FB_CMA_SparseSpectrum

Calculation of individual spectral values for real-valued input signals

The function block FB_CMA_SparseSpectrum provides a configurable number of individual spectral values, which are scaled in compliance with the function blocks FB_CMA_RealFFT, FB_CMA_MagnitudeSpectrum or FB_CMA_PowerSpectrum. The DFT coefficients are calculated

with the Goertzel algorithm. This is more efficient than a radix-2 FFT if the following applies to the number M of the coefficients to be calculated with a window length L:

Here, N is the next greater power of 2 with respect to the window length L. If only a few/individual spectral values are required, these can be calculated with the function block, if necessary directly in the (fast) sampling task, so that spontaneous changes in the spectrum can be reacted to more quickly.

The highest frequency of a component in the input signal should be at the most around half of the sampling rate of the input signal so that aliasing effects are avoided.

The function block performs several functions, see Analysis of data streams and Frequency analysis.

The input data buffer is first overlapped with the immediately preceding buffers and multiplied with a window function. The DFT coefficients are then calculated using the Goertzel algorithm. The parameter eSpectrumType defines whether the absolute magnitude or its square is calculated from the resulting complex values. If the parameter bTransformToDecibel is TRUE, the values are transformed to decibel values if magnitude or power values have been calculated. These decibel values are the same for both spectral values, i.e. the influence of the squaring with the power values is taken into account in the calculation of decibel values by a factor of two for the magnitude values. Furthermore, scaling of the results is feasible via the parameter eScalingType, see Scaling of spectra.

Scaling

The scaling of the result values, e.g. the Acceleration Spectral Densities matches the definition of the FFT by default. This means that the influence of the window length and the window function are eliminated.
Tabulated parameters described in the section "Options for spectrum scaling " can be used for the arithmetic scaling of absolute measurements.

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.

	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 showing the possible uses of the function block and its configuration is available under the following link: Calculation of individual spectral values

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 variant DFT (`nChannels = 1, eSpectrumType = eCM_DFT`)	`LREAL, 1,`nWindowLength-nOverlap	`LCOMPLEX, 1,`nBins
Standard variant Spectrum (`nChannels = 1, eSpectrumType <> eCM_DFT`)	`LREAL, 1,`nWindowLength-nOverlap	`LREAL, 1,`nBins
Multi-channel variant DFT (`nChannels > 1, eSpectrumType = eCM_DFT`)	`LREAL, 2,`nChannels x nWindowLength-nOverlap	`LCOMPLEX, 2,`nChannels x nBins
Multi-channel variant Spectrum (`nChannels > 1, eSpectrumType <> eCM_DFT`)	`LREAL, 2,`nChannels x nWindowLength-nOverlap	`LREAL, 2,`nChannels x nBins

VAR_INPUT
    stInitPars       : ST_CM_SparseSpectrum_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.

stInitPars: Function block-specific structure with initialization parameters of the type ST_CM_SparseSpectrum_InitPars. The parameters must correlate to the above definition of the input and output buffers.
nOwnID: Identifies the function block instance with a unique ID. This must always be greater than zero. A proven approach is to define an enumeration for this purpose.
aDestIDs: Defines the destinations to which the results are to be forwarded by specifying the IDs of the destinations. The definition of the output buffer (as described above) must correlate to the definition of the input buffer of each selected destination.
nResultBuffers: The function block initializes a Transfer Tray Stream with the specified number of MultiArray buffers. The default value is four.
tTransferTimeout: Setting of the synchronous timeout for internal MultiArray forwardings. See section Parallel processing.

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

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.

	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.

Configure():

On calling this method, the spectral values must be configured at the beginning. The DFT index is calculated for the frequency f to k = f * fSampleRate / nWindowLength. If f is not an integer multiple of the frequency resolution fSampleRate / nWindowLength, the spectral portions are distributed to two consecutive spectral values.

The corresponding PLC array must be defined as follows. The Configure() method can also be used for a new configuration with a different set of arguments.

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 Configure : HRESULT
VAR_INPUT
    pArg     : PVOID;    // pointer to array of arguments
    nArgSize : UDINT;    // size of arguments buffer in bytes 
END_VAR

The input buffers correspond to one of the following definitions (input 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
Identical configuration of all channels	`UDINT, 1,`nBins
Channel-specific configuration (`nChannels > 1`)	`UDINT, 2,`nChannels x nBins

METHOD Init : HRESULT
VAR_INPUT
    stInitPars     : ST_CM_SparseSpectrum_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

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.

stInitPars: Function block-specific structure with initialization parameters of the type ST_CM_SparseSpectrum_InitPars. The parameters must correlate to the above definition of the input and output buffers.
nOwnID: Identifies the function block instance with a unique ID. This must always be greater than zero. A proven approach is to define an enumeration for this purpose.
aDestIDs: Defines the destinations to which the results are to be forwarded by specifying the IDs of the destinations. The definition of the output buffer (as described above) must correlate to the definition of the input buffer of each selected destination.
nResultBuffers: The function block initializes a Transfer Tray Stream with the specified number of MultiArray buffers. The default value is four.

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_RealFFT calculates the Fast Fourier Transform for real-valued input signals.

The function block FB_CMA_MagnitudeSpectrum calculates the magnitude spectrum of a real-valued input signal.

The function block FB_CMA_PowerSpectrum calculates the power spectrum by means of squaring of the values in the last step.

Requirements

Development environment	Target platform	PLC libraries to include
TwinCAT v3.1.4022.25	PC or CX (x86, x64)	Tc3_CM, Tc3_CM_Base