ABSTRACT

INTRODUCTION

The theoretical method is a powerful tool for a precise determination of the remaining life cycle of existing structures as well, if it is used in combination with monitoring. This method is more precise in an order of magnitude compared with usual methods using the Palmgren-Miner concept, the local method or the fracture mechanics method. The reliabilities of the resulting life time is only small. Differences between theoretically calculated and observed life cycles may differ in an order of magnitude. The life cycle assessment via parallel structural health monitoring (SHM) can considerably improve the accuracy of the prediction [1, 2, 3].

ANAMNESIS OF THE EXISTING STRUCTURE

Since the owner of a bridge usually has to maintain a large number of bridges the choice of the most critical structure has to be performed. In [4] the basics of this procedure are presented. At the beginning of any monitoring measure a conscientious check up of the state of the structure and its accumulated damage is indispensable (anamnesis). This procedure is explained in detail in [3].

Fig 1. Life time determination procedure

At the very end of the anamnesis procedure the inherent damage must be assessed. This is one of the most difficult parts of the whole procedure. To possibilities are available to determine the damage state, a more theoretically based and an experimentally based procedure, see Fig. 2. Both methods are described in the following.

Fig 2. Determination of the actual damage

MEASURING OF THE INHERENT DAMAGE

The start of an acoustic emission signal supplies the substantial information about its source, because reflections are not yet superimposed. Thus this initial range is used for the extraction of features. Up to now the coefficients of a windowed Fourier-Transformation of the signal are used as signal features, fig.3.

Fig 3. Feature extraction

The comparison of the feature vector with the center vectors of signal classes defined before allows the classification into the associated signal classes. The easiest way to do this comparison would be to determine the average geometrical distance over all selected features. This would not take into account, that different classes may have different statistical spread within their features. This case is shown in Fig. 4. A signal (fat point) could be classified as being member of class 2, because its geometrical distance to this class is smaller than its distance to class 1 with wide-spread features. To avoid this, the scale-invariant Mahalanobis-distance is introduced [5]. The covariance matrix C is defined as

(1)

where: E {...} expected value of ... and m = E {x}
When used as a weighing matrix, the inverse covariance matrix of a class produces the Mahalanobis distance to its center vector

(2)

Fig 4. Mahalanobis distance

Single step tests with steel S355-J2G3 revealed characteristic signal forms for certain life span phases. The evaluation of acoustic emission activity over the number of load cycles of a test with a strain amplitude of ±3 micro-strain is represented here exemplarily.

Fig 5. Correlation of signal classes and damage state

The ordinate shows both the accumulated number of events and the amplitude of typical measured and classified events. These events are represented by different symbols according to their class. Four different stages of acoustic emission activity can be observed: An initial very short phase, which is coupled with the formation of shear bands. The acoustic emission activity then continues with the evolution of micro cracks. A further signal class is assigned to the evolution of main cracks. At the very end of the life time the number of events rises strongly, due to the macro cracks, which is accompanied by a large number of typical signals as well.

Up to now the results shown here are only carried out for identical test conditions (geometry, sensors and sensor arrangement, material). The search for additional signal classes is continued. Additionally wavelet coefficients are tested as signal features.

MODELLING OF THE INHERENT DAMAGE

Traffic data and axle loads are usually known by traffic authorities for different regions. Also WIM data on a lot of structures are available nowadays [7]. If measurements are not available (which is normal), re-extrapolated or estimated load probability distribution functions should be used. Figure 7 shows the density distributions of four vehicle classes. Density function 1 (in Figure 7 truncated) describes the probability of occurrence of cars, function 2 of light or empty trucks, functions 3 and 4 represent ordinary and heavy trucks [6].

The type of the micro traffic (typical vehicle sequences, clustering of trucks , typical temporal distances between vehicles) must be taken into account as well, because it influences the fatigue state remarkably. The simplest way is to start from the present, i.e. to measure the actual micro traffic and to extrapolate it into the past. In [3] the procedure is shown more in detail. As an example in Fig. 6 the distributions of the weights of four vehicle classes, are shown, Fig. 7 shows the sequence of vehicles resulting from a probability of occurrence which depends on the type of two preceding vehicle classes. Fig. 8 shows in similar manner the temporal distances between two vehicles.

Fig 6. Load Distribution as Histogram and Fitted Density Function Combination

Fig 7. Matrix of Temporal Distance Densities               Fig 8. Matrix of Sequence Densities

These statistical input information are now used to generate a synthetic time history of the traffic of the past, using the Monte-Carlo-Method. A random generator produces vehicle types which always consider the most recent sequence. The strains in the structure must be determined by means of a precise model, preferably a FE-Model. Heavy structures may be investigated purely statically, excluding dynamic effects. Moving loads on slender structures like bridges, however, may cause remarkable additional dynamic effects. An additional dynamic influence develops from the roughness of the road surface (the pavement) [8]. This influence is taken into account using measured different pavement states and describes them by means of a Gaussian, stationary, ergodic process, characterized by a power spectral density function (PSD). For use in the presented simulation, a discrete realization of the roughness function is needed. It can be generated from a finite Fourier series with random phase, where the amplitude of each term is determined in accordance with the chosen PSD. Because the system changes at each time step, the submodels (bridge and vehicles) have to be treated separately. The coupling forces of both systems are calculated and iterations must be performed until the Euclidean Norm of the interactive forces falls below a given threshold.

The calculated time histories for the past for typical traffic situations and the monitored actual strains at typical weak points can be used to calculate the actual damage via a model. Fracture mechanics, Palmgren-Miner or local concepts are just key words for possible methods. On the other hand an experimental approach gives a very precise prognosis of the life cycle of a bridge. If a specimen of the critical detail is tested in a numerical controlled test rig under a representative time history of strains the result is better in an order of magnitude. A flowchart is shown in fig. 13, [1].

ACKNOWLEDGEMENTS

Fig 9. Flowchart of the experimentally oriented procedure

REFERENCES

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