Analytical assessment of the reliability of the FBG multi-sensor network for monitoring CFRP structures based on the k-out-of-n model

In this paper, an analytical assessment of the long-term operability of the FBG multi-sensor network used for monitoring defects in CFRP structures was carried out. The main focus of the article is devoted to assessing the reliability level of a generalized FBG sensor network, and not the effectiveness of experimental detection of a defect in a specific CFRP sample. For this reason, the study does not consider the diagnostic sensitivity of the structural health monitoring system or the probability of detecting a defect, but the functional stability of the network in the event of sensor failure. The system reliability was calculated using the k-out-of-n model, and the time-dependent reliability of an individual sensor was characterized by an exponential law. The configuration <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mi> </mml:mi> </mml:math> 120 and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>k</mml:mi> <mml:mo>=</mml:mo> <mml:mi> </mml:mi> </mml:math> 100 was chosen as the main calculation scenario. This configuration was considered a representative redundancy model that characterized the system’s operability even in the event of a failure of about 16.7 % of the sensors. Calculations were carried out for 0-60 months for failure intensities <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:mi> </mml:mi> </mml:math> 0.005, 0.01, 0.02 and 0.05 months -1 . The results showed that as the degradation intensity of an individual sensor increases, system reliability decreases dramatically. At the same time, a sensitivity analysis of k/n configurations was performed, demonstrating an engineering trade-off between redundancy and the minimum number of operating sensors. The results obtained enable the selection of the maintenance interval, sensor replacement strategy, and level of redundancy on a scientific basis when designing SHM systems based on FBG.