In power transformer vibration analysis, the quantities of interest are the individual vibration characteristics of the internal core and windings, as they carry direct fault signatures. In practical, however, vibration measurements are constrained to the external tank surface. The acquired signals are therefore a mixture of vibrations from core and windings, which are large-scale spatial distributed sources and have overlapped spectrum. The statistically dependent nature and the complex mixing due to the coupled transmission paths make isolating individual source signals inherently challenging.To address these challenges, this paper proposes a physics-informed blind source separation (BSS) framework. It enhances the Time-Frequency Ratio of Mixtures (TIFROM) method by integrating a delay estimation technique and a two-dimensional subspace clustering strategy. It is designed to separate transformer vibrations while preserves both spectral and phase information under a single-sensor configuration.Validated on vibrations acquired from healthy and faulty transformers, the proposed method consistently outperforms other benchmark algorithms across sensor locations under all conditions. The effect of correct phase estimation is discussed in detail. Analysis further reveals that mechanical faults such as winding deformation would generate more clustering peaks and introduce modulation effects that manifest as distinctive patterns in the scattered plot. Notably, the method shows robust performance under real-world operational conditions. Therefore, this work enables the measurement of individual vibration characteristics of core and windings, provides an efficient preprocessing solution for vibration-based transformer diagnosis and offers new insights through the analysis of source-domain signals, thus adding practical values in the transformer fault detection area.

Previous studies on Erhu acoustics have primarily focused on the symmetric vibration of the python skin, its coupling with the attached soundbox, and sound radiation. Since the bridge is positioned at the centre of the skin, the input admittance at the bridge exhibits negligible response to antisymmetric modes. However, our recent measurements of the transfer admittance between off-centred skin vibrations and the force at the bridge reveal the presence of antisymmetric modes and their significant contribution to radiated sound, particularly around 1000 Hz- a frequency range where symmetric modes are less dominant. This paper presents experimental results on the antisymmetric modes of the Erhu and their sound radiation, along with a discussion of the possible excitation mechanisms.

This paper presents a comprehensive investigation, comprised of analytical, experimental and numerical approaches, into the interaction between a water cavity of varying fluid cavity height and the vibration of a thin circular plate subjected to its hydro-static pressure. We extend the application of the strong modal coupling method to derive a solution for this unexplored physical problem by utilising classic plate theory, Fourier-Bessel series formulation and the uncoupled solution of a thin clamped circular plate with uniform radial tension. Using a set of geometric and physical properties for the system, the resonance frequencies, response functions and non-dimensionalised added virtual mass incremental (NAVMI) factors are calculated and investigated as a function of hydro-static pressure and fluid cavity height, providing novel fundamental insights into the physical system. We construct an experimental rig to embody the conditions of the analytical investigation for the purpose of validation and to uncover experimental insights into the physical problem. Finite element analysis (FEA), employing modal analysis and transient dynamic analysis, is used to further validate and extend the analytical insights while more accurately mirroring the experimental conditions. The response functions, resonance frequencies and NAVMI factors and their dependence on the cavity pressure were experimentally measured and numerically simulated, with direct comparisons made with the analytical model. A high degree of accuracy for the analytical model is validated, along with its ability to describe the underlying physical phenomena. The validated analytical model is then leveraged to perform fundamental explorations into the modal compositions of the coupled system modes as a function of cavity height and hydro-pressure, the deformation of the coupled system mode shapes and a parametric sensitivity analysis on the effects of plate radii and plate thickness on the coupled system resonance frequencies and NAVMI factors. In totality, this study provides detailed modelling and prediction of the frequency response, resonance frequencies, added mass factors, modal contributions, and deformation of the coupled mode shapes, offering comprehensive insights with wide applicability.

This paper introduces an analytical method for predicting the acoustic response of a finite circular cylinder to internal monopole source excitation. The cylindrical shell is attached to rigid end plates. The proposed method accurately predicts the system response, irrespective of whether the internal and external media surrounding the shell are air or water. When the cylinder is filled with a heavy fluid, the cross-coupling between internal acoustical modes and shell structural modes becomes crucial in determining the accurate response both on the shell and inside the cylinder. Similarly, if the cylinder is submerged in a heavy fluid, the cross-coupling between shell modes through modal sound radiation also plays a significant role in determining the shell's response and the radiated sound field. The accuracy of our method is validated through excellent agreement with calculated results obtained from finite element / boundary element models.

This paper presents a comprehensive investigation, comprised of analytical, experimental and numerical approaches, into the interaction between the sound field produced within a pressurised air-filled back cavity and the vibration of a thin clamped circular plate subjected to its pressure. Previous investigations into the interaction of sound fields with vibrating boundaries have primarily been restricted to non-pressurised cavities. We extend the application of the weak modal coupling method to derive a solution for this unexplored physical problem by utilising classic plate theory, Fourier-Bessel series formulation and the uncoupled solutions for a pressurised cylindrical sound field and a thin clamped circular plate with uniform radial tension. We describe the vibration response of the coupled system in terms of the uncoupled cavity and plate modes. Using a set of geometric and physical properties for the system, the resonance frequencies and response functions are calculated and the coupling between the sound field and the plate is investigated as a function of cavity pressure, providing novel fundamental insights into the physical system. We construct an experimental rig to embody the conditions of the analytical investigation for the purpose of validation. Finite element analysis (FEA), employing modal analysis and transient dynamic analysis, is used to further validate and extend the analytical insights while more accurately mirroring the experimental conditions. The response functions, mode shapes, resonance frequencies and their dependence on the cavity pressure were experimentally measured and numerically simulated, with direct comparisons made with the analytical model. A high degree of accuracy for the analytical model is validated along with its ability to describe the underlying physical phenomena. The validated analytical model is then leveraged to perform fundamental explorations into the modal contributions as a function of cavity pressure and a parametric sensitivity analysis on the effects of plate radii and plate thickness on the coupled system resonance frequencies.

This paper examines the vibration and force properties of an actuator formed from a piezoelectric stack within a frame structure. Such configuration avoids the use of the traditional “earth-connected” support and allows the convenient attachment of the actuator to structures, such as power transformer tanks. The steady-state sensitivity of the actuator is analyzed, which comprised a linear frequency response function of the actuator system and a steady-state line frequency spectra of the transducer force at the frequency of the input voltage and its odd harmonics. The sensitivity is first analyzed by examining the forces transmitted to a rigid base structure through the stack and two legs of the frame when the actuator is excited by a single-frequency voltage input. The magnitude of the steady-state sensitivity at the frequency of the input voltage is approximately 15 dB higher than that at the other frequencies. The force transmitted through the piezoelectric stack is approximately twice as large as that through the two frame legs and with opposite phase. Next, the properties of transmitted forces when the rigid base structure is replaced by a beam and a plate of infinite size are also investigated. The interaction between the actuator and the elastic base structure has little effect on the magnitudes of the transmitted forces except at the resonace frequency of the actuator structure. However, the induced structural response is greatly affected and should be considered when describing the excitation capacity of the actuator. This capacity could be illustrated by the power flow between the actuator and the base structure and by the spatial distribution of the structural vibration induced by the actuator.

This paper experimentally investigates the performance of piezoelectric force actuators. Using the same encapsulated piezoelectric stack, an inertial-type actuator and a frame-type actuator are constructed for performance comparison. The experimental results are also used to validate the recently established actuator models, whilst the mechanical and piezoelectrical parameters of the models are experimentally identified. The performance of the actuators is described by the transmitted force(s) and input power flow from the actuators to the base structure with reference to the same electrical input voltage to the stack. The validation is deemed successful due to the strong agreement observed between the measured and predicted actuator performances. Additionally, it is discovered that the frame-type actuator has the capacity to produce significantly higher transmitted forces and input power flow to the base structure compared to the inertial-type actuator. The mechanism underlying the performance disparity between these two types of actuators is also examined. This paper clarifies the mechanism, shedding light on the design and optimization of piezoelectric actuators.

An analytical solution is presented in this study for the vibro-acoustic analysis of a cavity coupled with a ribbed panel due to an internal point sound source excitation. The solution is validated by comparing the result with that obtained using finite element analysis. Generally good agreements are found between the results. The model is then used to examine the sound transmission either through a single ribbed–panel or multiple ribbed–panels separated by air gaps. Results demonstrate that the rib enhancement is effective to reduce the energy transmission controlled by the panel control modes. Whereas the attenuation of the energy transmission to the panels is more effective for the cavity control modes when multiple ribbed panels with air gaps are used. The result also shows that the depth of the air gaps will also play a part on the sound attenuation across the panel system where a larger air gap will lead to a better sound attenuation.

In our previous work we demonstrated the feasibility of using Polyvinylidene Fluoride (PVDF) sensors inside an operational thrust bearing and were able to measure the blade passing frequencies (BPF) due to an asymmetric flow around different propellers. In that work however the sensors were positioned inside the flat surface of the stationary portion of the bearing with the tilted pads rotated on the opposite side. Due to this configuration the output signal of the PVDF consisted of a superposition of the pad passing frequency (PPF) and the blade passing frequency (BPF) making it difficult to extract useful information from the results. Here, an improved bearing pad-film configuration is proposed in order to minimise the effects of the PPF. By embedding the films inside the pads, positioned on the stationary side of bearing, and rotating the flat surface, it was possible to eliminate the PPF and significantly increase the signal to noise ratio. The measured results give a better understanding of the fundamental vibratory components that arise from the propeller-shaft system.

This paper investigates the properties of a mass−attached piezoelectric stack actuator and analyzes its sensitivity, which is defined as the spectrum of the driving force (the output) caused by a single−frequency voltage (the input). The force spectrum is utilized because of the nonlinear hysteresis effect of the piezoelectric stack. The sensitivity analysis shows that the nonlinear dynamics of the actuator can be interpreted as a cascade of two subsystems: a nonlinear hysteresis subsystem and a linear mechanical subsystem. Analytical solutions of the nonlinear differential equations are proposed, which show that the nonlinear transformation can be described by a steady−state mapping of a single−frequency voltage input to a multiple−frequency driving force at the driving frequency and its odd harmonics. The steady−state sensitivity is then determined by the response of the mechanical subsystem to the line spectrum of the driving force. The maximum sensitivity can be achieved by setting the frequency of the input voltage close to the natural frequency of the mechanical subsystem. The analytical model is also validated by a numerical model and experimental results and it may be used for the analysis and design of piezoelectric actuators with different structural configurations.

This paper reports a series of experimental and modeling investigations on two piezoelectric arrays made of polyvinylidene fluoride (PVDF) films. They were embedded inside rubber cylinders and used to directly measure the internal stresses generated by various external excitations applied to the top surface of the cylinder. Corresponding finite element (FE) models were established to reveal the relationship between the PVDF output and the stress field applied to it. This research improves the understanding of the output mechanism of the embedded PVDF and provides useful information for the design of PVDF sensors.

This paper presents an experimental study on the effect of an elastic coating on the sensitivity to an impact force on a polyvinylidene fluoride (PVDF) film by using a model consisting of a top mass, a coated/uncoated PVDF film, and a base block. The sensitivity of the PVDF film is determined by measuring the voltage outputs from the PVDF film and an impact hammer, which is used to excite the top mass. The effects of the constraints at the top and bottom surfaces of an uncoated PVDF film on the sensitivity are examined first. Experimentally, the shear-free and perfectly bonded constraints are approximated by applying oil and epoxy glue to the interfaces between the PVDF film and the top mass/base block. The sensitivities of the PVDF film for these two constraints are determined analytically, thus explaining the roles of the stress components in the thickness and in-plane directions of the film in generating the voltage outputs. The approximated shear-free boundary condition using oil at the interface allows an experimental determination of the piezoelectric voltage constant of the PVDF film in the poling direction. Rubber and polyurethane are used for constructing the coated PVDF films. Even a thin layer of elastic coating is capable of significantly increasing the sensitivity of the PVDF film. For example, 3 mm rubber layers allow a 27 dB increase in the low-frequency sensitivity. A system including an elastically coated PVDF film provides an additional 10 dB increase at frequencies close to its first resonance frequency, resulting in a total 37 dB increase in the system sensitivity. The increased sensitivity may be explained as being due to the increased shear force between the elastic material and PVDF film as the thickness of the elastic layer increases. The dominating effect of the shear force is illustrated by the experimental and finite-element analysis as the thickness of the rubber coating gradually increases. The high rate of increase of the sensitivity as a function of rubber thickness can be observed when the thickness is under 0.8 mm. (c) 2022 Elsevier Ltd. All rights reserved.

This study investigates the feasibility of a laminated polyvinylidene fluoride (PVDF) structure for realising a pressure-pressure (P-P) intensity probe, as well as the effects of various backing materials on the performance of the probe. The PVDF structure consists of two parallel PVDF films that serve roles as pressure sensors, and each of them is laminated between stiff plates. The sensitivity and directivity of these pressure sensors are examined numerically and experimentally. The physical properties and configuration of the PVDF sensing structure are optimised for the best sensing performance. For frequencies below 15 kHz, the averaged voltage outputs of the two PVDF films are proportional to the sound pressure of the incident plane sound wave. It has a flat frequency response and omni-directional directivity pattern. The difference between the outputs is proportional to the particle velocity of the incident sound, featured by a dipole directivity pattern and almost-linear dependence upon frequency. Such under-covered properties of the pressure- and velocity-generated voltages for the integrated sensing structure demonstrate its suitability for intensity estimation in the aforementioned frequency range. This study shows that the probe can determine the intensity of a plane wave field below an upperfrequency limit with pre-determined probe gains. The upper limit is determined by the finite-difference approximation error introduced by the pressure gradient method. Small errors exist in narrow frequency bands around resonances and are sensitive to the pressure-intensity index, which is the ratio of the mean square pressure to the sound intensity. These errors are caused by variations of probe gains due to the resonances and can be reduced by careful calibration around the resonance frequencies.

The structural discontinuities in the form of air gaps in transformer cores cause the concentration of electromagnetic force, which is an important source of transformer vibration and noise. In this paper, an engineering model of magnetic flux density and electromagnetic force density on transformer core discontinuities is analytically developed. Based on a reasonable structural simplification and assumptions, magnetic flux density and electromagnetic force density are deduced as explicit functions of the geometric, material, and electrical excitation characteristics of the gap region and the transformer core. The accuracy of the established model is validated by the finite element method (FEM) combined with a magnetic measurement experiment. According to this engineering model, the electromagnetic force density can be reduced by decreasing the gap ratio and increasing the gap thickness to a reasonable level. The outcome of this paper can help to understand the physical mechanism of the electromagnetic force generated by core air gap discontinuities, which is meaningful for noise control and the condition monitoring of transformers.

In this paper, the relationship between the phase variation in transformer vibration and the mechanical stability of the transformer is presented for the first time. First, the systems of winding vibration and core vibration are both described by Hammerstein-type models consisting of linear and nonlinear parts. Then the links between the phase angle of the fundamental winding/core vibration and system properties are established based on those Hammerstein-type models. They indicate that the phase variation can be used as an effective indicator of deterioration in transformer stability due to mechanical defects in the winding and core. To validate this claim, laboratory experiments and field tests are conducted. In the laboratory experiment, two mechanical faults-looseness of the winding clamping structure and winding deformation-are introduced to a 110 kV power transformer. The results show that both winding clamping looseness and winding deformation will cause larger phase variation in the winding-induced vibration and core-induced vibration. In the field tests, this relationship is also observed on an abnormal 220 kV power transformer. All the findings show that the proposed indicators can provide efficient fault-related information for evaluation of a winding's mechanical health condition. (C) 2021 Elsevier Ltd. All rights reserved.

The effect of a coating on the sensitivity of polyvinylidene fluoride (PVDF) is investigated in this study and the underlying physical mechanisms are explained. The spectral and directional sensitivity of a coated PVDF film are significantly different from that of an uncoated PVDF film, and this can be explained by the amplification of the in-plane stress component by the transmitted shear stress at the PVDF–coating interface. The amplification is dependent on the elastic property and thickness of the coating material. The sensitivity of the coated PVDF film below the first resonance frequency, owing to the destructive superposition of in-plane and normal voltage components, can be increased by adding a thick and soft coating or a thin and stiff coating. A thick and soft coating significantly amplifies the in-plane voltage component and makes it dominant, while a thin and stiff coating reduces the in-plane voltage component and hence the normal voltage component becomes dominant. The directivity sensitivity of the film at low frequency is also explained by the angular dependence of the PVDF–coating interaction. The demonstrated effect of the coating material on the spectral and directional sensitivity of PVDF helps in understanding the measured results of existing PVDF hydrophones, and in designing PVDF-based hydrophones and acoustical intensity probes with a desired response.

This study investigates complex acoustical intensity using a polyvinylidene fluoride (PVDF) bimorph. Analytical models of the open-circuit voltage outputs of an infinite-strip-shaped PVDF bimorph cantilever in an underwater sound field are developed. Results show that the sound pressure generates the sum of the outputs, while the particle velocity normal to the PVDF surface generates the difference. The sensitivities of the pressure- and velocity-generated voltage responses with respect to an incident plane sound field demonstrate uniform directivity in a low-frequency range, which is suitable for acoustical intensity determination. The higher velocity sensitivity confirms the advantage of using a PVDF bimorph as a velocity sensor, owing to its light weight and flexibility. An algorithm for determining the complex acoustical intensity normal to the surface is proposed by utilizing those voltage responses and the probe gain calibrated with a given angle of incident sound. This algorithm allows accurate determination of sound intensity of a plane wave field, where the reactive part of intensity is absent. However, a small error may exist when the reactive intensity is large and active intensity is small. This small discrepancy arises from the inherent variation in the phase directivity of the gains, which decrease with frequency.

The sensitivity of an infinite-strip-shaped polyvinylidene fluoride (PVDF) film in an underwater plane sound field is analyzed in this paper. The high-frequency sensitivity is characterized by the resonances of the symmetrical in-plane stress modes with traction-free boundary conditions at the ends of the film and by the anti-resonances due to the superposition of the stress components. The low-frequency sensitivity exhibits a simple hydrostatic response. The directional property of the in-plane stress component, generated by the incident sound across the thickness, has two contributions. The first is from the aperture and dipolar functions of the incident sound pressure over the PVDF surfaces and at the two ends of the film. The second is from an amplitude modulation by an angle-dependent gain. The directional property of the in-plane stress component by the sound pressure at the two ends of the film is only controlled by the dipolar function, and that of the stress component in the thickness direction is only determined by the aperture function. The illustration of the frequency and directional features of the PVDF film may advance understanding of the mechanisms involved in generating the voltage output of PVDF by an incident sound field.

This paper presents a new analytical solution for the vibration response of plates stiffened by orthogonal beams using a double finite sine integral transform technique. The compatibility conditions at the coupling interfaces and the boundary conditions of the plate are automatically defined in the transform. It is shown that the analytical model can accommodate various combinations of clamped and simply supported boundary conditions. The analytical model is then used to study the reproduction of the vibration response of an orthotropic plate. It is shown that an orthogonally ribbed isotropic plate can produce a closely matching vibration response to that of an orthotropic plate by carefully choosing an appropriate number of ribs and the rib properties in each plate direction.

Study of the vibration mechanisms of transformer windings may lead to useful applications of vibration techniques to transformer online diagnosis. In a power transformer, the clamping force provides a boundary mechanical constraint to ensure the integrity of the winding. Thus, the looseness of the clamping force is an important health indicator for a transformer. Although the effect of clamping force on a winding's stiffness and natural frequencies is known, the effect of time-varying load current on these natural frequencies remains unsolved. In this paper, this effect is investigated by studying the mechanical frequency response function of an on-load single-phase winding under different clamping forces and variation of the harmonic amplitude of in-service transformers with load current. Then, a gated recurrent unit (GRU) neural network is used to explore the relationship between current sequence and vibration sequence for operating transformers. This study shows that the electromagnetic force induced by the load current affects the vibration response of the winding structure, especially when the looseness of the clamping force is significant. A potential application of the observed phenomenon for online detection of winding conditions is also illustrated.