Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Porto, Portugal, 30 June - 2 July 2014 A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.) ISSN: 2311-9020; ISBN: 978-972-752-165-4 Diagnosis performance of vibration-based structural identification and health monitoring Guido De Roeck1 Department of Civil Eng., Faculty of Engineering, University of Leuven, Kasteelpark Arenberg 40, 3001 Leuven, Belgium email: [email protected] 1 ABSTRACT: Vibration-based Structural Identification has become an increasingly popular experimental technique, e.g. for model calibration, control of structural behavior during construction, assessment of the efficiency of structural repair, … Main breakthrough was the development of operational modal analysis (OMA), avoiding the use of artificial vibration sources. Vibration-based Structural Health Monitoring is based on the principle that modal parameters of a structure are stiffness dependent. Changes in natural frequencies, damping ratios, mode shapes or combinations can therefore be used as features to detect and to identify damage. Challenges for the four levels of damage assessment will be treated. From the measurement side, wireless sensors and optimal sensor placement strategies will be addressed. KEY WORDS: System identification; Operational modal analysis; Elimination environmental influences; Damage assessment; Wireless sensor networks; Optimal sensor placement. 1 INTRODUCTION Vibration-based damage identification is based on the principle that modal parameters of a structure are stiffness dependent. Changes in natural frequencies, damping ratios, and mode shapes can therefore be used as features to detect and to identify damage. Compared to other approaches for structural damage identification, vibration-based damage identification has the advantages of (1) being nondestructive, (2) being able to identify damage that is invisible at the surface, (3) being ‘global’ because no a priori location of the damage needs to be assumed as opposed to local methods such as ultrasonic testing. A good overview of recent trends is given in [18]. Output-only or operational modal analysis became very popular as no artificial vibration source is needed which is anyhow impossible in many cases. Powerful time domain system identification algorithms like Stochastic Subspace Iteration (SSI) have replaced the obsolete “peak-picking” method [1], [2]. Although theoretically a white noise (unmeasured) excitation is assumed, in practice these algorithms provide accurate lower modes and good damping estimates, even in case of (moderately) “colored” excitation. Moreover, operational modal analysis can be used for a permanent monitoring installation. In this case automated system identification (i.e. automatic treatment of response data with minimum or zero user intervention) is mandatory, while it is highly advisable for periodic monitoring [6]. To cope with the quite distinct vibration levels during operational and ambient loading, a large dynamic range of the sensors is required and a 24 bits resolution for the A/D conversion is advised. Main disadvantage is the dependence on the temporal and spatial characteristics of the unmeasured ambient loads, exciting a limited number of the lowest modes. A possible to circumvent this drawback is to supplement the present ambient excitation with a relatively small artificial excitation. System identification algorithms to deal with this hybrid stochastic-deterministic loading have been developed successfully [3], [4]. Results can be used for calibration of numerical FE-models inherently containing uncertainties especially related to boundary conditions, joint stiffnesses, structural contribution of non-bearing parts, material parameters, damping, … Subsequently, properly calibrated FE-models can be used to derive from response measurements the actual excitation like moving loads on road or railway bridges and wind forces on tall structures. Moreover, these models can be used to obtain from the response measurements in a limited number of sensors information in otherwise difficult to assess points, like strains close to weldings or forces in bolts [5]. Other interesting applications relate to the follow-up of critical phases during erection of constructions. However, one of the main applications remains vibrationbased damage identification. In general four levels are discriminated in damage assessment. Challenges for each of these levels will be addressed. The first level, damage detection (also called the “alarm level”) is mainly situated in the context of permanent monitoring. A damage related dynamic feature is permanently registered and a statistically relevant deviation is considered as a sign of possibly occurred damage. Probably this warning will then be followed by a more thorough inspection. Although a lot of potential damage features have been proposed, natural frequencies and mode shapes are still the most appealing. They are rather insensitive to the influence of unknown excitation, easy to extract by applying state-of-theart system identification algorithms and many other features (like strain energies) can just be derived from them. Unfortunately, natural frequencies are not only sensitive to damage, but also to changing environmental conditions such as temperature variations, and moreover, their estimation from vibration response data is also prone to experimental errors [7],[8],[9]. So far the influence of the environment on mode 11 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 shapes and modal strains is less understood. Challenge is to eliminate the environmental influences by prediction models that rely just on estimated modal properties (i.e. output-only models) or on the measured environment as input and the estimated modal parameters as output (i.e. input-output models). These models are trained by using data gathered in undamaged condition. Concerning levels two and three, localization and quantification of damage, the most powerful methodology is based on FE-model updating. It means that, by an optimization process, differences between measured and calculated modal parameters are minimized, taking parameterized damage patterns as updating variables. A probabilistic approach is necessary to account not only for the remaining uncertainty after filtering the environmental influence, but also the imperfections of the assumed numerical model. So far, mostly quasi-linear behavior of the damaged structure under small vibrations is assumed. Another challenge for the future is updating of nonlinear models of the damaged structure, which might be a step closer to level four. To localize and to quantify damage can be an objective of a permanent monitoring system interrogating a relatively low number of sensors or the goal of a periodic inspection making use of a more or less dense network of sensors. In the latter case, the use of wireless sensors can greatly reduce the cost of the measurement campaign. Level four, prediction of the remaining life time, is still an unresolved issue as changes in the dynamic behavior are basically related to stiffness degradation and not directly to strength reduction. Anyhow, in many cases there is at least some relation between the two. In fatigue assessment, vibration monitoring can deliver the true fatigue load. This load can be introduced in a (calibrated) FE-model to predict the remaining capacity by applying standard procedures for fatigue analysis. This is of growing importance for bridges because the dynamic loading due to traffic has increased severely during the past decades. A particular challenge for all four levels is the discovery of small local damage. Not only natural frequencies and mode shapes will hardly be affected but also its influence hidden in the uncertainty blur. Therefore, the development of a distributed strain sensor network able to cope with the very low strain intensities during ambient excitation is a challenge for future developments. Optical fiber sensors with Bragg grating technology permanently attached to the structure could be a good choice in this respect. Interrogation units are still quite expensive but can be coupled and uncoupled when adopting a periodic monitoring maintenance strategy. An additional advantage of the measured strain field is that it can be directly related to the stress field. Such a system will also be able to measure quasi-static deformation as occurs in case of shrinkage, creep, thermal expansion and very slowly applied dynamic loads. This paper will focus on some advances linked to the previously mentioned challenges: the elimination of environmental influences, the use of wireless sensors and the design of an optimal sensor placement strategy. 12 2 FILTERING OF ENVIRONMENTAL INFLUENCES It is well known that environmental changes like temperature variations may have an important influence on features of the dynamic characteristics such as natural frequencies [7],[8]. So they may mask the influence of damage completely. A second cause of inherent variance is due to estimation errors while applying system identification algorithms to the measured response data [9]. When monitored over a short period of time, in which the rather slowly varying environmental influences remain constant, a structure behaves like a linear time-invariant system. However, over longer time spans, the dynamic features change in a nonlinear way because of the nonlinear relationships between environmental parameters (like temperature) and stiffness of structural materials or boundary conditions. Moreover, due to the large thermal inertia of most structures, there can be a time delay between environmental changes and adaptation of dynamic features. To connect changes of dynamic features, e.g. natural frequencies, mode shapes and/or modal strains, to damage, it is of paramount importance to account for this environmental variability. Therefore, global prediction models should be derived from measurements over a long time span, preferentially covering the complete range of possible environmental parameter values. A possible approach for constructing the global prediction model is measuring the environmental factors that influence the damage-sensitive features, and identifying a black-box input model with these environmental factors as inputs and the corresponding features as outputs. However, a major difficulty with this input-output approach is to determine which environmental (or even operational) influences should be measured, and where the corresponding sensors should be placed. This can be overcome by employing output-only system identification methods, for which measurement of the environmental parameters is not necessary. 2.1 Output-only prediction model [10],[11] An output-only technique that has been applied for eliminating environmental influences on features such as natural frequencies is linear static principal component analysis (PCA), estimating a static linear relationship between the modal parameters and the unknown environmental parameters. However, in practice, this relationship may be strongly nonlinear. A very promising method for SHM in changing environmental conditions is kernel principal component analysis. This is a nonlinear version of PCA for which the type of nonlinearity does not need to be defined explicitly. Moreover, it is easy to implement and computationally very robust and efficient. In [10], an improved output-only technique for constructing a nonlinear prediction model is developed and validated on real-life monitoring data. It is based on Gaussian kernel PCA, where the two parameters of the model are automatically determined. The first parameter, which represents the standard deviation of the Gaussian (or radial basis function) kernel is chosen in such a way that the matrix of mapped output correlations is maximally informative, as measured by Shannon’s information entropy. The second parameter, which equals the number of principal components in the mapped feature space, Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 is chosen in such a way that the retained principal components amount for nearly all normal environmental and operational variability. In a first (training) step the available data are split in time sequences that are short compared to the parameter variations, and damage-sensitive features are estimated for each individual sequence. Then the second step consists in identifying a nonlinear prediction model, where the time-varying features of the first step are considered as outputs. The validity of this model can be checked by applying it to new data of the still intact structure. After that, the structure can be monitored by continuously repeating the first step. The features found in this way are compared with the ones predicted by the model of the second step. When the discrepancy becomes large, the model alone insufficiently explains the evolution of the features, so the structure may be damaged. This methodology is illustrated by application to the data set of the Z24, a bridge monitored for almost a year before realistic damage patterns where introduced in a controlled way. These tests were performed in the framework of the Brite-EuRam project CT96 0277 SIMCES. Figure 1. Z24 bridge. The Z24 bridge was part of the road connection between the villages of Koppigen and Utzenstorf, Switzerland, overpassing the A1 highway between Bern and Zürich (Figure 1). It was a classical post-tensioned concrete two-cell boxgirder bridge with a main span of 30m and two side spans of 14m. The bridge, which dated from 1963, was demolished at the end of 1998, because a new railway adjacent to the highway required a new bridge with a larger side span. Before complete demolition, the bridge was subjected to a short-term progressive damage test, in which 17 different damage scenarios were applied. During the year before demolition, a long-term continuous monitoring test took place to quantify the environmental variability of the bridge dynamics. Every hour, 65536 acceleration samples from 16 sensors at different points and in different directions were collected. The continuous monitoring system was still running during the damage tests preceding the demolition. In [10] the Z24 data are used for to apply both linear and kernel PCA. Selection of the modal parameters from the stabilization diagram was done in an automated way. The first four natural frequencies are taken as damage-sensitive features. They correspond with a vertical bending mode around 4 Hz, a lateral bending mode around 5 Hz, and two modes combining vertical bending and torsion around 10 and 11 Hz. A total of nt = 3000 data points, which amounts to about 50% of the number of data points available, are used for training the model. The other data points are used for monitoring. Figure 2 shows the result of the misfit ek when applying linear PCA: as can be seen only part of the environmental variation is covered by the training data. Figure 2. Z24 bridge, misfit of the linear output-only model constructed with 3000 data points. Blue: training data. Green: monitoring data in undamaged condition. Red: monitoring data in damaged condition. For the application of the kernel PCA again a total of nt = 3000 data points are used for training the model. The parameter in the radial basis function kernel is determined by maximizing the information entropy. Next, the number of retained principal components nu is determined based on the criterion that nu should account for at least a certain fraction F (e.g. 99%) of the normal variability. Figure 3. Z24 bridge, misfit of the nonlinear output-only model constructed with 3000 data points. Blue: training data. Green: monitoring data in undamaged condition. Red: monitoring data in damaged condition. The evolution of the misfit is shown in Figure 3. In the validation phase, the prediction error is not higher than during the training phase when the bridge is still in undamaged condition, except that there is a slight increase after 25 May, when the undamaged bridge is subjected to environmental conditions that are not covered by the training data. As soon as progressive damage is applied to the structure, the prediction error grows very significantly, so these unwanted 13 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 system changes can be clearly detected, either visually or with a novelty detection algorithm. It can be concluded that, when monitoring the misfit between the model predictions and the observed natural frequency data with linear PCA, it was difficult to discriminate the damaged from the undamaged condition. On the other hand, the nonlinear PCA approach allowed a clear detection of the onset of damage. 2.2 Input-output prediction model [12] As an alternative to eliminate the environmental influence, a nonlinear prediction model, that takes the measured temperatures as inputs and the estimated modal characteristics (e.g. the natural frequencies) as outputs, can be constructed. This influence is in general nonlinear and it affects different modal characteristics in a different way, so nonlinear system identification techniques are required. The nonlinear system model is identified using modal characteristics that have been obtained during a reference period in which the structure is undamaged. During the subsequent monitoring period, the values that are predicted by this model (using the measured environmental variables such as temperatures as inputs) are compared with the modal characteristics that are actually observed. If this difference is small, then the variations in measured modal characteristics can be well explained by environmental variations. If on the other hand this difference is large, then the observed variations in modal characteristics are caused by other factors, possibly structural damage. It is possible to account for uncertainty on both the predicted and the measured modal characteristics. It is then possible to apply robust decision rules for deciding whether or not the structure may be damaged and should be inspected. An efficient method for the identification of a nonlinear input-output environmental model is proposed. The output of the model is a sequence of vectors mk ∈ Rnm containing modal characteristics that have been estimated from short-term acceleration data. The input is a vector sequence of corresponding environmental variables uk ∈ Rnu. Only the first nt input-output samples (out of a total of ns samples) are used as training data for identifying the model. After removal of the DC input component, this model reads mk = WTφ(uk) + b + ek (1) where uk ∈ Rnu is the vector with known inputs and ek an error term that accounts for the misfit between the data and the model. The term b is the DC component of the output. φ represents a nonlinear mapping of (uk) onto a possibly very high-dimensional or even infinite-dimensional mapped feature space G: φ : Rnu → G, uk → φ(uk) (2) In LS-SVM, the model (1) is identified in a least-squares sense under the additional constraint that the regression should be smooth. Further, the uncertainties of the experimentally determined modal characteristics can be quantified. The environmental variables such as temperature are directly measured with high 14 accuracy, so their uncertainty is negligible with respect to that of the modal characteristics. Next, propagating these uncertainties through the SVM model delivers the probability distribution of the normalized modal characteristics. Once an environmental model is identified, the considered structure can be monitored by regular experimental determination of a modal characteristics vector mk and comparing it with the corresponding environmental model prediction ḿk An unwanted change causes the system to behave differently as in the period during which the environmental model was trained, so that the misfit ek grows. In a stochastic analysis, the misfit is a random variable. Since both mk and ḿk are normally distributed, the misfit, which is the difference between both, is also normally distributed. A probabilistic damage indicator can now be adopted. One possibility is to use the Mahalanobis distance between the misfit and zero as damage indicator. Figure 4. Cross section of the Z24 showing the temperature sensors. The data of the Z24 bridge are used to investigate the performance of LS-SVM in solving the monitoring problem. The lowest two monitored natural frequencies, corresponding to the first vertical and first lateral mode, are taken as outputs and a subset of nine measured temperatures (Figure 4) as inputs for the environmental model. A total of nt = 2664 data points were used for training the model; in this way a large portion of the temperature range is covered by the training data. The other data points were used for monitoring. There are approximately as many monitoring data in undamaged condition as there are monitoring data in damaged condition. The evolution of the misfit between the predictions of the environmental model and the observed natural frequencies, as measured by the Mahalanobis distance is shown in Figure 5. In the validation phase, the prediction error is not significantly higher than during the training phase when the bridge is still in undamaged condition. As soon as progressive damage is applied to the structure however, the prediction error grows very significantly, so these unwanted system changes can be clearly detected, either visually or with a novelty detection algorithm. The computational effort is largely reduced by changing the objective function in the Support Vector Machines (SVM) approach, so that a linear least squares problem needs to be solved for identifying a nonlinear system model instead of a quadratic programming one. The robustness issue is tackled by quantifying the uncertainty on the modal characteristics that are used as output data, and by propagating these through the SVM model, so that the probability distribution of the normalized modal characteristics is obtained. Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Figure 5. Z24 bridge, Mahalanobis distance of the prediction error from zero. Blue: training data. Green: monitoring data in undamaged condition. Red: monitoring data in damaged condition. 3 measurements, the modal parameters of the bridge structure can be extracted. The ADC includes a high-performance, linear-phase, digital and antialiasing filter; a high-pass integrated filter; and digital control of the sample rate. The signal conditioning circuit adapts common signals from the ICP sensors to differential, filters the noise, and supplies the necessary current for the ADCs. The Zigbee protocol, defined in IEEE standard 802.15.4, is used for the wireless synchronization module. This synchronization module provides an initial reference to the system, with less than 125-ns difference between all boxes. The next pulses to the boxes are used to fix derivations in the frequency clock. For communications between the boxes and transmission/reception of data the 802.11 protocol, also known as Wi-Fi, is exploited. It is possible to add as many clients as there are boxes, and they are automatically assigned an IP address. This feature provides a scalable architecture. Measurements are stored temporarily on a 2-GB SD card. This system has been tested successfully on a number of bridges (Figure 7). WIRELESS SENSOR NETWORKS Because of the omission of cables, wireless networks (WNs) have a lot of evident advantages, like the ease of system setup, the largely reduced installation time, the possibility of local data processing, data interpretation and anomaly detection. Nevertheless, there is still a need for improvements of the current WNs: 1) Reliability: packet collisions can occur in WNs because a share transmission medium is used. Moreover, when the distance between the nodes is too far, packets may not reach the destination. 2) Scalability: to characterize the state of the structure, a lot of raw data have to be sent over the air. This poses the problem of the scalability for an increasing number of modes. 3) Synchronization: time-synchronization errors can cause inaccuracy in the extracted mode shapes. Each sensor has its own local clock, which is not initially synchronized with the other sensor nodes. Synchronization errors affect the process of obtaining mode shapes. There are two primary sources of jitter: temporal jitter and spatial jitter. Temporal jitter takes place inside a node, and spatial jitter occurs between different nodes due to variation in node oscillator crystals and imperfect time synchronization. In a recent project a wireless measurement with high timesynchronization accuracy was developed [13]. Spatial jitter was reduced to 125 ns, far below the 120 µs required for highprecision acquisition systems and much better than the 10-µs current solutions, without adding complexity. Moreover, the system is scalable to a large number of nodes to allow for dense sensor coverage of real-world structures The system has two components: a host laptop (server) and boxes or nodes (clients). The architecture of a box is shown in Figure 6. The acquisition module contains a signal conditioning circuit, two low-noise ADCs with a sample rate between 1 and 192 kHz and a 24-bit resolution, and a PIC32 microcontroller. The ADC has two differential inputs that provide up to four channels in each box, allowing connection of 4 piezoelectric ICP accelerometers. From the acceleration Figure 6. Block diagram of a wireless box. Figure 7. Wireless boxes in use for a bridge test. 4 OPTIMAL SENSOR PLACEMENT In most of modal testing campaigns, there are more degreesof-freedom (DOFs) to be measured than sensors available. The whole measurement grid then needs to be covered in several phases by different measurement setups. A number of reference locations is then selected and transducers at these points are often kept fixed in all setups. The ideal location for a reference sensor is a position where all modes have 15 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 relatively large modal amplitudes. However, there exists no guidelines or general principles for evaluating whether a chosen number of reference sensors leads to sufficiently accurate mode shape estimates. In practice, even when measuring large structures, often a very limited number of reference sensors is allocated. The other transducers are roved in successive setups, hence these transducers are often termed `roving' sensors, so that by the end of the last setup, vibration responses at all grid points will have been recorded. So for any measurement campaign, the following questions have to be answered: (i) the location of the reference sensors, (ii) their number, (iii) the location of the roving sensors in the different setups. Answers can be given by applying Optimal sensor location (OSL) approaches. Their practical applicability will be illustrated on a large-scale operational modal test of a ﬁvespan steel truss railway bridge [15]. The measurement layout was designed according to intuitive reasoning, based on the modal results of a preliminary Finite Element analysis. Afterwards, this test design is reviewed using OSL. 4.1 The Guadalquivir railway bridge The Guadalquivir railway bridge in Andalusia, Spain, is a five-span continuous twin steel truss with one track in each direction (Figure 8). The spans have almost equal length: 50.48 + 50.94 + 50.94 + 50.94 + 50.61 (m). The abutments are labeled as E-1 and E-2 and the four piers as P-1, P-2, P-3, P-4 (Figure 9). The fixed bearings of the bridge are located on top of pier P-2. nodes, except a limited number of nodes in the upper chords at the end portal frames. Figure 10. Measurement layout: grid and position of reference sensors. The design of the measurement layout (Figure 10) was based on the modal results of a preliminary Finite Element analysis. To cover all measurement points, twenty-seven test setups were needed. Four fixed reference sensors were placed on the right main truss at bay numbers 9, 27, 43 and 63. These reference sensors were positioned at the locations of significant modal displacements of many lower modes. The fifth fixed reference sensor was placed at node 63 on the left main truss to provide comparison signals between the two main trusses. The remaining seven ‘roving’ sensors were distributed in a way that, at each particular setup, there is at least one sensor in each of the five spans. The last setup (27) was designed to measure the vibration of the transversal portal frame and also helped in distinguishing the global torsion modes. In this setup, four sensors were installed on a few accessible upper chord nodes at the end portal frames 0, 86 and 90. The sampling frequency was 200 Hz and the measurement duration was about fifteen minutes per setup. On average it took about 30 minutes to complete one setup including the time to relocate the roving sensors. Rail traffic was operating normally, with up to 5 train passages during rush hours. 4.3 Figure 8. The Guadalquivir railway bridge. Figure 9. Structural overview of the Guadalquivir bridge. 4.2 Test setup The bridge was extensively tested by making use of twelve wireless sensor units (GeoSIG GMS-18) which are connected by a time-synchronous wiﬁ network. Each unit is equipped with a triaxial accelerometer. Due to safety reasons, the measurement could only be performed on the bottom chord 16 Modal analysis results After the test operational modal analysis was performed using the Matlab toolbox MACEC 3.2 [17]. Thirty-seven modes have been identified within the frequency range from 2.78 Hz to 14.21 Hz. The identiﬁed modal characteristics are given in Table 3. The identiﬁed modes are all characterized by a low damping ratio. Most of them have a mode shape that is almost purely real, as evidenced by high MPC and low mean phase deviation (MPD) values, thus indicating a high estimation accuracy. All modes with a natural frequency between 2.78 and 3.36 Hz are transverse modes. In the frequency range from 4.36 to 7.37 Hz, seven vertical modes are identiﬁed. The other six modes in this frequency range are either transverse modes or modes with coupled transverse and vertical displacements. Mode 11 (5.16 Hz) and mode 12 (5.22 Hz) are closely spaced. The quality of the higher transverse mode shapes 19 and 20 is not as good as for the other four transverse modes of the same frequency range. The ﬁrst two modes in the frequency range from 8.46 to 14.21 Hz also belong to the transverse mode type combined with vertical modal deformation. Almost all modes from 23 onward are torsional modes of increasing frequency (from 8.90 Hz to 14.21 Hz) and modal order, in both vertical and transverse directions. Modes 31 and 32 can also be considered as transverse/combination modes. Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Table 1. Summary of identified modes (transverse ; vertical ; torsional/combined ). 4.4 No. Type f [Hz] ξ [%] MPC [-] ⁰ MP [ ] ⁰ MPD [ ] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 2.78 2.90 2.99 3.13 3.24 3.36 4.36 4.48 4.65 4.78 5.16 5.22 5.36 5.51 5.59 6.06 6.70 7.04 7.19 7.37 8.46 8.52 8.90 9.11 9.33 9.44 9.65 9.87 10.02 10.48 10.55 10.79 11.09 11.61 12.02 12.59 14.21 0.73 0.65 0.64 0.72 0.45 0.59 0.55 0.37 0.67 0.90 0.40 0.24 0.63 0.23 0.94 0.45 0.72 0.63 0.71 0.73 0.60 0.67 0.31 0.24 0.25 0.29 0.35 0.43 0.29 0.21 0.38 0.41 0.37 0.43 0.40 0.26 0.28 0.976 0.985 0.876 0.962 0.972 0.912 0.984 0.980 0.878 0.890 0.907 0.953 0.961 0.936 0.842 0.961 0.935 0.759 0.811 0.791 0.854 0.847 0.945 0.950 0.933 0.951 0.936 0.835 0.837 0.926 0.878 0.935 0.947 0.914 0.905 0.841 0.843 2.2 0.9 14.3 1.7 0.1 1.5 0.6 2.4 9.8 9.5 4.6 0.4 5 0.1 3.7 5.6 5.9 11 3.6 7.2 5.1 6.1 1.1 3 0.5 1 3.7 0.9 12.4 0.2 9.2 8 0.7 4.4 8 2.1 9.6 5.7 5.1 13 6.5 5.7 12.9 3.5 3.8 10.6 10.4 12.7 9.8 6.4 9.1 12.9 6.8 8.5 16.3 13.4 15.2 12.5 12.1 6.7 6.4 7.8 7.3 7.5 13.9 12.6 8.2 11.1 7.9 7.1 7.6 8.2 13 11.7 Comparison measured and calculated modes In Figures 11 and 12 the vertical and the transverse modes are compared. Some modes didn’t appear in the FE calculation. The longitudinal displacements of the nodes at the lower chords are relatively small compared to those in other directions. Especially at the supports, the almost zero longitudinal displacements indicate that they behave as practically ﬁxed in the longitudinal direction. It seems that the rollers allow free longitudinal displacement for static loading and thermal expansion but behave as ﬁxed under small amplitude vibration. 4.5 response and the modal coordinates of the finite element model is Review of the test design using optimal sensor placement After the field test, the original design of the test setups is reviewed by using an optimal sensor location (OSL) algorithm, which was recently developed [14]. Papadimitriou and Lombaert have proposed to choose the sensor locations so that the uncertainty of the identified modal coordinates, as measured by their information entropy, is minimized. When yk denotes the measured response, Φ the matrix with mode shapes computed from the preliminary finite element model, ξk the modal coordinates corresponding to this model and ek the prediction error due to both modeling inaccuracies and measurement errors, the relationship between the measured Figure 11. The identified vertical modes and the corresponding modes computed with the finite element model. yk = L[Φ ξk + ek] (3) where L denotes the observation matrix. This matrix is comprised of ones and zeros and maps, for a given configuration, the measured DOFs to the DOFs of the finite element model. Determining the optimal sensor configuration is equivalent to choosing the observation matrix L in such a way that the information entropy of the estimated modal coordinates ξk is minimized. This is equivalent to maximizing the determinant of the Fisher information matrix of ξk (as a function of L), which reads Q(L; Σ) = (L Φ)T (LΣLT)-1(L Φ) (4) where Σ denotes the covariance matrix of the prediction error ek. Since the objective function det Q(L; Σ) depends on the covariance of the prediction error ek,, the same holds for the optimal sensor configuration. The following model for the prediction error covariance was proposed in [14]: Σij =E[ek,iek,j ]= Σii Σ jj exp(-δij /λ) (5) 17 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 where δij denotes the distance between DOFs i and j, and λ is a scalar defining the degree of spatial correlation, called the correlation length. A value of λ = 0 means there is no correlation in the prediction error between any two measurement DOFs. Figure 12. The identified transverse modes and the corresponding modes computed with the FE model. An information entropy index (IEI) was also introduced as a normalized value to compare the difference between any configuration to the full configuration where all possible measurement locations are equipped with sensors: (6) IEI is a function of three variables that are unknown in the design stage. It depends on the number of sensors employed, their configuration and the prediction error correlation matrix among different channels. A large value of IEI means that the information content is small in relation to the full configuration. IEI should go down to unity as the number of sensors deployed approaches the full mesh. Two heuristic sequential sensor placement (SSP) algorithms, the forward (FSSP) and the backward (BSSP), 18 were proposed for solving the optimal sensor configuration problem as formulated in Equation (4). FSSP starts without any sensor. The positions of sensors are computed sequentially by placing one sensor at a time in the structure at a position that results in the highest reduction in information entropy. Specifically, at each iteration, combinations with an additional sensor to the previous configuration are considered, and the information entropy of all new sensor configurations are evaluated. The one that minimizes the information entropy is selected. On the contrary, BSSP is accomplished in a reverse order, starting with sensors placed at all measurable nodes on the structure and removing successively one sensor at a time from the position that results in the smallest increase in the information entropy. The actual test was very extensive with all truss nodal joints measured. Now, we retrospect whether we can coarsen the measurement grid and reduce the number of fixed reference sensors to make more sensors available for roving, in this way reducing the number of setups and so to speed up the test. Since upper chord access is prohibited, therefore 2 × 91 = 182 measurable locations have to be considered. In the transverse Y-direction it is expected that a sensor gives the same response whether put on the left main truss node or the right one of the same portal frame (section). Moreover, taken into account the longitudinal plane of the bridge, measuring on one truss plane is enough to characterize the dynamic properties of the bridge. So, the problem of finding several optimal locations for the fixed reference sensors is restricted to one measurement line along the lower chord of either truss plane, with 91 nodes from the section 0 to section 90. The OSL problem is run considering seven FE vertical modes. As the 91 measurable locations form a relatively dense grid, it can already be anticipated that taking into account correlation between sensors is important to maximize the quality of the data. It is assumed that the prediction errors between measurement channels are mutually correlated depending on their relative distance. The correlation length is chosen as = 0.001 (m), corresponding to the uncorrelated scenario and = 2d = 5.66 (m), with d the typical length of the truss bay and also the minimum distance between the two consecutive nodes of the mesh, corresponding to the correlated scenario. The IEI for the correlated scenario is shown in Figure 13. The change in IEI indices is signiﬁcant when the number of sensors is less than 4. When there are more than ﬁve sensors, they are distributed over all spans. If the number of sensors is further increased, there is a tendency of a spread-out over the measurement line. If we position 4 reference sensors, according to the correlated scenario and BSSP, the conﬁguration would be L = {9, 27, 44, 63} (Figure 14). This setting has a fairly low IEI and is actually very close to the choice L = {9, 27, 43, 63} based on intuition and experience (see Figure 13 □). Next, the method is employed again for one measurement line but using all 19 FE mode shapes up to a frequency of 7.70 Hz (the ﬁrst 7 vertical modes, the ﬁrst 11 lateral ones and one torsion mode) instead of the 7 vertical modes that were used before. Question is now to choose the optimal position of the triaxial sensors. It is assumed that there is no correlation Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 among the vertical, transverse and longitudinal directions. The correlation length in any ﬁxed direction is taken the same as before. Figure 15 suggests that at least 10 or 11 sensors have to be used. In Figure 15 IEIs of the correlated one with 7 vertical modes using BSSP are superimposed. Figure 16 shows the arrangement of triaxial sensors for the correlated scenario (from 6 to 20 sensors) when using 19 modes. Figure 16. Optimal sensor location for the correlated scenario when using 19 modes (× FSSP; ● BSSP). Figure 13. IEI for the correlated scenario when using 7 vertical modes. The previous analysis is not conclusive, however, on the number of ﬁxed reference sensors that is actually needed. In [16] the eﬀect of the number of reference sensors on the identiﬁcation results is studied by considering three cases. Case 1 is with only one reference sensor and its optimal location is L = {43} (Figure 14, BSSP). Case 2 is with two reference sensors at L = {27, 43}. Finally, case 3 is with three reference sensors in conﬁguration L = {9, 27, 43}. Then we compare the identification results with the previous case of four reference sensors L = {9, 27, 43, 63} (Figure 10). From this study [16] it can be concluded that, with optimal sensor placement techniques, the number of references employed (four in the present case) can be reduced to three or even to two without a signiﬁcant loss of quality of the modal estimates and without losing the ability to detect most modes of interest. A single reference however does not result in estimates of acceptable quality for most modes, even when placed at an optimal position. 4.6 Roving strategy The OSL methodology is used next to verify the strategy for the positions of roving sensors in successive test setups. Two roving strategies are often used in practice. One is to “rove in modules" or RIM (distributed roving) and the other is “rove in groups" or RIG (concentrated roving). Figure 14. OSL for the correlated scenario when using 7 vertical modes (× FSSP; ● BSSP; □ actual test). Figure 17. Roving configurations: in modules (top: RIM) or in groups (bottom: RIG). Figure15. IEI for the correlated scenario when using 19 modes. The RIM case has been implemented in the actual test with 7 sensors in 13 setups to cover 91 bottom nodes in one measurement line. In the RIM case the first setup would be L = {0, 13, 26, 39, 52, 65, 78}. The next setup is built by advancing every sensor in setup 1 by one truss bay to L = {1, 14, 27, 40, 53, 66, 79}. Following setups proceed successively after one another. Finally, the last one - setup 13 - will have a configuration of L = {12, 25, 38, 51, 64, 77, 90}. In the RIG case, the first seven nodes L = {1, 2, 3, 4, 5, 6, 7} will be measured in the first setup. Then, the next seven nodes are measured at configuration L = {7, 8, 9, 10, 11, 12, 13} in setup 2. In this roving strategy, the experiment finishes at setup 13 where the last seven nodes are measured L = {84, 85, 86, 87, 88, 89, 90}. The information entropy (IEI) values are computed directly considering 19 FE mode shapes (7 vertical modes, 11 lateral 19 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 and one torsional mode up to a frequency of 7.70 Hz). In general, the IEI values for setups in RIM case are signiﬁcantly lower – consequently much richer information content – than those calculated for the RIG case, except for setup 12 (Figure 18). REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] Figure 18. IEI values for the RIG and RIM strategies. 5 CONCLUSIONS A crucial aspect for a correct diagnosis from vibration-based structural health monitoring is the elimination of environmental influences. Powerful output-only or inputoutput methods allow to reduce the remaining variance significantly. The influence of environmental influences on mode shapes and modal strains is less studied but could help to discriminate structural changes, e.g. due to damage, from environmental effects. Wireless systems can reduce the measurement time for an operational modal analysis drastically, certainly in the case of large structures, and so contribute to an even more widespread use of it. To keep the same performance as a wired system, data synchronization, scalability and robustness are critical issues. A substantial improvement of the diagnosis capability to discover also small local damages is possible if the rather small dynamic strains during operation can be measured accurately. Optimal sensor placement methodologies, where the effect of spatial correlation of sensors into the prediction error is considered in order to avoid redundant information, provide very valuable insights into important choices in the test designing stage such as, an adequate measurement grid, locations of reference sensors and a suitable roving scheme. They are also very useful to decide upon the sensor positions in case of a permanent monitoring system, usually based on a limited number of sensors. [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] ACKNOWLEDGMENTS This research is partially supported by the Spanish Ministry of Science and Innovation (Sub-program INNPACTO 2010 Viadintegra research project). 20 B. Peeters and G. De Roeck. Reference-based stochastic subspace identification for output only modal analysis. Mechanical Systems and Signal Processing, 13(6):855–878, 1999. E. Reynders. System identification methods for (operational) modal analysis: review and comparison. Archives of Computational Methods in Engineering, 19(1):51-124, 2012. E. Reynders and G. De Roeck. Reference-based combined deterministic-stochastic subspace identification for experimental and operational modal analysis. Mechanical Systems and Signal Processing, 22(3):617-637, 2008. E. Reynders, A. Teughels, and G. De Roeck. Finite element model updating and structural damage identification using OMAX data. Mechanical Systems and Signal Processing, 24(5):1306-1323, 2010. E. Lourens, C. Papadimitriou, S. Gillijns, E. Reynders, G. De Roeck, and G. Lombaert. Joint input-response estimation for structural systems based on reduced-order models and vibration data from a limited number of sensors. Mechanical Systems and Signal Processing, 29:310327, 2012. E. Reynders, J. Houbrechts, and G. De Roeck. Fully automated (operational) modal analysis. Mechanical Systems and Signal Processing, 29:228-250, 2012. B. Peeters and G. De Roeck. One-year monitoring of the Z24-bridge: environmental effects versus damage events. Earthquake Engineering and Structural Dynamics, 30(2):149–171, 2001. A.Deraemaeker, E. Reynders, G. De Roeck, and J. Kullaa. Vibration based Structural Health Monitoring using output-only measurements under changing environment. Mechanical Systems and Signal Processing, 22(1):34-56, 2008. E. Reynders, R. Pintelon, and G. De Roeck. Uncertainty bounds on modal parameters obtained from Stochastic Subspace Identification. Mechanical Systems and Signal Processing, 22(4):948-969, 2008. E. Reynders, G. Wursten, and G. De Roeck. Output-only structural health monitoring in changing environmental conditions by means of nonlinear system identification. Structural Health Monitoring, 13(1):8293, 2014. E. Reynders, G. Wursten, and G. De Roeck. Output-only structural health monitoring by vibration measurements under changing weather conditions. In A. Strauss, D.M. Frangopol, and K. Bergmeister, editors, Proceedings of IALCCE 2012, 3rd International Symposium on LifeCycle Civil Engineering, pages 185-191, Vienna, Austria, October 2012. Taylor & Francis. E. Reynders and G. De Roeck. Robust structural health monitoring in changing environmental conditions with uncertain data. In Proceedings of the 11th International Conference On Structural Safety And Reliability: ICOSSAR 2013, New York, NY, USA, June 16-20 2013. Alvaro Araujo, Jaime García-Palacios, Javier Blesa, Francisco Tirado, Elena Romero, Avelino Samartín, and Octavio Nieto-Taladriz. Wireless Measurement System for Structural Health Monitoring With High Time-Synchronization Accuracy. IEEE Transactions On Instrumentation And Measurement, Vol. 61, No. 3, March 2012. C. Papadimitriou and G. Lombaert. The effect of prediction error correlation on optimal sensor placement in structural dynamics. Mechanical Systems and Signal Processing, 28:105-127, 2012. T.T. Bui, Reynders E., G. Lombaert, and G. De Roeck. Ambient vibration testing of a large truss bridge with optimal sensor placement. In G. Gao, E. Tutumluer, and Y. Chen, editors, Recent Advances in Environmental Vibration. Proceedings of the 6th International Symposium on Environmental Vibration. ISEV 2013, pages 15-30, Shanghai, China, November 2013. Tongji University, Shanghai, China. Keynote lecture. T.T. Bui, E. Reynders, G. Lombaert, and G. De Roeck. Operational modal analysis of large structures using optimal sensor placement. Paper submitted to Computer-Aided Civil and Infrastructure Engineering. E. Reynders, M. Schevenels, G. De Roeck, MACEC 3.2: a Matlab toolbox for experimental and operational modal analysis, Report BWM2011-01, Department of Civil Engineering, K.U.Leuven, 2011. A. Cunha, E. Caetano, F. Magalhães and C. Moutinho. Recent perspectives in dynamic testing and monitoring of bridges. Structural Control & Health Monitoring, 20 (6):853-877, 2013.

© Copyright 2020