An output-only ARX model-based sensor fusion framework on structural dynamic measurements using distributed optical fiber sensors and fiber Bragg grating sensors

The advent of distributed optical fiber sensing technologies has made continuous and dense measurement possible, and has a very broad application prospect in the field of structural health monitoring. However, not all of them are able to guarantee measurement accuracy in a good condition compared to traditional fiber sensors, such as FBGs (Fiber Bragg Grating sensor), strain gauges, etc. In our previous study (Cheng et al., 2019) of the calibration on static measurements for distributed sensors, it turns out that the signal to noise ratio from each single sensing point has proven to be much higher for FBGs than for distributed sensors. This paper presents a novel sensor fusion approach aiming to enhance the measurement quality of distributed fiber optical sensors in dynamic strain measurement. First of all, an output-only common-structured ARX (Auto-Regressive with exogenous input) model for dynamic MDOF (Multiple Degree of Freedom) systems with n degrees of freedom is studied where one of the measurement outputs is utilized as the input rather than actual external force, thus avoiding the inaccessibility of input signals in real structural engineering campaigns. After applying this model into a measurement system using a limited number of sensing points but with high fidelity, the outputs at unobserved points can then be roughly predicted using various curve fitting techniques on the ARX model coefficients against structural positions. However, the quality of the predicted performance cannot be guaranteed. Benefiting from a dense measurement but with low fidelity, the variation trend of the built ARX model coefficients against structural locations can be evaluated. Combined with EKR interpolation technique, the built ARX model from a high-fidelity system is then coupled to the evaluated trend of ARX model coefficients from a low-fidelity system, which leads to a further enhancement of its measurement quality at the unobserved points. To verify the feasibility and effectiveness of the presented sensor fusion approach, numerical studies on a 10-DOF MDOF system are conducted, indicating a satisfactory forecast with very small values of mean square errors for the unobserved DOFs. To further investigate the benefits of the proposed sensor fusion approach, experimental activities on a steel-beam are performed, aiming to enhance/calibrate the measurement performance on distributed fiber sensor (low fidelity) by incorporating four FBG sensors (high fidelity) as a calibration reference. The experimental results show that the intervention of the proposed approach yields significant improvement in the measurement quality for distributed fiber optic sensors.