Detection of Shifts in GPS Measurements for a Long-Span Bridge Using CUSUM Chart

Timely and correctly evaluating the quality of Global Positioning System (GPS) data is essential for reduction in the number of false alarms and missed detection of a GPS-based bridge deformation monitoring system. This paper investigates how to use the statistical process control technique, known as the cumulative sum (CUSUM) chart, for the detection of small but persistent shifts in the high-rate GPS carrier-phase measurements. First, a mathematical model for the shift detection based on the continuous hypothesis testing is established. The main features and implementation procedure of the CUSUM chart for the shift detection are then summarized, and the corresponding parameter selection method is discussed in detail. To meet the normality requirement of the CUSUM chart, a novel method that transfers the data to the Q-statistic by the estimated cumulative distribution functions is proposed according to the probability integral transform theory. This is followed by a simulation carried out to evaluate the detection performance of the CUSUM chart and exploit its advantages to the commonly used Shewhart chart for the high-rate GPS monitoring data with different shift sizes. Experimental results have showed that the CUSUM chart is sensitive to small persistent shifts compared to the Shewhart chart although it has a delay problem. The integration of CUSUM chart and Shewhart chart would be a reliable approach for the shift detection. Finally, an on-site dynamic monitoring experiment is carried out on a long-span bridge to validate the proposed approach’s effectiveness in detecting an actual deformation shift, and the experimental results proved to be very encouraging.