Vertical Deflection Research Articles

Experiment and Numerical simulation on Bearing Capacity of Partial Steel-ultra-high-performance Concrete Continuous Composite beams

Due to high strength, toughness and durability, ultra-high-performance concrete (UHPC) can be applied in replacing the cracked concrete slab in the negative moment region of newly built steel-ordinary concrete (OC) continuous composite beams, as well as in repairing old composite beams. To investigate the failure mode, crack propagation, stiffness degradation and bearing capacity of the partial steel-UHPC continuous composite beam, a test model with an UHPC slab over the negative moment region were designed and fabricated to compare with a steel-OC model with the same conditions. Similar failure mode was observed in the loading test of two models. Nevertheless, the maximum crack width in the UHPC slab is only 0.17mm, much smaller than that in the OC slab. Compared with the steel-OC composite beam, vertical deflection of the partial steel-UHPC composite beam decreases by 32.7%, and its cracking load and ultimate bearing capacity increase by 50% and 6.4%, respectively. The results show that the substitution of the OC with the UHPC in the negative bending moment area significantly improves the crack resistance, delays the crack propagation, increases the bending stiffness, and improves the working performance of composite beams with cracks, displaying good advantages in economy and in reality. Parametric analysis demonstrates that the height of steel beam is the most important factor, and cross section of the steel beam is suggested to be given priority in design so as to take advantages of partial steel-UHPC composite beams. The research also provides an option for the repair of old concrete slabs in steel-OC continuous composite beams.

A Novel Method of Bridge Deflection Prediction Using Probabilistic Deep Learning and Measured Data

The deflection control of the main girder in suspension bridges, as flexible structures, is critically important during their operation. To predict the vertical deflection of existing suspension bridge girders under the combined effects of stochastic traffic loads and environmental temperature, this paper proposes an integrated deflection interval prediction method based on a Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), a probability density estimation layer, and bridge monitoring data. A time-series training dataset consisting of environmental temperature, vehicle load, and deflection monitoring data was built based on bridge health monitoring data. The CNN-LSTM combined layer is used to capture both local features and long-term dependencies in the time series. A Gaussian distribution (GD) is adopted as the probability density function, and its parameters are estimated using the maximum likelihood method, which outputs the optimal deflection prediction and probability intervals. Furthermore, this paper proposes a method for identifying abnormal deflections of the main girder in existing suspension bridges and establishes warning thresholds. This study indicates that, for short time scales, the CNN-LSTM-GD model achieves a 47.22% improvement in Root Mean Squared Error (RMSE) and a 12.37% increase in the coefficient of determination (R2) compared to the LSTM model. When compared to the CNN-LSTM model, it shows an improvement of 28.30% in RMSE and 6.55% in R2. For long time scales, the CNN-LSTM-GD model shows a 54.40% improvement in RMSE and a 10.22% increase in R2 compared to the LSTM model. Compared to the CNN-LSTM model, it improves RMSE by 38.43% and R2 by 5.31%. This model is instrumental in more accurately identifying abnormal deflections and determining deflection thresholds, making it applicable to bridge deflection early-warning systems.

Backtesting the iconic Polyfytos balanced-cantilever bridge to enhance condition assessment

This paper introduces a comprehensive framework for reliable damage assessment and decision-making for bridge intervention planning. By utilizing historical data and 3D-UAV photogrammetry, a detailed 3D numerical model is created, incorporating advanced modeling and scenario-based approaches. The methodology is applied to the Polyfytos bridge in Greece, which faces significant vertical deck deflections that disrupt traffic and impact local communities. This approach offers a reliable, cost-effective, and efficient process, allowing stakeholders to make informed decisions with minimal physical interaction with the bridge. The integration of advanced modeling with in-situ measurements and expert judgment is emphasized. For the Polyfytos bridge, the framework helps prioritize retrofits and assess the deck’s remaining strength under various loads, providing estimates of its overstrength. This aids in evaluating the bridge’s ability to handle additional vertical loads through pushdown analysis. Overall, the framework is valuable for rapid infrastructure assessment, identifying damage patterns, severity, and the urgency of interventions related to structural strength.

A convolutional neural network to optimize multi-mission satellite altimeter fusion for improving the marine gravity field

Satellite altimetry is the main tool for constructing global or regional marine gravity fields. To improve the accuracy and spatial resolution, it is necessary to fuse multi-mission altimeters. How to determine the weights of multi-mission altimeters is a crucial issue, making the conventional calculation process very complex. In addition, traditional satellite inversion methods are often independent of shipborne gravity, which is used only as validation data, thus not take full advantages of high accuracy and resolution of shipborne gravity. In this study, we introduce a convolutional neural network (CNN) to merge the vertical deflections (DOVs) obtained from multi-altimeter missions to construct a marine gravity model in the South China Sea. High-accuracy shipborne gravity and a dataset comprising DOVs and geo-locations are employed as input data for neural network training. For the validation of CNN method, the gravity model is also computed by conventional Inverse Vening Meinesz (IVM) method. Independent shipborne gravity measurements and SIO V32.1, DTU17 models are used as validation data. The evaluation results show that the CNN-derived model achieves a higher level of accuracy, yielding a standard deviation (STD) of 3.21 mGal, with an improvement of 36.56% compared to IVM-derived model. More than 92% of the differences between the CNN-derived model and shipborne gravity are less than 5 mGal. In addition, spectral analysis results further show that the CNN-derived model has stronger energy at short wavelengths (less than 25 km) compared to other models. These findings reveal that CNN method is feasible for marine gravity recovery and the CNN-derived model can achieve higher accuracy. The CNN method can improve the accuracy and spectral characteristics of the constructed gravity model by taking advantage of the high accuracy and high resolution of shipborne gravity.Graphical

Structural Behaviour and Mechanical Characteristics of BlueDeck Profiled Steel Sheeting for Use in Composite Flooring Systems

The BlueDeck profiled steel sheeting system offers an innovative composite flooring solution, integrating high-strength steel sheets with reinforced concrete to form a unified structure. This study aimed to evaluate the development of full composite action, the ultimate bearing capacity, and the flexural stiffness of the system. A comprehensive experimental programme involving 18 four-point bending tests and 6 shear tests was conducted to quantify the mechanical interaction between the steel deck and concrete slab. This study specifically examined bending capacity and vertical deflection, comparing the results with predictions from AS/NZS 2327. It was found that the system consistently achieved full composite action, with composite specimens demonstrating higher flexural stiffness and load-bearing capacity as the concrete depth increased. For example, specimens with 200 mm slab depths exhibited a 60% improvement in ultimate capacity compared to those with 150 mm slabs, while those with 175 mm depths saw a 27% increase. Additionally, the BlueDeck system showed an 81% improvement in de-bonding resistance in thicker slabs. The experimental results exceeded the bending moment and deflection limits prescribed by AS/NZS 2327, confirming that the system is structurally sound for use in buildings. This study provides quantitative evidence supporting the system’s compliance with Australian standards, highlighting its potential for improving construction efficiency through reduced material use, while maintaining structural integrity under imposed loads.

Static analysis of violin bow behavior under playing loads.

After discussing the relationship between taper and camber typically used by bowmakers, energy methods are then employed to develop nonlinear boundary value problems describing both the hair tightening problem and static deflection analysis of the violin bow under playing loads, including an analysis of possible hair tension asymmetry by employing a linear springs in series model of the hair. A simple algebraic condition for the distance the frog travels in reaching maximum tension is also presented. Boundary value problems are then applied using tools in scilab, comparing the idealized Tourte taper exhibiting a linear stiffness profile and an alternative design with a significantly different profile, revealing small differences in their behavior under static playing loads and validating previously observed significant increase in hair tension when approaching the tip. While the difference in vertical hair deflection as a function of bow position is extremely small, the Tourte design exhibits somewhat more compliance in the stick when approaching the tip, possibly desirable by players given increasing hair tension. An interesting small loss of hair tension in the lower section of the bow stroke is also discussed, representing additional slight differences in the initial compliance felt by the player when engaging the strings.

Investigating the interactions between wakes and floating wind turbines using FAST.Farm

Abstract. As floating offshore wind progresses to commercial maturity, wake and array effects across a farm of floating offshore wind turbines (FOWTs) will become increasingly important. While wakes of land-based and bottom-fixed offshore wind turbines have been extensively studied, only recently has this topic become relevant for floating turbines. This work presents an investigation of the mutual interaction between the motions of floating wind turbines and wakes using FAST.Farm. While FAST.Farm has been extensively validated across a wide range of conditions, it has never been validated for FOWT applications. Hence, in the first part of this work, we validate FAST.Farm by comparing simulations of a single FOWT against high-fidelity results from large-eddy simulations available in the literature. The validation is based on wake meandering, mean wake deflection, and velocity deficit at different downstream locations. This validation showed that the original axisymmetric (polar) wake model of FAST.Farm overpredicts the vertical wake deflection induced by shaft tilt and floater pitch, while the new curled wake model is capable of properly capturing the vertical wake deflection. In the second part, we use FAST.Farm to analyze a small three-unit array of FOWTs with a spacing of 7 diameters across a wide range of environmental conditions. The same National Renewable Energy Laboratory 5 MW reference wind turbine atop the OC4-DeepCwind semisubmersible is adopted for the three FOWTs and for the validation against high-fidelity simulations. To assess the effect of the floating substructure, we compare the power production, tower-base moments, and blade-root moments obtained for the floating turbines with the results obtained in a fixed-bottom configuration. The main differences introduced by the floating substructure are the motions induced by the waves, the change in the natural frequencies of the tower caused by differences in the boundary condition at its base, and the larger vertical deflection of the wake deficit due to the mean pitch of the platform. The impact of these differences, as well as other minor effects, are analyzed in detail.

Deflection estimation of reinforced concrete beams using long-gauge optic sensors

Deflection is a crucial indicator in structural health monitoring, directly impacting the service life, safety, and economic viability of structures. However, current indirect methods for measuring deflection, such as multi-element FBG sensors or accelerometers, often have limitations. While they may be suitable for flexure-dominated reinforced concrete (RC) specimens in the elastic stage, they neglect the significant influence of nonlinearity and shear deformation. This paper introduces a new approach for estimating the deflection of reinforced concrete (RC) beams using distributed long-gauge optic sensors. The method tackles the limitations of current methods by incorporating the crucial factors of shear deformation, neutral axis position variation and shear stiffness degradation. Experimental studies are first conducted to validate the accuracy and stability of long-gauge optic sensors in small-scale RC members. Algorithms are then utilized the measurement data to estimate the deflection. The results demonstrate the excellent performance of long-gauge optic sensors in measuring shear deformation and vertical deflection of RC beams, as evidenced by comparisons with LVDT measurements. Additionally, a method for decoupling flexural and shear deformation is proposed. This method offers a preliminary assessment of the reinforced concrete (RC) beam type by quantifying the relative significance of shear deformation.

Load resistance of masonry infilled panels for steel frames to mitigate progressive collapse caused by middle column missing

The load resistance of masonry infilled panels in upgrading the steel frame to mitigate progressive collapse was quantified experimentally and analytically in the current study. Four 1/2-scale steel subframes were tested, including two bare subframes without infilled panels for reference and two infilled subframes to assess the effects of infilled panels. Two types of connection were investigated in current study: welded connection and top and seat angle connection. The test result showed that infilled panels provided a greater improvement in initial stiffness and peak load of the steel subframe with top and seat angle connections compared to the infilled steel subframe with welded connections. On the premise that the connections retained their integrity, the strut mechanism of infilled panels could change from a diagonal strut mechanism forming in the whole panel to an off-diagonal strut mechanism formed in the remaining intact corner region with increasing vertical deflection. A novel equivalent multi-strut modelling method was proposed for the prediction of the infilled panel behavior with an acceptable level of accuracy. This model incorporates the shifts in the position of plastic hinges, which were influenced by the specific types of connection and the load-resisting mechanisms of the infilled panel. The analysis result demonstrated that the model slightly overestimated the load resistance of infilled panels within the steel frame with simple connections and slightly underestimated the load resistance of infilled panels within steel frame with semi-rigid or rigid connections.

Research on Ride Comfort Control of Air Suspension Based on Genetic Algorithm Optimized Fuzzy PID

The air suspension system’s superior variable stiffness, low vibration frequency, and resistance to road impacts significantly elevate both the comfort of vehicle occupants and the overall ride quality. By effectively controlling the air suspension system, its superior characteristics can be fully exploited to enhance the overall performance of vehicles. However, the parameter tuning process of the fuzzy PID controller for air suspension involves subjectivity and blindness, which affects the performance of the suspension system. To overcome these shortcomings, a control strategy combining genetic algorithms with fuzzy PID control is proposed. This strategy involves a genetic algorithm-optimized fuzzy PID air suspension control approach specifically targeting the fuzzy PID controller for air suspension. A 1/4 two-degree-of-freedom air suspension fuzzy PID controller is designed in MATLAB 2019a, utilizing genetic algorithms to optimize the PID parameter tuning process. The ride comfort of the fuzzy PID air suspension after tuning is then investigated. In the study of ride comfort on Class B road surfaces, the simulation and experimental results were consistent. Using a genetic algorithm to optimize a fuzzy PID-controlled air suspension resulted in reductions of the root mean square values for vertical body acceleration, suspension deflection, and wheel dynamic load by 30%, 26%, and 9%, respectively, compared to passive suspension. These reductions are further improvements over the corresponding indices controlled by the fuzzy PID alone, which decreased by 23%, 18%, and 6%, respectively. Thus, the control effect of the genetic algorithm-optimized fuzzy PID is superior to that of the fuzzy PID control. This demonstrates that the fuzzy PID control of air suspension optimized by genetic algorithms can further improve the comfort of vehicle occupants and the ride comfort of driving, providing a reference for active control of air suspension systems.

Modelling the maximum ceiling temperature with bifurcated plume in tunnel fires

Evaluation of the temperature profile induced by tunnel fire is of great significance for fire detection and structural damage assessment. In this work, a special plume model, namely, the “plume bifurcation” is introduced, and its impact on the temperature distribution is analysed theoretically. Full-scale tunnel fire experiments and numerical simulations are conducted to investigate the plume evolution under various heat release rates and ventilation conditions. Results show that the plume will sperate into two sub-streams under strong ventilation condition, resulting in the multi-dimensional plume movement pattern when rising. The sub-plume impingement point location, quantified by the longitudinal vertical deflection angle θv and horizontal bifurcation angle θh, is correlated with the fire heat release rate and ventilation condition. The plume bifurcation angle is 0 when the dimensionless ventilation velocity V′≤0.33, marking a single-stream plume; and rapidly increase and then slowly decrease with V′ when V′>0.33, representing the sudden occurrence and decay trend of plume bifurcation with the ventilation velocity. Finally, a novel bifurcated plume-based model to estimate the maximum ceiling temperature is proposed. This study reveals the role of multi-dimensional smoke movement in reshaping the temperature field, providing new perspectives for a deeper understanding of the smoke transport behaviour in longitudinally ventilated tunnel fires.

The Variable Stiffness Treadmill 2: Development and Validation of a Unique Tool to Investigate Locomotion on Compliant Terrains

Abstract Understanding legged locomotion in various environments is valuable for many fields, including robotics, biomechanics, rehabilitation, and motor control. Specifically, investigating legged locomotion in compliant terrains has recently been gaining interest for the robust control of legged robots over natural environments. At the same time, the importance of ground compliance has also been highlighted in poststroke gait rehabilitation. Currently, there are not many ways to investigate walking surfaces of varying stiffness. This article introduces the variable stiffness treadmill (VST) 2, an improvement of the first version of the VST, which was the first treadmill able to vary belt stiffness. In contrast to the VST 1, the device presented in this paper (VST 2) can reduce the stiffness of both belts independently, by generating vertical deflection instead of angular, while increasing the walking surface area from 0.20m2 to 0.74m2. In addition, both treadmill belts are now driven independently, while high-spatial-resolution force sensors under each belt allow for measurement of ground reaction forces and center of pressure. Through validation experiments, the VST 2 displays high accuracy and precision. The VST 2 has a stiffness range of 13kN/m to 1.5MN/m, error of less than 1%, and standard deviations of less than 2.2kN/m, demonstrating its ability to simulate low-stiffness environments reliably. The VST 2 constitutes a drastic improvement of the VST platform, a one-of-its-kind system that can improve our understanding of human and robotic gait while creating new avenues of research on biped locomotion, athletic training, and rehabilitation of gait after injury or disease.

The performance of Tiangong-2 InIRA in gravity anomaly recovery from fused conventional nadir-observing altimeter data

Satellite altimetry has emerged as the primary data source for deriving marine gravity, owing to advancements in satellite altimetry technologies. The Tiangong-2 interferometric imaging radar altimeter (TG2 InIRA) is a new generation wide-swath altimeter (WSA) launched by China on 15 September 2016. TG2 InIRA employs a short-baseline interferometry measurement method at a small incidence angle, thereby enabling the precise measurement of wide-swath sea surface heights (SSHs). The present study demonstrates the efficacy of utilizing data from the TG2 InIRA in conjunction with data from the CryoSat-2 (CS2) satellite to recover marine gravity anomalies. In the Northwest Pacific region (15°N ∼ 25°N, 140°E ∼ 150°E), the TG2 InIRA data were filtered to a 2 km × 2 km grid and any anomalous values were excluded using a mean sea surface model. Deflections of the vertical (DOVs) were calculated using the remove-restore technique, and the inverse Vening-Meinesz formula was applied to invert the gravity anomaly. A power spectral density analysis was conducted to assess variations in gravity anomalies at ship locations in the frequency domain. The results, based on the SIO V31.1 (DOV) model, indicate that the gridded vertical deflections derived from CS2 and TG2 InIRA data achieve more balanced accuracy in the east–west and north–south directions. The integration of TG2 InIRA and CS2 data yielded gravity results exhibiting a root mean square (RMS) of 0.519 mGal lower than those derived from TG2 InIRA data alone, and 0.034 mGal lower than those derived from CS2 data. These findings were derived from shipborne gravity data. Furthermore, the inversion of gravity anomalies from TG2 InIRA demonstrated an enhanced capability in the reduction of high-frequency gravity noise.

Experimental Study on Shear Strengthening of Reinforced Concrete Beams by Fabric-Reinforced Cementitious Matrix.

In this study, an experiment was conducted to investigate the shear performance of reinforced concrete (RC) beams strengthened using fabric-reinforced cementitious matrices (FRCM). Four reinforced concrete beams, including a control specimen, were fabricated, and the shear strengthening effect of the FRCM was investigated on eight shear specimens, with the strengthening type and shear reinforcement as key variables. In particular, the digital image correlation (DIC) technique was applied to closely analyze the deformation of reinforced concrete beams subjected to shear forces. The average shear strain-shear stress curve of each specimen was derived, and the contributions of shear and bending to the vertical deflection and the change in the principal strain angle with increasing shear force were analyzed. The experiment results showed that all specimens failed with diagonal cracks within the shear span. In the specimens without shear reinforcement, the shear strength increased by up to 65% according to the FRCM strengthening, while in the specimens with shear reinforcement, only the sided bond strengthened specimen showed a strength increase of 16% compared to the control specimen. Based on displacement data of the DIC, it was confirmed that FRCM strengthening can control the deformation of the RC beam. To evaluate the shear strength of the FRCM-strengthened RC beams, a shear strength model was proposed by considering the contributions of the concrete section, shear reinforcement, and FRCM. The proposed model was capable of reasonably evaluating the shear strength of RC beams strengthened with FRCM, considering the shear contribution of FRCM and bond capacity between FRCM and concrete substrate, in which the shear strength of specimens was underestimated by 28% to 35%.

Dynamic Characteristics of LIT Girder Railway Bridges

This study analyzed the dynamic characteristics of railway bridges with low-weight, innovative truss (LIT) girders and evaluated their dynamic behavior under general and high-speed railway operating conditions. A dynamic analysis was performed considering various variables, including the span length (30, 35, 40, or 45 m), track (single or double), main girder type (three or five girders), track type (concrete or ballast), and train type (KTX, HEMU, freight train, Mugunghwa, or express EMU). The train load was modeled as a moving concentrated load, and the damping ratio was applied according to railway design standards. The results of the dynamic analysis showed that in most cases, railway bridges with LIT girders met the allowable criteria for vertical deflection, vertical acceleration, and warping. However, in the case of a 30 m span bridge, the vertical acceleration exceeded the allowable limit at a specific speed of the HEMU-430X high-speed train. The results of this study can be used to evaluate the applicability of LIT girders in railway bridges and provide useful information for future design and construction.

Predicting bathymetry using multisource differential marine geodetic data with multilayer perceptron neural network

ABSTRACT We propose a method for enhancing the accuracy of bathymetry models based on a multilayer perceptron (MLP) neural network that integrates the differences in multisource marine geodetic data (MMGD) (longitude, latitude, reference bathymetry, slope, the meridional and prime components of vertical deflection, gravity anomaly, vertical gravity gradient, and mean dynamic topography). First, we use the MMGD differences between the shipborne sounding control points within 8′ × 8′ grid points and shipborne sounding control points as input data, as well as the differences between the topo_24.1 model and the measured bathymetric values at the control points as output data to train the MLP model. Second, we feed the input data from the central point of a 1′ × 1′ grid into the MLP model to obtain predictions, and then use the topo_24.1 model to recover the predicted bathymetry at the prediction point. We focus on the Caribbean Sea, and construct a Caribbean Bathymetric Chart of the Oceans (CBCO1) model using MLP neural network. The reliability of MMGD, a CBCO2 model using MMGD, and the reliability and effectiveness of the overall method are demonstrated through comparisons with the CBCO2, GEBCO_2022, topo_24.1, DTU18 models at the checkpoints.

Analytical solutions for out-of-plane response of curved beams resting on an elastic foundation under a random moving load

In this study, the vibration behaviour of a horizontally curved beam resting on an elastic foundation and subjected to a random moving force is studied. The governing coupled differential equations for the out-of-plane vibration of curved beams are derived based on the mode superposition method, Duhamel's integral, and the Laplace transformation. Note that the out-of-dynamic responses of curved beams induced by a random moving load are composed of the centred random and mean value. Analytical solutions are proposed for the beam’s vertical and torsional deflections and the bending moment, where the rotary inertia, warping constant, and foundation stiffness are incorporated in these formulations. Because analytical studies on the random vibration of a curved beam resting on an elastic foundation are very limited, the aim of this study is to investigate the effect of relative parameters, namely, high-mode vibrations, the radius of curvature, the moving velocity, and foundation vertical and torsional stiffnesses, on the centred random and mean values of the beam dynamic responses. The results show that high-mode vibrations have a greater impact on the beam responses at higher velocities. To obtain precise results, the first 30 modes are considered in the calculation for the dynamic responses of the beams. The critical velocity is an inherent property of bridges, and it increases as the radius of curvature and foundation stiffness increase. In addition, an increase in the velocity and foundation stiffness results in a reduction in the centred random values for responses.

Construction control of rigid frame-continuous girder bridge based on grey theory

To address the issue of excessive mid-span deflection in rigid frame-continuous girder bridges during the later stages of normal use and to provide a basis for setting the pre-camber of this bridge type. This study focused on a specific rigid frame-continuous girder bridge. Based on the outcomes of finite element analysis, a GM(1,1) model developed using grey theory was utilized to forecast the vertical deflection of the primary girder in the construction phase of a rigid frame-continuous girder bridge, resulting in notable outcomes. The results suggest that the GM(1,1) model grounded in grey theory offers precise estimations of the vertical deflection of the primary girder during the prestressing tendon tensioning stage, displaying a minimal deviation of merely 1.73 mm compared to actual measurements. Consequently, applying the GM(1,1) model based on grey theory for projecting the vertical deflection of the primary girder in the construction process of rigid frame-continuous girder bridges can advance the accuracy of construction management. Through comparative analysis of measured values estimated values and theoretical values at the construction site, it is evident that the predictive model effectively controls the displacement, thus serving as a reference for construction control in similar projects.

Optimized estimation of marine deflection of the vertical from multibeam laser altimeter data of ICESat-2

SUMMARY Satellite altimetry data, with its increasing density and quality, has become the primary source for marine deflection of the vertical (DOV) and gravity anomaly modelling. Limited by orbital inclinations, the precision of the meridian component of the gridded deflection of the vertical (GDOV) calculated by traditional altimetry satellites is significantly better than that of the prime vertical component, and the excessive precision difference between these two components restricts the inversion precision of marine gravity anomaly model. The study of cross-track deflection of the vertical (CTDOV) is enabled by the multibeam synchronous observation mode of the new laser altimetry satellite, Ice, Cloud and Land Elevation Satellite-2 (ICESat-2). Based on the remove-restore method, residual geoid gradients are first calculated in this paper using three approaches: along-track (A-T), cross-track (C-T) and an integration of along-track and cross-track. Vertical deflections are then computed on a 1′ × 1′ grid using the least squares collocation (LSC) method, and the precision is verified against the SIO V32.1_DOV model. An optimized combination is proposed to address the issue of precision differences between the meridian and prime vertical components, and to enhance the precision of DOV inversion. A new DOV combination is formed by combining the meridian component from along-track deflection of the vertical (ATDOV) with the prime vertical component from cross-track deflection of the vertical (CTDOV) based on the remove-restore method. The Philippine Sea (0°–35°N, 120°–150°E) is selected as the test area to verify the feasibility of the optimized combination. The results indicate that the optimized combination of the meridian and prime vertical components achieved test precision of 2.63 and 3.33 μrad, respectively, when compared against the SIO V32.1_DOV model. The precision gap between the components is effectively narrowed by this approach, which maintains the precision of the meridian component and enhances that of the prime vertical component, thereby achieving optimal inversion precision for gravity anomalies.

The Influence of Seasonal Effects on Railway Vertical Track Modulus

Adequate vertical track support is essential for safe and efficient railway operations. Insufficient support leads to distorted track geometry, increased dynamic loads, component stress, poor ride quality, rolling stock damage, and derailment risks. Current inspection practices focus on assessing the condition of the track components and geometry, rather than the root causes of degradation. To improve this condition, this study presents the use of a methodology that utilizes an autonomous vertical track deflection measurement system mounted on a loaded rail car (36 tonnes/axle) to support track maintenance decisions in a heavy haul railroad located in southeast Brazil. The system continuously measured substructure stiffness along the railway line. Over one year, data were collected from over 8000 km of track. The study highlighted seasonal effects on track degradation over time, identifying areas with significant deflections and high deflection rates, which contribute to issues such as differential settlement and reduced lifespan of track components. Additionally, the study revealed seasonal effects, with deflections peaking during wet weather and decreasing during dry cycles. A method to classify weak track areas was developed, facilitating monitoring and enabling more effective maintenance planning, contributing to the reduction of overall track maintenance costs and enhancing safety and operational efficiency.