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A special issue of Sensors (ISSN 1424-8220). This special issue belongs to the section "Physical Sensors".

Deadline for manuscript submissions: closed (15 December 2020) | Viewed by 42158

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Prof. Dr. Marco Gherlone

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Guest Editor

Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Torino, Italy
Interests: multilayered composite and sandwich structures; structural health monitoring; shape sensing; finite element method
Special Issues, Collections and Topics in MDPI journals

Dr. Alexander Tessler

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Guest Editor

NASA Langley Research Center, Structural Mechanics & Concepts Branch, Hampton, VA 23681 USA
Interests: Beam, plate, and shell theoris; Laminated composite and sandwich structures; Structural Health Monitoring; Shape- and stress sensing; Penalty methods; Damage assessment; Finite Element Technology

Special Issue Information

Dear Colleagues,

Structural Health Monitoring/Management (SHM) is the latest technology utilizing advanced sensor networks for real-time monitoring and assessment of structural integrity. This technology is of an increased interest for application to existing and next generation aerospace and naval vehicles and structures. Current areas for application of SHM include civilian and military aircraft, spacecraft, naval and off-shore structures, and civil engineering structures, such as bridges and tunnels. The massive amounts of sensor data can be processed and analyzed using physics-based inverse and direct discretization methods, similar to the widely used direct Finite Element Method for structural analysis and design. Damage detection can also be inferred from the processed in-situ temperature and strain-sensor data, thus enabling improved maintanance of structural components based on the actual structural loads sustained during operational service environment.

This Special Issue is focuced on bringing together the latest advances in physics-based solution methods suitable for the large-scale structural applications to enable real-time structural health monitoring of aerospace, civil, and marine structures. The topics include but are not limited to:

Shape sensing
Inverse Finite Element Methods
Modal reconstruction methods
Methods for real-time damage assessment
Methods for real-time delamination damage assessment in laminated composite structures
Sensor optimization methods and studies
Advanced and affordable strain sensor technologies for large-scale applications
Method for material characterization inferred from sensor data

Dr. Marco Gherlone
Dr. Alexander Tessler
Guest Editors

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Keywords

Inverse Finite Element Methods
Modal reconstruction methods
Shape sensing algorithms
Damage assessment
Delamination identification
Sensor optimization
Material characterization
Laminated composites

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Published Papers (11 papers)

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Research

25 pages, 15442 KiB

Open AccessArticle

Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

by Daniele Oboe, Luca Colombo, Claudio Sbarufatti and Marco Giglio

Sensors 2021, 21(4), 1388; https://doi.org/10.3390/s21041388 - 17 Feb 2021

Cited by 30 | Viewed by 3378

Abstract

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty. Full article

(This article belongs to the Special Issue Shape Sensing)

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16 pages, 4011 KiB

Open AccessArticle

Natural Frequencies Identification by FEM Applied to a 2-DOF Planar Robot and Its Validation Using MUSIC Algorithm

by Salvador Martínez-Cruz, Juan P. Amézquita-Sánchez, Gerardo I. Pérez-Soto, Jesús R. Rivera-Guillén, Luis A. Morales-Hernández and Karla A. Camarillo-Gómez

Sensors 2021, 21(4), 1209; https://doi.org/10.3390/s21041209 - 9 Feb 2021

Cited by 3 | Viewed by 2314

Abstract

In this paper, the natural frequencies (NFs) identification by finite element method (FEM) is applied to a two degrees-of-freedom (2-DOF) planar robot, and its validation through a novel experimental methodology, the Multiple Signal Classification (MUSIC) algorithm, is presented. The experimental platforms are two different 2-DOF planar robots with different materials for the links and different types of actuators. The FEM is carried out using ANSYS™ software for the experiments, with vibration signal analysis by MUSIC algorithm. The advantages of the MUSIC algorithm against the commonly used fast Fourier transform (FFT) method are also presented for a synthetic signal contaminated by three different noise levels. The analytical and experimental results show that the proposed methodology identifies the NFs of a high-resolution robot even when they are very closed and when the signal is embedded in high-level noise. Furthermore, the results show that the proposed methodology can obtain a high-frequency resolution with a short sample data set. Identifying the NFs of robots is useful for avoiding such frequencies in the path planning and in the selection of controller gains that establish the bandwidth. Full article

(This article belongs to the Special Issue Shape Sensing)

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17 pages, 8418 KiB

Open AccessArticle

Shape-Sensing of Beam Elements Undergoing Material Nonlinearities

by Pierclaudio Savino, Marco Gherlone, Francesco Tondolo and Rita Greco

Sensors 2021, 21(2), 528; https://doi.org/10.3390/s21020528 - 13 Jan 2021

Cited by 8 | Viewed by 2073

Abstract

The use of in situ strain measurements to reconstruct the deformed shape of structures is a key technology for real-time monitoring. A particularly promising, versatile and computationally efficient method is the inverse finite element method (iFEM), which can be used to reconstruct the displacement field of beam elements, plate and shell structures from some discrete strain measurements. The iFEM does not require the knowledge of the material properties. Nevertheless, it has always been applied to structures with linear material constitutive behavior. In the present work, advances are proposed to use the method also for concrete structures in civil engineering field such as bridges normally characterized by material nonlinearities due to the behavior of both steel and concrete. The effectiveness of iFEM, for simply supported reinforced concrete beam and continuous beams with load conditions that determine the yielding of reinforcing steel, is studied. In order to assess the influence on displacements and strains reconstructions, different measurement stations and mesh configurations are considered. Hybrid procedures employing iFEM analysis supported by bending moment-curvature relationship are proposed in case of lack of input data in plastic zones. The reliability of the results obtained is tested and commented on to highlight the effectiveness of the approach. Full article

(This article belongs to the Special Issue Shape Sensing)

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24 pages, 10931 KiB

Open AccessArticle

Shape Sensing of Plate Structures Using the Inverse Finite Element Method: Investigation of Efficient Strain–Sensor Patterns

by Rinto Roy, Alexander Tessler, Cecilia Surace and Marco Gherlone

Sensors 2020, 20(24), 7049; https://doi.org/10.3390/s20247049 - 9 Dec 2020

Cited by 16 | Viewed by 2787

Abstract

Methods for real-time reconstruction of structural displacements using measured strain data is an area of active research due to its potential application for Structural Health Monitoring (SHM) and morphing structure control. The inverse Finite Element Method (iFEM) has been shown to be well suited for the full-field reconstruction of displacements, strains, and stresses of structures instrumented with discrete or continuous strain sensors. In practical applications, where the available number of sensors may be limited, the number and sensor positions constitute the key parameters. Understanding changes in the reconstruction quality with respect to sensor position is generally difficult and is the aim of the present work. This paper attempts to supplement the current iFEM modeling knowledge through a rigorous evaluation of several strain–sensor patterns for shape sensing of a rectangular plate. Line plots along various sections of the plate are used to assess the reconstruction quality near and far away from strain sensors, and the nodal displacements are studied as the sensor density increases. The numerical results clearly demonstrate the effectiveness of the strain sensors distributed along the plate boundary for reconstructing relatively simple displacement patterns, and highlight the potential of cross-diagonal strain–sensor patterns to improve the displacement reconstruction of more complex deformation patterns. Full article

(This article belongs to the Special Issue Shape Sensing)

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16 pages, 2907 KiB

Open AccessArticle

Application of Inverse Finite Element Method to Shape Sensing of Curved Beams

by Pierclaudio Savino, Francesco Tondolo, Marco Gherlone and Alexander Tessler

Sensors 2020, 20(24), 7012; https://doi.org/10.3390/s20247012 - 8 Dec 2020

Cited by 22 | Viewed by 4894

Abstract

Curved beam, plate, and shell finite elements are commonly used in the finite element modeling of a wide range of civil and mechanical engineering structures. In civil engineering, curved elements are used to model tunnels, arch bridges, pipelines, and domes. Such structures provide a more efficient load transfer than their straight/flat counterparts due to the additional strength provided by their curved geometry. The load transfer is characterized by the bending, shear, and membrane actions. In this paper, a higher-order curved inverse beam element is developed for the inverse Finite Element Method (iFEM), which is aimed at reconstructing the deformed structural shapes based on real-time, in situ strain measurements. The proposed two-node inverse beam element is based on the quintic-degree polynomial shape functions that interpolate the kinematic variables. The element is C² continuous and has rapid convergence characteristics. To assess the element predictive capabilities, several circular arch structures subjected to static loading are analyzed, under the assumption of linear elasticity and isotropic material behavior. Comparisons between direct FEM and iFEM results are presented. It is demonstrated that the present inverse beam finite element is both efficient and accurate, requiring only a few element subdivisions to reconstruct an accurate displacement field of shallow and deep curved beams. Full article

(This article belongs to the Special Issue Shape Sensing)

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19 pages, 1243 KiB

Open AccessArticle

State and Force Estimation on a Rotating Helicopter Blade through a Kalman-Based Approach

by Roberta Cumbo, Tommaso Tamarozzi, Pavel Jiranek, Wim Desmet and Pierangelo Masarati

Sensors 2020, 20(15), 4196; https://doi.org/10.3390/s20154196 - 28 Jul 2020

Cited by 5 | Viewed by 3091

Abstract

The interaction between the rotating blades and the external fluid in non-axial flow conditions is the main source of vibratory loads on the main rotor of helicopters. The knowledge or prediction of the produced aerodynamic loads and of the dynamic behavior of the components could represent an advantage in preventing failures of the entire rotorcraft. Some techniques have been explored in the literature, but in this field of application, high accuracy can be reached if a large amount of sensor data and/or a high-fidelity numerical model is available. This paper applies the Kalman filtering technique to rotor load estimation. The nature of the filter allows the usage of a minimum set of sensors. The compensation of a low-fidelity model is also possible by accounting for sensors and model uncertainties. The efficiency of the filter for state and load estimation on a rotating blade is tested in this contribution, considering two different sources of uncertainties on a coupled multibody-aerodynamic model. Numerical results show an accurate state reconstruction with respect to the selected sensor layout. The aerodynamic loads are accurately evaluated in post-processing. Full article

(This article belongs to the Special Issue Shape Sensing)

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19 pages, 10603 KiB

Open AccessArticle

Shape Sensing with Rayleigh Backscattering Fibre Optic Sensor

by Cheng Xu and Zahra Sharif Khodaei

Sensors 2020, 20(14), 4040; https://doi.org/10.3390/s20144040 - 21 Jul 2020

Cited by 23 | Viewed by 4645

Abstract

In this paper, Rayleigh backscattering sensors (RBS) are used to realize shape sensing of beam-like structures. Compared to conventional shape sensing systems based on fibre Bragg grating (FBG) sensors, RBS are capable of continuous lateral sensing. Compared to other types of distributed fibre optic sensors (FOS), RBS have a higher spatial resolution. First, the RBS’s strain sensing accuracy is validated by an experiment comparing it with strain gauge response. After that, two shape sensing algorithms (the coordinate transformation method (CTM) and the strain-deflection equation method (SDEM)) based on the distributed FOS’ input strain data are derived. The algorithms are then optimized according to the distributed FOS’ features, to make it applicable to complex and/or combine loading situations while maintaining high reliability in case of sensing part malfunction. Numerical simulations are carried out to validate the algorithms’ accuracy and compare their accuracy. The simulation shows that compared to the FBG-based system, the RBS system has a better performance in configuring the shape when the structure is under complex loading. Finally, a validation experiment is conducted in which the RBS-based shape sensing system is used to configure the shape of a composite cantilever-beam-like specimen under concentrated loading. The result is then compared with the optical camera-measured shape. The experimental results show that both shape sensing algorithms predict the shape with high accuracy comparable with the optical camera result. Full article

(This article belongs to the Special Issue Shape Sensing)

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22 pages, 12108 KiB

Open AccessArticle

A Comparative and Review Study on Shape and Stress Sensing of Flat/Curved Shell Geometries Using C⁰-Continuous Family of iFEM Elements

by Mohammad Amin Abdollahzadeh, Adnan Kefal and Mehmet Yildiz

Sensors 2020, 20(14), 3808; https://doi.org/10.3390/s20143808 - 8 Jul 2020

Cited by 36 | Viewed by 4185

Abstract

In this study, we methodologically compare and review the accuracy and performance of C⁰-continuous flat and curved inverse-shell elements (i.e., iMIN3, iQS4, and iCS8) for inverse finite element method (iFEM) in terms of shape, strain, and stress monitoring, and damage detection on various plane and curved geometries subjected to different loading and constraint conditions. For this purpose, four different benchmark problems are proposed, namely, a tapered plate, a quarter of a cylindrical shell, a stiffened curved plate, and a curved plate with a degraded material region in stiffness, representing a damage. The complexity of these test cases is increased systematically to reveal the advantages and shortcomings of the elements under different sensor density deployments. The reference displacement solutions and strain-sensor data used in the benchmark problems are established numerically, utilizing direct finite element analysis. After performing shape-, strain-, and stress-sensing analyses, the reference solutions are compared to the reconstructed solutions of iMIN3, iQS4, and iCS8 models. For plane geometries with sparse sensor configurations, these three elements provide rather close reconstructed-displacement fields with slightly more accurate stress sensing using iCS8 than when using iMIN3/iQS4. It is demonstrated on the curved geometry that the cross-diagonal meshing of a quadrilateral element pattern (e.g., leading to four iMIN3 elements) improves the accuracy of the displacement reconstruction as compared to a single-diagonal meshing strategy (e.g., two iMIN3 elements in a quad-shape element) utilizing iMIN3 element. Nevertheless, regardless of any geometry, sensor density, and meshing strategy, iQS4 has better shape and stress-sensing than iMIN3. As the complexity of the problem is elevated, the predictive capabilities of iCS8 element become obviously superior to that of flat inverse-shell elements (e.g., iMIN3 and iQS4) in terms of both shape sensing and damage detection. Comprehensively speaking, we envisage that the set of scrupulously selected test cases proposed herein can be reliable benchmarks for testing/validating/comparing for the features of newly developed inverse elements. Full article

(This article belongs to the Special Issue Shape Sensing)

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14 pages, 1515 KiB

Open AccessArticle

Measurement of Shear Strain Field in a Soft Material Using a Sensor System Consisting of Distributed Piezoelectric Polymer Film

by Fengyu Li, Yasuhiro Akiyama, Xianglong Wan, Shogo Okamoto and Yoji Yamada

Sensors 2020, 20(12), 3484; https://doi.org/10.3390/s20123484 - 19 Jun 2020

Cited by 10 | Viewed by 3874

Abstract

Measurement of the internal stress and strain distributions within soft materials is necessary in the field of skin contact safety. However, conventional interactive force sensors cannot efficiently obtain or estimate these distributions. Herein, a shear strain sensor system consisting of distributed built-in piezoelectric polyvinylidene fluoride (PVDF) polymer films was developed to measure the internal shear strain field of a soft material. A shear strain sensing model was mathematically established, based on the piezoelectricity and mechanical behavior of a bending cantilever beam, to explain the sensing principle. An experiment in three-dimensional measurement of the shear strain distribution within an artificial skin was designed and conducted to assess the sensitivity of the sensing model. This sensor system could visualize the shear strain field and was sensitive to different contact conditions. The measurement results agreed well with the results of numerical simulation of the substrate, based on contact mechanics. The proposed sensor system was confirmed to provide a new sensing method for the field of shape analysis. The sensor system can be applied to develop sufficiently sensitive electronic skin and can significantly contribute to skin damage analysis and skin contact safety assessment. Full article

(This article belongs to the Special Issue Shape Sensing)

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24 pages, 5385 KiB

Open AccessArticle

Isogeometric iFEM Analysis of Thin Shell Structures

by Adnan Kefal and Erkan Oterkus

Sensors 2020, 20(9), 2685; https://doi.org/10.3390/s20092685 - 8 May 2020

Cited by 57 | Viewed by 4814

Abstract

Shape sensing is one of most crucial components of typical structural health monitoring systems and has become a promising technology for future large-scale engineering structures to achieve significant improvement in their safety, reliability, and affordability. The inverse finite element method (iFEM) is an innovative shape-sensing technique that was introduced to perform three-dimensional displacement reconstruction of structures using in situ surface strain measurements. Moreover, isogeometric analysis (IGA) presents smooth function spaces such as non-uniform rational basis splines (NURBS), to numerically solve a number of engineering problems, and recently received a great deal of attention from both academy and industry. In this study, we propose a novel “isogeometric iFEM approach” for the shape sensing of thin and curved shell structures, through coupling the NURBS-based IGA together with the iFEM methodology. The main aim is to represent exact computational geometry, simplify mesh refinement, use smooth basis/shape functions, and allocate a lower number of strain sensors for shape sensing. For numerical implementation, a rotation-free isogeometric inverse-shell element (isogeometric Kirchhoff–Love inverse-shell element (iKLS)) is developed by utilizing the kinematics of the Kirchhoff–Love shell theory in convected curvilinear coordinates. Therefore, the isogeometric iFEM methodology presented herein minimizes a weighted-least-squares functional that uses membrane and bending section strains, consistent with the classical shell theory. Various validation and demonstration cases are presented, including Scordelis–Lo roof, pinched hemisphere, and partly clamped hyperbolic paraboloid. Finally, the effect of sensor locations, number of sensors, and the discretization of the geometry on solution accuracy is examined and the high accuracy and practical aspects of isogeometric iFEM analysis for linear/nonlinear shape sensing of curved shells are clearly demonstrated. Full article

(This article belongs to the Special Issue Shape Sensing)

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19 pages, 12417 KiB

Open AccessArticle

A LiDAR Point Cloud Data-Based Method for Evaluating Strain on a Curved Steel Plate Subjected to Lateral Pressure

by Hyeon Cheol Jo, Hong-Gyoo Sohn and Yun Mook Lim

Sensors 2020, 20(3), 721; https://doi.org/10.3390/s20030721 - 28 Jan 2020

Cited by 6 | Viewed by 4767

Abstract

Structural health monitoring (SHM) and safety assessment are very important areas for evaluating the behavior of structures. Various wired and wireless sensors can measure the physical responses of structures, such as displacement or strain. One recently developed wireless technique is a light imaging detection and ranging (LiDAR) system that can remotely acquire three-dimensional (3D) high-precision coordinate information using 3D laser scanning. LiDAR systems have been previously used in geographic information systems (GIS) to collect information on geography and terrain. Recently, however, LiDAR is used in the SHM field to analyze structural behavior, as it can remotely detect the surface and deformation shape of structures without the need for attached sensors. This study demonstrates a strain evaluation method using a LiDAR system in order to analyze the behavior of steel structures. To evaluate the strains of structures from the initial and deformed shape, a combination of distributed 3D point cloud data and finite element methods (FEM) was used. The distributed 3D point cloud data were reconstructed into a 3D mesh model, and strains were calculated using the FEM. By using the proposed method, the strain could be calculated at any point on a structure for SHM and safety assessment during construction. Full article

(This article belongs to the Special Issue Shape Sensing)

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