This paper attempts to determine the time delay between the sequence of system behaviors and that of influencing factors on system behaviors. Firstly, a new concept was coined called the representative subsequence (RS), and the RSs of influencing factors were selected. Next, a new geometric similarity grey relational grade (GRG) model was set up to compute the time delay of each influencing factor RS relative to the sequence of system behaviors. On this basis, the time-delay corresponding to the maximum GRG was taken as the desired time-delay. The verification on actual data shows that the concept and extraction rule of the RS are feasible, and our geometric similarity GRG model outperforms the conventional model in predicting time delay. The research findings lay the basis for grey prediction modelling of time sequences and optimizing the prediction effect of grey prediction models.

The gas holdup of oil-gas-water three-phase flow is intimately connected with stream pattern, flow rate and tension. Regarding the deviation problem in the measurement of fiber optic probe gas holdup in oil-gas-water three-phase flow, this paper presents an evaluation method to measure the gas holdup of fiber optic probe based on data fusion. Firstly, the method applies the Grubbs criterion to eliminate the omission errors in the gas holdup data collected by a single fiber optic probe in a period of time. Secondly, it acquires the optimal value of the fiber optic probe in a certain time quantum by estimating the data collected by the fiber optic probe in batches. After obtaining the optimal value of the data collected by the four fiber optic probes in the downhole optical fiber probe array, the author adopts the self-adaptive weighted fusion algorithm, fuses data according to the optimization principle of the total minimum mean squared error and calculates the accurate value of the gas holdup of oil-gas-water three-phase flow in the wellbore in a certain time quantum. The experimental results show that this kind of method can improve the measurement accuracy of gas holdup and achieve more accurate estimate in oil-gas-water three-phase flow.