PSI - Issue 64

Philipp Kähler et al. / Procedia Structural Integrity 64 (2024) 1248–1255 Kähler / Petryna / Structural Integrity Procedia 00 (2019) 000 – 000

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Keywords: Kalman Filter; Neural Network; Load Identification; Model Update; Damage Detection

1. Introduction Most of the bridges in Germany have been built between 1960 and 1985 and, thus, have reached a critical age. To challenge this problem, the Germany Research Foundation (DFG) has launched the priority program SPP 2388 100+ to develop new methods for digital representation, structural health monitoring (SHM) and lifetime management of complex infrastructure buildings. In the present contribution, an approach based on the Kalman update for data assimilation between model predictions and noisy measurements is applied and further developed. A sound numerical model, the measurement system, a permanent data flow and different assimilation techniques shall provide an online prediction of the state and model parameters of the structure. Various KF have already been implemented in the field of SHM in the past. Mostly, these were used for virtual sensing Maes et al. (2018), system identification Askari et al. (2016), or damage detection Xie et al. (2018). With the development of ensemble-based KF, which use a Monte Carlo sampling technique to generate a small number of ensembles from the a-priori probability density function of the state variables, the filters became able to solve nonlinear problems in a fast pace. They introduce, however, the problem of filter divergence due to undersampling and consequently an erroneous approximation of the ensemble variance, see Ehrendorfer (2007). Therefore, a wide variety of different ensemble-based KF have been further developed to solve this problem, two of which are used in this contribution. However, the current load on the real system needs to be identified and remodeled, to ensure that the measured behavior of the structure and the predicted behavior of the model are based on the same underlying cause. Thus, a two-step update procedure for SHM is proposed and applied in this context. One part of the measurement system is solely used for the load identification with artificial neural networks similar to Lan et al. (2017). The type of sensors, their position, and the measured values must ensure that the measurement data correlates well with the load itself and is less influenced by possible system changes or damage. In the second step, a different set of sensors is used for the data assimilation process. There, the previously determined load is used as input force on the model to generate the model prediction, which can then be compared with the response measurement of the real structure. Subsequently, the state and model parameters are adjusted using the KF to detect, localize and potentially quantify damages or changes in the structure. The load identification procedure is tested numerically, and the data assimilation technique is tested on a laboratory structure. The combination of the measurement of the dynamic behavior of a real structure, a numerical model as well as the assimilation techniques combining these two can be considered as a digital twin for SHM. 2. Continuous load identification using convolutional neural networks The identification of traffic loads can be very complex, difficult, and dependent on the level of detail required for the results. If only load models are to be generated for design verifications or fatigue analysis of a specific bridge, a simple load counting based on individual strain measurements can suffice. However, if actual, real-time load data is required, including load parameters like magnitude, velocity, location, and count, sensor data must be evaluated for multiple characteristic variables simultaneously. Through the sensor position and the corresponding time-delayed deviations in the time series of strain or acceleration sensors, time- and location-dependent information of the load can be determined. Additionally, random effects such as wind excitations, passages of smaller vehicles, or measurement noise pose a negative effect on the accuracy of load identification. The goal of the present load identification approach is the continuous determination of all characteristic features of the traffic load online in order to use them as input force on the model in the prediction step of the KF. Simple feedforward neural networks cannot be used to solve this task. Thus, a more sophisticated neural network structure is required to utilize the time series of multiple sensors simultaneously. Here, CNNs seem to provide the best results, see Goodfellow et al. (2016).

2.1. Cluster structure of the load identification process

CNNs were originally created to classify the content of images or speech time-series. Nowadays, their scope of application has greatly expanded. Due to their ability to recognize local features in complex datasets, CNNs are