Custom Anomaly Detection

Warning! This page documents an old version of Kapacitor, which is no longer actively developed. Kapacitor v1.3 is the most recent stable version of Kapacitor.

Everyone has their own anomaly detection algorithm, so we have built Kapacitor to integrate easily with which ever algorithm fits your domain. Kapacitor calls these custom algorithms UDFs for User Defined Functions. This guide will walk through the necessary steps for writing and using your own UDFs within Kapacitor.

If you haven’t already, we recommend following the getting started guide for Kapacitor prior to continuing.

3D Printing

If you own or have recently purchased a 3D printer, you may know that 3D printing requires the environment to be at certain temperatures in order to ensure quality prints. Prints can also take a long time (some can take more than 24 hours), so you can’t just watch the temperature graphs the whole time to make sure the print is going well. Also, if a print goes bad early, you want to make sure and stop it so that you can restart it, and not waste materials on continuing a bad print.

Due to the physical limitations of 3D printing, the printer software is typically designed to keep the temperatures within certain tolerances. For the sake of argument, let’s say that you don’t trust the software to do it’s job (or want to create your own), and want to be alerted when the temperature reaches an abnormal level.

There are three temperatures when it comes to 3D printing:

  1. The temperature of the hot end (where the plastic is melted before being printed).
  2. The temperature of the bed (where the part is being printed).
  3. The temperature of the ambient air (the air around the printer).

All three of these temperatures affect the quality of the print (some being more important than others), but we want to make sure and track all of them.

To keep our anomaly detection algorithm simple, let’s compute a p-value for each window of data we receive, and then emit a single data point with that p-value. To compute the p-value, we will use Welch’s t-test. For a null hypothesis, we will state that a new window is from the same population as the historical windows. If the p-value drops low enough, we can reject the null hypothesis and conclude that the window must be from something different than the historical data population, or an anomaly. This is an oversimplified approach, but we are learning how to write UDFs, not statistics.

Writing a UDF

Now that we have an idea of what we want to do, let’s understand how Kapacitor wants to communicate with our process. From the UDF README we learn that Kapacitor will spawn a process called an agent. The agent is responsible for describing what options it has, and then initializing itself with a set of options. As data is received by the UDF, the agent performs its computation and then returns the resulting data to Kapacitor. All of this communication occurs over STDIN and STDOUT using protocol buffers. As of this writing, Kapacitor has agents implemented in Go and Python that take care of the communication details and expose an interface for doing the actual work. For this guide, we will be using the Python agent.

The Handler Interface

Here is the Python handler interface for the agent:

# The Agent calls the appropriate methods on the Handler as requests are read off STDIN.
#
# Throwing an exception will cause the Agent to stop and an ErrorResponse to be sent.
# Some *Response objects (like SnapshotResponse) allow for returning their own error within the object itself.
# These types of errors will not stop the Agent and Kapacitor will deal with them appropriately.
#
# The Handler is called from a single thread, meaning methods will not be called concurrently.
#
# To write Points/Batches back to the Agent/Kapacitor use the Agent.write_response method, which is thread safe.
class Handler(object):
    def info(self):
        pass
    def init(self, init_req):
        pass
    def snapshot(self):
        pass
    def restore(self, restore_req):
        pass
    def begin_batch(self):
        pass
    def point(self):
        pass
    def end_batch(self, end_req):
        pass

The Info Method

Let’s start with the info method. When Kapacitor starts up it will call info and expect in return some information about how this UDF behaves. Specifically, Kapacitor expects the kind of edge the UDF wants and provides.

Remember: within Kapacitor, data is transported in streams or batches, so the UDF must declare what it expects.

In addition, UDFs can accept certain options so that they are individually configurable. The info response can contain a list of options, their names, and expected arguments.

For our example UDF, we need to know three things:

  1. The field to operate on.
  2. The size of the historical window to keep.
  3. The significance level or alpha being used.

Below we have the implementation of the info method for our handler that defines the edge types and options available:

...
    def info(self):
        """
        Respond with which type of edges we want/provide and any options we have.
        """
        response = udf_pb2.Response()

        # We will consume batch edges aka windows of data.
        response.info.wants = udf_pb2.BATCH
        # We will produce single points of data aka stream.
        response.info.provides = udf_pb2.STREAM

        # Here we can define options for the UDF.
        # Define which field we should process.
        response.info.options['field'].valueTypes.append(udf_pb2.STRING)

        # Since we will be computing a moving average let's make the size configurable.
        # Define an option 'size' that takes one integer argument.
        response.info.options['size'].valueTypes.append(udf_pb2.INT)

        # We need to know the alpha level so that we can ignore bad windows.
        # Define an option 'alpha' that takes one double valued argument.
        response.info.options['alpha'].valueTypes.append(udf_pb2.DOUBLE)

        return response
...

When Kapacitor starts, it will spawn our UDF process and request the info data and then shutdown the process. Kapacitor will remember this information for each UDF. This way, Kapacitor can understand the available options for a given UDF before its executed inside of a task.

The Init Method

Next let’s implement the init method, which is called once the task starts executing. The init method receives a list of chosen options, which are then used to configure the handler appropriately. In response, we indicate whether the init request was successful, and, if not, any error messages if the options were invalid.

...
    def init(self, init_req):
        """
        Given a list of options initialize this instance of the handler
        """
        success = True
        msg = ''
        size = 0
        for opt in init_req.options:
            if opt.name == 'field':
                self._field = opt.values[0].stringValue
            elif opt.name == 'size':
                size = opt.values[0].intValue
            elif opt.name == 'alpha':
                self._alpha = opt.values[0].doubleValue

        if size <= 1:
            success = False
            msg += ' must supply window size > 1'
        if self._field == '':
            success = False
            msg += ' must supply a field name'
        if self._alpha == 0:
            success = False
            msg += ' must supply an alpha value'

        # Initialize our historical window
        # We will define MovingStats in the next step
        self._history = MovingStats(size)

        response = udf_pb2.Response()
        response.init.success = success
        response.init.error = msg[1:]

        return response
...

When a task starts, Kapacitor spawns a new process for the UDF and calls init, passing any specified options from the TICKscript. Once initialized, the process will remain running and Kapacitor will begin sending data as it arrives.

The Batch and Point Methods

Our task wants a batch edge, meaning it expects to get data in batches or windows. To send a batch of data to the UDF process, Kapacitor first calls the begin_batch method, which indicates that all subsequent points belong to a batch. Once the batch is complete, the end_batch method is called with some metadata about the batch.

At a high level, this is what our UDF code will do for each of the begin_batch, point, and end_batch calls:

  • begin_batch – mark the start of a new batch and initialize a structure for it
  • point – store the point
  • end_batch – perform the t-test and then update the historical data

The Complete UDF Script

What follows is the complete UDF implementation with our info, init, and batching methods (as well as everything else we need).


from agent import Agent, Handler
from scipy import stats
import math
import udf_pb2
import sys

class TTestHandler(Handler):
    """
    Keep a rolling window of historically normal data
    When a new window arrives use a two-sided t-test to determine
    if the new window is statistically significantly different.
    """
    def __init__(self, agent):
        self._agent = agent

        self._field = ''
        self._history = None

        self._batch = None

        self._alpha = 0.0

    def info(self):
        """
        Respond with which type of edges we want/provide and any options we have.
        """
        response = udf_pb2.Response()
        # We will consume batch edges aka windows of data.
        response.info.wants = udf_pb2.BATCH
        # We will produce single points of data aka stream.
        response.info.provides = udf_pb2.STREAM

        # Here we can define options for the UDF.
        # Define which field we should process
        response.info.options['field'].valueTypes.append(udf_pb2.STRING)

        # Since we will be computing a moving average let's make the size configurable.
        # Define an option 'size' that takes one integer argument.
        response.info.options['size'].valueTypes.append(udf_pb2.INT)

        # We need to know the alpha level so that we can ignore bad windows
        # Define an option 'alpha' that takes one double argument.
        response.info.options['alpha'].valueTypes.append(udf_pb2.DOUBLE)

        return response

    def init(self, init_req):
        """
        Given a list of options initialize this instance of the handler
        """
        success = True
        msg = ''
        size = 0
        for opt in init_req.options:
            if opt.name == 'field':
                self._field = opt.values[0].stringValue
            elif opt.name == 'size':
                size = opt.values[0].intValue
            elif opt.name == 'alpha':
                self._alpha = opt.values[0].doubleValue

        if size <= 1:
            success = False
            msg += ' must supply window size > 1'
        if self._field == '':
            success = False
            msg += ' must supply a field name'
        if self._alpha == 0:
            success = False
            msg += ' must supply an alpha value'

        # Initialize our historical window
        self._history = MovingStats(size)

        response = udf_pb2.Response()
        response.init.success = success
        response.init.error = msg[1:]

        return response

    def begin_batch(self):
        # create new window for batch
        self._batch = MovingStats(-1)

    def point(self, point):
        self._batch.update(point.fieldsDouble[self._field])

    def end_batch(self, batch_meta):
        pvalue = 1.0
        if self._history.n != 0:
            # Perform Welch's t test
            t, pvalue = stats.ttest_ind_from_stats(
                    self._history.mean, self._history.stddev(), self._history.n,
                    self._batch.mean, self._batch.stddev(), self._batch.n,
                    equal_var=False)


            # Send pvalue point back to Kapacitor
            response = udf_pb2.Response()
            response.point.time = batch_meta.tmax
            response.point.name = batch_meta.name
            response.point.group = batch_meta.group
            response.point.tags.update(batch_meta.tags)
            response.point.fieldsDouble["t"] = t
            response.point.fieldsDouble["pvalue"] = pvalue
            self._agent.write_response(response)

        # Update historical stats with batch, but only if it was normal.
        if pvalue > self._alpha:
            for value in self._batch._window:
                self._history.update(value)


class MovingStats(object):
    """
    Calculate the moving mean and variance of a window.
    Uses Welford's Algorithm.
    """
    def __init__(self, size):
        """
        Create new MovingStats object.
        Size can be -1, infinite size or > 1 meaning static size
        """
        self.size = size
        if not (self.size == -1 or self.size > 1):
            raise Exception("size must be -1 or > 1")


        self._window = []
        self.n = 0.0
        self.mean = 0.0
        self._s = 0.0

    def stddev(self):
        """
        Return the standard deviation
        """
        if self.n == 1:
            return 0.0
        return math.sqrt(self._s / (self.n - 1))

    def update(self, value):

        # update stats for new value
        self.n += 1.0
        diff = (value - self.mean)
        self.mean += diff / self.n
        self._s += diff * (value - self.mean)

        if self.n == self.size + 1:
            # update stats for removing old value
            old = self._window.pop(0)
            oldM = (self.n * self.mean - old)/(self.n - 1)
            self._s -= (old - self.mean) * (old - oldM)
            self.mean = oldM
            self.n -= 1

        self._window.append(value)

if __name__ == '__main__':
    # Create an agent
    agent = Agent()

    # Create a handler and pass it an agent so it can write points
    h = TTestHandler(agent)

    # Set the handler on the agent
    agent.handler = h

    # Anything printed to STDERR from a UDF process gets captured into the Kapacitor logs.
    print >> sys.stderr, "Starting agent for TTestHandler"
    agent.start()
    agent.wait()
    print >> sys.stderr, "Agent finished"

That was a lot, but now we are ready to configure Kapacitor to run our code. Create a scratch dir for working through the rest of this guide:

mkdir /tmp/kapacitor_udf
cd /tmp/kapacitor_udf

Save the above UDF python script into /tmp/kapacitor_udf/ttest.py.

Configuring Kapacitor for our UDF

Add this snippet to your Kapacitor configuration file (typically located at /etc/kapacitor/kapacitor.conf):

[udf]
[udf.functions]
    [udf.functions.tTest]
        # Run python
        prog = "/usr/bin/python2"
        # Pass args to python
        # -u for unbuffered STDIN and STDOUT
        # and the path to the script
        args = ["-u", "/tmp/kapacitor_udf/ttest.py"]
        # If the python process is unresponsive for 10s kill it
        timeout = "10s"
        # Define env vars for the process, in this case the PYTHONPATH
        [udf.functions.tTest.env]
            PYTHONPATH = "/tmp/kapacitor_udf/kapacitor/udf/agent/py"

In the configuration we called the function tTest. That is also how we will reference it in the TICKscript.

Notice that our Python script imported the Agent object, and we set the PYTHONPATH in the configuration. Clone the Kapacitor source into the tmp dir so we can point the PYTHONPATH at the necessary python code. This is typically overkill since it’s just two Python files, but it makes it easy to follow:

git clone https://github.com/influxdata/kapacitor.git /tmp/kapacitor_udf/kapacitor

Running Kapacitor with the UDF

Restart the Kapacitor daemon to make sure everything is configured correctly:

service kapacitor restart

Check the logs (/var/log/kapacitor/) to make sure you see a Listening for signals line and that no errors occurred. If you don’t see the line, it’s because the UDF process is hung and not responding. It should be killed after a timeout, so give it a moment to stop properly. Once stopped, you can fix any errors and try again.

The TICKscript

If everything was started correctly, then it’s time to write our TICKscript to use the tTest UDF method:

// This TICKscript monitors the three temperatures for a 3d printing job,
// and triggers alerts if the temperatures start to experience abnormal behavior.

// Define our desired significance level.
var alpha = 0.001

// Select the temperatures measurements
var data = stream
    |from()
        .measurement('temperatures')
    |window()
        .period(5m)
        .every(5m)

data
    //Run our tTest UDF on the hotend temperature
    |tTest()
        // specify the hotend field
        .field('hotend')
        // Keep a 1h rolling window
        .size(3600)
        // pass in the alpha value
        .alpha(alpha)
    |alert()
        .id('hotend')
        .crit(lambda: "pvalue" < alpha)
        .log('/tmp/kapacitor_udf/hotend_failure.log')

// Do the same for the bed and air temperature.
data
    |tTest()
        .field('bed')
        .size(3600)
        .alpha(alpha)
    |alert()
        .id('bed')
        .crit(lambda: "pvalue" < alpha)
        .log('/tmp/kapacitor_udf/bed_failure.log')

data
    |tTest()
        .field('air')
        .size(3600)
        .alpha(alpha)
    |alert()
        .id('air')
        .crit(lambda: "pvalue" < alpha)
        .log('/tmp/kapacitor_udf/air_failure.log')

Notice that we have called tTest three times. This means that Kapacitor will spawn three different Python processes and pass the respective init option to each one.

Save this script as /tmp/kapacitor_udf/print_temps.tick and define the Kapacitor task:

kapacitor define -name print_temps -type stream -dbrp printer.default -tick print_temps.tick

Generating Test Data

To simulate our printer for testing, we will write a simple Python script to generate temperatures. This script generates random temperatures that are normally distributed around a target temperature. At specified times, the variation and offset of the temperatures changes, creating an anomaly.

Don’t worry too much about the details here. It would be much better to use real data for testing our TICKscript and UDF, but this is faster (and much cheaper than a 3D printer).

#!/usr/bin/python2

from numpy import random
from datetime import timedelta, datetime
import sys
import time
import requests


# Target temperatures in C
hotend_t = 220
bed_t = 90
air_t = 70

# Connection info
write_url = 'http://localhost:9092/write?db=printer&rp=default&precision=s'
measurement = 'temperatures'

def temp(target, sigma):
    """
    Pick a random temperature from a normal distribution
    centered on target temperature.
    """
    return random.normal(target, sigma)

def main():
    hotend_sigma = 0
    bed_sigma = 0
    air_sigma = 0
    hotend_offset = 0
    bed_offset = 0
    air_offset = 0

    # Define some anomalies by changing sigma at certain times
    # list of sigma values to start at a specified iteration
    hotend_anomalies =[
        (0, 0.5, 0), # normal sigma
        (3600, 3.0, -1.5), # at one hour the hotend goes bad
        (3900, 0.5, 0), # 5 minutes later recovers
    ]
    bed_anomalies =[
        (0, 1.0, 0), # normal sigma
        (28800, 5.0, 2.0), # at 8 hours the bed goes bad
        (29700, 1.0, 0), # 15 minutes later recovers
    ]
    air_anomalies = [
        (0, 3.0, 0), # normal sigma
        (10800, 5.0, 0), # at 3 hours air starts to fluctuate more
        (43200, 15.0, -5.0), # at 12 hours air goes really bad
        (45000, 5.0, 0), # 30 minutes later recovers
        (72000, 3.0, 0), # at 20 hours goes back to normal
    ]

    # Start from 2016-01-01 00:00:00 UTC
    # This makes it easy to reason about the data later
    now = datetime(2016, 1, 1)
    second = timedelta(seconds=1)
    epoch = datetime(1970,1,1)

    # 24 hours of temperatures once per second
    points = []
    for i in range(60*60*24+2):
        # update sigma values
        if len(hotend_anomalies) > 0 and i == hotend_anomalies[0][0]:
            hotend_sigma = hotend_anomalies[0][1]
            hotend_offset = hotend_anomalies[0][2]
            hotend_anomalies = hotend_anomalies[1:]

        if len(bed_anomalies) > 0 and i == bed_anomalies[0][0]:
            bed_sigma = bed_anomalies[0][1]
            bed_offset = bed_anomalies[0][2]
            bed_anomalies = bed_anomalies[1:]

        if len(air_anomalies) > 0 and i == air_anomalies[0][0]:
            air_sigma = air_anomalies[0][1]
            air_offset = air_anomalies[0][2]
            air_anomalies = air_anomalies[1:]

        # generate temps
        hotend = temp(hotend_t+hotend_offset, hotend_sigma)
        bed = temp(bed_t+bed_offset, bed_sigma)
        air = temp(air_t+air_offset, air_sigma)
        points.append("%s hotend=%f,bed=%f,air=%f %d" % (
            measurement,
            hotend,
            bed,
            air,
            (now - epoch).total_seconds(),
        ))
        now += second

    # Write data to Kapacitor
    r = requests.post(write_url, data='\n'.join(points))
    if r.status_code != 204:
        print >> sys.stderr, r.text
        return 1
    return 0

if __name__ == '__main__':
    exit(main())

Save the above script as /tmp/kapacitor_udf/printer_data.py.

This Python script has two Python dependencies: requests and numpy. They can easily be installed via pip or your package manager.

At this point we have a task ready to go, and a script to generate some fake data with anomalies. Now we can create a recording of our fake data so that we can easily iterate on the task:

# Start the recording in the background
kapacitor record stream -name print_temps -duration 24h &
# Run our python script to generate data
chmod +x ./printer_data.py
./printer_data.py
# Grab the ID from the output and store it in a var
# The ID will appear on a line above the last line about the background task finishing.
rid=7bd3ced5-5e95-4a67-a0e1-f00860b1af47

We can verify it worked by listing information about the recording. Our recording came out to 1.6MB, so yours should come out somewhere close to that:

$ kapacitor list recordings $rid
ID                                      Type    Size      Created
7bd3ced5-5e95-4a67-a0e1-f00860b1af47    stream  1.6 MB    21 Jan 16 12:43 MST

Detecting Anomalies

Finally, let’s run the play against our task and see how it works:

kapacitor replay -name print_temps -id $rid -fast -rec-time

Check the various log files to see if the algorithm caught the anomalies:

cat /tmp/kapacitor_udf/{hotend,bed,air}_failure.log

Based on the printer_data.py script above, there should be anomalies at:

  • 1hr – hotend
  • 8hr – bed
  • 12hr – air

There may be some false positives as well, but, since we want this to work with real data (not our nice clean fake data), it doesn’t help much to tweak it at this point.

Well, there we have it. We can now get alerts when the temperatures for our prints deviates from the norm. Hopefully you now have a better understanding of how Kapacitor UDFs work, and have a good working example as a launching point into further work with UDFS.

The framework is in place, now go plug in a real anomaly detection algorithm that works for your domain!

Extending This Example

There are a few things that we have left as exercises to the reader:

  1. Snapshot/Restore – Kapacitor will regularly snapshot the state of your UDF process so that it can be restored if the process is restarted. The examples here have implementations for the snapshot and restore methods. Implement them for the TTestHandler handler as an exercise.

  2. Change the algorithm from a t-test to something more fitting for your domain. Both numpy and scipy have a wealth of algorithms.

  3. The options returned by the info request can contain multiple arguments. Modify the field option to accept three field names and change the TTestHandler to maintain historical data and batches for each field instead of just the one. That way only one ttest.py process needs to be running.