This dissertation describes the work conducted on error analysis for Brillouin Optical Time Domain Reflectometry (BOTDR), a distributed strain sensing technology used for monitoring the structural performance of infrastructures. Although BOTDR has been recently applied to many infrastructure monitoring applications, its measurement error has not yet been thoroughly investigated. The challenge to accurately monitor structures using BOTDR sensors lies in the fact that the measurement error is dependent on the noise and the spatial resolution of the sensor as well as the non-uniformity of the monitored infrastructure strain conditions. To improve the reliability of this technology, measurement errors (including precision error and systematic error) need to be carefully investigated through fundamental analysis, lab testing, numerical modelling, and real site monitoring verification. The relationship between measurement error and sensor characteristics is firstly studied experimentally and theoretically. In the lab, different types of sensing cables are compared with regard to their measurement errors. Influences of factors including fibre diameters, polarization and cable jacket on measurement error are characterized. Based on experimental characterization results, an optics model is constructed to simulate the Brillouin back scattering process. The basic principle behind this model is the convolution between the injected pulse and the intrinsic Brillouin spectrum. Using this model, parametric studies are conducted to theoretically investigate the impacts of noise, frequency step and spectrum bandwidth on final strain measurement error. The measurement precision and systematic error are then investigated numerically and experimentally. Measurement results of field sites with installed optical fibres displayed that a more complicated strain profile leads to a larger measurement error. Through extensive experimental and numerical verifications using a Brillouin Optical Time Domain Reflectometry (BOTDR), the dependence of precision error and systematic error on input strain were then characterized in the laboratory and the results indicated that a) the measurement precision error can be predicted using analyzer frequency resolution and the location determination error and b) the characteristics of the measurement systematic error can be described using the error to strain gradient curve. This is significant because for current data interpretation process, data quality is supposed to be constant along the fibre although the monitored strain for most of the site cases is non-uniformly distributed, which is verified in this thesis leading to a varying data quality. A novel data quality quantification method is therefore proposed as a function of the measured strain shape. Although BOTDR has been extensively applied in infrastructure monitoring in the past decade, their data interpretation has been proven to be nontrivial, due to the nature of field monitoring. Based on the measurement precision and systematic error characterization results, a novel data interpretation methodology is constructed using the regularization decomposing method, taking advantages of the measured data quality. Experimental results indicate that this algorithm can be applied to various strain shapes and levels, and the accuracy of the reconstructed strain can be greatly improved. The developed algorithm is finally applied to real site applications where BOTDR sensing cables were implemented in two load bearing piles to monitor the construction loading and ground heaving processes.

We quantified confidence intervals (CIs) for T-scores for the lumbar spine and hip and determined the practical effect (impact on diagnosis) of variability around the T-score cutpoint of -2.5. Using precision data from the literature for GE Lunar Prodigy dual-energy X-ray absorptiometry (DXA) systems, the 95% CI for the T-score was ±0.23 at the lumbar spine (L1-L4), ± 0.20 at the total hip, and ±0.41 at the femoral neck. Thus, T-score variations of ±0.23 or less at the spine, ±0.20 at the total hip, and ±0.41 at the femoral neck are not statistically significant. When diagnosing osteoporosis, T-scores in the interval -2.3 to -2.7 for spine or total hip (after rounding to conform to guidelines from the International Society for Clinical Densitometry) and -2.1 to -2.9 for femoral neck are not statistically different from -2.5. Better precision values resulted in smaller 95% CIs. This concept was applied to actual clinical data using Hologic DXA systems. The study cohort comprised 2388 white women with either normal or osteopenic spines in whom the densitometric diagnosis of osteoporosis would be determined by hip T-scores. When evaluating actual patient T-scores in the range -2.5 ± 95% CI, we found that the diagnosis was indeterminate in approximately 12% of women when T-scores for femoral neck were used and in 4% of women when T-scores for total hip were used, with uncertainty as to whether the classification was osteopenia or osteoporosis. We conclude that precision influences the variability around T-scores and that this variability affects the reliability of diagnostic classification.