Correlation Function Reference

The Correlation Function Reference function block calculates the discrete correlation function between a recorded signal (referred to below as reference signal), which is read from a tcab file, and one or more input signals (Channel 00, ..., Channel 0n).

The correlation coefficients are calculated for time shifts of m cycles between the two signals, with the maximum and minimum values for m being limited by the parameters Minimum Lag (negative integer) and Maximum Lag (positive integer).

The Step Size parameter determines the number of cycles by which the signals are moved to calculate two consecutive correlation coefficients. I.e. m is always a multiple of the Step Size. Accordingly, only multiples of the Step Size are also allowed for Minimum Lag and Maximum Lag. If the Step Size is set to one, Minimum Lag to -6 and Maximum Lag to +4, for example, coefficients are calculated for shifts by -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, and +4 cycles. If the Step Size is set to two, coefficients are calculated for shifts by -6, -4, -2, 0, +2, and +4 cycles.

From the start of the analysis, a value is processed from the read-in signal per cycle. When the end of the file is reached, the process starts again with the first value of the file. The read-in signal is therefore assumed to be periodic. If you only want to correlate certain periods of the input signal with the reference signal, you can control this via the Enable Execution and Reset inputs as well as via the New Result output.

The correlation coefficients can be calculated over different timeframes. which are set by the Window Mode parameter. In Continuous mode, all values since the beginning of the analysis are included in the calculations. In SlidingWindow mode, the calculation runs continuously for the last number of cycles set by the Window Size. In FixWindow mode, the calculation is done over the length of the reference signal and the output values are always updated at the end of the recorded sequence.

If m is not zero, the window for the corresponding signal shifts by m cycles. The number of values included in the calculation of the coefficients is the same for all values of m. The only exceptions to this are the results from the first cycles after the start of the analysis. If the number of elapsed cycles is less than |m|, correspondingly fewer values are included in the calculation.

For positive values of m, the values of the reference signal (Channel Ref) are stored in a ring memory, so that the respective value of the reference signal received before m cycles can be compared with the current values from Channel 00 to Channel 0n. This corresponds to a shift of the reference signal into the past. For negative values of m, the reference signal would accordingly have to be moved into the future. Since this is obviously not possible, the second signal (Channel 00, .. Channel0n) is saved and moved backward instead.

The correlation coefficients can be calculated according to different calculation rules. This is determined by the Correlation Mode. In the Base and Normed modes, the coefficients are calculated analogously to the definition from signal processing, which calculates the correlation over the convolution. In Normed mode, the coefficients are also divided by the number of summands. Covariance and CovarianceBessel calculate the covariance without and with Bessel correction. Pearson mode uses the definition of the Pearson correlation coefficient commonly used in statistics. The exact calculation rules are mathematically listed in the configuration options. Here, x_n denotes the value of the reference signal and y_n denotes the value of the input signal (in each case Channel00, ..., Channel0n) at the timestamp t_n (corresponding to the n^th cycle since the start of the analysis or since reset, except for the cycles in which Enable Execution = FALSE). The value of N depends on the WindowMode you select. For SlidingWindow mode and FixWindow mode, N is equal to the WindowSize, provided a corresponding number of cycles have already elapsed since the start of the analysis, so that x_n-N-m (or y_n-N+m) has been recorded, otherwise N will be reduced to n-m+1 or n+m+1 respectively. In FixWindow mode, the window size is not to be set manually, but corresponds to the length of the read-in signal section (reference signal) and the output values are updated at the end of the signal section. In Continuous mode, N = n+1 always applies.

The illustration shows the different input and output values of the function block for a configuration (Correlation Mode = Pearson, Window Mode = FixWindow, Window Size = 120 (= number of values in the file), Step Size = 5, Maximum Lag = 20, Minimum Lag = -20) and an input channel. On the left side, the input signals Channel 00 and Reset are shown in the two lower plots, above which the read-in sequence is shown on the same timeline, according to its processing. The signal starts to be read in at the beginning of the analysis. If the last value from the file is processed in the 120^th (or 240^th) cycle, the process starts again with the first one. In the 300^th cycle, a reset is performed and the process starts again with the first value of the file. In addition, all values are deleted from the internal memories and the calculation of the coefficients begins again. For example, it was detected here that Channel 00 did not contain valid values in the previous cycles and the vibration has now been re-energized. In this area the analysis could also be interrupted by Enable Execution = FALSE. Since WindowMode = FixWindow, the outputs are updated only in the 120^th, 240^th and 420^th cycle. The corresponding coefficients (from Output00) are shown in the right plot. From the value pairs (Maximizing Lag, Maximum Coefficient) you can read how much the input signal is shifted with respect to the reference signal. For example, in the 420^th cycle (Maximizing Lag, Maximum Coefficient) = (-10.1). This means that if the Reset had taken place 10 cycles earlier, the reference signal and Channel 00 would have matched each other exactly in this window.

Correlation Function Reference 2:

Optionally, a Boolean signal can be selected for the Enable Execution input so that the algorithm is only active if the value of the selected signal is TRUE.

Configuration options

Num Channels: The number of channels that are correlated with the reference signal. This can be set via Add/Remove Channel
File Path: Path to the data file.
Maximum Lag: Specifies the maximum number of cycles by which the two signals are shifted to calculate the correlation to each other. This is a positive integer.
Minimum Lag: Specifies the minimum number of cycles by which the two signals are shifted to calculate the correlation to each other. This is a negative integer.
Step Size: Specifies by how many cycles the signals are shifted to calculate two consecutive correlation coefficients.
Window Size: For the SlidingWindow and FixWindow window modes, specifies the number of cycles over which the coefficients are calculated. The windowing has no effect for the Continuous Window Mode and cannot be set. In SlidingWindow mode, Window Size values for all channels are buffered in addition to Maximum Lag values from the Reference Channel and Minimum Lag values for Channel 00 to Channel 0n. The size of the router memory should therefore be taken into account when setting these parameters.
Correlation Mode: The correlation coefficients are calculated according to one of the following definitions:
Base:

Correlation Function Reference 3:

Normed:

Correlation Function Reference 4:

Covariance:

Correlation Function Reference 5:

CovarianceBessel:

Correlation Function Reference 6:

Pearson:

Correlation Function Reference 7:

Window Mode: Specifies the type of window used to calculate the coefficients:

Continuous: All values since the start of the analysis are included in the analysis with equal weighting.

SlidingWindow: The calculation is done via a window of the size Window Size. The current values are always included in the analysis and outputs are updated with each cycle.

FixWindow: The coefficients are calculated over the entire length of the read-in signal section and the outputs are updated after processing the last value.

Output values

Output00 .. Output0n: Shows for each input (Channel00, ..., Channel0n) the coefficients for the shifts m = Minimum Lag, m = Minimum Lag + Step Size, ..., m = - Step Size, m = 0, m = +StepSize,..., m = Maximum Lag as an array.
Minimizing Lag00..Minimizing Lag0n: For each channel, specifies the shift for which the coefficient becomes minimum.
Minimum Coefficient00..Minimum Coefficient0n: Specifies the minimum coefficient for each channel.
Maximizing Lag00..Maximizing Lag0n: for each channel, specifies the shift for which the coefficient becomes maximum.
Maximum Coefficient 00..00.. Maximum Coefficient0n: Specifies the maximum coefficient for each channel.

Standard HMI Controls

For the Correlation Function Reference algorithm, the following HMI controls are available for generating an Analytics Dashboard:

1. The Table Control or Multivalue Control visualizes all output values: read value, minimum coefficient, maximum coefficient, minimum lag, maximum lag and the coefficient array.

Alternatively, customer-specific HMI controls can be mapped in the Correlation Function Reference algorithm using the Mapping Wizard.