## 1 Introduction  
Concept drift is a phenomenon in which data distribution changes over time. It often appears in time series data. In today's world, a large amount of data are generated every moment, and concept drift phenomena are also emerging endlessly, such as the decline in product reputation caused by emergencies, public opinion drift, etc. Decrease in sales of certain types of goods due to changes in living habits, etc. Traditional machine learning models assume that the data distribution is stable. The occurrence of concept drift greatly reduces the performance of the original learning model. Therefore, rapid detection or response to concept drift is crucial to ensure the high learning efficiency of the classifier. Active detection mechanisms represent one of the effective strategies for addressing concept drift. In this approach, a classifier employs a drift detector to discern shifts in the data stream's underlying concepts. Upon detecting a drift risk, the drift detector promptly alerts the classifier, enabling timely adjustments. A prevalent approach for drift detection involves monitoring the classification performance of the model. According to the Probably Approximately Correct (PAC) theory [1], classifier performance tends to stabilize with increased learning time under stable conditions. Therefore, significant changes in the error rate of the base classifier can be viewed as indicators of concept drift. Concept drift typically arises from changes in the underlying data distribution. While monitoring the underlying data distribution facilitates a deeper understanding of concept drift, such methods are often complex and unsuitable for online environments dealing with massive data scales [2]. Consequently, drift detection methods based on classifier performance monitoring are frequently favored for their expedited processing speed and practicality. To date, numerous drift detection algorithms have been proposed, encompassing both classic and more recent methods. Classic approaches include the Drift Detection Method (DDM) [3], Early Drift Detection Method (EDDM) [4], and Adaptive Sliding Window (ADWIN) [5]. Additionally, newer algorithms have emerged with notable efficacy, such as the Online and Non-Parametric Drift Detection Methods Based on Hoeffding's Bounds (HDDM) [2] and the Fast Hoeffding Drift Detection Method (FHDDM) [6]. Recent advancements include the Multi-level Weighted Drift Detection Method (MWDDM) [7], and the Group Drift Detection Method (GDDM) [8], among others. However, many existing drift detection methods encounter several common challenges: (1) Most current drift detection methods use the same detection approach for different data streams, which limits the flexibility and generalizability of drift detection; (2) Most current drift detection methods face a trade-off between false positives and detection speed, which affects the classification performance of base classifiers. Thus, to address these key concerns and optimize the performance of drift detection, we introduced a unique solution and a novel drift detection method. This method tailors its strategies to different data streams, considering their unique characteristics. By doing so, it aids classifiers in achieving superior classification performance. The main contributions of this article include four aspects:  
* **Fast Variance Estimation Strategy for Small-scale Sliding Windows**: We introduce a swift variance estimation strategy tailored for small-scale sliding windows that addresses the issue of small sample effects. This approach ensures both speed and flexibility in mutation drift detection. * **Variance Feedback Strategy**: We propose a variance feedback strategy that utilizes the variance calculated through the estimation strategy. This feedback dynamically adjusts the weighting of window data instances within the drift detector, amplifying the window mean. This enhancement significantly boosts detection speed while maintaining low false positive rates.