Chillers, as primary energy consumers in heating, ventilating, and air conditioning (HVAC) systems, play a critical role in maintaining indoor comfort. However, traditional data-driven methods often fail to recognize chiller incipient faults, leading to operational disruptions and increased energy consumption. To address this challenge, this article proposes an innovative chiller incipient fault detection method based on local anomaly kernel entropy component analysis (LOKECA). This method selects kernel entropy component analysis (KECA) for feature extraction and uses local anomaly factor (LOF) as a statistic for incipient fault detection. By introducing the mean square error (MSE) to analyze variable data in the principal component subspace and residual subspace. In addition, this method also utilizes a Bayesian inference mechanism to fuse detection results to enhance robustness. The innovation of our method is that it adopts k-means clustering to integrate the chiller's operating conditions to reduce the influence of different operating conditions on the detection results. Notably, our approach exhibits superior performance in identifying chiller incipient faults. For most of the incipient faults, PCA, KECA and SFA only have a detection rate of about 60 %, but the method has a detection rate of up to 90 %, which can identify the incipient faults well. Especially for RL incipient faults, the detection rate is improved by 27.5 %-60.5 % compared to the other three algorithms, which is a significant improvement. The validity and superiority of the method were validated by the ASHRAE RP-1043 chiller multi-condition dataset. The findings underscore its potential in enhancing chiller fault detection, consequently optimizing HVAC system performance and longevity.