Train and Test Time Series Statistical Process Control Anomaly Detector

This example uses:

Open Live Script

Load the file sineWaveAnomalyData.mat, which contains two sets of synthetic three-channel sinusoidal signals.

sineWaveNormal contains 10 sinusoids of stable frequency and amplitude. Each signal has a series of small-amplitude impact-like imperfections. The signals have different lengths and initial phases. sineWaveAbnormal contains the same sinusoids as sineWaveNormal, but also includes anomalous data.

load sineWaveAnomalyData.mat
s1 = 3;

Plot input signals

Plot the first three anomalous input signals.

tiledlayout("vertical")
ax = zeros(s1,1);
for kj = 1:s1
    ax(kj) = nexttile;
    plot(sineWaveAbnormal{kj})
    title("Anomalous Signals")
end

Figure contains 3 axes objects. Axes object 1 with title Anomalous Signals contains 3 objects of type line. Axes object 2 with title Anomalous Signals contains 3 objects of type line. Axes object 3 with title Anomalous Signals contains 3 objects of type line.

sineWaveAbnormal contains three signals, all of the same length. Each signal in the set has one or more anomalies.

  • All channels of the first signal have an abrupt change in frequency that lasts for a finite time.

  • The second signal has a finite-duration amplitude change in one of its channels.

  • The third signal has spikes at random times in all channels.

Create detector

Use the timeSeriesSpcAD command to create a detector with 3 channels that tracks the exponentially weighted mean average of the data.

detector_tsspc = timeSeriesSpcAD(3, Method="ewma",WindowLength=10);

Train detector

Train the detector using normal data and default settings.

detector_tsspc = train(detector_tsspc,sineWaveNormal)
detector_tsspc = 
  TimeSeriesSPCDetector with properties:

       NumChannels: 3
      WindowLength: 10
            Stride: 10
            Method: "ewma"
            Lambda: 0.4000
    DetectionRules: "n1"
             Level: 3
        CenterLine: [0.0056 -0.0030 -2.9131e-04]
     StandardError: [0.3533 0.3504 0.3538]
              Mean: [0.0056 -0.0030 -2.9131e-04]
             Sigma: [0.7067 0.7008 0.7075]
         MeanRange: [0.1533 0.3004 0.0925]
         IsTrained: 1

Plot detection results

Plot the detection results for sineWaveAbnormal(2)

figure(1);
detector_tsspc.plot(sineWaveAbnormal{2})

Figure contains 3 axes objects. Axes object 1 with title Anomalies, xlabel Samples, ylabel Signal contains 7 objects of type patch, line. These objects represent Labeled Anomalies, Raw Signal (Channel 3), Raw Signal (Channel 2), Raw Signal (Channel 1), Detected Anomalies (Channel 3), Detected Anomalies (Channel 2), Detected Anomalies (Channel 1). Axes object 2 with title EWMA Control Chart, xlabel Window Start Index, ylabel Batch-Means Signal contains 5 objects of type line, constantline. One or more of the lines displays its values using only markers These objects represent Batch-Means Signal (Channel 3), Batch-Means Signal (Channel 2), Batch-Means Signal (Channel 1), Detected Anomalies (across all channels), UCL, CL, LCL. Axes object 3 with title Anomaly Scores, xlabel Window Start Index, ylabel Score contains 3 objects of type stem, line, constantline. One or more of the lines displays its values using only markers These objects represent Anomaly Scores, Detected Anomalies.

The plot shows that the detector successfully detects the anomaly.

Plot histogram

Plot the histogram of the anomaly scores.

figure(2);
detector_tsspc.plotHistogram(sineWaveNormal{2}, sineWaveAbnormal{2})

Figure contains an axes object. The axes object with title Anomaly Score Distribution, xlabel Anomaly Scores, ylabel Probability (Histogram) contains 3 objects of type histogram, constantline. These objects represent Anomaly Scores 1, Anomaly Scores 2.

See Also

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