In most cases, cavitation is highly dangerous and should be avoided [1], [2]. Cavitation onset in the pump system begins with transient noise that gradually becomes persistent and highly intense as the inlet pressure decreases.

This phenomenon is also accompanied by increasing vibrations [3–5]. Cavitation arises when the local absolute pressure falls below the liquid's vapor pressure, leading to bubble formation. When the bubble moves into regions of higher pressure, it implodes, producing highly pressurized fluid jets that impact solid surfaces, resulting in vibrations, erosion, and noise [6]. Cavitation in a centrifugal pump usually starts near the impeller inlet, where the velocity is maximum, and the pressure is minimum. It causes a reduction in flow rate, a decrease in head, and deterioration of impeller blade performance [6]. Thus, detecting cavitation is important to avoid pump failures.

Over the past 20 years, various approaches have been proposed for detecting cavitation in centrifugal pumps. Alfayez et al. [1] employed Acoustic Emission (AE) technology to identify incipient cavitation and determine the Best Efficiency Point (BEP) for a 60 kW centrifugal pump, demonstrating that AE signals are highly sensitive to bubble collapse. Over the past two decades, many investigators have attempted to develop various techniques for detecting cavitation in centrifugal pumps.

Čudina and Prezelj [5] applied the approach of using frequency tones in the audible range to monitor cavitation phenomena, while later Čudina and Prezelj [3], [4] conducted a comparison study of sound pressure, underwater sound, and vibrations. The authors concluded that vibration measurement is a more practical approach that strikes an effective balance between sensitivity and technical simplicity. Measurement uncertainties in detecting cavitation phenomena were estimated by Černetič and Čudina [7] using various approaches, including frequency analysis of wide-band and discrete frequency components. Cavitation noise parameters in a centrifugal pump were analyzed experimentally using power spectral density and wavelet transform techniques by Wang et al. [8].

Al Obaidi [9], [10] studied vibration-based cavitation diagnosis techniques in time and frequency domains, proving that vibration patterns are substantially altered as cavitation progresses. Sakthivel et al. [11] employed decision trees for vibration-based fault diagnosis of monoblock centrifugal pumps, with cavitation as a possible fault.

Azizi et al. [12] focused solely on the detection of cavitation severity and proposed cavitation-related vibration indices. Cavitation was detected using vibration signal analysis by Ganeriwala and Kanakasabai [13], emphasizing the role of high-frequency components. Spectral kurtosis method for cavitation detection using vibration data was introduced by Yiakopoulos et al. [14].

Mousmoulis et al. [15] conducted an experiment that included AE, vibration monitoring, and flow visualization to investigate cavitation formation in a centrifugal pump. Li et al. [16] combined numerical, experimental, and deep learning approaches to characterize hydrodynamic performance and cavitation evolution. McKee et al. [17] proposed a vibration-based cavitation-sensitivity parameter that enables quantitative estimation of cavitation severity from spectral and statistical vibration characteristics.

Among these techniques, vibration analysis has been found interesting due to its stability and insensitivity to environmental changes, as well as its ease of measurement using industrial accelerometers [3–5]. Despite being unstable (i.e., nonstationary), vibration signal analysis in a centrifugal pump is relatively simple, since cavity bubble collapse occurs in a broad-band manner and involves transient phenomena. This aspect cannot be captured using conventional spectral analysis techniques like the FFT, which suffer from the time-average problem. STFT, on the other hand, is used to overcome such a problem but is subject to a constant trade-off between time and frequency. Continuous Wavelet Transform (CWT) provides an ideal solution to such issues because multi-resolution analysis allows the use of a small window at higher frequencies (time resolution) and a larger window at lower frequencies (frequency resolution) [8], [11], [12].

In this work, vibration data are obtained for four operating conditions of the centrifugal pump: normal operation, early-stage cavitation, mature cavitation, and severe cavitation. The CWT technique is implemented using the db9 mother wavelet, and the scales of interest are determined, which are strongly affected by cavitation in the rotor flow. In addition, a simulation of the effect of white Gaussian noise is performed.

An experimental setup was developed as a closed-loop circuit to produce controlled cavitation conditions (Fig. 1). The test pump consists of a 10-blade centrifugal pump driven by a 2850 rpm electric motor (shaft rotation frequency = approx. 50 Hz; Blade Passing Frequency (BPF)= approx. 500 Hz). A piezoelectric accelerometer (0.5 Hz–20 kHz) was placed in proximity to the pump outlet, where bubbles collapse under high pressure, generating maximum vibrations. A magnetic clamp was used to ensure proper sensor mounting. Signals were collected at 32 L/min flow using an A/D converter board (4 channels, ±5 V; max output frequency 10 kHz; anti-aliasing filter) with a sampling frequency of 4096 Hz, yielding an effective sampling frequency of 2048 Hz after the anti-aliasing filter.

Four distinct modes of operation were identified from the observations and sounds:

I. Normal condition: No cavitation, smooth functioning, no bubble collapse sound.

II. Incipient cavitation: Emergence of bubble collapse sound for the first time, weak intensity, no performance decrease.

III. Developed cavitation: Continuous sound, increased vibrations, and performance reduction start.

IV. Extensive cavitation: Well-developed cavitation, heavy vibrations, noise, and a decrease in flow rate and head.

A vibration signal captured in the time domain by an accelerometer when it is functioning normally is shown

The CWT is an approach that uses time-frequency analysis to represent signals using wavelets. The definition of the CWT is provided below.

ψ ψ 1 +∞ ∗ t − τ

CWTx (τ, s) = Ψx (τ, s) = ∫ x(t)ψ ( ) dt. (1)

√|s| −∞ s

Here, x(t) represents the signal, ψ(t) denotes the mother wavelet, ss represents the scaling factor, and τ is the translation parameter. In this work, db9 (Daubechies 9) was used as the mother wavelet, which has good localization characteristics and has been previously applied successfully for fault detection in mechanical systems [8], [12]. Scale ss is inversely proportional to frequency; small scales are associated with higher frequencies (better time resolution), while larger scales are associated with lower frequencies (better frequency resolution). The equation relating scale s and the corresponding frequency f is:

fc

f = , (2)

sΔt

where fc is the central frequency of the mother wavelet (for db9, fc ≈ 0. 714 Hz for each sampling time interval), s is the scale, and Δ t is the sampling interval. For a sampling rate of 2048 Hz, Δ t = 1/2048 ≈ 0. 000488.

The paper assessed the feasibility of the CWT for cavitation detection in a centrifugal pump using vibration signals. Key conclusions drawn are:

I. Sensitivities to specific scales: Cavitation is found to consistently excite scales 2 (≈725 Hz) and 5–10 (≈145– 290 Hz) in the CWT analysis of pump casing vibration signals.

II. Monotonic progression: The magnitude of CWT coefficients of the aforementioned scales progressively increases with increasing cavitation severity–normal, incipient, developed, and extensive cavitations. This phenomenon makes the method suitable not only for cavitation detection but also for estimating cavitation severity.

III. Resilience to noise: Despite the presence of a 0 dB signal-to-noise ratio white Gaussian noise, where noise and signal have equal amplitudes, the sensitivities of these scales remain detectable. This phenomenon confirms the feasibility of the proposed technique for practical industrial applications.

IV. Feasibility: Real-time monitoring of these scales using a simple thresholding algorithm is a reliable, low-cost cavitation warning system that requires only a basic accelerometer and an average sample frequency.

Further research can be conducted using different mother wavelets such as Morlet, Symlet, and Coiflet. Moreover, the combination of CWT and Machine Learning (ML) models, such as Convolution Neural Networks (CNNs), can be used for cavitation detection and classification.

The authors declare that there is no conflict of interest regarding the publication of this article.

All data generated or analyzed during this study are included in this published article. No additional data are available.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.