Vibration

24 pages, 6980 KiB

Open AccessArticle

Vibration Signal-Based Fault Diagnosis of Rotary Machinery Through Convolutional Neural Network and Transfer Learning Method

by Chirag Mongia and Shankar Sehgal

Vibration 2025, 8(2), 27; https://doi.org/10.3390/vibration8020027 - 25 May 2025

Viewed by 114

Abstract

Artificial Intelligence (AI) is revolutionizing proactive repair systems by enabling real-time identification of bearing faults in industrial machinery. However, traditional fault detection methods often struggle in dynamic environments due to their dependence on specific training conditions. To address this limitation, a transfer learning [...] Read more.

Artificial Intelligence (AI) is revolutionizing proactive repair systems by enabling real-time identification of bearing faults in industrial machinery. However, traditional fault detection methods often struggle in dynamic environments due to their dependence on specific training conditions. To address this limitation, a transfer learning (TL)-based methodology has been developed for bearing fault detection, so that the model trained under some specific training conditions can perform accurately under significantly different real-time working conditions, thereby significantly improving diagnostic efficiency while reducing training time. Initially, a deep learning approach utilizing convolutional neural networks (CNNs) has been employed to diagnose faults based on vibration data. After achieving high classification performance at source domain conditions, the performance of the model is re-evaluated by applying it to the Case Western Reserve University (CWRU) dataset as the target domain through the TL method. short-time Fourier transform is employed for signal preprocessing, enhancing feature extraction and model performance. The proposed methodology has been validated across various CWRU dataset configurations under different operating conditions and environments. The proposed approach achieved a 99.7% classification accuracy in the target domain, demonstrating effective adaptability and robustness under domain shifts. The results demonstrate how TL-enhanced CNNs can be used as a scalable and efficient way to diagnose bearing faults in industrial environments. Full article

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11 pages, 2038 KiB

Open AccessArticle

EU Vibration Limit Values May Be Too Strict for Evaluating the Effect of Impact Loading on the Lower Back During Horse Riding

by Nerissa A. Smit, Jelte E. Bos, Jaap H. van Dieën and Idsart Kingma

Vibration 2025, 8(2), 26; https://doi.org/10.3390/vibration8020026 - 21 May 2025

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Abstract

This study evaluated the suitability of the vibration dose value (VDV) and action and limit values from the EU Directive 2002/44/EC in assessing lower back health risks due to repeated shocks using common horse riding as an example. The difference between pelvis- and [...] Read more.

This study evaluated the suitability of the vibration dose value (VDV) and action and limit values from the EU Directive 2002/44/EC in assessing lower back health risks due to repeated shocks using common horse riding as an example. The difference between pelvis- and saddle-based VDV calculations was assessed. VDVs were calculated from accelerations measured using inertial measurement units (IMUs) on the saddle and the rider’s pelvis during walking (30 min) and cantering (10 min). Saddle and pelvis VDVs were similar, 12–31 m/s^1.75 for walking and 46–69 m/s^1.75 for cantering. Accelerations reached the action value (9.1 m/s^1.75) within 03:16 min of walking and 00:08 min of cantering. Accelerations reached the limit value (21 m/s^1.75) within 30:00 min or 00:26 min of cantering. Although VDV reached limits quickly, walking and cantering are generally harmless for the lower back. Application of the VDV and associated limits for repeated shocks assessment might need reconsideration. Full article

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20 pages, 2949 KiB

Open AccessArticle

Optimal Design Methodology of Maxwell–Coulomb Friction Damper

by Chun-Nam Wong and Wai-On Wong

Vibration 2025, 8(2), 25; https://doi.org/10.3390/vibration8020025 - 19 May 2025

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Abstract

The optimal design methodology for a Maxwell–Coulomb friction damper is proposed to minimize the resonant vibration of dynamic structures. The simple Coulomb friction damper has the problem of zero or little damping effect of the vibration of the spring–mass dynamic system at resonance. [...] Read more.

The optimal design methodology for a Maxwell–Coulomb friction damper is proposed to minimize the resonant vibration of dynamic structures. The simple Coulomb friction damper has the problem of zero or little damping effect of the vibration of the spring–mass dynamic system at resonance. This problem is solved in the case of the Maxwell–Coulomb friction damper, which is formed by combining a Coulomb friction damper with a spring element in series. However, the design and analysis of the Maxwell–Coulomb friction damper become much more complicated. The optimal design methodology for this nonlinear damper is proposed in this article. The nonlinear equations of motion of the proposed damper are modelled, and its hysteresis loop can be constructed by combining four different cases of stick–slide motion. Motion responses of the turbine blade with the proposed damper are solved by a central difference solver. Optimal paths of damping and stiffness ratios are determined by the central difference Newton search method. The optimal experimental design is ascertained using a prototype damper test. Close correlation with its numerical simulations is observed in our hysteresis loop comparison. The performance of the proposed damper is also compared to that of a viscous damper in the seismic response design of adjacent single-story buildings. Full article

(This article belongs to the Special Issue Vibration Damping)

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20 pages, 3429 KiB

Open AccessArticle

Damping Identification Sensitivity in Flutter Speed Estimation

by Gabriele Dessena, Alessandro Pontillo, Marco Civera, Dmitry I. Ignatyev, James F. Whidborne and Luca Zanotti Fragonara

Vibration 2025, 8(2), 24; https://doi.org/10.3390/vibration8020024 - 16 May 2025

Viewed by 84

Abstract

Predicting flutter remains a key challenge in aeroelastic research, with certain models relying on modal parameters, such as natural frequencies and damping ratios. These models are particularly useful in early design stages or for the development of small Unmanned Aerial Vehicles (maximum take-off [...] Read more.

Predicting flutter remains a key challenge in aeroelastic research, with certain models relying on modal parameters, such as natural frequencies and damping ratios. These models are particularly useful in early design stages or for the development of small Unmanned Aerial Vehicles (maximum take-off mass below 7 kg). This study evaluates two frequency-domain system identification methods, Fast Relaxed Vector Fitting (FRVF) and the Loewner Framework (LF), for predicting the flutter onset speed of a flexible wing model. Both methods are applied to extract modal parameters from Ground Vibration Testing data, which are subsequently used to develop a reduced-order model with two degrees of freedom. The results indicate that FRVF- and LF-informed models provide reliable flutter speed, with predictions deviating by no more than 3% (FRVF) and 5% (LF) from the N4SID-informed benchmark. The findings highlight the sensitivity of flutter speed predictions to damping ratio identification accuracy and demonstrate the potential of these methods as computationally efficient alternatives for preliminary aeroelastic assessments. Full article

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17 pages, 7015 KiB

Open AccessArticle

Studying the Behavior of a Paperboard Box: Experiment and Finite Element Model

by Boussad Abbès, Fazilay Abbès, Lien Tien Dao, Pham Tuong Minh Duong and Viet Dung Luong

Vibration 2025, 8(2), 23; https://doi.org/10.3390/vibration8020023 - 6 May 2025

Viewed by 158

Abstract

In the transportation and distribution of goods, cardboard boxes are often subjected to mechanical impacts such as shocks and random vibrations, which can cause damage to the goods. In this study, static and dynamic tests on cardboard boxes were designed and conducted to [...] Read more.

In the transportation and distribution of goods, cardboard boxes are often subjected to mechanical impacts such as shocks and random vibrations, which can cause damage to the goods. In this study, static and dynamic tests on cardboard boxes were designed and conducted to determine the compression strength, natural frequencies, and modal characteristics of the boxes. A finite element model of cardboard boxes considering the in-plane orthotropic elastic–plastic behavior of the cardboard was implemented in the Abaqus software through a VUMAT subroutine to perform numerical simulations under compression and random vibrations. The parameters of the model were determined through an inverse identification process. As a first result, the predicted force–displacement curves show good agreement with the measured curves. Furthermore, the power spectral density (PSD) response of the mass/box system under random vibrations obtained through numerical simulations is consistent with the responses obtained from experimental measurements. Full article

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20 pages, 4484 KiB

Open AccessArticle

Feasibility Analysis of Monitoring Contact Wire Rupture in High-Speed Catenary Systems

by Andrea Collina, Antonietta Lo Conte and Giuseppe Bucca

Vibration 2025, 8(2), 22; https://doi.org/10.3390/vibration8020022 - 3 May 2025

Viewed by 160

Abstract

The rupture of the contact wire (CW) of a railway overhead contact line (OCL or catenary) is expected to be a rare event. However, when it occurs, and a pantograph transits under the already broken section of the CW, this can have catastrophic [...] Read more.

The rupture of the contact wire (CW) of a railway overhead contact line (OCL or catenary) is expected to be a rare event. However, when it occurs, and a pantograph transits under the already broken section of the CW, this can have catastrophic consequences for the pantograph which in turn can cause a further extension of the damaged portion on the OCL with a consequent disruption in the service and cause there to be a long time before the operating condition can be restored. Therefore, the prevention of such events through effective catenary monitoring is gaining significant attention. The purpose of this work is to investigate the feasibility of a monitoring system that can be installed at each end of an OCL section which is able to detect the occurrence of a broken CW event, sending an alert to the management traffic system, so as to stop the train traffic before the damaged catenary is reached by other trains. A nonlinear dynamic analysis is employed to model the OCL’s response following a simulated CW rupture and identify a set of variables that can be measured at the line’s extremities related to the occurrence of breakage in the CW. Several locations of the rupture of a CW section along the line are simulated to investigate the influence on the time pattern of the measured variables and consequently on the extraction of a signature. Finally, a proposed measurement setup is presented, combining accelerometers and displacement transducers, instead of the direct measurement of the axial load of the OCL conductors. Full article

(This article belongs to the Special Issue Railway Dynamics and Ground-Borne Vibrations)

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16 pages, 2584 KiB

Open AccessArticle

Comparative Study of Different Linear Analysis for Seismic Resistance of Buildings According to Eurocode 8

by Ivelin Ivanov and Dimitar Velchev

Vibration 2025, 8(2), 21; https://doi.org/10.3390/vibration8020021 - 3 May 2025

Viewed by 182

Abstract

Structural design in Europe should strongly follow EN 1998-1 or so called Eurocode 8 (EC8), for a seismic resistance assessment of structures. Eurocode 8 recommends two linear methods and two nonlinear methods. The nonlinear methods require some knowledge about the nonlinear behavior of [...] Read more.

Structural design in Europe should strongly follow EN 1998-1 or so called Eurocode 8 (EC8), for a seismic resistance assessment of structures. Eurocode 8 recommends two linear methods and two nonlinear methods. The nonlinear methods require some knowledge about the nonlinear behavior of beams and joints in the structure, which makes the linear methods preferable. An alternative method of the seismic loading representation is to use artificial accelerograms with the same or similar spectra as the response spectrum used for modal spectrum analysis. Using an artificial diagram, three approaches in finite element methods exist: explicit time integration, implicit time integration, and modal dynamics. A typical six-story steel structure is modeled using the finite element method, and all linear methods are examined in both horizontal directions. The structure is examined by the modal response spectrum method using sufficient modes, as well as with and without the residual mode. The results are compared, and conclusions concerning the efficiency and precision of methods are deduced. Time history loading by accelerograms reveals higher dynamics and stress in the structural response than the modal response spectrum and lateral forces methods. The time history analysis methods have almost no difference in accuracy, and the modal dynamics method is the cheapest one. Full article

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17 pages, 3642 KiB

Open AccessArticle

Crack Location in Wind Turbine Blades Using Vibration Signal and Support Vector Machine

by Perla Y. Sevilla-Camacho, José B. Robles-Ocampo, Juvenal Rodríguez-Resendíz, Sergio De la Cruz-Arreola, Marco A. Zuñiga-Reyes and Edwin N. Hernández-Estrada

Vibration 2025, 8(2), 20; https://doi.org/10.3390/vibration8020020 - 21 Apr 2025

Viewed by 364

Abstract

This study introduces a new method to locate cracks in wind turbine blades using the support vector machine algorithm and the tangential vibration signal measured at the root blade in static conditions. The method was implemented in hardware and experimentally validated on 200 [...] Read more.

This study introduces a new method to locate cracks in wind turbine blades using the support vector machine algorithm and the tangential vibration signal measured at the root blade in static conditions. The method was implemented in hardware and experimentally validated on 200 W wind turbine blades. The blade conditions were healthy, and transverse cracked at the root, midsection, and tip. The experimental procedure is easy, and only one low-cost piezoelectric accelerometer is needed, which is affordable and straightforward to install. The machine learning technique used requires a small dataset and low computing power. The results show exceptional performance, achieving an accuracy of 99.37% and a precision of 98.77%. This approach enhances the reliability of wind turbine blade monitoring. It provides a robust early detection and maintenance solution, improving operational efficiency and safety in wind energy production. K-nearest neighbors and decision trees are also used for comparison purposes. Full article

(This article belongs to the Special Issue Machine Learning Applications to Vibration Problems)

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30 pages, 39645 KiB

Open AccessArticle

Global Admittance: A New Modeling Approach to Dynamic Performance Analysis of Dynamic Vibration Absorbers

by Cuauhtémoc Mazón-Valadez, Eduardo Barredo, Jorge Colín-Ocampo, Javier A. Pérez-Molina, Demetrio Pérez-Vigueras, Ernesto E. Mazón-Valadez and Agustín Barrera-Sánchez

Vibration 2025, 8(2), 19; https://doi.org/10.3390/vibration8020019 - 16 Apr 2025

Viewed by 193

Abstract

The vibration control in structural design has long been a critical area of study, particularly in mitigating undesirable resonant vibrations using dynamic vibration absorbers (DVAs). Traditional approaches to tuning DVAs have relied on complex mathematical models based on Newtonian or Euler–Lagrange equations, often [...] Read more.

The vibration control in structural design has long been a critical area of study, particularly in mitigating undesirable resonant vibrations using dynamic vibration absorbers (DVAs). Traditional approaches to tuning DVAs have relied on complex mathematical models based on Newtonian or Euler–Lagrange equations, often leading to intricate systems requiring simplification of the analysis of multi-degree-of-freedom structures. This paper introduces a novel modeling approach for analyzing DVAs based on the concept of global admittance, which stems from mechanical admittance and network simplifications. This model streamlines the representation of structures with DVAs as one-degree-of-freedom systems coupled with a global admittance function, which emulates additional damping coupled to the primary structure. In this work, global admittance functions are determined by the independent analysis of the mechanical networks of the DVA, restructuring the process of obtaining the system’s transfer function. The model was validated using different classical DVA configurations, demonstrating total accuracy in its applicability across designs concerning conventional modeling. Our most remarkable finding was that the dimensionless function,

γ_{g} (Ω)

, resulting from the global admittance, partially decouples the dynamics of the DVAs from the primary structure, facilitating the implementation of passive vibration control strategies in more realistic structural models. Additionally, this work establishes a significant advancement in vibration control analysis, providing a flexible tool for control strategies in real-world structural systems. Full article

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13 pages, 2097 KiB

Open AccessArticle

A Coupled Harmonic Balance-Based Approach for the Non-Linear Dynamics of Spur-Gear Pairs

by Giacomo Saletti, Giuseppe Battiato and Stefano Zucca

Vibration 2025, 8(2), 18; https://doi.org/10.3390/vibration8020018 - 10 Apr 2025

Viewed by 337

Abstract

Noise, vibration and harshness analyses are of great interest for the latest developments of the gearboxes of electric vehicles. Gearboxes are now the main source of vibrations, since electric powertrains are much quieter than internal combustion engines. Traditionally, the simulation of the non-linear [...] Read more.

Noise, vibration and harshness analyses are of great interest for the latest developments of the gearboxes of electric vehicles. Gearboxes are now the main source of vibrations, since electric powertrains are much quieter than internal combustion engines. Traditionally, the simulation of the non-linear gear dynamics is studied by first performing a series of preliminary static analyses to compute the static transmission error (STE). The STE (i.e., in the form of varying mesh stiffness) is then accepted as the system’s excitation source to compute the dynamic transmission error (DTE). This paper presents a novel approach to analyze the non-linear dynamics of gears which does not require any preliminary static analyses. The method consists of a frequency–domain approach based on the Harmonic Balance Method (HBM) and the Alternating Frequency–Time (AFT) scheme, allowing for much faster simulations when compared to the widely used direct–time integration (DTI). The contact between the teeth is modeled as intermittent and penalty based with a varying gap. The time–varying gap between the teeth is initially approximated to a step function that guarantees the design contact ratio. The methodology introduced is tested on a lumped parameter model of a spur–gear pair already proposed and simulated in the literature. The results obtained with the novel approach are compared with the DTI simulation of the model as a reference. The excellent match between the different approaches validates the reliability of developed methodology. Full article

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11 pages, 2759 KiB

Open AccessTechnical Note

User-Friendly Tool for Expedited Ground Vibration Assessment Induced by Impact Pile Driving

by Ahmed M. Abouelmaty, Aires Colaço and Pedro Alves Costa

Vibration 2025, 8(2), 17; https://doi.org/10.3390/vibration8020017 - 4 Apr 2025

Viewed by 370

Abstract

Driven piles are a common geotechnical solution for foundations in weak soil profiles. However, hammer impacts during the driving process can generate excessive levels of ground vibration, which, in extreme cases, can affect nearby structures and people. Due to the complexity of wave [...] Read more.

Driven piles are a common geotechnical solution for foundations in weak soil profiles. However, hammer impacts during the driving process can generate excessive levels of ground vibration, which, in extreme cases, can affect nearby structures and people. Due to the complexity of wave propagation in soils, the accurate prediction of these vibrations typically requires advanced numerical modeling approaches. To address this challenge, a surrogate modeling framework was developed by integrating Artificial Neural Networks (ANNs) and Extreme Gradient Boosting (XGBoost), trained on a synthetic dataset generated from an experimentally validated numerical model. The proposed surrogate model enables the rapid prediction of ground vibration characteristics, including peak particle velocity (PPV) and frequency content, across a broad range of soil, pile, and hammer conditions. In addition to its predictive capabilities, the tool allows users to design a specific mitigation measure (open trench) and compare the vibration levels with international standards. Experimental validation confirmed the model’s ability to replicate field measurements with acceptable accuracy. The expedited prediction tool is available as supplemental data and can be used by other researchers and technicians for quick and accurate ground vibration predictions. Full article

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29 pages, 2815 KiB

Open AccessArticle

Linearly Perturbed Frequency Equation, New Frequency Formula, and a Linearized Galerkin Method for Nonlinear Vibrational Oscillators

by Chein-Shan Liu, Chia-Cheng Tsai and Chih-Wen Chang

Vibration 2025, 8(2), 16; https://doi.org/10.3390/vibration8020016 - 2 Apr 2025

Viewed by 251

Abstract

A new frequency–amplitude formula by improving an ancient Chinese mathematics method results in a modification of He’s formula. The Chinese mathematics method that expresses via a fixed-point Newton form is proven to be equivalent to the original nonlinear frequency equation. We modify the [...] Read more.

A new frequency–amplitude formula by improving an ancient Chinese mathematics method results in a modification of He’s formula. The Chinese mathematics method that expresses via a fixed-point Newton form is proven to be equivalent to the original nonlinear frequency equation. We modify the fixed-point Newton method by adding a term in the denominator, and then a new frequency–amplitude formula including a parameter is derived. Upon using the new frequency formula with the parameter by minimizing the absolute error of the periodicity condition, one can significantly raise the accuracy of the frequency several orders. The innovative idea of a linearly perturbed frequency equation is a simple extension of the original frequency equation, which is supplemented by a linear term to acquire a highly precise frequency for the nonlinear oscillators. In terms of a differentiable weight function, an integral-type formula is coined to expeditiously estimate the frequency; it is a generalized conservation law for the damped nonlinear oscillator. To seek second-order periodic solutions of nonlinear oscillators, a linearized residual Galerkin method (LRGM) is developed whose process to find the second-order periodic solution and the vibrational frequency is quite simple. A hybrid method is achieved through a combination of the linearly perturbed frequency equation and the LRGM; very accurate frequency and second-order periodic solutions can be obtained. Examples reveal high efficacy and accuracy of the proposed methods; the mathematical reliability of these methods is clarified. Full article

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20 pages, 2487 KiB

Open AccessArticle

Comparison of Piezoelectric Stack-Based Passive and Active Vibration Suppression Systems for Satellite Solar Panels

by Carmelo Rosario Vindigni, Antonio Esposito, Calogero Orlando and Andrea Alaimo

Vibration 2025, 8(2), 15; https://doi.org/10.3390/vibration8020015 - 1 Apr 2025

Viewed by 361

Abstract

This study proposes a piezoelectric device for vibration damping in satellite solar panels. The design features a structural arrangement with piezoelectric stacks configured in a V-shape and hinged to the main yoke structure. The satellite structure is modeled using an Euler–Bernoulli beam finite [...] Read more.

This study proposes a piezoelectric device for vibration damping in satellite solar panels. The design features a structural arrangement with piezoelectric stacks configured in a V-shape and hinged to the main yoke structure. The satellite structure is modeled using an Euler–Bernoulli beam finite element framework, incorporating the electro-mechanical coupling of active elements through equivalent nodal piezoelectric loads. Various shunt circuits are designed to mitigate vibrations, with a parametric study conducted to optimize the key circuit parameters. Additionally, a filtered PID active suppression system is developed and tuned using a meta-heuristic algorithm to determine optimal controller gains. Numerical simulations are performed to evaluate and compare the effectiveness of the proposed vibration suppression systems, demonstrating the efficiency of the smart structure configuration and providing performance analysis. Full article

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17 pages, 3602 KiB

Open AccessArticle

Vibration Characteristics of Carbon Nanotube-Reinforced Sandwich Nanobeams with Hybrid Cellular Core

by Mohammad Javad Khoshgoftar, Pejman Mehdianfar, Yasin Shabani, Mahdi Shaban and Hamed Kalhori

Vibration 2025, 8(2), 14; https://doi.org/10.3390/vibration8020014 - 25 Mar 2025

Viewed by 298

Abstract

This research explores the dynamic characteristics of composite nano-beams with a hybrid cellular structure (HCS) core, composed of two segments with distinct unit cell configurations, and face sheets reinforced with carbon nanotube (CNT) composites. By considering three-layered sandwich beams with aluminum cores of [...] Read more.

This research explores the dynamic characteristics of composite nano-beams with a hybrid cellular structure (HCS) core, composed of two segments with distinct unit cell configurations, and face sheets reinforced with carbon nanotube (CNT) composites. By considering three-layered sandwich beams with aluminum cores of varying unit cell angles, the study explores a broad spectrum of achievable Poisson’s ratios. The top and bottom face sheets incorporate CNTs, distributed either uniformly or in a functionally graded manner. The governing equations are derived using Eringen’s nonlocal elasticity framework and the modified theory of shear deformation, with solutions obtained via the Galerkin method. A detailed parametric analysis is conducted to evaluate the effects of CNT content, arrangement configurations, hybrid core cellular angles, nonlocal parameters, and slenderness ratio (L/h) on the dimensionless natural frequencies of sandwich nanobeams with hybrid cellular cores. A key contribution of this study is the presentation of natural frequencies for nanobeams with hybrid cellular cores and composite face sheets reinforced with functionally graded CNTs, derived from advanced theoretical formulations. These findings offer new insights into design optimization and highlight the potential applications of hybrid cellular sandwich nanobeams in cutting-edge engineering systems. Full article

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35 pages, 8042 KiB

Open AccessArticle

Instability of a Moving Bogie: Analysis of Vibrations and Possibility of Instability in Subcritical Velocity Range

by Zuzana Dimitrovová

Vibration 2025, 8(2), 13; https://doi.org/10.3390/vibration8020013 - 24 Mar 2025

Viewed by 227

Abstract

This paper analyzes vibrations induced by a moving bogie passing through a single-layer railway track model. The emphasis is placed on the possibility of unstable behavior in the subcritical velocity range. All results are presented in dimensionless form to encompass a wide range [...] Read more.

This paper analyzes vibrations induced by a moving bogie passing through a single-layer railway track model. The emphasis is placed on the possibility of unstable behavior in the subcritical velocity range. All results are presented in dimensionless form to encompass a wide range of possible scenarios. The results are obtained semi-analytically, however, the only numerical step involves solving the roots of polynomial expressions. No numerical integration is used, allowing for the straightforward solution of completely undamped scenarios, as damping is not required for numerical stability. The vibration shapes are presented in the time domain in closed form. It is concluded that increased foundation damping worsens the situation. However, in general, the risk of instability in the subcritical velocity range for a moving bogie is lower than that of two moving masses, particularly for higher mass moments of inertia of the bogie bar and primary suspension damping. The study also examines how the results change when a Timoshenko-Rayleigh beam is considered instead of an Euler-Bernoulli beam. Although some cases may appear academic, it is demonstrated that instability in the supercritical velocity range cannot be assumed to be guaranteed. Full article

(This article belongs to the Special Issue Railway Dynamics and Ground-Borne Vibrations)

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14 pages, 1025 KiB

Open AccessArticle

Rhythmic Analysis in Animal Communication, Speech, and Music: The Normalized Pairwise Variability Index Is a Summary Statistic of Rhythm Ratios

by Yannick Jadoul, Francesca D’Orazio, Vesta Eleuteri, Jelle van der Werff, Tommaso Tufarelli, Marco Gamba, Teresa Raimondi and Andrea Ravignani

Vibration 2025, 8(2), 12; https://doi.org/10.3390/vibration8020012 - 24 Mar 2025

Viewed by 627

Abstract

Rhythm is fundamental in many physical and biological systems. Rhythm is relevant to a broad range of phenomena across different fields, including animal bioacoustics, speech sciences, and music cognition. As a result, the interest in developing consistent quantitative measures for cross-disciplinary rhythmic analysis [...] Read more.

Rhythm is fundamental in many physical and biological systems. Rhythm is relevant to a broad range of phenomena across different fields, including animal bioacoustics, speech sciences, and music cognition. As a result, the interest in developing consistent quantitative measures for cross-disciplinary rhythmic analysis is growing. Two quantitative measures that can be directly applied to any temporal structure are the normalized pairwise variability index (nPVI) and rhythm ratios (r_k). The nPVI summarizes the overall isochrony of a sequence, i.e., how regularly spaced a sequence’s events are, as a single value. Meanwhile, r_k quantifies ratios between a sequence’s adjacent intervals and is often used for identifying rhythmic categories. Here, we show that these two rhythmic measures are fundamentally connected: the nPVI is a summary static of the r_k values of a temporal sequence. This result offers a deeper understanding of how these measures are applied. It also opens the door for creating novel, custom measures to quantify rhythmic patterns based on a sequence’s r_k distribution and compare rhythmic patterns across different domains. The explicit connection between nPVI and r_k is one further step towards a common quantitative toolkit for rhythm research across disciplines. Full article

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Vibration, Volume 8, Issue 2 (June 2025) – 16 articles

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