FB_CMA_PowerCepstrum

The function block calculates the power cepstrum for a real-valued input signal.

The power cepstrum Cp(τ) is defined as follows, in this case in time-continuous representation:

FB_CMA_PowerCepstrum 1:

Accordingly, it is defined as inverse Fourier transform of the logarithmized power spectrum (see FB_CMA_PowerSpectrum). Forward and inverse transform bring the result back into the time range.

The function block is helpful for monitoring of gear units, see Gearbox monitoring.

In the numerical implementation the PowerSpectrum is calculated first. The input data buffer is overlapped with the immediately preceding buffers and multiplied with a window function. If the value of parameter nFFT_Length is greater than the parameter nWindowLength, the windowed time signal is filled with the same number of zeros at the beginning and the end, in order to reach the required FFT input length (zero padding). Subsequently a FFT for real values is applied, and the absolute value of the resulting complex values and the square of the values is calculated. The values are then logarithmized. Before the logarithmization the argument is compared with the value of the parameter fLogThreshold. If they are smaller they are set to this value in order to avoid value range errors or the attempt to calculate the logarithm of zero. This is followed by another inverse Fourier transform. The result is an array with complex values.

FB_CMA_PowerCepstrum 2:

Evaluation of the complex-valued result

In practice the absolute value, the squared absolute value or only the real part of the complex-valued power cepstrum is evaluated, depending on the application. This has to be implemented by the user as required.

A number of slightly different definitions exist for the power cepstrum. The definition used here is based on common definitions by J. Korelus and Robert B. Randall, see bibliography.

Differentiation to the complex cepstrum:

The power cepstrum differs from the complex cepstrum, which is defined as logarithmized Fourier inverse transform of a complex signal spectrum. Due to the absolute value calculation the power cepstrum is less sensitive to the properties of the phase angle of the signal, compared with the complex cepstrum. In addition, the complex cepstrum directly provides a real-valued result.

Memory properties

Due to the use of the Welch method, the current input data buffer, together with the last-transferred buffers, is used for the calculation. The number of buffers incorporated depends on the selected overlap (nOverlap).
The frequency analysis takes step changes in the time series into account. In order to achieve a correct result, therefore, the input data buffers used must be concatenated without gaps and without jumps.

NaN occurrence

If the input vector contains one or more NaN (Not a Number) values, the entire output sector is filled with NaN. See separate section for further information on NaN values.

FB_CMA_PowerCepstrum 3:

Handling of NaN values

If the situations described above, which lead to NaN values, cannot be ruled out or safely neglected, the application program must be able to handle these error values.

Behavior when processing multi-channel input data

When processing several channels (nChannels > 1), there is a possibility of each channel having different return values. In this case, return values can be queried separately on the function block. If the results from one or more channels are impermissible, but not all channels, the value on the function block corresponds to eCM_InfRTime_AmbiguousChannelResults. If the results of all channels are impermissible, then the value on the function block corresponds to eCM_ErrRTime_ErrornousChannelResults.

A list of return values of all channels can be queried using the method GetChannelErrors().

Sample implementation

A sample implementation is available under the following link: Power cepstrum.

Inputs and outputs

The input and output buffers correspond to one of the following definitions (input / output shape). The variable parameters are part of the function block input stInitPars.

Versions

Input buffer (MultiArray input stream)
Element type, number of dimensions, dimension sizes

Output buffer (MultiArray output stream)
Element type, number of dimensions, dimension sizes

Standard version
(nChannels = 1)

LREAL, 1,
nWindowLength-nOverlap

LCOMPLEX, 1,
nFFT_Length/2+1

Multi-channel version
(nChannels > 1)

LREAL, 2,
nChannels x nWindowLength-nOverlap

LCOMPLEX, 2,
nChannels x nFFT_Length/2+1

VAR_INPUT
    stInitPars       : ST_CM_PowerCepstrum_InitPars;     // init parameter
    nOwnID           : UDINT;                            // ID for this FB instance
    aDestIDs         : ARRAY[1..cCMA_MaxDest] OF UDINT;  // IDs of destinations for output
    nResultBuffers   : UDINT := 4;                       // number of MultiArrays which should be initialized for results (0 for no initialization)
    tTransferTimeout : LTIME := LTIME#500US;             // timeout checking off during access to inter-task FIFOs
END_VAR

Input parameters

The input parameters of this function block represent initialization parameters and must already be assigned in the declaration of the FB instance! (Alternatively: Init() method). They may only be assigned once. A change at runtime is not possible.

Output parameters

VAR_OUTPUT
    bError         : BOOL;                           // TRUE if an error occurs. Reset by next method call.
    hrErrorCode    : HRESULT;                        // '< 0' = error; '> 0' = info; '0' = no error/info
    ipErrorMessage : I_TcMessage := fbErrorMessage;  // Shows detailed information about occurred errors, warnings and more.
    nCntResults    : ULINT;                          // Counts outgoing results (MultiArrays were calculated and sent to transfer tray).
END_VAR
  • bError: The output is TRUE if an error occurs.
  • hrErrorCode: If an error occurs, a corresponding error code of the type HRESULT is output. Possible values are described in the List of error codes.
  • ipErrorMessage: Contains more detailed information on the current return value. Refer here to the section Error description and information. This special interface pointer is internally secured so that it is always valid/assigned.

Methods

METHOD Init : HRESULT
VAR_INPUT
    stInitPars     : ST_CM_PowerCepstrum_InitPars;     // init parameter
    nOwnID         : UDINT;         // ID for this FB instance
    aDestIDs       : ARRAY[1..cCMA_MaxDest] OF UDINT;  // IDs of destinations for output
    nResultBuffers : UDINT := 4;    // number of MultiArrays which should be initialized for results (0 for no initialization)
END_VAR

Call():

The method is called each cycle in order to apply the algorithm to the current input data. The function block waits for input data if the method indicates neither new results nor an error. This is a regular behavior in the process of the analysis chain.

  • Return value: If an error occurs, a corresponding error code of the type HRESULT is output. Possible values are described in the List of error codes.
METHOD Call : HRESULT
VAR_OUTPUT
    bNewResult   : BOOL;       // TRUE every time when outgoing MultiArray was calculated and sent to transfer tray.
    bError       : BOOL;       // TRUE if an error occurs.
    hrErrorCode  : HRESULT;    // '< 0' = error; '> 0' = info; '0' = no error/info
END_VAR
  • bError: The output is TRUE if an error occurs.
  • hrErrorCode: If an error occurs, a corresponding error code of the type HRESULT is output. Possible values are described in the List of error codes. This output is identical to the return value of the method.
FB_CMA_PowerCepstrum 4:

If a timeout occurs or no MultiArray buffer is available for the result, then neither the input data nor the result data are lost. They are forwarded on the next call.

Init():

This method is not usually necessary in a Condition Monitoring application. It offers an alternative to the function block initialization. The Init() method may only be called during the initialization phase of the PLC. It cannot be used at runtime. You are referred to the use of an FB_init method or the attribute 'call_after_init' (see TwinCAT PLC reference). In addition, this facilitates the function block encapsulation.

The input parameters of the function block instance may not be assigned in the declaration if the initialization is to take place using the Init() method.

  • Return value: If an error occurs, a corresponding error code of the type HRESULT is output. Possible values are described in the List of error codes.

ResetData():

The method deletes all data records that have already been added, see Memory property of the function block. If the Call() method is called again after a ResetData(), the internal memory must be replenished in order to calculate a valid result.

  • Return value: If an error occurs, a corresponding error code of the type HRESULT is output. Possible values are described in the List of error codes.
METHOD ResetData : HRESULT
VAR_INPUT
END_VAR

PassInputs():

As long as an FB_CMA_Source instance is called and signal data are thus transferred to a target block, all further function blocks of the analysis chain have to be called cyclically as explained in the API PLC Reference.
Sometimes it is useful not to execute an algorithm for a certain time. For example, some algorithms should be executed only after prior training or configuration. The function block must be called cyclically, but it is sufficient for the data arriving at the function block to be forwarded in the communication ring. This is done using the PassInputs() method in place of the Call() method. The algorithm itself is not called here, and accordingly no result is calculated and no output buffer generated.

  • Return value: If an error occurs, a corresponding error code of the type HRESULT is output. Possible values are described in the List of error codes.
METHOD PassInputs : HRESULT
VAR_INPUT
END_VAR

GetChannelErrors():

The method enables the querying of a list of the channel-specific return values when processing several channels (nChannels > 1). A call is useful in the case that the return value of the function block corresponds to one of the values eCM_InfRTime_AmbiguousChannelResults or eCM_ErrRTime_ErrornousChannelResults.

  • Return value: Information on the reading process of the list of error codes. The value is set to TRUE if the query was successful, otherwise to FALSE.
    METHOD GetChannelErrors : BOOL
VAR_IN_OUT
    aChannelErrors : ARRAY[*] OF HRESULT;
END_VAR
  • aChannelErrors: Error list of the type HRESULT of the length nChannels.

Similar function blocks

The function block FB_CMA_Envelope is also suitable for the analysis of pulse-like excitations with linear and non-linear system components.

Requirements

Development environment

Target platform

PLC libraries to include

TwinCAT v3.1.4022.25

PC or CX (x86, x64)

Tc3_CM, Tc3_CM_Base

FB_CMA_PowerCepstrum 5:

Limited functional scope already available with CM 3.1. See section Compatibility.