Petroleum equipment fault diagnosis method

Fault diagnosis technology is a technology that uses analysis algorithms to judge the status of equipment through the current data information and historical data information of the equipment. Fault diagnosis includes dynamic analysis, signal processing, and intelligent diagnosis, in which signal processing relies on experience for manual discrimination, and ideal discrimination results can be obtained without the support of data samples; Intelligent diagnostics are automatically classified by machine learning and deep learning, but their accuracy is too dependent on sample size.

Signal processing

Vibration signals are widely used in signal processing methods for feature extraction, and the vibration signals of equipment are mainly extracted by time domain statistical analysis, spectral analysis, time-frequency analysis, deconvolution, and other methods.

（1）Time domain statistical analysis Time domain statistical characteristic analysis is to calculate and analyze the time domain amplitude of the equipment vibration signal to complete the fault diagnosis of the equipment. Commonly used time-domain statistical characteristic indicators include dimensioned indicators and dimensionless indicators. Dimensional indicators include root mean square value, peak, variance, standard deviation, skewness, steepness, etc., and one or more dimensional indicators are often selected to monitor the status of the equipment. Dimensional statistical indicators will not only change with the aggravation of faults, but also change differently with the change of equipment operating state, and it is impossible to effectively divide the fault interval of characteristic indicators.

Therefore, dimensionless characteristic indicators are introduced in the analysis of statistical characteristics in the time domain, and dimensionless characteristic indicators are obtained by dividing two identical characteristic indicators, which are more sensitive to fault characteristics and less affected by changes in equipment operation conditions, and the probability of equipment failure is judged by calculating whether the dimensionless characteristic indicators during equipment operation reach the fault interval, mainly including waveform indicators, peak indicators, pulse indicators, margin indicators, steepness indicators, skewness indicators, etc.

The dimensionless time domain index is not affected by changes such as equipment speed, and when the operating state of the equipment changes, good diagnostic results can still be obtained. Among them, the most widely used is the slope indicator, which can well identify the impact signal, it is generally believed that the slope index is greater than 3 when the signal is impacted, the more obvious the impact, the greater the steepness indicator.

(2) Spectral analysis is a method of analyzing the characteristics of the fault by mathematically calculating the working signal of petroleum and petrochemical equipment and converting it into the frequency domain, including classical spectrum estimation methods and modern spectral estimation methods.

In classical spectral estimation, the Fourier transform is the basis of many frequency domain analysis methods, which maps the time domain signal to the frequency domain, and more intuitively display the correspondence between frequency and amplitude and phase and amplitude, among which amplitude-frequency maps are more widely used. It is worth noting that the Fourier transform requires the signal to have linear and stable properties and meet the Diriheli condition, while the signal in reality is mostly random signals and does not meet the transformation conditions, so it is necessary to find the autocorrelation of the signal first, and then perform the Fourier transform on the autocorrelation signal to obtain the power spectrum.

To find the signal envelope spectrum, you first need to perform the Hilbert transform on the signal, and then modulus it, and then perform the Fourier transform. Envelope spectroscopy is widely used in the demodulation of modulated signals, such as the extraction of fault characteristics of bearing shock signals. Parametric model power spectrum estimation is a modern spectrum estimation method based on time series analysis, mainly including the AR model method, MA model method, ARMA model method, etc., which has a higher resolution than classical spectrum estimation and can obtain better power spectrum estimation effect, but it has problems such as high computational complexity, large computing power requirements,  and requires exponential time and more efficient hardware to support algorithms with higher time complexity and spatial complexity.

(3) Time-frequency analysis Although the spectral analysis method can better describe the composition of the signal, it cannot explain the signal locally.

The time-frequency analysis method introduces the concept of instantaneous frequency based on traditional frequency domain analysis, which is a signal processing method that can describe the time dimension characteristics and frequency dimension characteristics of non-stationary signals at the same time, which can display the relative frequencies corresponding to different times when the equipment is working. According to different means of analysis, it can be divided into time-frequency analysis method based on basis function and time-frequency analysis method based on modal decomposition. Time-frequency analysis methods based on basis functions include short-time Fourier transform, wavelet transform, Weigel transform, etc.

Gabor et al. proposed the short-time Fourier transform (STFT) in 1946, STFT first divides the time domain signal into several overlapping sub-periods of equal length, and there is a certain overlap between each sub-period to prevent the loss of the corresponding time-frequency information during the analysis process, and then performs a Fourier transform on each sub-period signal, and finally stitches the Fourier transform results of all sub-time periods, that is, the energy distribution of the signal at different times and different frequencies in the period is obtained. Although STFT is widely used in signal processing, it also has some drawbacks. When the length of the sub-period is selected, the time domain resolution is fixed, and the frequency domain resolution obtained by the uncertainty principle is also fixed, and the higher time domain resolution will cause the signal center energy to diverge along the frequency, and the obtained time-frequency map has blurred high-frequency details. Conversely, higher frequency resolution can obtain compact signal frequency components but will increase the overlap of signal time-frequency diagrams in time.

Therefore, Morlet proposed the wavelet transform in 1984, which can localize the analysis of the signal in time and frequency, compared with the short-time Fourier transform, the wavelet transform constructs an adjustable wavelet basis function, constantly changes the time domain scale factor and the frequency domain translation factor, and stitches the final result. Although wavelet transforms alleviate the problem that STFT is solidified in the time and frequency dimensions to a certain extent and the corresponding accuracy cannot be selected in a targeted manner, there is still a problem of spectral blurring under the influence of the uncertainty principle, and different wavelet bases will affect the analysis results of the time-frequency map, and improper selection will lead to errors and distortions, and may even miss important information.

Daubechies et al. proposed the simultaneous compression wavelet transform (SWT) in 2011, which rearranges the time-frequency coefficients through synchronous compression operators, and moves the time-frequency distribution of the signal at any point in the time-frequency plane to the center of gravity of the energy, so that the energy of the instantaneous frequency becomes concentrated, thereby solving the problem of spectral blurring. Ville introduced the Wigner distribution to the field of signal processing in 1948, thus developing into a representative signal processing method. As a new time-frequency analysis method, Wigne-Ville distribution (WVD) can effectively overcome the shortcomings of the short-time Fourier transform and is an effective method for processing non-stationary signals. WVD is obtained by Fourier transform according to the instantaneous autocorrelation function of the signal, because it has a quadratic term coefficient, resulting in cross-interference in the time-frequency analysis method, and when the multi-component signal is analyzed in time-frequency analysis, the interference interval and influence are expanded, so that a large number of false components are generated around the actual component. Therefore, it is necessary to find a suitable basis function to suppress cross-interference terms.

Equipment Fault Detection – Oil & Gas Use Case – YouTube.