CN116378912A - Early compound fault diagnosis method and device for wind driven generator and readable storage medium - Google Patents
Early compound fault diagnosis method and device for wind driven generator and readable storage medium Download PDFInfo
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Abstract
The invention belongs to the field of mechanical fault diagnosis, and particularly relates to a method and a device for diagnosing early compound faults of a wind driven generator and a readable storage medium, wherein the method comprises the following steps: step 1, collecting vibration signals of mechanical parts; step 2, decomposing the RSSD signal; and 3, analyzing the Teager energy spectrum, and judging the reason of the fault according to the Teager energy spectrum. The invention can realize the early diagnosis of single/composite faults of mechanical parts such as bearings, gear boxes and the like, provide early warning for monitoring and realize the early fault diagnosis of the mechanical parts. Meanwhile, the method provided by the invention can avoid the interference of noise and has the advantages of accurate diagnosis, high reliability and low cost.
Description
Technical Field
The invention belongs to the field of mechanical fault diagnosis, and particularly relates to a method and a device for diagnosing early compound faults of a wind driven generator and a readable storage medium.
Background
Offshore wind power is increasingly gaining attention as a renewable green energy source, and wind generators are important mechanical equipment for offshore wind power. Mechanical parts of the wind driven generator such as bearings, gears and the like run in a high-speed and heavy-load environment for a long time, and are extremely easy to damage. Damage to mechanical parts is a progressive process, typically from early weak damage failure to late severe damage. If the fault can be identified in the early stage of the fault occurrence, the serious property loss caused by serious damage of mechanical parts can be effectively avoided, and even the casualties caused by the mechanical fault can be avoided. And thus has significance for early failure diagnosis of mechanical equipment. However, the early fault signal is relatively weak, is extremely submerged in background noise, and is particularly difficult to diagnose. In addition, mechanical parts may be damaged in many places, such as bearing parts, rolling elements, cages, outer rings, etc., may be damaged at the same time. When multiple faults coexist, mutual interference and coupling can occur among different fault impact signals, the additional weak faults are easily submerged in background noise, and the identification and extraction of early weak composite fault signals are particularly difficult. Early composite fault feature separation and extraction has been one of the difficulties in mechanical fault diagnosis.
In combination with the above related problems, the applicant has proposed an early compound fault diagnosis method based on resonance sparse decomposition (RSSD) and Teager energy operators. The structure provided by the invention can realize early diagnosis of single/composite faults of mechanical parts such as bearings, gear boxes and the like in the wind driven generator, provide early warning for monitoring and realize early fault diagnosis of the mechanical parts. Meanwhile, the method provided by the invention can avoid the interference of noise and has the advantages of accurate diagnosis, high reliability and low cost.
Disclosure of Invention
In order to make up for the defects of the prior art, the invention provides a method and a device for diagnosing early compound faults of a wind driven generator and a technical scheme of a readable storage medium.
An early compound fault diagnosis method for a wind driven generator, comprising the following steps:
step 1, collecting vibration signals of mechanical parts;
step 2, decomposing the RSSD signal;
and 3, analyzing the Teager energy spectrum, and judging the reason of the fault according to the Teager energy spectrum.
Further, step 1 includes:
step 1.1, acquiring vibration signals of mechanical parts through a vibration sensor, and storing acquired data into a data acquisition instrument;
and 1.2, exporting the data in the data acquisition instrument as an input of RSSD signal decomposition.
Further, in step 1.1, the mechanical parts include one or more of a gearbox, a bearing, and a gear component.
Further, step 2 includes:
first, the quality factor of the high resonance component is given
Is->
And the quality factor of the optimal low resonance component +.>
Is in the range of +.>
The quality factor of the optimal high-resonance component is obtained through a particle swarm optimization algorithm
And the quality factor of the optimal low resonance component +.>
The method comprises the steps of carrying out a first treatment on the surface of the Second according to the quality factor/>
And->
Determining the number of decomposition layers->
And
is optimized to obtain the optimal +.>
And->
The method comprises the steps of carrying out a first treatment on the surface of the Finally according to the optimum->
、/>
、/>
And->
The optimal high and low resonance components are obtained by RSSD decomposition.
Further, step 2 specifically includes:
step 2.1, quality factor
Defining the resonance properties of the input signal, < >>
The BW is bandwidth, and a low resonance component signal containing the impulse signal and a high resonance component containing the harmonic signal are obtained according to the difference of quality factors of the impulse signal and the harmonic signal;
step 2.2, according to the scale parameters of the high-pass filter bank and the low-pass filter bankNumber of digits
And->
() Determining the maximum number of layers of the RSSD decomposition +.>
Wherein->
For redundancy, N is the data length, < ->
Rounding down the symbol;
step 2.3, according to the quality factor
And redundancy->
Determining the low-pass filter in the signal reconstruction process>
The expression of (2) is:
Step 2.4, according to steps 2.1-2.3, the basic parameters of the decomposition filter bank can be determined, and the vibration signal obtained in step 1 can be expressed as
Wherein->
Representing a high resonance component>
Representing a low resonance component>
Representing the redundant component; establishing a sparsely resolved objective function using morphological component analysis as
Wherein->
And->
Inverse wavelet transforms representing high and low quality factors, respectively;
step 2.5, utilizing a split augmented Lagrangian contraction algorithm to coefficient the wavelet
And->
Performing iterative calculation to obtain +.>
、/>
And->
Expression of (2)The following are provided:
in the middle of
And->
Transform coefficients optimal for the objective function, respectively;
step 2.6, calculating FCFR;
step 2.7, using FCFR as an objective function, giving
And->
Parameter range, repeating step 2.1-step 2.5, optimizing quality factor by PSO algorithm>
And->
；
Step 2.8, using FCFR as an objective function, giving
And->
Parameter range, repeating step 2.1-step 2.5, optimizing quality factor by PSO algorithm>
And->
；
Step 2.9, optimal according to step 2.7 and step 2.8
、/>
、/>
And->
And (3) performing RSSD decomposition to obtain optimal high and low resonance components and residual components.
Further, step 2.6 specifically includes:
step 2.6.1, carrying out resonance sparse decomposition on an original signal to obtain a high resonance component and a low resonance component;
step 2.6.2, HT change is carried out on the low resonance component, and instantaneous amplitude response is obtained;
step 2.6.3, performing fast Fourier transform on the amplitude response obtained in step 2.6.2 to obtain a spectrogram, and finding the amplitudes of all possible fault characteristic frequencies;
step 2.6.4, calculating the FCFR based on the amplitude of the fault signature frequency.
Further, step 3 includes calculating kurtosis spectra of the high and low resonance components according to the optimal high and low resonance components, determining a period range of multi-point optimal minimum entropy deconvolution according to the kurtosis spectra, performing MOMEDA deconvolution calculation on signals in the given period range, calculating a Teager energy spectrum on the MOMEDA deconvolution signals, and finally judging a cause of the fault according to the Teager energy spectrum.
Further, the step 3 specifically includes:
step 3.1, selecting a failure period
The corresponding sampling number is taken as the fault period of the input, sampling period +.>
Defined as->
；
Step 3.2, by the formula
Calculating the multi-point kurtosis value of the deconvolution output signal of the high and low resonance components to obtain a multi-point kurtosis spectrum, wherein +.>
Is the target vector, can pass the fault impact period +.>
To determine that the number of the groups of groups,
，/>
is a window function for expanding the target vector;
step 3.3, determining the calculated period interval of MOMEDA deconvolution according to the multi-point kurtosis spectrum of the high and low resonance components
；
Step 3.4, according to the formula
Solving the maximum value of the D-norm to enable the deconvolution effect to obtain an optimal MOMEDA deconvolution signal in a given period interval;
step 3.5, given Window function
And filter length->
Is optimized by PSO algorithm with FCFR as objective function>
And->
Obtain the optimal window function->
And filter length->
；
Step 3.6, according to the optimum
And->
Parameters, performing MOMEDA deconvolution to obtain a deconvolution time sequence of a given period range;
step 3.7, based on the time series obtained after MOMEDA deconvolution, according to
Calculate +.>
Obtaining a Teager energy sequence of the MOMEDA deconvolution signal;
step 3.8, performing fast Fourier transform on the Teager energy sequence to obtain a Teager energy spectrum;
and 3.9, identifying faults according to the fault characteristic frequency in the Teager energy spectrum.
The invention also provides an early compound fault diagnosis device, which comprises a processor and a memory connected with the processor, wherein a computer program for the processor to execute is stored in the memory, and the early compound fault diagnosis method is carried out when the processor executes the computer program.
The present invention also provides a readable storage medium storing a computer program for execution by a processor, which when executing the computer program, performs the early compound fault diagnosis method as described above.
Compared with the prior art, the invention has the beneficial effects that:
1) The method combining the RSSD decomposition algorithm with the Teager energy spectrum is used for early compound fault diagnosis of mechanical parts of the wind driven generator, the RSSD decomposition algorithm can be used for dividing the early compound fault diagnosis into basic high-low resonance signals according to different quality factors, the early weak fault signals submerged in noise can be effectively extracted, the Teager energy operator is further used for enhancing the capability of the impact characteristic of the fault signals, the Teager energy spectrum is obtained, and the early weak fault signals can be more effectively extracted;
2) The invention provides the method for optimizing the reliability of PSO algorithm optimization by utilizing the frequency ratio of the fault characteristic signals as the optimized objective function of the RSSD decomposition algorithm and the MOMEDA deconvolution algorithm, which can be effectively used for decomposing the multi-fault coupling signals;
3) The invention utilizes PSO algorithm to optimize parameters of RSSD decomposition algorithm, so as to obtain optimal high and low resonance decomposition components, and further to improve reliability of fault diagnosis;
4) The invention provides the method for optimizing the algorithm parameters of MOMEDA by using the PSO algorithm, so that the optimal deconvolution signal of the MOMEDA can be obtained, and the reliability of fault diagnosis can be improved;
5) According to the invention, the fault signal period is positioned by utilizing the multi-point kurtosis spectrum, and the MOMEDA deconvolution calculation interval is intercepted according to the fault signal period, so that the calculated amount is reduced, the calculation efficiency is improved, and the fault characteristic frequency can be more reliably identified;
6) The invention utilizes Teager energy operators to enhance the impact characteristic of fault signals in the prominent vibration signals, can more reliably identify the fault characteristic frequency, locate the faults of mechanical parts, and extract more orders of frequency multiplication components compared with the traditional envelope spectrum analysis.
Drawings
FIG. 1 is a flow chart of a method for diagnosing early compound faults of a wind driven generator;
FIG. 2 is a flow chart of optimizing quality factors QH and QL by the PSO algorithm provided by the invention;
FIG. 3 is a flowchart of optimizing and decomposing the layer numbers JH and JL by the PSO algorithm provided by the invention;
FIG. 4 is a diagram showing the signal components after RSSD decomposition provided by the present invention;
FIG. 5 is a schematic diagram of a multi-point kurtosis spectrum provided by the invention;
FIG. 6 is a flow chart of MOMEDA parameter optimization provided by the invention;
FIG. 7 is a schematic diagram of a time domain waveform after deconvolution of MOMEDA provided by the present invention;
fig. 8 and fig. 9 are schematic diagrams of the Teager energy spectrum provided by the present invention.
Description of the embodiments
The invention is further described below with reference to the accompanying drawings.
Example 1
Referring to fig. 1, a method for diagnosing early compound faults of a wind driven generator includes:
step 1, data acquisition
Step 1.1, collecting vibration signals of a gear box, a bearing or a gear component through a vibration sensor, and storing the collected data into a data collecting instrument.
Step 1.2, data in a data acquisition instrument are exported to file formats such as Excel or Text and the like and used as input for decomposing RSSD signals; the data aiming at the SCADA system of the offshore/onshore wind turbine can be directly exported, and the exported data is converted into a specified format and then is directly used as the input of an RSSD algorithm.
Step 2, RSSD signal decomposition
To obtain optimal high and low resonance decomposition components, the quality factor of the high resonance component is given first
Is->
And the quality factor of the optimal low resonance component +.>
Is in the range of +.>
Obtaining the quality factor of the optimal high resonance component by a particle swarm optimization (Particle Swarm Optimization, PSO) optimization algorithm>
And the quality factor of the optimal low resonance component +.>
The method comprises the steps of carrying out a first treatment on the surface of the Second according to the quality factor>
And->
Determining the number of decomposition layers->
And->
Is optimized to obtain the optimal +.>
And->
The method comprises the steps of carrying out a first treatment on the surface of the Finally according to the optimum->
、/>
、/>
And->
The optimal high and low resonance components are obtained by RSSD decomposition. The detailed steps of the process are as follows:
step 2.1, quality factor
Defining a resonance property of the input signal, wherein +.>
The BW is bandwidth, and the low resonance component signal containing the impulse signal and the high resonance component containing the harmonic signal are obtained according to the difference of the quality factors of the impulse signal and the harmonic signal.
Step 2.2, according to the scale parameters of the high-pass filter bank and the low-pass filter bank
And->
Determining the maximum number of layers of the RSSD decomposition +.>
Wherein->
For redundancy, N is the data length, < ->
To round down the symbol.
Step 2.3, according to the quality factor
And redundancy->
Determining the low-pass filter in the signal reconstruction process>
The expression of (2) is:
high-pass filter
The expression of (2) is:
wherein, the liquid crystal display device comprises a liquid crystal display device,
as a function, it can be expressed as: />
，/>
It can be found that the high-pass filter parameters are completely dependent on the quality factor +.>
And redundancy->
。
Step 2.4, according to step 2.1-step 2.3, basic parameters of the decomposition filter bank may be determined. The vibration signal obtained in the step 1 can be expressed as
Wherein->
Representing a high resonance component>
Representing a low resonance component>
Representing the redundant component. Establishing a sparsely resolved objective function using morphological component analysis as
Wherein->
And->
The inverse wavelet transform of high and low quality factors are shown, respectively.
Step 2.5, utilizing a split augmented Lagrangian contraction algorithm to coefficient the wavelet
And->
Performing iterative calculation to obtain ++when the objective function takes the minimum value>
、/>
And->
The expression of (2) is as follows:
in the middle of
And->
The transform coefficients that are optimal for the objective function, respectively.
Step 2.6, RSSD decomposition is completed once according to steps 2.1-2.5, but since the type of failure is unknown at the time of early failure of the mechanical system, for a given quality factor
Optimal decomposition is not guaranteed. To select the optimal quality factor->
The best decomposition component is obtained. The invention provides a selection strategy based on fault characteristic frequency ratio (Fault Characteristic Frequency Ratio, FCFR), wherein the FCFR can directly reflect the proportion of fault signals in signals, and the larger the FCFR is, the more fault information is contained, and the better the RSSD decomposition effect is. Based on the Hilbert transform (Hilbert Transform, HT), the FCFR definition is given as +.>
Wherein M represents the number of possible faults in the mechanical transmission system, +.>
Representing the +.>
The harmonic component of the wave is transmitted,
representing the number of harmonics for each fault, +.>
Representing the frequency amplitude in the HT spectrum, +.>
Representing the total number of frequency components in the frequency.
For a given signal, the detailed FCFR calculation steps are as follows:
and 2.6.1, carrying out resonance sparse decomposition on the original signal to obtain a high resonance component and a low resonance component.
And 2.6.2, HT change is carried out on the low resonance component, and instantaneous amplitude response is obtained.
And 2.6.3, performing fast Fourier transform on the amplitude response obtained in the step 2.6.2 to obtain a spectrogram, and finding the amplitudes of all possible fault characteristic frequencies.
Step 2.6.4, calculating the FCFR based on the amplitude of the fault signature frequency.
Step 2.7, using FCFR as an objective function, giving
And->
Parameter range, repeating step 2.1-step 2.5, optimizing quality factor by PSO algorithm>
And->
The specific optimization flow chart is shown in FIG. 2Shown.
Step 2.8, using FCFR as an objective function, giving
And->
Parameter range, repeating step 2.1-step 2.5, optimizing quality factor by PSO algorithm>
And->
A specific optimization flow chart is shown in fig. 3.
Step 2.9, obtaining an optimal according to step 2.7 and step 2.8
、/>
、/>
And->
RSSD decomposition is performed to obtain the optimal high and low resonance components and residual components as shown in fig. 4.
Step 3, teager energy Spectrum analysis
According to the optimal high and low resonance components, calculating kurtosis spectrums of the high and low resonance components, and determining a periodic range of a multipoint optimal minimum entropy deconvolution (Multipoint optimal Minimum Entropy Deconvolution Adjusted, MOMEDA) according to the kurtosis spectrums; performing MOMEDA deconvolution calculation on signals in a given period range; and calculating a Teager energy spectrum for the MOMEDA deconvolution signal, and finally judging the reason of the fault according to the Teager energy spectrum. The detailed steps of the process are as follows:
step 3.1, selecting a failure period
Corresponding sampling points (sampling period +.>
) Fault period as input, sampling period +.>
Defined as->
。
Step 3.2, calculating by a formula
The multi-point kurtosis value of the deconvolution output signal of the high and low resonance components, a multi-point kurtosis spectrum is obtained, wherein +.>
Is the target vector, can pass the fault impact period +.>
To determine that the number of the groups of groups,
wherein->
Is a window function for expanding a target vector, and the obtained kurtosis spectrum is shown in FIG. 5, in which +.>
And->
Respectively representing the fault periods corresponding to the two faults.
Step 3.3, determining the calculated period interval of MOMEDA deconvolution according to the multi-point kurtosis spectrum of the high and low resonance components
。
Step 3.4, according to the formula
And solving the maximum value of the D-norm to enable the deconvolution effect to obtain the optimal MOMEDA deconvolution signal in the given period interval.
Step 3.5, given Window function
And filter length->
Also using FCFR as target function, optimizing +.>
And->
Obtain the optimal window function->
And filter length->
，/>
And->
The optimized PSO algorithm optimization process is shown in FIG. 6.
Step 3.6, according to the optimum
And->
Parameters, MOMEDA deconvolution, are performed to obtain a deconvolution time series for a given period range, as shown in FIG. 7.
Step 3.7, based on the time series obtained after MOMEDA deconvolution, according to
Calculate +.>
To obtain a Teager energy sequence of the MOMEDA deconvolution signal.
And 3.8, performing fast Fourier transform on the Teager energy sequence to obtain a Teager energy spectrum.
Step 3.9, calculating according to the faults
And->
The corresponding Teager energy spectrum, as shown in fig. 8 and 9, identifies faults according to the fault feature frequency in the Teager energy spectrum. From fig. 8 it can be seen that the failure period +.>
And the period times thereof can be effectively extracted, and it can be seen from FIG. 9 that the failure period +.>
And the double period of the method can be effectively extracted, and the result proves the effectiveness of the method, so that the early compound faults can be effectively identified.
Example 2
An early compound fault diagnosis apparatus comprising a processor and a memory connected to the processor, wherein the memory stores a computer program for execution by the processor, and wherein the early compound fault diagnosis method of embodiment 1 is performed when the processor executes the computer program.
Example 3
A readable storage medium storing a computer program for execution by a processor, the processor performing the early compound fault diagnosis method of embodiment 1 when executing the computer program.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (8)
1. An early compound fault diagnosis method for a wind driven generator is characterized by comprising the following steps:
step 1, collecting vibration signals of mechanical parts;
step 2, decomposing the RSSD signal, specifically including:
step 2.1, quality factor
Defining the resonance properties of the input signal, < >>
The BW is bandwidth, and a low resonance component signal containing the impulse signal and a high resonance component containing the harmonic signal are obtained according to the difference of quality factors of the impulse signal and the harmonic signal;
step 2.2, according to the scale parameters of the high-pass filter bank and the low-pass filter bank
And->
Determining the maximum number of layers of the RSSD decomposition +.>
Wherein->
For redundancy, N is the data length, < ->
Rounding down the symbol;
step 2.3, according to the quality factor
And redundancy->
Determining the low-pass filter in the signal reconstruction process>
The expression of (2) is:
Step 2.4, according to steps 2.1-2.3, the basic parameters of the decomposition filter bank can be determined, and the vibration signal obtained in step 1 can be expressed as
Wherein->
Representing a high resonance component>
Indicating a low-resonance component of the wave,
representing the redundant component; establishing a sparsely resolved objective function using morphological component analysis as
Wherein->
And->
Inverse wavelet transforms representing high and low quality factors, respectively;
step 2.5, utilizing a split augmented Lagrangian contraction algorithm to coefficient the wavelet
And->
Performing iterative calculation to obtain +.>
、/>
And->
The expression of (2) is as follows:
in the middle of
And->
Transform coefficients optimal for the objective function, respectively;
step 2.6, calculating FCFR;
step 2.7, using FCFR as an objective function, giving
And->
Parameter range, repeating step 2.1-step 2.5, optimizing quality factor by PSO algorithm>
And->
；
Step 2.8, using FCFR as an objective function, giving
And->
Parameter range, repeating step 2.1-step 2.5, optimizing quality factor by PSO algorithm>
And->
；
Step 2.9, optimal according to step 2.7 and step 2.8
、/>
、/>
And->
Performing RSSD decomposition to obtain optimal high and low resonance components and residual components;
and 3, analyzing the Teager energy spectrum, and judging the reason of the fault according to the Teager energy spectrum.
2. The method for diagnosing an early compound fault in a wind turbine generator as set forth in claim 1, wherein step 1 includes:
step 1.1, acquiring vibration signals of mechanical parts through a vibration sensor, and storing acquired data into a data acquisition instrument;
and 1.2, exporting the data in the data acquisition instrument as an input of RSSD signal decomposition.
3. The method for diagnosing early compound faults of a wind turbine of claim 1 in which in step 1 the mechanical components include one or more of a gearbox, bearings, gear components.
4. The method for diagnosing early compound faults of a wind turbine as claimed in claim 1, wherein the step 2.6 specifically includes:
step 2.6.1, carrying out resonance sparse decomposition on an original signal to obtain a high resonance component and a low resonance component;
step 2.6.2, HT change is carried out on the low resonance component, and instantaneous amplitude response is obtained;
step 2.6.3, performing fast Fourier transform on the amplitude response obtained in step 2.6.2 to obtain a spectrogram, and finding the amplitudes of all possible fault characteristic frequencies;
step 2.6.4, calculating the FCFR based on the amplitude of the fault signature frequency.
5. The early compound fault diagnosis method for the wind driven generator according to claim 1, wherein the step 3 comprises calculating kurtosis spectra of high and low resonance components according to optimal high and low resonance components, determining a period range of multi-point optimal minimum entropy deconvolution according to the kurtosis spectra, performing MOMEDA deconvolution calculation on signals in the given period range, calculating a Teager energy spectrum on the MOMEDA deconvolution signals, and finally judging the cause of the fault according to the Teager energy spectrum.
6. The method for diagnosing early compound faults of a wind turbine as claimed in claim 5, wherein the step 3 specifically includes:
step 3.1, selecting a failure period
The corresponding sampling number is taken as the fault period of the input, sampling period +.>
Is defined as
；
Step 3.2, by the formula
Calculating the multi-point kurtosis value of the deconvolution output signal of the high and low resonance components to obtain a multi-point kurtosis spectrum, wherein +.>
Is the target vector, can pass the fault impact period +.>
To determine that the number of the groups of groups,
，/>
is a window function for expanding the target vector;
in the step 3.3 of the method,determining the calculated period interval of MOMEDA deconvolution according to the multi-point kurtosis spectrum of high and low resonance components
；
Step 3.4, according to the formula
Solving the maximum value of the D-norm to enable the deconvolution effect to obtain an optimal MOMEDA deconvolution signal in a given period interval;
step 3.5, given Window function
And filter length->
Is optimized by PSO algorithm with FCFR as objective function>
And->
Obtain the optimal window function->
And filter length->
；
Step 3.6, according to the optimum
And->
Parameters, performing MOMEDA deconvolution to obtain a deconvolution time sequence of a given period range;
step 3.7, based on the time series obtained after MOMEDA deconvolution, according to
Calculate +.>
Obtaining a Teager energy sequence of the MOMEDA deconvolution signal;
step 3.8, performing fast Fourier transform on the Teager energy sequence to obtain a Teager energy spectrum;
and 3.9, identifying faults according to the fault characteristic frequency in the Teager energy spectrum.
7. An early compound fault diagnosis apparatus comprising a processor and a memory connected to the processor, the memory storing a computer program for execution by the processor, wherein the early compound fault diagnosis method of any one of claims 1-6 is performed when the processor executes the computer program.
8. A readable storage medium storing a computer program for execution by a processor, wherein the early compound fault diagnosis method of any one of claims 1-6 is performed when the processor executes the computer program.
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