Deflection Data Research Articles

Mechanical Response of Hot-Mixed Epoxy Asphalt Concrete Steel Deck Pavement Under Thermal and Load

In recent years, fatigue cracking in orthotropic steel bridge deck pavements has become a significant concern, so the investigation of the mechanical response of the pavement layer has become a central focus in pavement structure design. This experiment subjected a full-scale specimen to a constant amplitude dynamic load of 60 kN to 300 kN over 2 million cycles. Throughout the testing, a circulating water bath elevated the temperature of the pavement layer from 15 °C to 50 °C. Key locations were monitored for strain and deflection data, facilitating an investigation into the mechanical response of the epoxy asphalt pavement system under the effects of temperature and load. The results indicate that the maximum transverse strain at the bottom of the steel deck occurs at the U-rib weld aligned with the load center, reaching 190% of the initial loading strain. Meanwhile, the maximum transverse strain on the pavement surface is observed at the U-rib weld adjacent to the loaded area, measuring 167% of the initial strain. The maximum longitudinal strain is lower than the maximum transverse strain. In the load zone, the longitudinal strain between the U-ribs exceeds that at the U-rib weld. Both transverse strain and relative deflection increase as the load intensifies. The relationship between transverse strain and applied load is characterized by an exponential function, while deflection exhibits a cubic relationship with the applied load. Elevated temperatures also contribute to increased transverse strains at both the bottom of the steel deck and the pavement surface, following an exponential trend. Relative deflection is primarily influenced by the applied load and remains relatively unaffected by temperature variations. When accounting for the coupling of load and temperature, the maximum transverse strains at both the bottom of the steel deck and the pavement surface can be modeled as an exponential function of the independent variables: load and temperature.

Physics-informed neural networks with data-driven in modeling and characterizing piezoelectric micro-bender

Abstract Despite the rapid development and widespread adoption of physics-informed neural networks (PINNs) in various engineering fields, their applications in microelectromechanical coupling systems (MEMS) remain relatively unexplored. In this study, we demonstrate a novel implementation of PINNs for modeling and characterizing a piezoelectric microactuator. By leveraging the beam-like structure, the governing equations for a multi-layered piezoelectric actuator are first derived and subsequently incorporated into the PINNs model to accurately predict the deformation of the piezoelectric actuator in response to a given voltage input. Furthermore, by integrating experimental deflection data obtained from Laser Doppler Vibrometer measurements into the neural network, we further demonstrate the potential of PINNs in identifying the piezoelectric material coefficient through inverse analysis. Our contribution in applying PINNs to models and characterizing piezoelectric actuators in MEMS serves as a promising starting point for the broader utilization of machine learning techniques in this field.

Effect of data censoring on thoracic injury risk curves

Objective The first objective was to evaluate the effect of using less censored (i.e., exact and interval-censored) data on thoracic injury risk curves and the resulting injury probabilities. The second objective was to generate new injury risk curves to predict Abbreviated Injury Scale (AIS) 3+ rib fractures based on chest deflection. Methods Two data sets consisting of postmortem human surrogate (PMHS) tests with multipoint chest deflection measurements were compiled: A less censored data set consisting of exact and interval-censored data and a doubly censored data set consisting of left- and right-censored data. Chest deflection data from both data sets were processed in a consistent manner to calculate the maximum deflections at different locations across the chest. Survival analysis methods were used to generate nonparametric and parametric injury risk curves for serious skeletal injury. The total sample sizes and proportions of less censored data used to generate the risk curves were varied for each curve to evaluate the effects of sample size and less censored data on risk curve shape and predicted injury thresholds. Results Increasing the proportion of less censored data resulted in steeper injury risk curves and a higher predicted risk for a given amount of deflection. Differences in injury risk were more pronounced in the upper half of the injury risk curves. Introducing less censored data also produced narrower confidence intervals. At a total sample size of 79, increasing the percentage of less censored data from 0 to 30 had minimal effect on the shape of the risk curve. Conclusions Doubly censored chest deflection data have historically been used to generate thoracic injury risk curves for frontal motor vehicle crash events. This study found that incorporating less censored data into thoracic injury risk curves meaningfully affected the shape of the injury risk curves and their resulting injury risk predictions. All of the injury risk curves generated in the study predicted a lower threshold for serious rib fracture injury compared to previously developed injury risks curves that are currently in use in the field. Based on the results of this study, adding less censored data to injury risk curves should be strongly considered to improve thoracic injury risk curve prediction and confidence, especially for smaller sample sizes.

Extension of paperboard modelling with Föppl–von Karman terms for improved stress state under suction pressure

A practical method for solving the bending stiffness of a thin orthotropic plate based on measured deflection and known loading was studied. The target application was paperboard manufacturing and related process control. Here, finite element (FE) method was used to create virtual paperboard and its deflection data. The accuracy of the linear Kirchhoff plate model used in the practical method was tested against the FE model with known load and material properties. It was found that in the case of significant deflections, the linear Kirchoff model was not accurate. The non-linear Föppl--von Kàrmàn model takes into account the occurring membrane stresses and extends on the Kirchhoff model, allowing for larger deflection. The non-linear Föppl--von Kàrmàn model was found to successfully describe the simulated situation and could be used to better solve for the paperboard's bending stiffness values over two axes.

Experimental and numerical study on polypropylene fibers reinforced concrete slabs with corroded reinforcement under monotonic loading

The degradation of structural performance due to reinforcement corrosion in reinforced concrete (RC) structures and the subsequent measures to improve the mechanical properties of corroded RC structures have garnered significant interest. This study investigates the structural performance of corroded polypropylene fiber RC slabs through both experimental and numerical approaches. Specimens were subjected to accelerated corrosion via electrochemical methods to simulate rebar corrosion. Key experimental parameters include polypropylene fiber volume fractions of 0% and 3%, design corrosion levels of 0%, 5%, and 10%, and both one-way and two-way constraints. The Digital Image Correlation (DIC) technique was employed for data acquisition. Load, deflection, strain, and crack morphology data were collected during loading. Results indicate that reinforcement corrosion increases the maximum crack width during loading, while a 3% polypropylene fiber volume fraction reduces this width by 20% to 48% at the same load level. Polypropylene fibers also enhance the peak loads and corresponding deflections of unidirectional and bidirectional specimens, with a more pronounced increase in unidirectional specimens of 11.3% and 15.4%, respectively. Although corrosion reduces the load-carrying capacity of the specimens, the inclusion of 3% polypropylene fibers significantly mitigates this reduction. A numerical model, incorporating rebar corrosion and polypropylene fibers through appropriate material constitutive models, was developed and validated against experimental results. The model accurately simulates the mechanical behavior of polypropylene fiber RC slabs with corroded reinforcement.

Calculation Thickness of the Added Flexural Layer on Composite Layer using a Light Weight Deflectometer (LWD) Pusjatan

Calculating the thickness of the flexible overlay needs to consider several factors, such as traffic load, soil characteristics, existing pavement conditions, and planned changes to the road design. This procedure generally uses recognized pavement design methods, such as the AASHTO 1993 method (Guide for Design of Pavement Structures). This research aims to determine the thickness of the added layer using an asphalt layer on composite roads in accordance with the 1993 AASHTO standards. It is hoped that this method can produce an effective overlay design, extend the life of the pavement, and increase the comfort and safety of road users. The data used in this research includes primary and secondary data. The results of this analysis are to calculate the STA 0 segment, for other STAs use the same method. From the Light Weight Deflectometer (LWD) deflection data, the Subgrade Reaction Modulus (k) value was 473 psi/in, the Concrete Elasticity Modulus (Ec) value was 4,843,105 psi and the Rupture Modulus (Sc') value was 699 psi. The traffic load used is 25.000.000, so the result of calculating the plate thickness to serve future traffic (Df) is 10.79 inches or 27.40 cm and the effective plate thickness value (Deff) is 9.13 inches or 23.30 cm, then the result is the added layer thickness (Dol) is 3.30 inches or 8.39 cm

Bending Analysis of Multiwall Carbon Nanotube Reinforced Functionally Graded Composite Cylindrical Shell

The curved structural components of aircraft, automobiles, and marine vessels, such as cylindrical panels, are primarily exposed to loading, which can result in bending failure, particularly in lightweight structures. The bending analysis of cylindrical panels made of functionally graded multiwall carbon nanotube (FG-MWCNT) epoxy composites is subjective in this study. In the first section, FG-MWCNT composite cylindrical panels are simulated in the ANSYS software. There are three methods for distributing uniaxially aligned reinforcements. The material properties of the carbon nanotubes uniformly distributed and functionally graded over the thickness of the shell structure are estimated using an extended rule of mixture micromechanical model that incorporates certain useful characteristics. To demonstrate the effectiveness and applicability of the proposed finite element approach, deflection data are presented. The analysis of the shell structure's bending includes an investigation of the impact of CNT volume fraction, boundary condition, lengthto-thickness ratio, and other geometrical factors

Time-convolutional network with joint time-frequency domain loss based on arithmetic optimization algorithm for dynamic response reconstruction

Structural Health Monitoring (SHM) systems provide extensive data on in-service bridges, which is crucial for evaluating structural performance. However, data loss frequently occurs due to environmental factors and technical failures. Although missing data reconstruction problem has been largely studied, the accuracy of response reconstruction in the frequency domain is often overlooked. To address this issue, this study proposes to integrate a time-frequency joint loss function within an Arithmetic Optimization Algorithm-Temporal Convolutional Network (AOA-TCN), which leverages temporal and spatial dependencies among measurement points to reconstruct missing dynamic deflection data. The time-frequency joint loss function is enhanced with linear decay weights to increase sensitivity to low-order modal contributions, with an adaptive weighting mechanism balancing loss contributions from time and frequency domains. These adaptive weight parameters are optimized through AOA to enhance the TCN's generalizability. The feasibility and effectiveness of the proposed method are first demonstrated using simulated dynamic deflection data of a finite element model of a continuous beam bridge, and then experimentally verified on a real-world simply-supported beam bridge. The results indicate that the proposed method achieves higher data reconstruction accuracy and more precise modal analysis results compared to existing methods. The Modal Assurance Criterion (MAC) between mode shapes identified using measured data and reconstructed response reached 96.9 %, proving that the proposed method is capable of reconstructing the missing structural response while retaining its frequency-domain information, which is valuable for structural integrity assessment based on modal parameter identification of operational bridges.

Bayesian Inference and Condition Assessment Based on the Deflection of Aging Reinforced Concrete Hollow Slab Bridges

This paper presents a Bayesian inference framework for updating the structural rigidity ratio of aging hollow slab RC bridges using deflection measurements. The framework models the structural rigidity ratio as a stochastic field along the hollow RC slabs, using the Karhunen–Loeve (KL) transform to capture spatial correlation and variation. Bayesian inference is then applied using deflection data from static loading tests, supported by a finite element model (FEM) and a Kriging surrogate model to enhance computational efficiency. The posterior distribution of the structural rigidity ratio is derived using a Markov chain Monte Carlo (MCMC) sampler. The proposed method was tested on an RC bridge with hollow slabs, using deflection measurements taken before and after reinforcement. The Bayesian updates indicated increased structural rigidity ratios after reinforcement, validating the effectiveness of the reinforcement. The deflection predictions from the updated models closely matched the measurements, with the 95% confidence bounds encompassing most of the data. This demonstrates the method’s validity and robustness in capturing the structural improvements post-reinforcement.

Deep learning-based minute-scale digital prediction model for temperature induced deflection of a multi-tower double-layer steel truss bridge

Bridge deflection serves as a vital and intuitive index for the evaluation of bridge safety. Temperature load has the greatest influence on the bridge deformation and studies on the temperature-induced deformation prediction of long-span bridge are in limited numbers. A digital prediction model based on deep learning in minute scale is established to study the bridge deflection caused by temperature. The wavelet transform (WT) is adopted to filter the high-frequency signals of the original deflection caused by the related load factors. Three different networks, long short-term memory (LSTM), bidirectional LSTM (Bi-LSTM), and Transformer variant, are studied and compared in the prediction process. Two different learning strategies considering different input data are also considered to optimize the prediction performance. The proposed prediction model is applied to the temperature induced deflection prediction of a multi-tower double-layer steel truss bridge. The results show that strategy A, which employs temperature time series data as input, is less effective than strategy B. Incorporating both temperature and deflection data as inputs is essential for predicting temperature-induced deflections. Moreover, the Transformer-variant network generally exhibits superior prediction performance compared to the LSTM and Bi-LSTM. The self-attention mechanism of the Transformer allows it to focus on key historical temperature points, thereby enhancing prediction accuracy.

Application of Digital Image Correlation to Small Punch Test for Determination of Stress–Strain Properties

The analysis of the small punch test is based on the force on the moving punch and the deflection data acquired at a single point of the specimen bottom. However, the spatial distribution of stress and strain at any given instant is non-uniform and its variations with increase in punch penetration are quite complex. In this work, the digital image correlation (DIC) technique is integrated with small punch test for in-situ full field strain measurement in the bottom surface of the specimen. The DIC results reveal that with the progression of deformation, the peak equivalent plastic strain at the bottom surface shifts from the center of the specimen to a characteristic radial location, where the strain rapidly builds up and concentrates leading to instability and cracking. Combining DIC-based strain results with finite element model-based stress estimation at the characteristic radial location, a methodology for determining the stress–strain curve from small punch test is formulated and the outcomes are compared with tensile test results for four different metallic alloys.

Enhancing structural analysis efficiency: a comprehensive review and experimental validation of advanced submodeling techniques, introducing the submodeling-density-shape-element removal (S-D-S-ER) method

PurposeThe paper's goal is to examine and illustrate the useful uses of submodeling in finite element modeling for topology optimization and stress analysis. The goal of the study is to demonstrate how submodeling – more especially, a 1D approach – can reliably and effectively produce ideal solutions for challenging structural issues. The paper aims to demonstrate the usefulness of submodeling in obtaining converged solutions for stress analysis and optimized geometry for improved fatigue life by studying a cantilever beam case and using beam formulations. In order to guarantee the precision and dependability of the optimization process, the developed approach will also be validated through experimental testing, such as 3-point bending tests and 3D printing. Using 3D finite element models, the 1D submodeling approach is further validated in the final step, showing a strong correlation with experimental data for deflection calculations.Design/methodology/approachThe authors conducted a literature review to understand the existing research on submodeling and its practical applications in finite element modeling. They selected a cantilever beam case as a test subject to demonstrate stress analysis and topology optimization through submodeling. They developed a 1D submodeling approach to streamline the optimization process and ensure result validity. The authors utilized beam formulations to optimize and validate the outcomes of the submodeling approach. They 3D-printed the optimized models and subjected them to a 3-point bending test to confirm the accuracy of the developed approach. They employed 3D finite element models for submodeling to validate the 1D approach, focusing on specific finite elements for deflection calculations and analyzed the results to demonstrate a strong correlation between the theoretical models and experimental data, showcasing the effectiveness of the submodeling methodology in achieving optimal solutions efficiently and accurately.FindingsThe findings of the paper are as follows: 1. The use of submodeling, specifically a 1D submodeling approach, proved to be effective in achieving optimal solutions more efficiently and accurately in finite element modeling. 2. The study conducted on a cantilever beam case demonstrated successful stress analysis and topology optimization through submodeling, resulting in optimized geometry for enhanced fatigue life. 3. Beam formulations were utilized to optimize and validate the outcomes of the submodeling approach, leading to the successful 3D printing and testing of the optimized models through a 3-point bending test. 4. Experimental results confirmed the accuracy and validity of the developed submodeling approach in streamlining the optimization process. 5. The use of 3D finite element models for submodeling further validated the 1D approach, with specific finite elements showing a strong correlation with experimental data in deflection calculations. Overall, the findings highlight the effectiveness of submodeling techniques in achieving optimal solutions and validating results in finite element modeling, stress analysis and optimization processes.Originality/valueThe originality and value of the paper lie in its innovative approach to utilizing submodeling techniques in finite element modeling for structural analysis and optimization. By focusing on the reduction of finite element models and the creation of smaller, more manageable models through submodeling, the paper offers designers a more efficient and accurate way to achieve optimal solutions for complex problems. The study's use of a cantilever beam case to demonstrate stress analysis and topology optimization showcases the practical applications of submodeling in real-world scenarios. The development of a 1D submodeling approach, along with the utilization of beam formulations and 3D printing for experimental validation, adds a novel dimension to the research. Furthermore, the paper's integration of 1D and 3D submodeling techniques for deflection calculations and validation highlights the thoroughness and rigor of the study. The strong correlation between the finite element models and experimental data underscores the reliability and accuracy of the developed approach. Overall, the originality and value of this paper lie in its comprehensive exploration of submodeling techniques, its practical applications in structural analysis and optimization and its successful validation through experimental testing.

Deflection and stress characteristics of single lap joint (adhesively bonded) theoretical analysis and experimental verification

The adhesively bonded single-lap joint strength is computed numerically and verified with the experiment. An ABAQUS model is prepared to analyze by adding the primary information, i.e., geometry, material properties, element, and solution type, including the boundary conditions. The model accuracy has been verified through two-step comparisons with published numerical deflection data and in-house experiments. The validated model is used to compute the energy-absorbing capacity better to understand lap joint strength. Further, the statistical analysis (variance-based sensitivity analysis) is conducted to measure the model output variability with the model input parameter. Additionally, the influences of geometry and property-dependent design parameters (layup schemes, loading position, adherend thickness ratio (L/t), and adhesive thickness ratio: (a/h), including the overlapping length (25, 30, 35, and 40 mm) are examined through several examples. The conclusions on the overlap length in bonded joints are that an increase in intact/lap length improves the joint stiffness and decreases the deflection. Similarly, a few insights on layer sequence (angle-ply) and shear stress thickness ratio are discussed in detail.

Adaptation of an alternative neural network instead of ANN for backcalculating pavement layer moduli

The structural condition of the pavement is often evaluated using deflection data from the non-destructive test such as the Falling Weight Deflectometer (FWD). Young's moduli calculated from surface deflections are used to characterize pavement layers. One of the most popular techniques for analyzing FWD data to determine pavement layer moduli is backcalculation. Artificial Neural Network (ANN) has been explored or used in studies to backcalculate layer moduli from FWD data, although its applications in this area are relatively recent. However, ANN suffers from limitations in terms of convergence accuracy and generalization capability. This research aims to develop an alternative neural network instead of ANN for backcalculating pavement layer moduli. Based on FWD data, Recurrent Neural Network (RNN) and Long-Short Term Memory (LSTM) networks were used to overcome the shortcomings of the traditional ANN. The LSTM, RNN, and ANN networks were developed and trained with the same training properties. The results revealed that LSTM attained high convergence accuracy and fastest convergence speed than ANN and RNN. LSTM network produced reasonable and accurate layer moduli values with determination coefficient (R2) of 0.9298 when compared to the measured values, while R2 values of the RNN and ANN networks were 0.906 and 0.8326, respectively. There was evidence that the LSTM network can learn the continuity pattern between the deflection basin points and enhance the FWD backcalculation accuracy.

A preliminary investigation of the inverse Finite Element Method applied to bridge structures

Deflection monitoring plays a key role in bridge Structural Health Monitoring, as deflection data may offer valuable insights into potential structural issues, such as cracks and corrosion. However, monitoring bridge deflections under operative loads presents challenges, particularly in scenarios where establishing a fixed reference point for displacement sensors is impractical, such as when a bridge spans a waterway or the sensors may be vulnerable to vandalism. In recent years, the inverse Finite Element Method (iFEM) has emerged as a possible solution. This method provides a load- and material-independent means of computing structural displacements from strain measurements, in real time at a minimal computational cost. Additionally, the iFEM can serve as a virtual sensing approach to monitor strains at locations lacking sensors, enabling the assessment of the fatigue life consumption at virtually any point in the structure. Despite its potential, applications of the iFEM in the civil engineering field are very limited, with no validation on full scale bridges has been performed to date. This study addresses this gap by investingating the application of the iFEM for bridge deflection monitoring through distributed strain measurements. The proposed approach is tested on experimental case studies, involving cross-validatiion of reference-free deflections inferred by the iFEM with those obtained from displacement sensors. This work contributes to the advancements of structural health monitoring methodologies in civil engineering, demonstrating the practicality and reliability of iFEM in bridge applications.

Signal Denoising of Traffic Speed Deflectometer Measurement Based on Partial Swarm Optimization-Variational Mode Decomposition Method.

To accurately identify the deflection data collected by a traffic speed deflectometer (TSD) and eliminate the noise in the measured signals, a TSD signal denoising method based on the partial swarm optimization-variational mode decomposition (PSO-VMD) method is proposed. Initially, the VMD algorithm is used for modal decomposition, calculating the correlation coefficients between each decomposed mode and the original signal for modal selection and signal reconstruction; Then, the particle swarm optimization algorithm is utilized to optimize the number of modes K and the value α for the VMD algorithm, adopting fuzzy entropy as the affinity function to circumvent effects from sequence decomposition and forecasting accuracy, thus identifying the optimal combination of hyperparameters. Finally, the analysis on simulated signals indicates that the PSO-VMD method secures the best parameters, showing a clear advantage in denoising. Denoising real TSD data validates that the approach proposed herein achieves commendable outcomes in TSD deflection noise reduction, offering a feasible strategy for TSD signal denoising.

Early Warning for Continuous Rigid Frame Bridges Based on Nonlinear Modeling for Temperature-Induced Deflection.

Bridge early warning based on structural health monitoring (SHM) system is of significant importance for ensuring bridge safe operation. The temperature-induced deflection (TID) is a sensitive indicator for performance degradation of continuous rigid frame bridges, but the time-lag effect makes it challenging to predict the TID accurately. A bridge early warning method based on nonlinear modeling for the TID is proposed in this article. Firstly, the SHM data of temperature and deflection of a continuous rigid frame bridge are analyzed to examine the temperature gradient variation patterns. Kernel principal component analysis (KPCA) is used to extract principal temperature components. Then, the TID is extracted through wavelet transform, and a nonlinear modeling method for the TID considering the temperature gradient is proposed using the support vector machine (SVM). Finally, the prediction errors of the KPCA-SVM algorithm are analyzed, and the early warning thresholds are determined based on the statistical patterns of the errors. The results show that the KPCA-SVM algorithm achieves high-precision nonlinear modeling for the TID while significantly reducing the computational load. The prediction results have coefficients of determination above 0.98 and fluctuate within a small range with clear statistical patterns. Setting the early warning thresholds based on the statistical patterns of errors enables dynamic and multi-level warnings for bridge structures.

Using machine learning algorithms for predicting bridge vertical deflection

Machine learning (ML) is being increasingly used to ease structural health monitoring and management of bridges. Therefore, the main objective of this study is to apply two state-of-the-art ML algorithms, namely locally weighted learning (LWL) and K-Star for the prediction of vertical deflection of composite bridges. To accomplish the objective, 83 track loading tests were carried out at various bridges located in Vietnam and deflection data was collected for models’ development. Model's validation and comparison were carried out using different popular methods, namely mean absolute error, root mean squared error and R on both training (70%) and validation (30%) datasets. The results of this study indicate that the K-Star algorithm outperforms LWL in predicting the vertical deflection of composite bridges. Consequently, K-Star can serve as an effective tool for rapidly predicting vertical deflection, thereby facilitating more efficient bridge health monitoring and management. This efficiency can lead to significant time and cost savings in maintaining the structural integrity of composite bridges.

Angular acceleration estimation and aerodynamic parameter identification based on angular velocity equivalent model

Conventional angular acceleration estimation methods generate non-negligible errors when the control surface rapidly deflects; hence, the estimated angular acceleration cannot be used for aerodynamic parameter identification directly. This paper proposes an angular acceleration estimation method based on angular velocity equivalent model. The angular acceleration of the angular velocity equivalent model, whose angular velocity response is consistent with the flight test data, is used as the estimated angular acceleration. Firstly, the equivalent angular velocity model is established by combining the generic aerodynamic model with the rotational dynamic equations of aircraft. Secondly, the angular velocity data and the control surface deflection data are synchronized. Finally, the angular velocity response of the equivalent model is used as the predictor, and the estimated angular acceleration is obtained by extended Kalman filter. The aerodynamic parameter identification and validation are carried out using the estimated angular acceleration of a large civil aircraft flight test data. The results show that the angular acceleration obtained through the proposed angular acceleration estimation method meets the accuracy requirement of aerodynamic parameter identification.

Three-dimensional diagnosis of lean premixed turbulent swirl flames using tomographic background oriented Schlieren

The necessity of minimizing NOx emissions drives the pursuit of ultra-lean premixed combustion in aeroengines and gas turbines, characterized by susceptibility to combustion instabilities. To tackle this issue, swirling flow design is widely incorporated into lean premixed combustor design, enhancing flame stability, and shortening flame length. This study utilizes the tomographic background-oriented Schlieren (TBOS) to reconstruct the spatial distribution of the refractive index gradient of lean premixed turbulent swirl flames with an aeroengine combustor configuration. A parametric study of the TBOS reconstruction quality is conducted, and the results reveal that view sparseness primarily degrades the reconstruction quality compared to the specific iterative algorithm used. The classic visual hull approach is explored to address this challenge, highlighting the significance of visual hull size. Furthermore, to improve the reconstruction quality, a posterior support constraint method is proposed, involving the removal of voxels of nearly constant refractive index within the central volume surrounded by flames. Results demonstrate that implementing this posterior support constraint further improves the reconstruction quality of lean premixed turbulent swirl flames. Finally, the robustness of this posterior support constraint method is validated by introducing high-level noise to the light deflection data, showcasing the potential of combining the dedicated designed visual hull and proposed posterior support constraint in addressing the view sparseness challenge for TBOS measurements.