Virtual Distortion Research Articles

Synchronized Assessment of Bridge Structural Damage and Moving Force via Truncated Load Shape Function

Moving load and structural damage assessment has always been a crucial topic in bridge health monitoring, as it helps analyze the daily operating status of bridges and provides fundamental information for bridge safety evaluation. However, most studies and research consider these issues as two separate problems. In practice, unknown moving loads and damage usually coexist and influence the bridge vibration synergically. This paper proposes an innovative synchronized assessment method that determines structural damages and moving forces simultaneously. The method firstly improves the virtual distortion method, which shifts the structural damage into external virtual forces and hence transforms the damage assessment as well as the moving force identification to a multi-force reconstruction problem. Secondly, a truncated load shape function (TLSF) technique is developed to solve the forces in the time domain. As the technique smoothens the pulse function via a limited number of TLSF, the singularity and dimension of the system matrix in the force reconstruction is largely reduced. A continuous beam and a three-dimensional truss bridge are simulated as examples. Case studies show that the method can effectively identify various speeds and numbers of moving loads, as well as different levels of structural damages. The calculation efficiency and robustness to white noise are also impressive.

Transparent type virtual image display using small mirror array

There is a demand to display image on a transparent medium. If we can show image superimposed on a window, it can attract interest of people. However, a current achieved transparent displays show images only on the display surface, hence it is difficult to show image superimposed on an object that exists behind the screen. Thus, it doesn't understand intuitively. On the other hand, a display which can be perceived the image behind the screen should be placed inclined. Therefore, it is difficult to apply to advertising and exhibition. The purpose of this study is to generate transparent display to show image superimposed on near an object that exists behind the screen. We propose a display which shows image not on display surface but at a different image of depth. In this system, to show the image at behind the screen, display device is reflected on the transparent screen which incorporates a half mirror array. In this study, we use the mirror array as screen in order to locate the display device at an appropriate place. We optimize the surface of display device and angle of all mirrors so as to minimize the virtual image distortion. To confirm the practicality of the proposed method, we conducted a simulation. From the result, we confirmed the virtual image was able to display designated position.

An Improved Objective Function for Modal-Based Damage Identification Using Substructural Virtual Distortion Method

Damage identification based on modal parameters is an important approach in structural health monitoring (SHM). Generally, traditional objective functions used for damage identification minimize the mismatch between measured modal parameters and the parameters obtained from the finite element (FE) model. However, during the optimization process, the repetitive calculation of structural modes is usually time-consuming and inefficient, especially for large-scale structures. In this paper, an improved objective function is proposed based on certain characteristics of the peaks of the frequency response function (FRF). Traditional objective functions contain terms that quantify modal shapes and/or natural frequencies. Here, it is proposed to replace them by the FRF of the FE model, which allows the repeated full modal analysis to be avoided and thus increases the computational efficiency. Moreover, the efficiency is further enhanced by employing the substructural virtual distortion method (SVDM), which allows the frequency response of the FE model of the damaged structure to be quickly computed without the costly re-analysis of the entire damaged structure. Finally, the effectiveness of the proposed method is verified using an eight-story frame structure model under several damage cases. The damage location and extent of each substructure can be identified accurately with 5% white Gaussian noise, and the optimization efficiency is greatly improved compared with the method using a traditional objective function.

Optimal Placement of Virtual Masses for Structural Damage Identification.

Adding virtual masses to a structure is an efficient way to generate a large number of natural frequencies for damage identification. The influence of a virtual mass can be expressed by Virtual Distortion Method (VDM) using the response measured by a sensor at the involved point. The proper placement of the virtual masses can improve the accuracy of damage identification, therefore the problem of their optimal placement is studied in this paper. Firstly, the damage sensitivity matrix of the structure with added virtual masses is built. The Volumetric Maximum Criterion of the sensitivity matrix is established to ensure the mutual independence of measurement points for the optimization of mass placement. Secondly, a method of sensitivity analysis and error analysis is proposed to determine the values of the virtual masses, and then an improved version of the Particle Swarm Optimization (PSO) algorithm is proposed for placement optimization of the virtual masses. Finally, the optimized placement is used to identify the damage of structures. The effectiveness of the proposed method is verified by a numerical simulation of a simply supported beam structure and a truss structure.

Experimental Study for Damage Identification of Storage Tanks by Adding Virtual Masses

This research proposes a damage identification approach for storage tanks that is based on adding virtual masses. First, the frequency response function of a structure with additional virtual masses is deduced based on the Virtual Distortion Method (VDM). Subsequently, a Finite Element (FE) model of a storage tank is established to verify the proposed method; the relation between the added virtual masses and the sensitivity of the virtual structure is analyzed to determine the optimal mass and the corresponding frequency with the highest sensitivity with respect to potential damages. Thereupon, the damage can be localized and quantified by comparing the damage factors of substructures. Finally, an experimental study is conducted on a storage tank. The results confirm that the proposed method is feasible and practical, and that it can be applied for damage identification of storage tanks.

Lens distortion correction method based on cross-ratio invariability and compressed sensing

Optical lens distortions will seriously affect the measurement accuracy of the vision system. An independent lens distortion correction method based on cross-ratio invariability and compressed sensing is, thus, proposed to improve the measurement accuracy of the system. A virtual distortion correction template is designed according to the characteristics of the lens distortion. The ideal projection coordinate in the imaging plane of the camera and the distortion correction value of the characteristic points in the virtual correction template can be calculated based on the four-point cross-ratio invariance principle. The ideal projection coordinate of the other pixels in the image can then be reconstructed based on compressed sensing theory and, thus, correcting the distortion of all pixels. The experimental results show that for the same vision measurement system, when the independent distortion correction algorithm is used, its measurement accuracy is significantly improved, and the maximum error is only 0.069 mm. This method can correct the distortion effectively, thus improving the precision of the system.

A numerical investigation for alternative toolpath deposition solutions for surface cladding of stainless steel P420 powder on AISI 1018 steel substrate

The thermal cycling in the coaxial laser cladding process can cause significant variations in the strength of cladded parts as well as the development of residual stresses, large distortions, and even cracking. In the current study, the hardness variations, induced residual stress distribution, and the developed distortion characteristics of cladded parts are examined for different deposition tool paths. The research is conducted by means of numerical simulations validated by experimental results for selected surface cladding deposition strategies. The specimens were made using P420 stainless steel powder clad onto an AISI 1918 substrate. In the previous studies by the authors, it was found that the transient thermal solution using a moving heat source simulation technique required several days of computational time for small cladded parts, making it impractical for industrial applications. In the present research work, a modeling approach using a steady-state thermal solution was proposed. This technique produced similar results for hardness and residual stress in a shorter time period, but the resulted distortion values were not accurate. Consequently, a thermo-mechanical modeling approach was adopted that provided virtual distortion solutions correlating well with the experimental results. These models were subsequently employed to explore various process planning scenarios. The effect of surface cladding deposition patterns, the substrate dimensions, the plate dimension’s aspect ratio, and the time gap between beads deposition were simulated and the strength and physical defects of the clad layer results are compared. Moreover, the mechanical response and properties for a full-scale gasket part is investigated as an example representing an industrial application.

Pipeline Damage Identification Based on Additional Virtual Masses

To improve the identification sensitivity of local damages in pipelines, we propose an added virtual mass method thatprevents adding real masses to the pipeline. First, we develop a method of adding virtual masses to pipelines based on the virtual distortion method (VDM). Second, a frequency response to the added mass is constructed using the excitation and acceleration responses. The quantity of mass and the corresponding selected natural frequency with high sensitivity are both determined by the analyzing the sensitivity of the relationship between mass and natural frequency. Finally, the degree of damage can be accurately identified by adding virtual masses on the substructure of the pipeline combined with sensitivity and frequency. Using numerical simulations and experiments, we verify the feasibility of the added virtual mass method for the identification of damages to pipeline structures.

Damage Detection in the Cable Structures of a Bridge Using the Virtual Distortion Method

Damage Detection in the Cable Structures of a Bridge Using the Virtual Distortion Method

Hybrid element-based virtual distortion method for finite element model updating of bridges with wide-box girders

A hybrid element-based virtual distortion method (VDM) is proposed to reduce the computational burden of finite element model (FEM) updating for bridges with wide-box girders. First, for the finite element modeling of wide bridges, a beam-shell hybrid element is proposed as an effective trade-off between the inadequate accuracy of beam-like elements and the low efficiency of solid or shell elements. Based on this, VDM is extended from a beam-like element to the proposed hybrid element to establish a metamodel for the FEM updating for wide bridges. Second, this paper describes in detail some key issues of this new type of VDM, such as generating the transfer and influence matrices, extracting the main virtual distortions and selecting the master degrees of freedom (DOFs) of the hybrid element. Finally, using the measured static deformation from a load test, the effectiveness of the proposed method is demonstrated by updating the FEM of an actual bridge.

Refined finite element modeling of a damaged bridge with virtual distortion method coupling solid superelement

A new type of metamodel, the virtual distortion method (VDM) coupling superelement, is proposed to alleviate the calculation burden of refined finite element (FE) modeling of existing damaged bridges. First, VDM based on a beam-like element is extended to a solid superelement, and the transfer matrix and influence matrices of a complicated superelement suitable for VDM are obtained. Second, aiming at an actual damaged bridge, a two-step procedure of refined modeling based on FE model updating is presented to precisely model the local damaged regions of the structure, which is difficult to achieve in FE analysis. Finally, using the measured static deformation from the load test, a precise FE model of this damaged bridge is obtained with high efficiency by importing the VDM coupling solid superelement into the above procedure of refined modeling.

Adaptive Bit Allocation for 3D Video Coding

In the multi-view video plus depth 3D video coding, texture image and depth map are coded jointly. The texture image is utilized for displaying and synthesizing the virtual view as reference image. The depth map provides the scene geometry information and is utilized to synthesize the virtual view at the terminal through Depth-Image Based Rendering technique. The distortion of the compressed texture image and depth map will be propagated to the synthesized virtual view. Besides the coding efficiency of texture image and depth map, bit allocation between texture image and depth map also has a great effect on the synthesized virtual view quality. Several methods are proposed for bit allocation between texture image and depth map, but most of them attempt to allocate a fixed target bitrate based on virtual view distortion model to achieve optimal synthesized virtual view quality, and the modeling process brings extra complexity. In practical application, the video sequence has different contents and fixed bit ratio cannot achieve optimal performance. In this paper, we propose an adaptive bit allocation algorithm for 3D video coding. First, we present a model to estimate the synthesized virtual view distortion, and then adjust the bit ratio between adjacent views and between texture image and depth map at Group of Picture level based on the virtual view quality fluctuation. We adjust the bit ratio to achieve the optimal virtual view quality for different video contents. Experimental results demonstrate that the proposed algorithm can optimally allocate bits to achieve optimal virtual view quality under different target bitrates and for different video contents, and the computational complexity of the proposed algorithm is extremely low.

Damage identification using structural modes based on substructure virtual distortion method

A damage identification approach is presented using substructure virtual distortion method which takes the advantage of the fast structural reanalysis technique of virtual distortion method. The formulas of substructure virtual distortion method are deduced in frequency domain, and then the frequency response function of the damaged structure is constructed quickly via the superposition of the frequency response function of the intact structure and the frequency responses caused by the damage-coupling virtual distortions of the substructures. The structural damage extents are identified using the measured modal parameters. Two steps are adopted to increase the efficiency of optimization: the modals of finite element model are estimated quickly from the fast constructed frequency response function during the optimization and the primary distortions of the substructures are extracted by contribution analysis to further reduce the computational work. A six-story frame numerical model and an experiment of a cantilever beam are carried out, respectively, to verify the efficiency and accuracy of the proposed method.

Synergic identification of prestress force and moving load on prestressed concrete beam based on virtual distortion method

In a prestressed concrete bridge, the magnitude of the prestress force (PF) decreases with time. This unexpected loss can cause failure of a bridge which makes prestress force identification (PFI) critical to evaluate bridge safety. However, it has been difficult to identify the PF non-destructively. Although some research has shown the feasibility of vibration based methods in PFI, the requirement of having a determinate exciting force in these methods hinders applications onto in-service bridges. Ideally, it will be efficient if the normal traffic could be treated as an excitation, but the load caused by vehicles is difficult to measure. Hence it prompts the need to investigate whether PF and moving load could be identified together. This paper presents a synergic identification method to determine PF and moving load applied on a simply supported prestressed concrete beam via the dynamic responses caused by this unknown moving load. This method consists of three parts: (i) the PF is transformed into an external pseudo-load localized in each beam element via virtual distortion method (VDM); (ii) then these pseudo-loads are identified simultaneously with the moving load via Duhamel Integral; (iii) the time consuming problem during the inversion of Duhamel Integral is overcome by the load-shape function (LSF). The method is examined against different cases of PFs, vehicle speeds and noise levels by means of simulations. Results show that this method attains a good degree of accuracy and efficiency, as well as robustness to noise.

Virtual Distortion Method-Based Finite Element Model Updating of Bridges by Using Static Deformation

AbstractA superelement-based virtual distortion method (VDM) was proposed to improve the efficiency of the finite element model (FEM) updating of large-scaled bridges by using static information. O...

Optimizing rate allocation between multiview videos and associated depth maps with quantization-based virtual view distortion model and genetic algorithm

In three-dimensional video coding (3-DVC), it is reasonable to allocate different coding bits for multiview videos and associated depth maps because of their different characteristics to meet the bits’ restraints of bandwidth/storage. We first propose a virtual view average distortion model. Then, based on the quantization parameter (QP), the average distortion-QP models and sum bitrate-QP models are proposed to depict the average distortions and sum bitrates of the referenced views for multiview videos and depth maps. Finally, the 3-DVC bit allocation problem is converted as a constrained optimization problem, which is solved by a genetic algorithm to search for the optimal QP pair. Experimental results demonstrate the effectiveness of our proposed models. Since the bit allocation scheme takes the performance of synthesized view and bitrate utilization into consideration, the absolute difference between the constraint and the actual coding bitrates (referred to as “rate inaccuracy”) of the proposed method is only 7.405% on average, which greatly outperforms the fixed 5 ∶ 1 ratio-based method with a rate inaccuracy of 19.103% and the planar model-based method with a rate inaccuracy of 20.556%. Compared with these two methods, our proposed method can achieve a maximum 1.951-dB gain under the same bitrates constraint.

Structural damage identification by adding virtual masses

This paper presents a method for damage identification by adding virtual masses to the structure in order to increase its sensitivity to local damages. The main concept is based on the Virtual Distortion Method (VDM), which is a fast structural reanalysis method that employs virtual distortions or pseudo loads to simulate structural modifications. In this paper, the structure with an added virtual mass is called the virtual structure. First, the acceleration frequency response of the virtual structure is constructed numerically by the VDM using local dynamic data measured only by a single excitation sensor and a single acceleration sensor. Second, the value of the additional mass is determined via sensitivity analysis of the constructed frequency responses of the virtual structure with respect to damage parameters; only the natural frequencies with high sensitivity are selected. This process is repeated for all the considered placements of the virtual mass. At last, the selected natural frequencies of all the virtual structures are used together for damage identification of the real structure. A finite element (FE) model of a plane frame is used to introduce and verify the proposed method. The damage can be identified precisely and effectively even under simulated 5 % Gaussian noise pollution.

Simultaneous Identification of Moving Vehicles and Bridge Damages Considering Road Rough Surface

A method for the simultaneous identification of moving vehicles and the damages of the supporting structure from measured responses is presented. A two-axle vehicle model with two degrees of freedom (DOF) is adopted. The extent of the damage and the vehicle parameters were chosen as the optimisation variables, which allow ill conditioning to be avoided and decrease the number of sensors required. The identification is performed by minimising the distance between the measured responses and the computed responses to given optimisation variables. The virtual distortion method (VDM) was used, such that the response of the damaged structure can be computed from comparison with the intact structure subjected to the same vehicle excitation and to the response-coupled virtual distortions. These are related to the optimisation variables by the system impulse response matrix and are expressed by a linear system, which allowed both types of optimisation variables to be treated in a unified way. The numerical cost is reduced by using a moving influence matrix. The adjoint variable method is used for fast sensitivity analysis. A three-span bridge numerical example is presented, where the identification was verified with 5% root mean square (RMS) measurement, and model, error whilst also considering the surface roughness of the road.

Simultaneous identification of excitation time histories and parametrized structural damages

This paper presents and experimentally verifies an effective method for simultaneous identification of excitations and damages, which are two crucial factors in structural health monitoring and which often coexist in practice. The unknowns are identified by minimizing a time-domain square distance between the measured and the computed responses. Even though both damage and excitation are unknown, only damage parameters are treated here as the optimization variables: given the damage, the excitation is uniquely determined from the measured responses. As a result, all unknowns are of the same type, which allows standard optimization algorithms to be used and obviates the need for two-step procedures. The sensitivity analysis is facilitated by interpolating in each iteration the relation between structural responses and damage parameters. The numerical costs are further decreased by the fast reanalysis approach of the virtual distortion method (VDM), which is used to compute exact impulse responses of the damaged structure. The proposed methodology is verified both numerically (using a multi-span frame) and experimentally (using a cantilever beam). Stiffness-related damages and mass-related modifications are identified successfully together with the three tested types of external excitation.

Monitoring of progressive collapse of skeletal structures

The authors propose an idea of monitoring the state of skeletal structures of high importance (e.g. roof structures over large area buildings) with the aim of identification of slowly-developing plastic zones. This is formulated as an inverse problem within the framework of the Virtual Distortion Method, which was used previously to identify stiffness/mass modifications in similar manner. Permanent plastic strains developed in a truss element can be modeled by an initial strain (virtual distortion) introduced to the structure. The formation of subsequent plastic zones in the structure is assumed to be slow. Consequently, the design variable (plastic strain) is time-independent, which makes the inverse analysis efficient. This article presents problem formulation and numerical algorithm for identification of the plastic strains int russ structures. The identification relies on gradient-based optimization. A numerical example is included to demonstrate the efficiency of th ealgorithm.