7.3.1 Using long-term SHM data for fatigue assessment
To compute the fatigue strength of a structural component, the resulting stress cycles at the component must be applied. Due to changes in bridge’s traffic loads, the induced stress ranges at the structural components of bridges have a variable property. Application of SHM data for fatigue assessment, benefits from considering the variable range of amplitude stress in fatigue responses. The time-history strain responses of strain gages are frequently applied for fatigue assessment. As the linear elastic relationship is valid, the collected strain responses are converted into stress responses. Furthermore, the cycles of stress ranges are extracted from the time-history stress responses, using the Rainflow cycle algorithm (14).
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It is recommended to use the Miner’s rule to compute the fatigue responses through the variable amplitude of stress range stress. Miner’s rule superposes the cycles of variable stress ranges to compute the fatigue damage index (15). Fatigue damage index expressed in Eq (7.1), is a ratio, varying from 0 to 1 that reflects the fatigue damage level of the investigating component.
Eq. (7.1) where N denotes the number of collected stress cycles and N represents the number of remaining cycles to failure. N can be determined through the appropriate S-N curves for an investigating component, recommended by AASHTO (16).
7.3.1.1Data collection period for fatigue assessment
The fatigue strength of in-service bridge’s structural components can be estimated over discrete periods of data collection, using the long-term SHM data. An exclusive data collection period helps to study the trend of the measured fatigue damage index in a long-term service life of a bridge. The period is required to include the frequent stress ranges, experienced by the structural components of the bridge. The choice of the optimum data collection interval depends on the traffic pattern, as well as the structure’s performance. The fatigue damage index may also have a variable trend due to the seasonal impacts, when the traffic pattern of the bridge is considerably associated with the seasonal variations. In addition, before computing the fatigue damage index, the existing outlier due to the random noise or malfunction of the sensor must be removed from the collected SHM data.
D= ni
Ni
i
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7.3.2 Using numerical data for fatigue assessment
Fatigue assessment of welded structural components using SHM data is restricted to the instrumented locations of the structural component. Welded structural component, prone to fatigue cracks are often less accessible areas for instrumentation. Consequently, the crack-induced stress concentration may not be detected through the fatigue damage index, measured which is measured through the long-term SHM data. Alternatively, it is possible to implement a model-based fatigue assessment method to obtain the numerical stress responses at the desired locations through a validated FE model. A validated FE model can mirror the structural responses of the objective component, if the model is appropriately created and calibrated corresponding to the field’s responses. The models also required to consider any inspection results concerning the structural defects. To compute the fatigue damage index, the required stress cycles can be counted for the equivalent stress ranges, through the SHM data.
The model-based fatigue assessment method also benefits from anticipating the remaining fatigue life and structural performance of the component, due to an induced fatigue crack, when a fatigue crack is simulated to the model. The crack propagation leading to fracture of a concerning component, and the structural responses variations are other advantages of model-based fatigue assessment method. However, if the bridge does not include any detected damage, using the cycle counts of the bridge for the crack-induced stress ranges is required to be implemented with caution. In addition, it is necessary to calculate the remaining cycles to failure, if the simulated fatigue cracks cause higher stress ranges than the experienced stresses at the bridge. The location and type of the crack is also required to be selected based on the structural analysis results.
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7.3.3 The Neural Network Method
Neural Network (NN) is a mathematical tool to predict the behavior of a system, through a learning algorithm of the connections between the neurons. The connection is provided by weight functions, which include the required information to solve the problem. The weights are then defined and allocated to the connections through a training process. A typical NN model consists of input, output and hidden layers, developing a multi-layer neural network. A Multilayer Perceptron (MLP) is a back-propagation algorithm, that trains the networks to correspond the nodes of the input layer to the output layer (17). In addition to the training process, estimating the error is required to evaluate the accuracy of the output (validation and test). During the training process, the MLP network modifies the weight and biases, resulting in a new output, through multiple attempts until the optimal responses (minimized error) are achieved In Figure 7-2, the schematic architecture for MLP network is shown. The error of the NN model is frequently measured, using the root mean square error (RMSE) or epoch value (18).
MLP models are extensively applied for damage detection purposes in conditional assessment of structural components. Long-term SHM data have the advantage of providing sufficient samples of the structural responses to train MLP model for predicting the structural condition goals. For damage detection purposes, however, samples of healthy and damaged structural components are necessary to input the network. Therefore, the trained model can accurately differentiate the healthy versus damage induced responses, when the features of each conditions are precisely extracted.
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Figure 7-2 Schematic Multi-layer Perceptron Neural Network Architecture