively. That means, 30% for testing (or 60% for learning) of 52 patterns will be well-predicted by the neural network with accuracy |ep| ≤ 10%. 5.4. Improvement of network generalization The main objective in this study is to achieve the most possible network generalization with good identification accuracy. The main reason that limits, in our case, the network’s performance is the small number of available training patterns. The relation between the input and output is, therefore, more difficult to be learnt. The second issue is that the function that we are trying to simulate should be smooth in the sense that a small change in the inputs should mostly produce a small change in the outputs, and this property is not guaranteed from the mechanics of the studied problem. One of the regularization techniques that may improve the network generalization is based on the addition of small amounts of an artificial noise (a jitter) into the inputs during training. In other words, if we have two cases with similar inputs, the desired outputs will usually be similar. As long as the amount of jitter is sufficiently small, we can assume that the output will not change enough to be of any consequence, so we can just use the same target value. Unfortunately, when the jitter is too high it will make the network learning quite difficult, while too small values of jitter will have a little effect on the results. In this section the optimal value of standard deviation (std) of the artificial noise will be studied. It was assumed that the noise will have random entries chosen from a normal distribution with mean value equal to zero, a variance equal to one and various values of standard deviation (in the range of 0.0001 to 0.1). The network 16-3-2 trained with trainrp algorithm was employed here. The selection of patterns in the training set is
Table 4 Average MSE values of damaged support location Network 16-3-2 16-4-3-2 MSE-learning x 0.0078 0.0052 z 0.0119 0.0052 MSE-testing x 0.0239 0.0293 z 0.0536 0.0530
followed by the scheme with support numbers {4 5 10 11 16 17 21 24 27 30 33 36 39 42 43 49 51}. As a result of the mentioned procedure, the number of patterns available for the network training increased from 52 to 520, where the first 52 patterns are related to the original data without noise. One important thing is that jitter was added after dividing the PD into learning and testing datasets. In that way, the sizes of these vectors were equal to 350 and 170 samples, respectively. Results of these simulations are shown on Fig. 10. A comparison with the results of networks training without jitter, with only 52 patterns (Fig. 7(b)), shows that, unfortunately, there is no significant improvement of the MSE values due to various std levels. The lowest error values for the vertical (worse predicted) coordinate were achieved with std equal to 0.0003. Finally, network simulations with various sizes of the hidden layer and considered std level were carried out (see Fig. 11). From the above it can be concluded that, by using classical techniques, there is no significant improvement of the prediction accuracy for the studied networks. Even when networks with two hidden layers were adopted, the obtained results have a comparable level of error. The best results are shown and compared in Table 4, whereas the damage support location for network 16-3-2 is shown on Fig. 12. The next graph (Fig. 13) is an SR plot corresponding to the results presented on Fig. 12. In this case the number of patterns predicted with error value |ep| ≤ 10% is approximately equal to 34% and 58% for testing and learning datasets respectively.
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Fig. 11. MSE of neural fault location with various sizes of the hidden layers.
Fig. 12. Damaged support location predicted by the network 16-3-2, trained with the noised input (std = 0.0003).
Fig. 13. Success ratio plot for learn and test datasets provided by network 16-3-2 trained with the noised input (std = 0.0003).
It seems that we have achieved small prediction improvement, of about 4% which is related with the training patterns. As a comparison, the exemplary results for networks training
with jitter and random selection of training dataset (mentioned in Section 5.1) was shown on Fig. 14. The assessment of damaged support position looks pretty good here, due to the fact
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Fig. 14. Damaged support location predicted by the network 16-3-2 trained with the noised input and randomly selected training set.
that learning and testing patterns are very similar to each other. Unfortunately, in this case the network generalization cannot be estimated. It should be noted, that the number of patterns in our case is rather poor for effective network learning. The strong dependence of the identification accuracy on the training set size has been already observed earlier [11]. In that paper it was mentioned that the number of training cases may determine the precision which a network can offer. In an investigation, where the damage cases were increased from 50 to 80, the absolute error decreased from 27.7% to 8.6%. Following this remark, the future works should consider computation of more damage patterns as a continuation of the present work. 6. Conclusions and final remarks In this paper, a method for structural health monitoring and fault detection in curtain-wall systems was presented. Several models of a damaged curtain-wall system and the respective numerical simulation were studied. A database (PD) was developed from the results of the parametric FE analysis of the models, concerning different fault positions. The first step was to set an initial position of control points, analyze it and find the optimal number of control points. The regularization technique (jittering) employed here has slightly improved network generalization and increased the identification accuracy. Moreover, the position (coordinates) of damaged supports was predicted by employing ANNs. Due to the presence of an error value within the identification results, a plethora of various activities proposed in the literature was used in order to increase the accuracy. The investigation presented in the present paper can be considered to be the early stage in the use of ANNs, as an efficient method for the identification and localization of imperfections in curtain-wall systems. Future work will be focused on the consideration of imperfections in more supports at the same time, in order to make the approach more realistic (multiple defect identification). Furthermore, due to the local changes in the deflection map under the static loads a proposal
for improving the damaged support identification accuracy, may be the employment of dynamic analysis i.e. dynamic or impact loads. Acknowledgment The financial support of the European Commission for this research activity is gratefully acknowledged (“Smart systems” – HPRN–CT–2002–00284). References
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Application of neural networks for the structural health monitoring in curtain-wall systems
Ch. Efstathiades a , C.C. Baniotopoulos a , P. Nazarko b,∗ , L. Ziemianski b , G.E. Stavroulakis c,d
a Institute of Steel Structures, Faculty of Engineering, Aristotle University of Thessaloniki, GR-54124, Greece b Department of Structural Mechanic, Rzeszow University of Technology, W. Pola 2, 35-959 Rzeszow, Poland c Department of Production Engineering and Management, Technical University of Crete, GR-73132 Chania, Greece d Department of Civil Engineering, Carolo Wilhelmina Technical University, D–38106 Braunschweig, Germany
Received 3 August 2006; received in revised form 21 August 2007; accepted 21 August 2007 Available online 25 September 2007
Abstract In a curtain-wall system, the main and the most possible cause of failures, is the total or partial destruction of its connections with the bearing structure. The present paper deals with the respective health monitoring problem and proposes an Artificial Neural Network (ANN) in order to identify possible imperfections in a typical curtain-wall system. Several Finite Element (FE) models of the curtain-wall system were developed and a parametric analysis was carried out dealing with the loss of rigidity in the aforementioned connections. During the numerical investigations, datasets containing the deflections of the columns of the curtain-wall structure were computed. The obtained results were used to create the Patterns Database, which, in turn, was used as the input for the training of the ANNs. Due to the relatively small number of training patterns, the regularization technique was also employed in order to improve the network generalization. The number of sensors and their optimal placement for appropriate network training were investigated. A wide variety of network architectures was studied and their influence on the network training was analyzed. The obtained results showed that ANNs can be an efficient method for the identification and localization of imperfections in curtain-wall systems. c 2007 Elsevier Ltd. All rights reserved.
Keywords: Curtain-wall system; Structural health monitoring; Artificial neural networks; Finite elements method; Damage detection; Regularization techniques
1. Introduction Curtain-wall systems are becoming one of the most important parts of modern structures, since they greatly improve both their serviceability and their appearance. This is due to the fact that curtain-wall systems recently began to be designed as a part of the principal load-bearing structure. In consequence, a wide research effort on the structural behavior of such facades is nowadays in progress having as final target ¸ the improvement of the response of such systems and the optimum design (from the financial and safety point of view) since in certain cases the cost of the facade exceeds the fifteen ¸ percent of the total cost of a structure [1]. Currently the curtain-wall systems are being used in various shapes and types, not only in new buildings but also during the
∗ Corresponding author. Tel.: +48 17 865 1535; fax: +48 17 865 1173.
E-mail address: [email protected] (P. Nazarko). 0141-0296/$ - see front matter c 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2007.08.017
renovation of existing structures, mainly in order to improve the physical properties of buildings (Fig. 1(a)). The early detection of damages in a curtain-wall system, by means of Structural Health Monitoring (SHM), is an important factor since it supports early decisions about necessary repair and helps the engineers to avoid unfortunate accidents. One of the most possible positions for a fault in a curtain-wall system is the connection of the facade with its bearing structure. In ¸ most cases, these connections are easily accessible during the construction of the facade (Fig. 1(b)), but they are not accessible ¸ during the operation life of the building. The curtain-wall system is suspended from the main structure through point connections in certain distances over the whole area. The bolted connections used in curtain-walls cannot be assumed to be either completely rigid or pinned, but in most cases they are semi-rigid. For the generation of the Patterns Database (PD), damage in these connections can be represented by introducing a different (much lower) stiffness
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Fig. 1. Curtain-walls used: (a) In the renovation of an existing building. (b) During the construction.
value to some of the degrees of freedom (different for each type of partial destruction) in the finite element (FE) model. The identification of such faults by means of locating their position and severity may prevent failures and the respective detrimental consequences. 2. SHM and artificial intelligence methods An employment of SHM systems may be very useful to improve the reliability of modern structures and study their behavior under various effects. In recent years, the development of Nondestructive Damage Testing and Assessment (NDT&E) techniques became an interesting topic of research, not only for civil infrastructure [2], but also for mechanical systems, aircrafts and aerospace structures [3]. As a matter of fact the integrity of the structure is a very important aspect, since it may reduce maintenance costs and, in extreme events, avoid the collapse (e.g. after infrequent but high forces like earthquakes, wind gusts, accidental impacts). Ideally, health monitoring of civil infrastructure consists of determining by measured parameters the location and severity of damage in structure in real time, as they happen. Currently, these methods can only determine whether or not damage is present [4], whereas information about the extent of damage is not sufficiently accurate. However, the preliminary results related to the failure of the supports in the curtain-wall system will be presented in this paper and only the position of the partial destruction of a single support will be predicted. Further work will be extended to damage severity assessment and recognition of failure in several locations at the same time (multiple damage sources). During the past decade, the concept of Artificial Intelligence (AI) has offered some useful methods, especially for the solution of the so-called inverse problems. In this area, Artificial Neural Networks (ANNs) are mostly in use for damage identification [5–10]. Employment of such novel techniques allows us to predict the structural health during the service, without the need to interrupt or terminate the usage of the structure.
The correct selection of the structural parameters susceptible to damage is a very important issue for the success of the task. Network training is usually carried out based on values like modal shapes, natural frequencies, displacements, acceleration spectra, strains, etc. [11]. The optimal positioning of the sensors is an additional critical factor for the effectiveness of monitoring techniques. Taking into account the cost of sensors, the installation of strain-gauges on every part of a structure is, from both the financial and the technological point of view, impractical. Due to this fact a simple analysis of sensor placement will be provided in order to focus regularities in damaged structure deflections. 3. Formulation of the problem In the present section the damage detection problem of a curtain-wall system is formulated. Exploration of partial destruction in supports (connections with the supporting structure) is the main objective of this study. Firstly, the FE model of the curtain-wall system was created and data was generated, defining the relationship between changes in boundary conditions and the different values of the deflections at the midpoints of the mullions in the curtain-wall system. Control points were located at midpoints of each part of the columns and displacements related to different damage patterns were computed. Only the horizontal displacements under static wind load are going to be measured. In addition we considered that each time only one connection will have partial destruction. The results from the above parametric analysis lead (together with related target vectors) to the formulation of the Patterns Database (PD). Based on the changes of the structural response due to the occurrence of a fault, NNs were trained to assess the position of damage. The following issues will be addressed in the following sections: • • • • • FE models of curtain-wall system Creation of the PD and data preprocessing Selection and optimal placement of control points Tuning the ANNs for damage detection Application of a regularization technique (jitter).
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Fig. 2. Details of the connection: (a) Cross-section of a typical bracket. (b) A bolt in the bracket with the slotted holes.
4. Numerical computations 4.1. Model description The FE model of the curtain-wall system is used to compute the required data for the ANNs training. It is composed of a typical grid of 1 m height and 1 m width, respectively, and comprises vertical aluminium members (mullions) interconnected by discontinuous horizontal aluminium members (transoms) [12]. The glass panels are continuously supported over all sides of the grid. For mullions and transoms beam elements are used, whereas glass panels are considered to be shell elements. The whole system of the curtain-wall is supported on the bearing structure (a building) with connections (in our model the supports), where it is assumed that the mid supports are partially, whereas the end supports are fully restrained. The main loads that are acting in the model are wind loads (acting perpendicular at the X –Z plane of the structure) along with the dead load of the elements of the curtain-wall system. Eurocode1 gives provisions for the calculation of the wind load, which is generally dependent on the location and the height of the structure. For the present study the value of the wind load was taken as equal to 1 kN/m2 . 4.2. Connections The connections of the curtain-wall system with its bearing structure consist of the brackets and the fixings (bolts) as it is shown on the simple cross-section through a typical support point (Fig. 2(a)). Brackets may be made of aluminum, steel or stainless steel and are required to: – transfer to the bearing structure vertical loads due to selfweight, – transfer to the bearing structure horizontal loads due to live loads (wind pressure), – help for the adjustment of the curtain-wall system and overcome dimensional variations (slotted holes for fixing) (Fig. 2(b)),
– allow to avoid imposed loads on the curtain-wall due to relative movement of the system and the structure. Moreover, they have to both resist the corrosion and be simple to construct since curtain-wall systems are mainly erected at a height. The type and the size of the fixings (bolts) depend on a number of requirements like load values, load nature, thickness of members etc. Concerning the adjustment of the curtain-wall systems to their bearing structure, brackets have slotted holes, that is “bolt 1” has a freedom to move slightly in the direction of the Y Y axis and “bolts 2” have a freedom to move slightly in the direction of the X X axis (Fig. 2(a)). When a fault is introduced to the structure (e.g. a bolt is partially slacked), the boundary conditions of the supports (Fig. 3(a)) in the FE model are changed. For instance, in an end support, when the bolt1 (Fig. 2(a)) is slacked out we have a reduction in the translational stiffness coefficients Rx, Rz and the rotational stiffness coefficient Rx x. On the other hand, when the bolt2 (Fig. 2(a)) is slacked out we have a reduction in Rz and Ryy. Considering that both bolts have been slacked out, we generate the data defining the relationship between changes in boundary conditions, i.e. due to the faults in the connections with the supporting structure, and the different structural responses, i.e. the deflections at the midpoints of the mullions of the curtain-wall system (exactly 117 control points, as showed on the Fig. 3(b)). 4.3. Results of the analysis A parametric analysis is performed by calculating each time the displacements in all 117 midpoints of the mullions (Figs. 3(b) and 4) by taking into consideration the changes of the boundary conditions and obtaining finally the displacements for all 53 cases: namely the 52 different possible faults in the connections (Fig. 3(a)) together with the case of the intact (healthy) structure. In such a way the table with 53x117 deflection values was developed, on the assumption that the severity of damage is the same and that the magnitude of
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Fig. 3. The finite element model of the curtain-wall system: (a) The numbering of the supports. (b) The numbering of the midpoints of the mullions.
loading is the same (see Table 1). An exemplary deflection value due to existing damage in one of the supports (marked as 3-3 on Fig. 3(a)) was presented in the Fig. 4. All data obtained from the analysis using the FEM were subsequently used for the ANN training. 5. Applications of ANNs The fault location problem in the proposed approach will be solved based on the prediction of ANNs. The basic and most important issue is the training of the networks which should lead to a sufficient approximation of the transformation between inputs and outputs. First of all, the learning and testing datasets are defined by selecting patterns (e.g. randomly) from the available PD. The learning process iteratively calculates the free parameters of the network by minimizing the computed error between the target and obtained network outputs. The testing is carried out based on data that the network has never seen before. The ability of such a prediction for the training set was named the “network generalization”. Feed-forward networks consisted of one or two hidden layers and trained by the backpropagation algorithm are proposed and tested in this paper. A constant, equivalent static wind loading is used. For each damage case, a number of 12 to 20 units, related with selected control points on the structure, were allocated in the input layer. The output layer consisted of the damaged support position (two units related with damaged support coordinates). The ANN simulations were implemented using the Neural Networks Toolbox of Matlab R . The logsigmoid transfer function, written as f (N ) = 1/(1+exp(−N )), was used to activate the neurons in both the hidden and the output layer. The functions trainrp and trainlm according to the resilient backpropagation algorithm (RPROP) were used for the training of the networks in this preliminary study. The evaluation of the accuracy of the neural approximation was done based on the most popular Mean Square Error (MSE) defined as: MSE = 1 V
V
Table 1 Some results of the parametric analysis of the glass–aluminium curtain-wall system Mullion midpoint deflection (mm) 1 2 3 ... 117 Deflections in certain control points due to a fault in a single support (coordinates) None 0–0 1–0 0–3 1–0 ... 3.920 5.735 6.238 3.922 3.921 5.735 6.238 3.922 3.921 5.736 6.239 3.922 3.893 5.725 6.239 3.922 3.897 5.705 6.216 3.922 ...
12–9 3.920 5.735 6.238 3.923
Fig. 4. The disturbance of the curtain-wall system deflections due to the existence of a fault in one support.
A second auxiliary factor, called the Success Ratio (SR), that follows the formula: SR = N Bep · 100% V (2)
[ti − oi ]2
i=1
(1)
has been introduced. Here N Bep is the number of patterns within the Bep area (where a relative error ep is not greater than the assumed level) and V is the number of patterns in the considered sets. For the estimation of the neural prediction the following relative error was used [8]: ep = 1 − yi /ti · 100%
p p p p
(3)
where ti and oi are the target and output vectors for every iteration respectively, and V = L , T denotes the number of elements in the target vectors (learn and test, respectively).
where, ti , yi are, respectively, the target and neurally computed ith outputs for the pth pattern.
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Fig. 5. Damage identification error (MSE) for the networks (16-H-2) trained with different input vectors (1, 2, 3) and various sizes of the hidden layer H ; manual selection of testing set.
5.1. Data preprocessing From a parametric numerical investigation the PD has been created. The displacements for all considered cases of partial defect at single supports were computed in 117 control points (Fig. 3(b)). The total number of achieved patterns consisted of 53 cases, from which 52 were related with damage in the single support and 1 with the undamaged structure. The input and output data for the network were first normalized to the range [0.1, 0.9] for all cases. Then, they were divided into learning and testing vectors with ratio of 70% and 30% respectively. In the early studies the selection of testing data was carried out randomly, during each time of simulation. That leads to multifold validation [8]. On the other hand, due to the relatively small number of damage patterns, it easily causes nonuniform distribution of testing patterns and produces high randomness. Due to this fact a manual selection (covering the whole dataset) was carried out in parallel, in order to avoid the above mentioned effects. It was assumed that every third support will be included in the testing set. In this study better precision was obtained for training with a pre-selected constant training vector. For a network with 16 inputs, 2 outputs and one hidden layer with 3 nodes, i.e. a 16-3-2 network, the MSE results for the case with the random test data selection, have values higher than 0.009 and 0.027, for the prediction of the x and z coordinates, respectively. For the subsequent sections of this paper, only manual selection of test data will be done. First, the network’s input vector xi was defined in three different ways, in order to find the most efficient data form: xi = di xi = d0 − di xi = (d0 − di ) /di (4) (5) (6)
these simulations (Fig. 5) showed that slightly lower level of error values were achieved for the first input vector, while the introduction of the information from the undamaged structure (inputs no. 2 and 3) led to worse precision in the prediction of the damaged support coordinates. It may be easily seen, especially for the learning rate (marked by circle), where for the same conditions (network architecture, activation functions, etc) the error level is significantly higher. Several tests related with various sizes of the hidden layer showed that the best results were achieved for the smallest networks (herein 16-3-2). It is a consequence of the small number of training patterns, because networks with large number of neurons in the hidden layer may easily overfit the learning dataset and give worse results for the testing set (the network generalization is impossible in this case). The validity of a neural network-based damage detection approach also depends on the initial weights and biases, the order in which the inputs are presented to the network, the choice of transfer functions, the training algorithm, etc. [10]. Thus, to achieve sufficient efficiency, the training procedure was repeated at least 50 times and the respective average error results are shown in this paper. 5.2. Brief analysis of PD Apparently, there are deflections in the PD that can vary more than the others. It is also possible that some control points occur more often in the set of the highest values. The effort in this section is to find the set of control points from the range of 117 values that are the most sensitive to the position of damage. All 52 damage cases were compared with the deflection for the undamaged structure and the number of 50 maximum values for each case was taken into consideration. Next, the number of control points that was included in this matrix was considered. The most frequent indices with 20 maximum and 20 minimum values were shown on Fig. 6 by squares and diamonds respectively. From this dataset the index 57 appears
where di , d0 are the displacements of the ith damage case and the undamaged structure, respectively. It was supposed that by including the information of the undamaged structure the accuracy of prediction will be improved. The results of
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Fig. 6. Position of the control points with the greatest and the most frequent variations of deflections due to the failure of one support.
36 times while some of the 2600 analyzed values appear merely 13 times. A first conclusion could be that the deflection at the center of the structure is more frequent and relatively high, while on the border of the structure it is smaller and less frequent. The second hint is that we should add to the input vector, values computed for the middle points of the columns. 5.3. Various sizes of the input vector An objective of the test presented here was the optimal selection of control points, their numbers and their position on the curtain-wall system. It has been already assumed at the beginning that the set of input data will be only consisting of the deflections at the middle point of each column. The studied input combinations are collected in Table 2. The size of network input vectors leads to different ANNs architectures. Moreover, the influence of the number of neurons in the hidden layer was evaluated in relation with the accuracy of the prediction. Our investigations started from networks with only one hidden layer and a small number (three units) of neurons in this layer. Next, the number of neurons and hidden layers was increased. The learning algorithms trianrp and trainlm were used for two independent networks. The obtained identification accuracy was better for the trainrp and only this case will be discussed in this paper. The results of this study for the input vector consisted of 12, 16 and 20 displacement values as shown in the following graphs (Fig. 7). As before, the output of the networks consisted of the two coordinates of the damaged support. In order to have better results for our case, since we have a poor number of patterns (here 52), a small number of neurons in the hidden layer have to be employed. Furthermore, it seems that the optimal input vector size is equal to 16 units and that a higher value of this number does not lead to significant improvement in the prediction accuracy (compare the graphs in the Fig. 7). Another conclusion is that the “x” coordinate was predicted with better precision than the “z” coordinate. Neural Networks with two hidden layers were also tested. There were no significant differences in the group of
Table 2 Assumed sets of control points Number of points 12 16 20 Combinations of control points 15 18 22 25 55 58 60 63 93 96 100 103 15 17 20 23 25 54 56 58 60 62 64 93 95 98 101 103 14 16 18 20 22 24 26 54 56 58 60 62 64 92 94 96 98 100 102 104
Table 3 Average MSE values of damaged support location Network 16-3-2 16-4-3-2 16-5-3-2 16-3-2 MSE-learning x 0.0060 0.0034 0.0046 0.0040 (*) z 0.0125 0.0053 0.0067 0.0093 (*) MSE-testing x 0.0243 0.0271 0.0228 0.0146 (*) z 0.0530 0.0515 0.0518 0.0492 (*)
trained architectures. The MSE values of damaged support identification for several networks are collected in the Table 3. It may be assessed that the lowest value of error was achieved for the network 16-4-3-2, but the loss of the network 16-3-2 is very small, especially in the testing results. As it was mentioned above, small architectures are privileged for this case of the PD. Based on exemplary results provided by the network 163-2 (adequate error values were distinguished by brackets with star in the Table 3), a graph with the predicted failure position was created (Fig. 8). On the graph, the location of the supports (target coordinates used to train the neural networks) was marked by circles (empty circles) and the position of the control points was marked by stars. Furthermore, the position of supports that were included in the testing set was marked by squares. Learn results after 2000 training epochs were shown by “+” while the testing set was presented by “X”. It may be seen that the precision for some damaged support locations is not sufficient enough and the accuracy of network prediction should be improved further. The results obtained in this section are shown also on the SR plot (Fig. 9), which in fact correspond to the cumulative probability function. For instance when the relative error is not
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Fig. 7. MSE of fault location for various inputs and number of neurons in hidden layer: (a) Networks trained with 12 control points. (b) Networks trained with 16 control points. (c) Networks trained with 20 control points.
Fig. 8. Identification of fault location by the network 16-3-2.
Fig. 9. Success ratio plot for learn and test datasets provided by the network 16-3-2.
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Fig. 10. MSE of neural fault location with various standard deviations of the artificial noise.
greater than i.e. Bep = 10% the identification is approximately on the level of SR = 30% and SR = 60% for testing and learning sets respectively. That means, 30% for testing (or 60% for learning) of 52 patterns will be well-predicted by the neural network with accuracy |ep| ≤ 10%. 5.4. Improvement of network generalization The main objective in this study is to achieve the most possible network generalization with good identification accuracy. The main reason that limits, in our case, the network’s performance is the small number of available training patterns. The relation between the input and output is, therefore, more difficult to be learnt. The second issue is that the function that we are trying to simulate should be smooth in the sense that a small change in the inputs should mostly produce a small change in the outputs, and this property is not guaranteed from the mechanics of the studied problem. One of the regularization techniques that may improve the network generalization is based on the addition of small amounts of an artificial noise (a jitter) into the inputs during training. In other words, if we have two cases with similar inputs, the desired outputs will usually be similar. As long as the amount of jitter is sufficiently small, we can assume that the output will not change enough to be of any consequence, so we can just use the same target value. Unfortunately, when the jitter is too high it will make the network learning quite difficult, while too small values of jitter will have a little effect on the results. In this section the optimal value of standard deviation (std) of the artificial noise will be studied. It was assumed that the noise will have random entries chosen from a normal distribution with mean value equal to zero, a variance equal to one and various values of standard deviation (in the range of 0.0001 to 0.1). The network 16-3-2 trained with trainrp algorithm was employed here. The selection of patterns in the training set is
Table 4 Average MSE values of damaged support location Network 16-3-2 16-4-3-2 MSE-learning x 0.0078 0.0052 z 0.0119 0.0052 MSE-testing x 0.0239 0.0293 z 0.0536 0.0530
followed by the scheme with support numbers {4 5 10 11 16 17 21 24 27 30 33 36 39 42 43 49 51}. As a result of the mentioned procedure, the number of patterns available for the network training increased from 52 to 520, where the first 52 patterns are related to the original data without noise. One important thing is that jitter was added after dividing the PD into learning and testing datasets. In that way, the sizes of these vectors were equal to 350 and 170 samples, respectively. Results of these simulations are shown on Fig. 10. A comparison with the results of networks training without jitter, with only 52 patterns (Fig. 7(b)), shows that, unfortunately, there is no significant improvement of the MSE values due to various std levels. The lowest error values for the vertical (worse predicted) coordinate were achieved with std equal to 0.0003. Finally, network simulations with various sizes of the hidden layer and considered std level were carried out (see Fig. 11). From the above it can be concluded that, by using classical techniques, there is no significant improvement of the prediction accuracy for the studied networks. Even when networks with two hidden layers were adopted, the obtained results have a comparable level of error. The best results are shown and compared in Table 4, whereas the damage support location for network 16-3-2 is shown on Fig. 12. The next graph (Fig. 13) is an SR plot corresponding to the results presented on Fig. 12. In this case the number of patterns predicted with error value |ep| ≤ 10% is approximately equal to 34% and 58% for testing and learning datasets respectively.
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Fig. 11. MSE of neural fault location with various sizes of the hidden layers.
Fig. 12. Damaged support location predicted by the network 16-3-2, trained with the noised input (std = 0.0003).
Fig. 13. Success ratio plot for learn and test datasets provided by network 16-3-2 trained with the noised input (std = 0.0003).
It seems that we have achieved small prediction improvement, of about 4% which is related with the training patterns. As a comparison, the exemplary results for networks training
with jitter and random selection of training dataset (mentioned in Section 5.1) was shown on Fig. 14. The assessment of damaged support position looks pretty good here, due to the fact
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Fig. 14. Damaged support location predicted by the network 16-3-2 trained with the noised input and randomly selected training set.
that learning and testing patterns are very similar to each other. Unfortunately, in this case the network generalization cannot be estimated. It should be noted, that the number of patterns in our case is rather poor for effective network learning. The strong dependence of the identification accuracy on the training set size has been already observed earlier [11]. In that paper it was mentioned that the number of training cases may determine the precision which a network can offer. In an investigation, where the damage cases were increased from 50 to 80, the absolute error decreased from 27.7% to 8.6%. Following this remark, the future works should consider computation of more damage patterns as a continuation of the present work. 6. Conclusions and final remarks In this paper, a method for structural health monitoring and fault detection in curtain-wall systems was presented. Several models of a damaged curtain-wall system and the respective numerical simulation were studied. A database (PD) was developed from the results of the parametric FE analysis of the models, concerning different fault positions. The first step was to set an initial position of control points, analyze it and find the optimal number of control points. The regularization technique (jittering) employed here has slightly improved network generalization and increased the identification accuracy. Moreover, the position (coordinates) of damaged supports was predicted by employing ANNs. Due to the presence of an error value within the identification results, a plethora of various activities proposed in the literature was used in order to increase the accuracy. The investigation presented in the present paper can be considered to be the early stage in the use of ANNs, as an efficient method for the identification and localization of imperfections in curtain-wall systems. Future work will be focused on the consideration of imperfections in more supports at the same time, in order to make the approach more realistic (multiple defect identification). Furthermore, due to the local changes in the deflection map under the static loads a proposal
for improving the damaged support identification accuracy, may be the employment of dynamic analysis i.e. dynamic or impact loads. Acknowledgment The financial support of the European Commission for this research activity is gratefully acknowledged (“Smart systems” – HPRN–CT–2002–00284). References
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