Special Issue "Inverse Dynamics Problems"

A special issue of Vibration (ISSN 2571-631X).

Deadline for manuscript submissions: closed (30 November 2020).

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Dr. Hamed Kalhori
E-Mail Website
Guest Editor
School of Mechanical and Mechatronic Engineering, The University of Technology Sydney, Sydney, NSW 2007, Australia
Interests: inverse dynamics problems; linear and nonlinear vibrations; structural health monitoring; smart materials and structures
Special Issues and Collections in MDPI journals

Special Issue Information

Estimation of system inputs or internal reactions by direct measurements for many real systems is complicated or impossible, either because the system input is inaccessible or unknown or simply because the nature of input is unknown and therefore cannot be instrumented. An inverse problem strategy is, therefore, a promising solution for such scenarios.

An inverse problem is about identifying the cause of an effect utilizing a set of observations and measurement of the system response. As opposed to a forward problem yielding the system response, an inverse problem manipulates the effects considering the system natural behavior to predict the inputs to the system.

Inverse dynamics, in particular, focusing on structural dynamics and/or inverse rigid body dynamics, calculates the applied forces or internal forces and moments from measurements of structural vibrations and/or rigid body motions. These types of problems are normally challenging as there are uncertainties that are usually amplified through the inverse process and therefore need to be properly addressed.

The objective of this Special Issue is to create a forum of discussion, for research scientists and engineers working in the area of inverse structural dynamics and inverse rigid body kinematics. We invite researchers to submit both original research and review articles.

The Special Issue will cover a range of topics including but not limited to the following:

  • Impact force identification;
  • Time-varying load identification;
  • Moving load identification;
  • Bridge-weight-in-motion systems;
  • Vehicle–bridge interaction dynamics;
  • Regularization in force identification;
  • Uncertainties in inverse dynamics problems;
  • Time-varying system identification;
  • Sound source reconstruction;
  • Experimental modal analysis;
  • Operational modal analysis;
  • Inverse dynamics with application in structural health monitoring;
  • Human body and animal body inverse dynamics problems.

Dr. Hamed Kalhori
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Vibration is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • inverse dynamics
  • force identification
  • force reconstruction
  • bridge-weigh-in-motion
  • modal analysis
  • structural health monitoring
  • human body dynamics
  • regularization

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Published Papers (12 papers)

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Editorial

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Editorial
Inverse Dynamics Problems for a Sustainable Future
Vibration 2021, 4(1), 130-132; https://0-doi-org.brum.beds.ac.uk/10.3390/vibration4010011 - 12 Feb 2021
Viewed by 629
Abstract
Inverse dynamics problems and associated aspects are all around us in everyday life but are commonly overlooked and/or not fully comprehended [...] Full article
(This article belongs to the Special Issue Inverse Dynamics Problems)
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Research

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Article
Effect of Impeller Diameter on Dynamic Response of a Centrifugal Pump Rotor
Vibration 2021, 4(1), 117-129; https://0-doi-org.brum.beds.ac.uk/10.3390/vibration4010010 - 09 Feb 2021
Cited by 1 | Viewed by 899
Abstract
This paper investigates the effect of impeller diameter on the dynamic response of a centrifugal pump using an inverse dynamic method. For this purpose, the equations of motion of the shaft and the impeller are derived based on Timoshenko beam theory considering the [...] Read more.
This paper investigates the effect of impeller diameter on the dynamic response of a centrifugal pump using an inverse dynamic method. For this purpose, the equations of motion of the shaft and the impeller are derived based on Timoshenko beam theory considering the impeller as a concentrated mass disk. For practical modeling, the model of Jones and Harris is added to the equation to include the effect of bearings. As a case study, the model is applied to a process pump used in an oil refinery. Computing the eigenvalues of the model and comparing them with the natural frequencies of the structure, the model updating of the problem is performed through an indirect method. Three impellers with different diameters are applied to the updated model. The results show that increasing the diameter of the pump impeller can increase the amplitude of vibration up to 52% at critical speeds of the rotor. It is found that in addition to the hydraulic condition and efficiency, the impeller diameter should be considered as an important factor in the selection of centrifugal pumps. Full article
(This article belongs to the Special Issue Inverse Dynamics Problems)
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Article
Experimental Study on Impact Force Identification on a Multi-Storey Tower Structure Using Different Transducers
Vibration 2021, 4(1), 101-116; https://0-doi-org.brum.beds.ac.uk/10.3390/vibration4010009 - 29 Jan 2021
Cited by 1 | Viewed by 905
Abstract
This paper presents the identification of both location and magnitude of impact forces applied on different positions of a multi-storey tower structure using different types of transducers, i.e., an accelerometer, a laser Doppler vibrometer, and a triangulation displacement sensor. Herein, a model-based inverse [...] Read more.
This paper presents the identification of both location and magnitude of impact forces applied on different positions of a multi-storey tower structure using different types of transducers, i.e., an accelerometer, a laser Doppler vibrometer, and a triangulation displacement sensor. Herein, a model-based inverse method is exploited to reconstruct unknown impact forces based on various recorded dynamic signals. Furthermore, the superposition approach is employed to identify the impact location. Therein, it is assumed that several impact forces are applied simultaneously on potential locations of the multi-storey tower structure, while only one impact has non-zero magnitude. The purpose is then to detect the location of that non-zero impact. The influence of using different hammer tip materials for establishing the transfer function is investigated, where it is concluded that the hammer with a harder tip leads to a more accurate transfer function. An accuracy error function is proposed to evaluate the reconstruction precision. Moreover, the effect of sensor type and location on the accuracy of the reconstruction is studied, where it is shown that the proximity between the impact and sensor locations is a dominant factor in impact force reconstruction. In addition, the efficacy of using different transducers is studied for the impact localization, where it is demonstrated that reducing the degree of under-determinacy by using a combination of system responses of the same type can improve the localization accuracy. Full article
(This article belongs to the Special Issue Inverse Dynamics Problems)
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Article
Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems
Vibration 2021, 4(1), 49-63; https://0-doi-org.brum.beds.ac.uk/10.3390/vibration4010004 - 31 Dec 2020
Cited by 1 | Viewed by 806
Abstract
Industrial dynamical systems often exhibit multi-scale responses due to material heterogeneity and complex operation conditions. The smallest length-scale of the systems dynamics controls the numerical resolution required to resolve the embedded physics. In practice however, high numerical resolution is only required in a [...] Read more.
Industrial dynamical systems often exhibit multi-scale responses due to material heterogeneity and complex operation conditions. The smallest length-scale of the systems dynamics controls the numerical resolution required to resolve the embedded physics. In practice however, high numerical resolution is only required in a confined region of the domain where fast dynamics or localized material variability is exhibited, whereas a coarser discretization can be sufficient in the rest majority of the domain. Partitioning the complex dynamical system into smaller easier-to-solve problems based on the localized dynamics and material variability can reduce the overall computational cost. The region of interest can be specified based on the localized features of the solution, user interest, and correlation length of the material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update the prior knowledge of the localized region of interest using measurements of the system response. Once, the region of interest is identified, the localized uncertainty is propagate forward through the computational domain. We demonstrate our framework using numerical experiments on a three-dimensional elastodynamic problem. Full article
(This article belongs to the Special Issue Inverse Dynamics Problems)
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Article
An Inverse Problem for Quantum Trees with Delta-Prime Vertex Conditions
Vibration 2020, 3(4), 448-463; https://0-doi-org.brum.beds.ac.uk/10.3390/vibration3040028 - 17 Nov 2020
Cited by 2 | Viewed by 866
Abstract
In this paper, we consider a non-standard dynamical inverse problem for the wave equation on a metric tree graph. We assume that the so-called delta-prime matching conditions are satisfied at the internal vertices of the graph. Another specific feature of our investigation is [...] Read more.
In this paper, we consider a non-standard dynamical inverse problem for the wave equation on a metric tree graph. We assume that the so-called delta-prime matching conditions are satisfied at the internal vertices of the graph. Another specific feature of our investigation is that we use only one boundary actuator and one boundary sensor, all other observations being internal. Using the Neumann-to-Dirichlet map (acting from one boundary vertex to one boundary and all internal vertices) we recover the topology and geometry of the graph together with the coefficients of the equations. Full article
(This article belongs to the Special Issue Inverse Dynamics Problems)
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Article
A Shake Table Frequency-Time Control Method Based on Inverse Model Identification and Servoactuator Feedback-Linearization
Vibration 2020, 3(4), 425-447; https://0-doi-org.brum.beds.ac.uk/10.3390/vibration3040027 - 03 Nov 2020
Cited by 1 | Viewed by 1018
Abstract
Shake tables are one of the most widespread means to perform vibration testing due to their ability to capture structural dynamic behavior. The shake table acceleration control problem represents a challenging task due to the inherent non-linearities associated to hydraulic servoactuators, their low [...] Read more.
Shake tables are one of the most widespread means to perform vibration testing due to their ability to capture structural dynamic behavior. The shake table acceleration control problem represents a challenging task due to the inherent non-linearities associated to hydraulic servoactuators, their low hydraulic resonance frequencies and the high frequency content of the target signals, among other factors. In this work, a new shake table control method is presented. The procedure relies on identifying the Frequency Response Function between the time derivative of pressure force exerted on the actuator’s piston rod and the resultant acceleration at the control point. Then, the Impedance Function is calculated, and the required pressure force time variation is estimated by multiplying the impedance by the target acceleration profile in frequency domain. The pressure force time derivative profile can be directly imposed on an actuator’s piston by means of a feedback linearization scheme, which approximately cancels out the actuator’s non-linearities leaving only those related to structure under test present in the control loop. The previous architecture is completed with a parallel Three Variable Controller to deal with disturbances. The effectiveness of the proposed method is demonstrated via simulations carried over a non-linear model of a one degree of freedom shake table, both in electrical noise free and contaminated scenarios. Numerical experiments results show an accurate tracking of the target acceleration profile and better performance than traditional control approaches, thus confirming the potential of the proposed method for its implementation in actual systems. Full article
(This article belongs to the Special Issue Inverse Dynamics Problems)
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Article
Dynamic Behaviour of High Performance of Sand Surfaces Used in the Sports Industry
Vibration 2020, 3(4), 410-424; https://0-doi-org.brum.beds.ac.uk/10.3390/vibration3040026 - 29 Oct 2020
Cited by 3 | Viewed by 1004
Abstract
The sand surface is considered a critical injury and performance contributing factor in different sports, from beach volleyball to greyhound racing. However, there is still a significant gap in understanding the dynamic behaviour of sport sand surfaces, particularly their vibration behaviour under impact [...] Read more.
The sand surface is considered a critical injury and performance contributing factor in different sports, from beach volleyball to greyhound racing. However, there is still a significant gap in understanding the dynamic behaviour of sport sand surfaces, particularly their vibration behaviour under impact loads. The purpose of this research was to introduce different measurement techniques to the study of sports sand surface dynamic behaviour. This study utilised an experimental drop test, accelerometry, in-situ moisture content and firmness data, to investigate the possible correlation between the sand surface and injuries. The analysis is underpinned by data gathered from greyhound racing and discussed where relevant. Full article
(This article belongs to the Special Issue Inverse Dynamics Problems)
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Article
A Comparison of Time-Frequency Methods for Real-Time Application to High-Rate Dynamic Systems
Vibration 2020, 3(3), 204-216; https://0-doi-org.brum.beds.ac.uk/10.3390/vibration3030016 - 24 Aug 2020
Cited by 5 | Viewed by 1247
Abstract
High-rate dynamic systems are defined as engineering systems experiencing dynamic events of typical amplitudes higher than 100 gn for a duration of less than 100 ms. The implementation of feedback decision mechanisms in high-rate systems could improve their operations and safety, and [...] Read more.
High-rate dynamic systems are defined as engineering systems experiencing dynamic events of typical amplitudes higher than 100 gn for a duration of less than 100 ms. The implementation of feedback decision mechanisms in high-rate systems could improve their operations and safety, and even be critical to their deployment. However, these systems are characterized by large uncertainties, high non-stationarities, and unmodeled dynamics, and it follows that the design of real-time state-estimators for such purpose is difficult. In this paper, we compare the promise of five time-frequency representation (TFR) methods at conducting real-time state estimation for high-rate systems, with the objective of providing a path to designing implementable algorithms. In particular, we examine the performance of the short-time Fourier transform (STFT), wavelet transformation (WT), Wigner–Ville distribution (WVD), synchrosqueezed transform (SST), and multi-synchrosqueezed transform (MSST) methods. This study is conducted using experimental data from the DROPBEAR (Dynamic Reproduction of Projectiles in Ballistic Environments for Advanced Research) testbed, consisting of a rapidly moving cart on a cantilever beam that acts as a moving boundary condition. The capability of each method at extracting the beam’s fundamental frequency is evaluated in terms of precision, spectral energy concentration, computation speed, and convergence speed. It is found that both the STFT and WT methods are promising methods due to their fast computation speed, with the WT showing particular promise due to its faster convergence, but at the cost of lower precision on the estimation depending on circumstances. Full article
(This article belongs to the Special Issue Inverse Dynamics Problems)
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Article
Experimental and Numerical Investigations into Dynamic Modal Parameters of Fiber-Reinforced Foamed Urethane Composite Beams in Railway Switches and Crossings
Vibration 2020, 3(3), 174-188; https://0-doi-org.brum.beds.ac.uk/10.3390/vibration3030014 - 20 Jul 2020
Cited by 4 | Viewed by 1630
Abstract
Dynamic behaviors of composite railway sleepers and bearers in railway switches and crossings are not well-known and have never been thoroughly investigated. In fact, the dynamic properties of the full-scale composite sleepers and bearers are not available in practice. Importantly, the deteriorated condition [...] Read more.
Dynamic behaviors of composite railway sleepers and bearers in railway switches and crossings are not well-known and have never been thoroughly investigated. In fact, the dynamic properties of the full-scale composite sleepers and bearers are not available in practice. Importantly, the deteriorated condition or even the failure of composite materials and components in the railway system can affect the functional limitations or serviceability of the switches and crossings. Especially, it is important to identify the dynamic modal parameters of Fiber-reinforced Foamed Urethane (FFU) composite railway sleepers and bearers so that track engineers can adequately design and optimize the structural components with their superior properties, for benchmarking with the conventional sleepers and bearers. This paper is the world’s first to investigate the vibration characteristics of full-scaled FFU composite beams in healthy and damaged conditions, using the impact hammer excitation technique. This study also determines the dynamic elastic modulus of FFU composite beams from experimental dynamic measurements. It is found that the first bending mode in a vertical plane obviously is the first dominant mode of resonance under a free-free condition. The dynamic modal parameters reduce when damages occur. In this study, finite-element modeling has been used to establish a realistic dynamic model of the railway track incorporating FFU composite sleepers and bearers. Then, numerical simulations and experimental campaigns have been performed to enable new insights into the dynamic behaviors of composite sleepers and bearers. These insights are fundamental to the performance benchmarking as well as the development of vibration-based condition monitoring and inspection for predictive track maintenance. Full article
(This article belongs to the Special Issue Inverse Dynamics Problems)
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Article
Continuous Evaluation of Track Modulus from a Moving Railcar Using ANN-Based Techniques
Vibration 2020, 3(2), 149-161; https://doi.org/10.3390/vibration3020012 - 22 Jun 2020
Cited by 3 | Viewed by 1107
Abstract
Track foundation stiffness (also referred as the track modulus) is one of the main parameters that affect the track performance, and thus, quantifying its magnitudes and variations along the track is widely accepted as a method for evaluating the track condition. In recent [...] Read more.
Track foundation stiffness (also referred as the track modulus) is one of the main parameters that affect the track performance, and thus, quantifying its magnitudes and variations along the track is widely accepted as a method for evaluating the track condition. In recent decades, the train-mounted vertical track deflection measurement system developed at the University of Nebraska–Lincoln (known as the MRail system) appears as a promising tool to assess track structures over long distances. Numerical methods with different levels of complexity have been proposed to simulate the MRail deflection measurements. These simulations facilitated the investigation and quantification of the relationship between the vertical deflections and the track modulus. In our previous study, finite element models (FEMs) with a stochastically varying track modulus were used for the simulation of the deflection measurements, and the relationships between the statistical properties of the track modulus and deflections were quantified over different track section lengths using curve-fitting approaches. The shortcoming is that decreasing the track section length resulted in a lower accuracy of estimations. In this study, the datasets from the same FEMs are used for the investigations, and the relationship between the measured deflection and track modulus averages and standard deviations are quantified using artificial neural networks (ANNs). Different approaches available for training the ANNs using FEM datasets are discussed. It is shown that the estimation accuracy can be significantly increased by using ANNs, especially when the estimations of track modulus and its variations are required over short track section lengths, ANNs result in more accurate estimations compared to the use of equations from curve-fitting approaches. Results also show that ANNs are effective for the estimations of track modulus even when the noisy datasets are used for training the ANNs. Full article
(This article belongs to the Special Issue Inverse Dynamics Problems)
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Article
H 2 and H Optimal Control Strategies for Energy Harvesting by Regenerative Shock Absorbers in Cars
Vibration 2020, 3(2), 99-115; https://0-doi-org.brum.beds.ac.uk/10.3390/vibration3020009 - 22 May 2020
Cited by 1 | Viewed by 1029
Abstract
Regenerative suspension systems, unlike traditional passive, semi-active or active setups, are able to convert the traditionally wasted kinetic energy into electricity. This paper discusses flexible multi-objective control design strategies based on LMI formulations to suitably trade-off between the usual road handling and ride [...] Read more.
Regenerative suspension systems, unlike traditional passive, semi-active or active setups, are able to convert the traditionally wasted kinetic energy into electricity. This paper discusses flexible multi-objective control design strategies based on LMI formulations to suitably trade-off between the usual road handling and ride comfort performance and the amount of energy to be harvested. An electromechanical regenerative vehicle suspension system is considered where the shock absorber of each wheel is replaced by a linear electrical motor which is actively governed. It is shown by simulations that multivariable centralized control laws designed on the basis of a full-car model of the suspension system are able to achieve larger amount of harvested energy under identical ride comfort prescriptions with respect to scalar decentralized control strategies, designed on the basis of a single quarter-car model and implemented independently on each wheel in a decentralized way. Improvements up to 40 % and 20 % of harvested energy are respectively achievable by the centralized multivariable H 2 and H optimal controllers under the same test conditions. Full article
(This article belongs to the Special Issue Inverse Dynamics Problems)
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Review

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Review
Jerk within the Context of Science and Engineering—A Systematic Review
Vibration 2020, 3(4), 371-409; https://0-doi-org.brum.beds.ac.uk/10.3390/vibration3040025 - 21 Oct 2020
Cited by 1 | Viewed by 1791
Abstract
Rapid changes in forces and the resulting changes in acceleration, jerk and higher order derivatives can have undesired consequences beyond the effect of the forces themselves. Jerk can cause injuries in humans and racing animals and induce fatigue cracks in metals and other [...] Read more.
Rapid changes in forces and the resulting changes in acceleration, jerk and higher order derivatives can have undesired consequences beyond the effect of the forces themselves. Jerk can cause injuries in humans and racing animals and induce fatigue cracks in metals and other materials, which may ultimately lead to structure failures. This is a reason that it is used within standards for limits states. Examples of standards which use jerk include amusement rides and lifts. Despite its use in standards and many science and engineering applications, jerk is rarely discussed in university science and engineering textbooks and it remains a relatively unfamiliar concept even in engineering. This paper presents a literature review of the jerk and higher derivatives of displacement, from terminology and historical background to standards, measurements and current applications. Full article
(This article belongs to the Special Issue Inverse Dynamics Problems)
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