{"id":103159,"date":"2026-09-10T00:25:24","date_gmt":"2026-09-09T16:25:24","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/103159.html"},"modified":"2026-09-10T00:25:24","modified_gmt":"2026-09-09T16:25:24","slug":"%e5%bc%82%e5%b8%b8%e6%a3%80%e6%b5%8b%e7%ae%97%e6%b3%95%e5%88%9d%e8%af%86%ef%bc%9a%e4%bb%8e-3-sigma-%e7%bb%9f%e8%ae%a1%e5%ad%a6%e5%88%b0%e5%8a%a8%e6%80%81%e6%97%b6%e9%97%b4%e8%a7%84%e6%95%b4-dtw","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/103159.html","title":{"rendered":"\u5f02\u5e38\u68c0\u6d4b\u7b97\u6cd5\u521d\u8bc6\uff1a\u4ece 3-Sigma \u7edf\u8ba1\u5b66\u5230\u52a8\u6001\u65f6\u95f4\u89c4\u6574 DTW"},"content":{"rendered":"<h2>\u5f02\u5e38\u68c0\u6d4b\u7b97\u6cd5\u521d\u8bc6&#xff1a;\u4ece 3-Sigma \u7edf\u8ba1\u5b66\u5230\u52a8\u6001\u65f6\u95f4\u89c4\u6574 DTW<\/h2>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260909162522-6aa18872d8980.webp\" alt=\"\u5c01\u9762\u4fe1\u606f\u56fe\" \/><\/p>\n<p>\u5728\u667a\u80fd\u8fd0\u7ef4&#xff08;AIOps&#xff09;\u7684\u65f6\u5e8f\u76d1\u63a7\u4e2d&#xff0c;\u6211\u4eec\u7ecf\u5e38\u9047\u5230\u4e00\u7c7b\u975e\u5e38\u7279\u6b8a\u7684\u201c\u5f62\u6001\u5f02\u5e38&#xff08;Shape Anomaly&#xff09;\u201d&#xff1a;<\/p>\n<ul>\n<li>\u67d0\u6838\u5fc3\u4e1a\u52a1\u5728\u6bcf\u5929\u65e9\u4e0a 09:00 \u4f1a\u51c6\u65f6\u8fce\u6765\u65e9\u9ad8\u5cf0\u6d41\u91cf\u722c\u5761&#xff0c;\u8017\u65f6\u4ece 40ms \u4e0a\u6da8\u81f3 90ms&#xff1b;<\/li>\n<li>\u4f46\u4eca\u5929\u65e9\u9ad8\u5cf0\u7531\u4e8e\u5916\u90e8\u7f51\u7edc\u6ce2\u52a8&#xff0c;\u6d41\u91cf\u722c\u5761\u63a8\u8fdf\u5230\u4e86 09:20 \u624d\u53d1\u751f\u3002<\/li>\n<\/ul>\n<p>\u5982\u679c\u4f7f\u7528\u4f20\u7edf\u7684 3-Sigma \u6216 \u6b27\u6c0f\u8ddd\u79bb&#xff08;Euclidean Distance&#xff09; \u9010\u70b9\u5bf9\u9f50\u6bd4\u5bf9&#xff0c;\u7b97\u6cd5\u4f1a\u5728 09:0009:20 \u4e4b\u95f4\u75af\u72c2\u62a5\u8b66&#xff08;\u56e0\u4e3a\u6b64\u65f6\u5b9e\u9645\u503c\u8fdc\u4f4e\u4e8e\u5386\u53f2\u671f\u671b\u5747\u503c&#xff09;&#xff0c;\u5e76\u5728 09:2009:40 \u518d\u6b21\u75af\u72c2\u62a5\u8b66&#xff08;\u5b9e\u9645\u503c\u8fdc\u9ad8\u4e8e\u5386\u53f2\u540c\u671f&#xff09;\u3002\u4f46\u4ece\u4e1a\u52a1\u5168\u5c40\u6765\u770b&#xff0c;\u8fd9\u53ea\u662f\u4e00\u4e2a\u5728\u65f6\u95f4\u8f74\u4e0a\u53d1\u751f\u4e86\u8f7b\u5fae\u62c9\u4f38\u6216\u76f8\u4f4d\u5ef6\u8fdf\u7684\u6b63\u5e38\u4e1a\u52a1\u5468\u671f&#xff0c;\u6839\u672c\u4e0d\u662f\u7cfb\u7edf\u6545\u969c\u3002<\/p>\n<p>\u4f20\u7edf\u7684\u9010\u70b9\u5bf9\u9f50\u7b97\u6cd5\u65e0\u6cd5\u5904\u7406\u65f6\u95f4\u8f74\u4e0a\u7684\u5c40\u90e8\u5f62\u53d8\u4e0e\u901f\u5ea6\u6f02\u79fb\u3002\u5f15\u5165\u6e90\u81ea\u8bed\u97f3\u8bc6\u522b\u9886\u57df\u7684 \u52a8\u6001\u65f6\u95f4\u89c4\u6574\u7b97\u6cd5&#xff08;Dynamic Time Warping, DTW&#xff09;&#xff0c;\u662f\u89e3\u51b3\u65f6\u5e8f\u5f62\u6001\u76f8\u4f3c\u5ea6\u8ba1\u7b97\u4e0e\u81ea\u9002\u5e94\u5f02\u5e38\u68c0\u6d4b\u7684\u7834\u5c40\u5229\u5668\u3002<\/p>\n<h3>\u6b27\u6c0f\u8ddd\u79bb vs \u52a8\u6001\u65f6\u95f4\u89c4\u6574&#xff08;DTW&#xff09;<\/h3>\n<p>\u3010\u6b27\u6c0f\u8ddd\u79bb (Euclidean Distance &#8211; \u4e00\u5bf9\u4e00\u786c\u5bf9\u9f50)\u3011<br \/>\n\u5e8f\u5217 A (\u4eca\u65e5\u65f6\u5e8f):   o\u2500\u2500\u2500o\u2500\u2500\u2500o\u2500\u2500\u2500\u2500\u2500\u2500\u2500o\u2500\u2500\u2500o (\u6ce2\u5cf0\u5728\u7b2c 4 \u70b9)<br \/>\n                     \u2502   \u2502   \u2502       \u2502   \u2502<br \/>\n\u5e8f\u5217 B (\u5386\u53f2\u57fa\u7ebf):   o\u2500\u2500\u2500o\u2500\u2500\u2500\u2500\u2500\u2500\u2500o\u2500\u2500\u2500o\u2500\u2500\u2500o (\u6ce2\u5cf0\u5728\u7b2c 3 \u70b9)<br \/>\n&#061;&#061;&gt; \u7f3a\u9677: \u5f3a\u884c\u5728\u76f8\u540c\u65f6\u95f4\u6233\u6c42\u5dee\u503c\u5e73\u65b9\u548c&#xff0c;\u65f6\u95f4\u8f74\u8f7b\u5fae\u5e73\u79fb\u5bfc\u81f4\u8bef\u5dee\u6025\u5267\u653e\u5927<\/p>\n<p>\u3010DTW \u52a8\u6001\u65f6\u95f4\u89c4\u6574 (\u4e00\u5bf9\u591a\u5f39\u6027\u626d\u66f2\u5bf9\u9f50)\u3011<br \/>\n\u5e8f\u5217 A (\u4eca\u65e5\u65f6\u5e8f):   o\u2500\u2500\u2500o\u2500\u2500\u2500o\u2500\u2500\u2500\u2500\u2500\u2500\u2500o\u2500\u2500\u2500o<br \/>\n                      \\\\   \\\\   \\\\     \/   \/<br \/>\n\u5e8f\u5217 B (\u5386\u53f2\u57fa\u7ebf):     o\u2500\u2500\u2500o\u2500\u2500\u2500o\u2500\u2500\u2500o\u2500\u2500\u2500o<br \/>\n&#061;&#061;&gt; \u4f18\u52bf: \u5141\u8bb8\u5728\u65f6\u95f4\u8f74\u4e0a\u201c\u538b\u7f29\u6216\u62c9\u4f38\u201d&#xff0c;\u627e\u5230\u4e24\u4e2a\u65f6\u5e8f\u4e4b\u95f4\u8ddd\u79bb\u6700\u5c0f\u7684\u6700\u4f18\u89c4\u6574\u8def\u5f84<\/p>\n<h3>DTW \u7b97\u6cd5\u7684\u6838\u5fc3\u6570\u5b66\u539f\u7406<\/h3>\n<p>\u7ed9\u5b9a\u4e24\u4e2a\u65f6\u5e8f\u5e8f\u5217 $X &#061; (x_1, x_2, \\\\dots, x_n)$ \u548c $Y &#061; (y_1, y_2, \\\\dots, y_m)$&#xff1a;<\/p>\n<li>\u6784\u5efa\u4e00\u4e2a $n \\\\times m$ \u7684\u70b9\u95f4\u8ddd\u79bb\u77e9\u9635 $D$&#xff0c;\u5176\u4e2d $D(i, j) &#061; |x_i &#8211; y_j|$ \u6216 $(x_i &#8211; y_j)^2$&#xff1b;<\/li>\n<li>\u5bfb\u627e\u4e00\u6761\u89c4\u6574\u8def\u5f84 $W &#061; (w_1, w_2, \\\\dots, w_k)$&#xff0c;\u6ee1\u8db3\u8fb9\u754c\u6761\u4ef6\u3001\u5355\u8c03\u6027\u4e0e\u8fde\u7eed\u6027\u7ea6\u675f&#xff1b;<\/li>\n<li>\u4f7f\u7528\u52a8\u6001\u89c4\u5212&#xff08;Dynamic Programming&#xff09;\u8ba1\u7b97\u7d2f\u79ef\u8ddd\u79bb\u77e9\u9635 $\\\\gamma(i, j)$&#xff1a;<\/li>\n<p>$$\\\\gamma(i, j) &#061; D(i, j) &#043; \\\\min \\\\Big( \\\\gamma(i-1, j), , \\\\gamma(i, j-1), , \\\\gamma(i-1, j-1) \\\\Big)$$<\/p>\n<p>\u6700\u7ec8 $\\\\gamma(n, m)$ \u5373\u4e3a\u4e24\u4e2a\u65f6\u5e8f\u5728\u6700\u4f18\u65f6\u95f4\u626d\u66f2\u4e0b\u7684\u6700\u5c0f\u5168\u5c40\u5f62\u6001\u8ddd\u79bb\u3002<\/p>\n<h3>\u6838\u5fc3\u5b9e\u73b0&#xff1a;\u57fa\u4e8e Python \u7684\u5feb\u901f DTW \u5f62\u6001\u5f02\u5e38\u68c0\u6d4b\u5668<\/h3>\n<p>\u6807\u51c6 DTW \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a $O(n \\\\cdot m)$\u3002\u5728\u751f\u4ea7\u65f6\u5e8f\u76d1\u63a7\u4e2d&#xff0c;\u901a\u5e38\u5f15\u5165 Sakoe-Chiba \u7ea6\u675f\u7a97\u53e3&#xff08;Warping Window Band&#xff09; \u5c06\u8ba1\u7b97\u590d\u6742\u5ea6\u4f18\u5316\u81f3\u63a5\u8fd1\u7ebf\u6027 $O(n \\\\cdot w)$&#xff1a;<\/p>\n<p>import numpy as np<br \/>\nfrom dataclasses import dataclass<br \/>\nfrom typing import List, Tuple<\/p>\n<p>&#064;dataclass<br \/>\nclass DtwAnomalyResult:<br \/>\n    is_anomaly: bool<br \/>\n    dtw_distance: float<br \/>\n    threshold: float<br \/>\n    warping_path_length: int<\/p>\n<p>class FastDtwDetector:<br \/>\n    def __init__(self, window_size: int &#061; 5, distance_threshold: float &#061; 15.0):<br \/>\n        &#034;&#034;&#034;<br \/>\n        window_size: Sakoe-Chiba \u5e26\u5bbd\u9650\u5236 (\u5141\u8bb8\u7684\u6700\u5927\u65f6\u95f4\u6f02\u79fb\u6b65\u6570)<br \/>\n        distance_threshold: \u5f62\u6001\u504f\u79bb\u62a5\u8b66\u9608\u503c<br \/>\n        &#034;&#034;&#034;<br \/>\n        self.w &#061; window_size<br \/>\n        self.threshold &#061; distance_threshold<\/p>\n<p>    def compute_dtw_distance(self, s1: np.ndarray, s2: np.ndarray) -&gt; float:<br \/>\n        n, m &#061; len(s1), len(s2)<br \/>\n        w &#061; max(self.w, abs(n &#8211; m))<\/p>\n<p>        # \u521d\u59cb\u5316\u7d2f\u79ef\u4ee3\u4ef7\u77e9\u9635<br \/>\n        dtw_matrix &#061; np.full((n &#043; 1, m &#043; 1), np.inf)<br \/>\n        dtw_matrix[0, 0] &#061; 0.0<\/p>\n<p>        for i in range(1, n &#043; 1):<br \/>\n            # \u4ec5\u5728\u5bf9\u89d2\u7ebf\u9644\u8fd1\u5e26\u5bbd\u5185\u8ba1\u7b97<br \/>\n            for j in range(max(1, i &#8211; w), min(m &#043; 1, i &#043; w &#043; 1)):<br \/>\n                cost &#061; (s1[i &#8211; 1] &#8211; s2[j &#8211; 1]) ** 2<br \/>\n                dtw_matrix[i, j] &#061; cost &#043; min(<br \/>\n                    dtw_matrix[i &#8211; 1, j],     # \u63d2\u5165 (\u65f6\u95f4\u62c9\u4f38)<br \/>\n                    dtw_matrix[i, j &#8211; 1],     # \u5220\u9664 (\u65f6\u95f4\u538b\u7f29)<br \/>\n                    dtw_matrix[i &#8211; 1, j &#8211; 1]  # \u5339\u914d<br \/>\n                )<\/p>\n<p>        return float(np.sqrt(dtw_matrix[n, m]))<\/p>\n<p>    def evaluate_shape_anomaly(self, current_series: List[float], baseline_series: List[float]) -&gt; DtwAnomalyResult:<br \/>\n        s1 &#061; np.array(current_series, dtype&#061;float)<br \/>\n        s2 &#061; np.array(baseline_series, dtype&#061;float)<\/p>\n<p>        # Z-Score \u6807\u51c6\u5316&#xff0c;\u6d88\u9664\u6574\u4f53\u91cf\u7eb2\u4e0e\u7edd\u5bf9\u503c\u504f\u79fb&#xff0c;\u4e13\u6ce8\u4e8e\u201c\u5f62\u6001\u66f2\u7ebf\u53d8\u5316\u201d<br \/>\n        s1_norm &#061; (s1 &#8211; np.mean(s1)) \/ (np.std(s1) &#043; 1e-6)<br \/>\n        s2_norm &#061; (s2 &#8211; np.mean(s2)) \/ (np.std(s2) &#043; 1e-6)<\/p>\n<p>        dist &#061; self.compute_dtw_distance(s1_norm, s2_norm)<br \/>\n        is_anomaly &#061; dist &gt; self.threshold<\/p>\n<p>        return DtwAnomalyResult(<br \/>\n            is_anomaly&#061;is_anomaly,<br \/>\n            dtw_distance&#061;round(dist, 2),<br \/>\n            threshold&#061;self.threshold,<br \/>\n            warping_path_length&#061;len(s1)<br \/>\n        )<\/p>\n<p># \u6d4b\u8bd5\u9a8c\u8bc1<br \/>\ndetector &#061; FastDtwDetector(window_size&#061;4, distance_threshold&#061;8.0)<\/p>\n<p># \u57fa\u51c6\u5e8f\u5217&#xff1a;\u6807\u51c6\u722c\u5761\u6ce2\u5f62<br \/>\nbaseline &#061; [10, 12, 15, 45, 80, 95, 100, 98, 85, 40, 20, 10]<\/p>\n<p># \u6d4b\u8bd5\u7528\u4f8b 1&#xff1a;\u65f6\u95f4\u6ede\u540e 2 \u4e2a\u5468\u671f\u7684\u6b63\u5e38\u722c\u5761&#xff08;\u7eaf\u65f6\u95f4\u8f74\u62c9\u4f38&#xff0c;\u5f62\u6001\u4e00\u81f4&#xff09;<br \/>\nlagged_normal &#061; [10, 10, 10, 13, 16, 46, 82, 96, 101, 97, 83, 38]<br \/>\nres1 &#061; detector.evaluate_shape_anomaly(lagged_normal, baseline)<br \/>\nprint(f&#034;\u65f6\u79fb\u6b63\u5e38\u6ce2\u5f62\u68c0\u6d4b: \u5f02\u5e38&#061;{res1.is_anomaly}, DTW\u8ddd\u79bb&#061;{res1.dtw_distance} (\u6b27\u6c0f\u8ddd\u79bb\u6781\u9ad8\u4f46DTW\u8bc6\u522b\u4e3a\u6b63\u5e38)&#034;)<\/p>\n<p># \u6d4b\u8bd5\u7528\u4f8b 2&#xff1a;\u7a81\u53d1\u66b4\u8dcc\u7578\u5f62\u6ce2&#xff08;\u4e2d\u9014\u65ad\u5d16\u5f0f\u4e0b\u8dcc&#xff0c;\u5f62\u6001\u4e25\u91cd\u7578\u53d8&#xff09;<br \/>\nabnormal_shape &#061; [10, 12, 15, 45, 12, 10, 10, 15, 85, 40, 20, 10]<br \/>\nres2 &#061; detector.evaluate_shape_anomaly(abnormal_shape, baseline)<br \/>\nprint(f&#034;\u7578\u5f62\u6ce2\u5f62\u68c0\u6d4b: \u5f02\u5e38&#061;{res2.is_anomaly}, DTW\u8ddd\u79bb&#061;{res2.dtw_distance} (\u6210\u529f\u89e6\u53d1\u62a5\u8b66)&#034;)<\/p>\n<h3>\u5728 AIOps \u751f\u4ea7\u73af\u5883\u4e2d\u7684\u5e94\u7528\u573a\u666f<\/h3>\n<li>\u5927\u4fc3\u6d41\u91cf\u722c\u5761\u81ea\u9002\u5e94\u8bc6\u522b&#xff1a;\u5728\u5927\u4fc3\u9884\u70ed\u671f&#xff0c;\u5404\u4e1a\u52a1\u7ebf\u6d41\u91cf\u722c\u5761\u65f6\u95f4\u5f80\u5f80\u524d\u540e\u76f8\u5dee\u6570\u5206\u949f\u3002DTW \u80fd\u81ea\u52a8\u81ea\u9002\u5e94\u8fd9\u79cd\u5fae\u5c0f\u76f8\u4f4d\u6f02\u79fb&#xff0c;\u907f\u514d\u56e0\u65f6\u95f4\u672a\u4e25\u683c\u5bf9\u9f50\u4ea7\u751f\u6d77\u91cf\u865a\u5047\u8bef\u62a5\u3002<\/li>\n<li>\u6279\u5904\u7406 Job \u8017\u65f6\u66f2\u7ebf\u8bca\u65ad&#xff1a;\u79bb\u7ebf\u5927\u6570\u636e\u4efb\u52a1\u7531\u4e8e\u6bcf\u65e5\u6570\u636e\u91cf\u4e0d\u540c&#xff0c;\u6267\u884c\u8017\u65f6\u66f2\u7ebf\u5b58\u5728\u5929\u7136\u62c9\u4f38\u3002DTW 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