Fill time gaps and imputing missing values
Important
Azure SQL Edge no longer supports the ARM64 platform.
When dealing with time series data, it's often possible that the time series data has missing values for the attributes. It's also possible that, because of the nature of the data, or because of interruptions in data collection, there are time gaps in the dataset.
For example, when collecting energy usage statistics for a smart device, whenever the device isn't operational there are gaps in the usage statistics. Similarly, in a machine telemetry data collection scenario, it's possible that the different sensors are configured to emit data at different frequencies, resulting in missing values for the sensors. For example, if there are two sensors, voltage and pressure, configured at 100 Hz and 10-Hz frequency respectively, the voltage sensor emits data every one-hundredth of a second, while the pressure sensor only emits data every one-tenth of a second.
The following table describes a machine telemetry dataset, which was collected at a one-second interval.
timestamp VoltageReading PressureReading
----------------------- --------------- ----------------
2020-09-07 06:14:41.000 164.990400 97.223600
2020-09-07 06:14:42.000 162.241300 93.992800
2020-09-07 06:14:43.000 163.271200 NULL
2020-09-07 06:14:44.000 161.368100 93.403700
2020-09-07 06:14:45.000 NULL NULL
2020-09-07 06:14:46.000 NULL 98.364800
2020-09-07 06:14:49.000 NULL 94.098300
2020-09-07 06:14:51.000 157.695700 103.359100
2020-09-07 06:14:52.000 157.019200 NULL
2020-09-07 06:14:54.000 NULL 95.352000
2020-09-07 06:14:56.000 159.183500 100.748200
There are two important characteristics of the preceding dataset.
- The dataset doesn't contain any data points related to several timestamps
2020-09-07 06:14:47.000,2020-09-07 06:14:48.000,2020-09-07 06:14:50.000,2020-09-07 06:14:53.000, and2020-09-07 06:14:55.000. These timestamps are gaps in the dataset. - There are missing values, represented as
null, for the Voltage and pressure readings.
Gap filling
Gap filling is a technique that helps create contiguous, ordered set of timestamps to ease the analysis of time series data. In Azure SQL Edge, the easiest way to fill gaps in the time series dataset is to define a temporary table with the desired time distribution and then do a LEFT OUTER JOIN or a RIGHT OUTER JOIN operation on the dataset table.
Taking the MachineTelemetry data represented previously as an example, the following query can be used to generate contiguous, ordered set of timestamps for analysis.
Note
The following query generates the missing rows, with the timestamp values and null values for the attributes.
CREATE TABLE #SeriesGenerate (dt DATETIME PRIMARY KEY CLUSTERED)
GO
DECLARE @startdate DATETIME = '2020-09-07 06:14:41.000',
@endtime DATETIME = '2020-09-07 06:14:56.000'
WHILE (@startdate <= @endtime)
BEGIN
INSERT INTO #SeriesGenerate
VALUES (@startdate)
SET @startdate = DATEADD(SECOND, 1, @startdate)
END
SELECT a.dt AS TIMESTAMP,
b.VoltageReading,
b.PressureReading
FROM #SeriesGenerate a
LEFT JOIN MachineTelemetry b
ON a.dt = b.[timestamp];
The above query produces the following output containing all one-second timestamps in the specified range.
Here's the result set:
timestamp VoltageReading PressureReading
----------------------- ----------------- ----------------
2020-09-07 06:14:41.000 164.990400 97.223600
2020-09-07 06:14:42.000 162.241300 93.992800
2020-09-07 06:14:43.000 163.271200 NULL
2020-09-07 06:14:44.000 161.368100 93.403700
2020-09-07 06:14:45.000 NULL NULL
2020-09-07 06:14:46.000 NULL 98.364800
2020-09-07 06:14:47.000 NULL NULL
2020-09-07 06:14:48.000 NULL NULL
2020-09-07 06:14:49.000 NULL 94.098300
2020-09-07 06:14:50.000 NULL NULL
2020-09-07 06:14:51.000 157.695700 103.359100
2020-09-07 06:14:52.000 157.019200 NULL
2020-09-07 06:14:53.000 NULL NULL
2020-09-07 06:14:54.000 NULL 95.352000
2020-09-07 06:14:55.000 NULL NULL
2020-09-07 06:14:56.000 159.183500 100.748200
Impute missing values
The preceding query generated the missing timestamps for data analysis, however it didn't replace any of the missing values (represented as null) for voltage and pressure readings. In Azure SQL Edge, a new syntax was added to the T-SQL LAST_VALUE() and FIRST_VALUE() functions, which provide mechanisms to impute missing values, based on the preceding or following values in the dataset.
The new syntax adds IGNORE NULLS and RESPECT NULLS clause to the LAST_VALUE() and FIRST_VALUE() functions. A following query on the MachineTelemetry dataset computes the missing values using the LAST_VALUE function, where missing values are replaced with the last observed value in the dataset.
SELECT timestamp,
VoltageReading AS OriginalVoltageValues,
LAST_VALUE(VoltageReading) IGNORE NULLS OVER (
ORDER BY timestamp
) AS ImputedUsingLastValue,
PressureReading AS OriginalPressureValues,
LAST_VALUE(PressureReading) IGNORE NULLS OVER (
ORDER BY timestamp
) AS ImputedUsingLastValue
FROM MachineTelemetry
ORDER BY timestamp;
Here's the result set:
timestamp OrigVoltageVals ImputedVoltage OrigPressureVals ImputedPressure
----------------------- ---------------- -------------- ----------------- ----------------
2020-09-07 06:14:41.000 164.990400 164.990400 97.223600 97.223600
2020-09-07 06:14:42.000 162.241300 162.241300 93.992800 93.992800
2020-09-07 06:14:43.000 163.271200 163.271200 NULL 93.992800
2020-09-07 06:14:44.000 161.368100 161.368100 93.403700 93.403700
2020-09-07 06:14:45.000 NULL 161.368100 NULL 93.403700
2020-09-07 06:14:46.000 NULL 161.368100 98.364800 98.364800
2020-09-07 06:14:49.000 NULL 161.368100 94.098300 94.098300
2020-09-07 06:14:51.000 157.695700 157.695700 103.359100 103.359100
2020-09-07 06:14:52.000 157.019200 157.019200 NULL 103.359100
2020-09-07 06:14:54.000 NULL 157.019200 95.352000 95.352000
2020-09-07 06:14:56.000 159.183500 159.183500 100.748200 100.748200
The following query imputes the missing values using both the LAST_VALUE() and the FIRST_VALUE function. For the output column ImputedVoltage, the last observed value replaces the missing values, while for the output column ImputedPressure the missing values are replaced by the next observed value in the dataset.
SELECT dt AS [timestamp],
VoltageReading AS OrigVoltageVals,
LAST_VALUE(VoltageReading) IGNORE NULLS OVER (
ORDER BY dt
) AS ImputedVoltage,
PressureReading AS OrigPressureVals,
FIRST_VALUE(PressureReading) IGNORE NULLS OVER (
ORDER BY dt ROWS BETWEEN CURRENT ROW
AND UNBOUNDED FOLLOWING
) AS ImputedPressure
FROM (
SELECT a.dt,
b.VoltageReading,
b.PressureReading
FROM #SeriesGenerate a
LEFT JOIN MachineTelemetry b
ON a.dt = b.[timestamp]
) A
ORDER BY timestamp;
Here's the result set:
timestamp OrigVoltageVals ImputedVoltage OrigPressureVals ImputedPressure
----------------------- ---------------- --------------- ----------------- ---------------
2020-09-07 06:14:41.000 164.990400 164.990400 97.223600 97.223600
2020-09-07 06:14:42.000 162.241300 162.241300 93.992800 93.992800
2020-09-07 06:14:43.000 163.271200 163.271200 NULL 93.403700
2020-09-07 06:14:44.000 161.368100 161.368100 93.403700 93.403700
2020-09-07 06:14:45.000 NULL 161.368100 NULL 98.364800
2020-09-07 06:14:46.000 NULL 161.368100 98.364800 98.364800
2020-09-07 06:14:47.000 NULL 161.368100 NULL 94.098300
2020-09-07 06:14:48.000 NULL 161.368100 NULL 94.098300
2020-09-07 06:14:49.000 NULL 161.368100 94.098300 94.098300
2020-09-07 06:14:50.000 NULL 161.368100 NULL 103.359100
2020-09-07 06:14:51.000 157.695700 157.695700 103.359100 103.359100
2020-09-07 06:14:52.000 157.019200 157.019200 NULL 95.352000
2020-09-07 06:14:53.000 NULL 157.019200 NULL 95.352000
2020-09-07 06:14:54.000 NULL 157.019200 95.352000 95.352000
2020-09-07 06:14:55.000 NULL 157.019200 NULL 100.748200
2020-09-07 06:14:56.000 159.183500 159.183500 100.748200 100.748200
Note
The above query uses the FIRST_VALUE() function to replace missing values with the next observed value. The same result can be achieved by using the LAST_VALUE() function with a ORDER BY <ordering_column> DESC clause.
Next steps
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