Non-intrusive load monitoring is an important development direction of load monitoring, and event detection is the key research content of non-intrusive load monitoring. Multidimensional signals can provide multi-source information compared with one-dimensional signals. If the correlation between different dimensions of signals is large, the detection accuracy can be improved. In this paper, the decision functions of BIC, CUSUM and GLRT are deduced for the first time based on statistical hypothesis, and two-dimensional signals are simulated to compare the results of the three algorithms. The simulation results show that adding the appropriate second dimension signal can improve the overall detection accuracy, and the applicable conditions of different algorithms are obtained. That is, CUSUM algorithm is suitable for high threshold detection, and GLRT algorithm is suitable for low threshold detection.