Vibration analysis is widely used for rotating machinery diagnostics; however measuring vibration of operational oil well pumps is not possible. The pump’s driver’s current signatures may provide condition-related information without the need for an access to the pump itself. This paper investigates the degree of relationship between the pump’s driver’s current signatures and its induced vibration. This relationship between the driver’s current signatures (DCS) and its vibration signatures (DVS) is studied by calculating magnitude-squared coherence and phase coherence parameters at a certain frequency band using continuous wavelet transform (CWT). The CWT coherence-based technique allows better analysis of temporal evolution of the frequency content of dynamic signals and areas in the time-frequency plane where the two signals exhibit common power or consistent phase behaviour indicating a relationship between the signals. This novel approach is validated by experimental data acquired from 3 kW petroleum pump’s driver. Both vibration and current signatures were acquired under different speed and load conditions. The outcomes of this research suggest the use of DCS analysis as reliable and inexpensive condition monitoring tool, which could be implemented for oil pumps, real-time monitoring associated with condition-based maintenance (CBM) program.

Pumps and their associated systems are essential in oil and gas facilities for the efficient transportation of fluids. Common pumps found in these facilities include centrifugal, reciprocating, diaphragm, and rotary pumps [

Vibration monitoring is particularly suited to pumps due to the number of integrated rotating parts, which may show additional movement when faults develop [

The most obvious technique for obtaining a vibration signal from pump driver’s “induction motor” is by direct measurement using vibration transducers (usually accelerometers) mounted on the driver. This requires a high-performance vibration transducer capable of withstanding harsh environmental conditions and which can cost several hundred dollars. When a large number of machines are concerned and more than one transducer is required per machine, the total cost can be high. A major disadvantage of vibration monitoring is that it requires access to the machine. For accurate measurements, sensors should be mounted rigidly on the machine, which requires expertise and trained personnel.

An increasing number of pumps are installed with electrical motors as their prime driver. This development has introduced new possibilities for condition monitoring by the use of driver’s electric signals such as current and voltage.

In response an indirect method, called sensorless detection and diagnosis intended for mechanical equipment driven by AC induction motors, has been developed over the past 20 years and is growing rapidly [

The relationship between the magnitudes of stator current harmonics, the magnitudes of the vibration harmonics, and specific machine faults types has been closely studied [

The cause and effect relationship between two signals or the commonality between them is generally estimated using the coherence function. Reference [

This paper aims at investigating the use of current signal as reliable and inexpensive tool for pump’s CBM programs. It is organised as follows. In Section

Figure

Time waveforms of current and vibration signatures.

Healthy motor with symmetrical supply voltages

Healthy motor with symmetrical supply voltages

One-phase supply voltage with 20 volts drop

One-phase supply voltage with 20 volts drop

Influence of load on the RMS current and vibration signals.

A common approach for extracting information concerning frequency features of a periodic signal is to transform the signal to the frequency domain using the discrete Fourier transform.

In Figure

Frequency spectra of current and vibration signatures.

Healthy motor with symmetrical supply voltages (current)

Healthy motor with symmetrical supply voltages (vibration)

One-phase supply voltage with 20 volts drop (current)

One-phase supply voltage with 20 volts drop (vibration)

The coherence is a function of the power spectral density (

An improved estimator of the PSD is the one proposed by Welch [

The averaging of modified periodograms tends to decrease the variance of the estimate relative to a single periodogram estimate of the entire data record. Although overlap between segments tends to introduce redundant information, this effect is diminished by the use of a nonrectangular window, which reduces the importance or weight given to the end samples of segments (the samples that overlap).

However, as mentioned above, the combined use of short data records and nonrectangular windows results in reduced resolution of the estimator. In summary, there is a trade-off between variance reduction and resolution. One can manipulate the parameters in Welch’s method to obtain improved estimates relative to the periodogram, especially when the SNR is low.

The coherence function between the motor current and vibration signature was computed and plotted in Figure

Coherence between DCS and DVS signals.

The CWT allows analysis of the temporal evolution of the frequency content of a given signal or time series. The application of the CWT to two time series and the cross-examination of the two decompositions can reveal localized similarities in time and scale. Areas in the time-frequency plane where the two time series exhibit common power or consistent phase behaviour indicate a relationship between the signals.

For jointly stationary time series, the cross spectrum and associated coherence function based on the Fourier transform are used to detect common behaviour in the frequency domain. In the general nonstationary case, wavelet-based counterparts can be defined to provide time-localized alternatives.

The wavelet coherence of two time series

Figure

Continuous wavelet transform of DCS and DVS signals.

The common periods of the current and vibration signals at scales 32 and 16, respectively are clearly detected in the moduli of the individual wavelet spectra and frequency at 50 and 100 Hz as shown in Figure

The wavelet spectrum, defined for each signal, is characterized by the modulus and the phase of the CWT obtained using the complex valued wavelet. The individual wavelet spectra are denoted as

Wavelet cross spectrum of DCS and DVS signals.

Figure

Wavelet coherence of DCS and DVS signals.

The common period of the signals at scale 192 is clearly detected using Freq = scal2frq(192,“mother wavelet”, 1/sample frequency); note that this corresponds to a frequency of 50 Hz.

The arrows in the figure represent the relative phase between the two signals as a function of scale and position. The relative phase information is obtained from the smoothed estimate of the wavelet cross spectrum,

This study utilized Welch’s method and continuous wavelet techniques for spectral estimation to investigate the coherence between the driver’s current DCS and the driver’s vibration signatures. The coherence between DCS and DVS signals was investigated at a particular frequency and in different frequency bands. Both signals are completely coherent if the magnitude-squared coherence is equal to 1; if MSC is equal to zero, then both signals are independent of each other. The results show that both signals are coherent at the frequencies at which the magnitude-squared coherence (DSC) is greater than 0.5 and both signals are incoherent (less coherent) if DSC is less than 0.5. Wavelet coherence analysis greatly facilitates the detection of the quasiperiodic component indicative of a system anomaly. Wavelet cross spectrum and wavelet coherence are useful to reveal localized similarities between DCS and DVS signals in the time-scale plane and to interpret the results. The results of this work show the possibility to estimate the DVS signal information from the DCS signal.