Strain Data Research Articles

Proposal of a Creep-Experiment Method and Superficial Creep Coefficient Model of CFT Considering a Stress-Redistribution Effect

Existing concrete creep coefficient prediction models have the limitation of not considering the structural characteristics of CFT. For this reason, these models tend to overestimate the creep deformation of CFT. Therefore, in order to overcome the limitations of existing CFT creep experiments, this study proposes a creep-experiment method involving the use of CFT that passively changes the load applied to a single concrete specimen by calculating the stress redistribution between the concrete and a steel tube in CFT based on a step-by-step method. Furthermore, by actually applying the proposed experimental method, a creep experiment of CFT lasting for approximately 163 days was performed and a superficial creep coefficient model of CFT was proposed based on long-term strain data from the experiment. In order to verify the proposed superficial creep coefficient model, it was compared with two design criteria (CEB-FIP and ACI) based on the experimental results of this study and references. As a result, compared to the existing design criteria, the value predicted by the proposed superficial creep coefficient model showed good agreement with the experimental results of this study and the references, proving that the proposed creep-experiment method of CFT and superficial creep coefficient model are reasonable.

Dynamic analysis and shape sensing of pipes subjected to water hammer by the inverse finite element method

Pipe structures are commonly employed in modern industries. However, the transient pressure induced by water hammer leads to a high risk of structural damage, highlighting the importance of Structural Health Monitoring (SHM). The inverse Finite Element Method (iFEM) offers a way to reverse structural deformations based on a set of discrete strain data. In this paper, the water hammer phenomenon in a Reservoir-Pipe-Valve (RPV) system is investigated. The element iQS4 is adopted to reconstruct dynamic deformations for the pipe using iFEM. The water hammer resulting from an instantaneous closure of the valve can generate significant fluid pressure, leading to severe pipe vibrations. The vibration deformations can be monitored by iFEM. The maximum error of the pipe nodal displacement is below 3 % and the average error is below 2 % in the proposed several sensor location cases, even the mesh of iFEM is coarser than the FE model. Among the sparse sensor location cases, the X path which is suitable for Fiber Bragg Grating (FBG) sensors has the highest accuracy of the displacement reconstruction. The results reveal a promising prospect in the real-time monitoring based on iFEM for pipes.

Demonstration of machine learning-assisted low-latency noise regression in gravitational wave detectors

Abstract Low-latency noise regression algorithms are crucial for maximizing the science outcomes of the LIGO, Virgo, and KAGRA gravitational-wave detectors. This includes improvements in the detectability, source localization and pre-merger detectability of signals thereby enabling rapid multi-messenger follow-up. In this paper, we demonstrate the effectiveness of DeepClean, a convolutional neural network architecture that uses witness sensors to estimate and subtract non-linear and non-stationary noise from gravitational-wave strain data. Our study uses LIGO data from the third observing run with injected compact binary signals. As a demonstration, we use DeepClean to subtract the noise at 60 Hz due to the power mains and their sidebands arising from non-linear coupling with other instrumental noise sources. Our parameter estimation study on the injected signals shows that DeepClean does not do any harm to the underlying astrophysical signals in the data while it can enhance the signal-to-noise ratio of potential signals. We show that DeepClean can be used for low-latency noise regression to produce cleaned output data at latencies ~1–2 s. We also discuss various considerations that may be made while training DeepClean for low latency applications.

Maternal Streptococcus agalactiae colonization in Europe: data from the multi-center DEVANI study.

Despite national guidelines and use of intrapartum antibiotic prophylaxis (IAP), Streptococcus agalactiae (group B streptococci (GBS)) is still a leading cause of morbidity and mortality in newborns in Europe and the United States. The European DEVANI (Design of a Vaccine Against Neonatal Infections) program assessed the neonatal GBS infection burden in Europe, the clinical characteristics of colonized women and microbiological data of GBS strains in colonized women and their infants with early-onset disease (EOD). Overall, 1083 pregnant women with a GBS-positive culture result from eight European countries were included in the study. Clinical obstetrical information was collected by a standardized questionnaire. GBS strains were characterized by serological and molecular methods. Among GBS carriers included in this study after testing positive for GBS by vaginal or recto-vaginal sampling, 13.4% had at least one additional obstetrical risk factor for EOD. The five most common capsular types (i.e., Ia, Ib, II, III and V) comprised ~ 93% of GBS carried. Of the colonized women, 77.8% received any IAP, and in 49.5% the IAP was considered appropriate. In our cohort, nine neonates presented with GBS early-onset disease (EOD) with significant regional heterogeneity. Screening methods and IAP rates need to be harmonized across Europe in order to reduce the rates of EOD. The epidemiological data from eight different European countries provides important information for the development of a successful GBS vaccine.

Effects of heat treatment and geometry on mechanical properties and precipitate development in martensitic additively manufactured 17-4 PH

Reliable mechanical properties of precipitation strengthened alloys like 17-4 PH stainless steel are conventionally obtained through tightly controlled thermomechanical processing to optimize the size and distribution of strengthening precipitates. In additive manufacturing, however, the thermal history (e.g. heating and cooling rates) can vary significantly across a part or individual layer causing the precipitate distribution and resulting mechanical properties to be non-uniform. This is especially true for precipitation strengthened alloys like 17-4 PH which require a specific thermal history to achieve the expected phases and properties. To explore this material and the effect that standard heat treatments have on the processing-structure-properties relationship for AM 17-4 PH, a series of thin-wall (0.8 mm) and ASTM E8 size dogbones were printed via SLM and tensile tested in the as-built, solution annealed, and H900 condition. A Vic-2D DIC system was used during tensile testing to obtain full-field strain data. SEM BSE imaging and TEM EDS were used to characterize the larger (60–120 nm) precipitate phases (SiO and NbC) along with the overall microstructure. GISAXS and TEM EDS were used to quantify the size (5–15 nm), shape, distribution, and composition of nanoscale copper-rich precipitates. Overall, the mechanical properties between the E8 and thin-wall samples were similar with yield strengths of 677 and 734 MPa and ultimate strengths of 1049 and 941 MPa in the H900 condition, respectively. The other sample conditions follow similar trends with the only significant difference being a drop in average ductility (0.27 vs 0.17) for the thin-wall geometry. These similarities were hypothesized to stem from several factors which work to lessen the cooling rate dependence of 17-4 PH.

Effect of vibration on the interface properties of welded steel joints and filled concrete in steel pipes

Concrete-filled steel tubes (CFSTs) have been increasingly utilized in engineering due to their excellent mechanical properties. Ensuring a solid bond between a steel tube and concrete is essential for optimizing their synergistic effect. This study introduces an internally welded steel bar structure within the inner wall of a steel tube to enhance the bond properties at the connection interface. The influence of various configurations of steel bars welded to the inner surface of the tube on the bond strength is investigated considering the impact of vibration on the load-bearing capacity of the component. This study comprises two groups of specimens, one with vibration and one without vibration, for a total of ten specimens. Each group included CFST members with five distinct internal welded steel bar structures. The experimental results, including load–displacement curves and strain data of the steel tube, were used to assess the impact of the internal welded steel bar configurations on the steel–concrete interface. The sliding process is described by correlating test data with curves and observed phenomena. To comprehensively compare the effects of structural dimensions on the bonding and slipping properties of the welded bars, finite element simulations replicating the experimental conditions were carried out using ABAQUS software, and the simulation results agreed with the experimental observations. The study demonstrated that incorporating internal welded steel bars substantially enhances the bond strength of steel pipe–concrete interfaces. While vibration weakens the bond strength in CFST members, internal welded steel bars mitigate this effect. These findings improve the structural performance of CFST structures and their resilience to external vibrations.

Fatigue life assessment of thermite welded rails based on laboratory tests and field measurement data

This in-depth study assesses the fatigue life of thermite-welded 60E1 rails by combining fatigue experimental tests with field measurement data. Material characterization, conducted using X-ray Diffraction (XRD), X-ray Fluorescence (XRF), and Scanning Electron Microscopy (SEM), aimed to understand the fatigue behavior of these materials. The research was particularly focused on high-speed rail lines in South Korea, targeting areas with influence of track condition to collect strain data. By combining dynamic modulus calculations from high-speed tensile tests with the rain flow counting method for determining wheel loads, and employing the Linear Cumulative Damage method for estimating rail fatigue life, this study provides novel insights into the maintenance and durability of thermite welded rails. The integration of detailed laboratory experiments with field stress data offers a significant contribution to the predictive maintenance and lifecycle management of high-speed railway infrastructure.

Research on prediction method of coal mining surface subsidence based on MMF optimization model

Coal seam mining causes fracture and movement of overlying strata in goaf, and endangers the safety of surface structures and underground pipelines. Based on the engineering geological conditions of 22,122 working face in Cuncaota No.2 Coal Mine of China Shenhua Shendong Coal Group Co., Ltd. a similar material model test of mining overburden rock was carried out. The subsidence of overburden rock was obtained through the full-section strain data of distributed optical fiber technology, and the characteristics of mining surface subsidence were studied. The Weibull model was used to adjust the mathematical form of the first half of the surface subsidence curve via the MMF function. On this basis, the prediction model of coal seam mining surface subsidence was established, and the parameters of the prediction model of surface subsidence were determined. The test results show that with the advancement of coal seam mining, the fit goodness of the surface subsidence prediction curve based on the MMF optimization model reaches 0.987. Compared with the measured values, the relative error of the surface subsidence prediction model is reduced to less than 10%. The model displays good prediction accuracy. The time required for settlement stability in the prediction model is positively correlated with parameter a and negatively correlated with parameter b. The research results can be further extended to the prediction of overburden “three zones” subsidence, and provide a scientific basis for the evaluation of surface subsidence compression potential in coal mine goaf.

Gravity dam displacement monitoring using in situ strain and deep learning

AbstractRecent studies in dam displacement monitoring primarily focus on single‐response monitoring or model updating using advanced techniques. Few studies involve the combination analysis of displacement with other synchronized responses utilizing their monitoring characteristics. In situ strain data provide a strength‐safety perspective for dam displacement monitoring. The challenge lies in that estimating displacement directly using limited discrete strain data may be misleading. This paper analyzes the relationship between displacement and global, and multipoint local strains from the perspective of the differences in load effects of gravity dams, and indicates that introducing appropriate state factors improves the estimation. A displacement estimation model driven by strain data and state factors is developed using stacked convolutional neural network, and the variable relationships within the model are interpretated via accumulated local effects. Incorporating specific strength criteria, a novel displacement monitoring indicator based on the tensile safety of the dam heel is proposed. A case study of a gravity dam showcases the effectiveness of the proposed approach in comparison with the solely strain‐based model and the traditional hydrostatic‐seasonal‐time factors‐based model.

Stress and Strain Characterization for Evaluating Mechanical Safety of Lithium-Ion Pouch Batteries under Static and Dynamic Loadings

The crashworthiness of electric vehicles depends on the response of lithium-ion cells to significant deformation and high strain rates. This study thoroughly explores the mechanical behavior due to damage of lithium-ion battery (LIB) cells, focusing on Lithium Nickel Manganese Cobalt Oxide (NMC) and Lithium Iron Phosphate (LFP) types during both quasi-static indentation and dynamic high-velocity penetration tests. Employing a novel approach, a hemispherical indenter addresses gaps in stress–strain data for pouch cells, considering crucial factors like strain rate/load rate and battery cell type. In the finite element method (FEM) analysis, the mechanical response is investigated in two stages. First, a viscoplastic model is developed in Abaqus/Standard to predict the indentation test. Subsequently, a thermomechanical model is formulated to predict the high-speed-impact penetration test. Considering the high plastic strain rate of the LIB cell, adiabatic heating effects are incorporated into this model, eliminating heat conduction between elements. Addressing a notable discrepancy from prior research, this work explores the substantial reduction in force observed when transitioning from a single cell to a stack of two cells. The study aims to unveil the underlying reasons and provide insights into the mechanical behavior of stacked cells.

Optimized identification process of equivalent wind load calculations for offshore wind turbines under standstill conditions

In engineering, the wind excitations acting on the offshore wind turbine (OWT) structure cannot be obtained directly by the measured method. The traditional load simulation way may lead to poor accuracy because of the deviation between actual operational conditions and simulation environment parameters or load coefficients, which are always selected based on load spectrums, small scale model tests and engineering experience. To solve this project problem, an equivalent wind load optimization model and parameter identification process of OWT was established under the standstill conditions. Afterwards, two key load parameters in load model respectively called constant drag coefficient and unsteady lift coefficient can be obtained through recursive call on numerical model and feedback analysis using particle swarm optimization (PSO) algorithm based on measured vibration data. The applicability and accuracy of proposed calculation process was verified through an equivalent numerical model of OWT considering different particle position and wind speed. Further, the optimization identification on equivalent wind load and the drag and lift coefficients of one OWT was achieved based on measured data. It is illustrated that the identified drag coefficients show a drop trend from 0.629 to 0.154, consistent with the parameter range of 0.20–0.60 obtained from model experiments, before the wind speed reaches 6.0 m/s and then rise obviously with the increase of wind speed. On the contrary, the range of optimized lift coefficients form 0.133–0.480, which is as familiar as the experimental parameter range of 0.10–0.30, reflects a certain increase trend. Finally, the comparison between identified wind excitations and calculated loads based on the measured strain data explain that the proposed load optimization identification process have a good credibility on actual OWT.

Damage Detection and Localization Methodology Based on Strain Measurements and Finite Element Analysis: Structural Health Monitoring in the Context of Industry 4.0

This paper investigates the integration of Structural Health Monitoring (SHM) within the frame of Industry 4.0 (I4.0) technologies, highlighting the potential for intelligent infrastructure management through the utilization of big data analytics, machine learning (ML), and the Internet of Things (IoT). This study presents a success case focused on a novel SHM methodology for detecting and locating damages in metallic aircraft structures, employing dimensional reduction techniques such as Principal Component Analysis (PCA). By analyzing strain data collected from a network of sensors and comparing it to a baseline pristine condition, the methodology aims to identify subtle changes in local strain distribution indicative of damage. Through extensive Finite Element Analysis (FEA) simulations and a PCA contribution analysis, the research explores the influence of various factors on damage detection, including sensor placement, noise levels, and damage size and type. The findings demonstrate the effectiveness of the proposed methodology in detecting cracks and holes as small as 2 mm in length, showcasing the potential for early damage identification and targeted interventions in diverse sectors such as aerospace, civil engineering, and manufacturing. Ultimately, this paper underscores the synergistic relationship between SHM and I4.0, paving the way for a future of intelligent, resilient, and sustainable infrastructure.

Experimental behavior and fracture prediction of a novel high-strength and high-toughness steel subjected to tension and shear loading tests

In this study, laboratory testing and numerical simulation methods are used to investigate the mechanical behavior and perform fracture prediction of a novel high-strength and high-toughness steel with a negative Poisson's ratio (NPR) effect under combined tensile-shear loading conditions. A test device capable of meeting different tensile-shear combination test angles is designed and manufactured, wherein the mechanical experiments on the NPR (Negative Poisson's Ratio) steel specimens are carried out at various testing angles. Q235 steel and MG400 steel are used as experimental control groups. The results show that the mechanical deformation of NPR steel is significantly better than that of Q235 steel and MG400 steel. Its tensile-shear test curve has no yield plateau and it has quasi-ideal elastic-plastic mechanical properties. The loading direction gradually changes from tension-dominated to shear-dominated as the tension-shear angle increases, and the strength and deformation of the specimens show a decreasing trend. Based on the laboratory test results, a finite element numerical model of NPR steel is established. A series of numerical simulations are carried out under the conditions of different tension and shear angles and the average stress triaxiality and fracture strain data are obtained. The fracture data of NPR steel are fitted using the Johnson-Cook fracture criterion, and the Johnson-Cook fracture parameters under the tensile-shear test conditions of NPR steel are thus obtained. The numerical simulation verifies that the fracture model can accurately predict the tensile-shear fracture behavior of NPR steel.

Understanding Structural Changes in Recycled Aggregate Concrete under Thermal Stress

Objective: This study investigates the influence of high-temperature treatment on the deformation properties and structural deformation of recycled aggregate concrete (RAC) in response to potential fire hazards in the construction industry. Methods: Standard-cured 28-day RAC specimens were subjected to microwave heating at 300 °C and 600 °C, with subsequent uniaxial compression tests utilizing a WDW-2000 machine and a VIC 3D strain measurement system to analyze strain data through digital image correlation (DIC) technology. Results: After treatment at 300 °C, recycled aggregate concrete (RAC) demonstrated superior mechanical properties to fresh concrete aggregates. This enhancement may be attributed to the more robust siloxane bonds (Si-O-Si) in the recycled materials. Conversely, exposure to 600 °C intensified internal structural damage, notably lowering the material’s elastic modulus and peak stress. DIC analysis highlighted the correlation among temperature, volumetric strain, and crack development patterns, with more extensive cracking at 600 °C. Conclusions: Moderate-temperature treatment enhances RAC’s structure and deformation properties, while high-temperature treatment diminishes its performance. These findings provide valuable insights for assessing building safety post-fire and the application of RAC, emphasizing its suitability at moderate temperatures and risks at high temperatures.

Time-domain expression and mechanical response of the viscoelastic Poisson's ratio in asphalt pavement

Poisson's ratio (PR) is a fundamental mechanical parameter for materials. Unlike the constant Elastic Poisson's Ratio (EPR), the Viscoelastic Poisson's Ratio (VEPR) is significantly influenced by external factors such as environmental temperature, stress level, and loading frequency. Using the VEPR to characterize the stress state of asphalt pavements provides a more accurate reflection of their actual service conditions. Moreover, the VEPR plays a more critical role than the EPR in predicting fatigue life, analyzing temperature sensitivity, and optimizing pavement structure design. In this study, the Elastic-Viscoelastic Correspondence Principle (EVCP) and the Zener mechanical model were combined to derive a time-domain expression for the VEPR of asphalt pavement. Fiber Bragg Grating (FBG) sensors were embedded within various structural layers of an in-service road to collect mechanical response and temperature data under traffic loads. Based on the measured temperature data, Finite Element Models (FEMs) were developed for both the VEPR and EPR conditions. The mechanical responses were validated using these FEMs, and the results were compared with the strain data collected by the FBG sensors. The results indicated that both VEPR and EPR increase most rapidly between 20°C and 35°C, with VEPR resulting in higher transverse and longitudinal strains and stresses than EPR, while vertical strain remained constant. Furthermore, the VEPR was better suited to actual driving conditions, with a peak error of only 3.97 % and an average error of 10.04 %.

Seismic performance of the ST-RC columns to RC beams exterior joint with assembled connection details

An innovative composite column type, the steel tube-reinforced concrete column (ST-RC), consists of a core of concrete-filled steel tube (CFST) and reinforced concrete (RC) encasement. This study aims to validate the reliability of two convenient and rapid assembly methods between RC beams and ST-RC columns. Four full-scale beam-column joint specimens were tested, comprising two prefabricated assembly joints of ST-RC column-RC beam frames, one integrally cast joint of ST-RC column-RC beam frames, and one traditional integrally cast joint of RC column-RC beam frames for comparison. The experiments were conducted based on the principles of a self-balanced system, and quasi-static tests under constant axial compression on the ST-RC columns were performed. Hysteresis curves, skeleton curves, failure modes, strength degradation, energy dissipation capacity, stiffness degradation, deformation capacity and the influence of connection method and joint form on mechanical performance were analyzed and obtained based on the test results. The results indicate that, compared to integral casting, the assembly surrounding method with steel sleeves reduces specimen energy dissipation by 19.8 % and damping ratio by 21 % at 4 % drift, with minimal impact on other mechanical properties. In contrast, reinforcement surrounded and connected by steel plates reduces initial stiffness and peak load-carrying capacity by 1.0 %, along with decreasing negative ductility. It also lowers total energy dissipation by 37.4 % and damping ratio by 45.4 % due to compressive effects from bottom steel plate connections. Despite these effects, its impact on negative ductility and load-carrying capacity remains minimal. Additionally, experimental observations and rebar strain data indicate higher stress on rebars at the base of steel plate connection beams, suggesting a need to strengthen transverse rebars at the beam’s base. The study confirms the feasibility of two convenient and rapid assembly methods for the joints of ST-RC column. Both methods meet current Chinese standards for MCE, with failure modes characterized by “strong columns and weak beams” in both cases.

Study on Strain Field Reconstruction Method of Long-Span Hull Box Girder Based on iFEM

The box girder’s condition significantly impacts the safety and overall performance of the entire ship because it is the primary stress component of the hull construction. This work used experimental research on the long-span hull box girder based on IFEM (Inverse Finite Element Method) technology to ensure the structural safety of the hull box girder. Due to the limitations of conventional experiments in this technical field, such as their reliance on finite element data and lack of input from physical tests, numerous research methods combining the strain sensing data from physical tests with the strain data from virtual sensors were conducted. The strain fields of the top plate, side plate, and bottom plate were each reconstructed in turn, and the verifier measuring points in the physical model test were used to assess the accuracy of the reconstruction results. The findings demonstrate that the top plate, side plate, and bottom plate reconstructions had relative errors of 0.24–7.86%, 0.75–8.13%, and 3.31–2.52%, respectively. This enables the reconstruction of the strain field of the long-span hull box girder using physical test data and promotes the use of iFEM technology in the field of structural health monitoring of large marine structures.

Applying a thermodynamic-based method to reveal the failure laws of CFRP stiffened plates

The high specific strength and stiffness of carbon fiber-reinforced polymer (CFRP) stiffened plates make them popular in aerospace and other fields. Nevertheless, CFRP stiffened plates have unique characteristics and complicated and diversified failure patterns, so it is impossible to determine its failure law with a uniform failure criterion accurately. Its load-carrying capacity has always been calculated on the conservative side of empirical estimation. This work uses the stressing state theory to investigate the stressing state evolution of composite stiffened plates under axial loading. It conducts three CFRP stiffened plates of the same configuration from a thermodynamic perspective. By equating stiffened plates to thermodynamic systems, the measured strain data are modeled as state variables, and renormalization and clustering algorithms are applied to determine the phase transition loads of the structure, while the characteristic points before and after normalization are verified for their reasonableness and stability. Accordingly, this work reveals the failure laws of CFRP stiffened plates by applying a thermodynamic-based method. It characterizes the structural failure features by defining catastrophe points throughout the failure process, which provides a new reference for the failure analysis and strength design of CFRP stiffened plates.

Chemotaxonomic and molecular phylogenetic studies of selected Hypoxylon species from the Neotropics

ABSTRACT Members of the genus Hypoxylon (Ascomycota) are pleomorphic fungi mostly forming conspicuous teleomorphs, consisting of perithecia embedded into stromal tissue, and their morphology has traditionally served for species delineation. However, analysis in tandem with other phenotypic characters, such as chemical and genetic traits, proved to be a more stable predictor of interspecies and intergeneric relationships. During 2014 and 2015, a set of species identified as Hypoxylon were described from the Neotropics, exclusively relying on morphological traits. The secondary metabolite profiles of their stromata were analysed by HPLC/DAD-ESI-MS, corroborating their classification within Xylariales. Additionally, molecular data for ex-type strains of H. dussii and H. sofaiense were incorporated into an inferred molecular phylogeny of the Hypoxylaceae and allies. Furthermore, a freshly collected specimen from North Carolina was selected as epitype of Sphaeria perforata Schweinitz (syn. Hypoxylon perforatum), as its morphological/chemotaxonomic characters matched those of the holotype. Our findings demonstrate that the secondary metabolism of Hypoxylon closely correlates with both morphological features and molecular data, serving as a complement for species identification.

Data-driven computational mechanics: comparison of model-free and model-based methods in constitutive modeling

In computational homogenization approaches, data-driven methods entail advantages due to their ability to capture complex behavior without assuming a specific material model. Within this domain, constitutive model-based and model-free data-driven methods are distinguished. The former employ artificial neural networks as models to approximate a constitutive relation, whereas the latter directly incorporate stress–strain data in the analysis. Neural network-based constitutive descriptions are one of the most widely used data-driven approaches in computational mechanics. In contrast, distance-minimizing data-driven computational mechanics enables substituting the material modeling step entirely by iteratively obtaining a physically consistent solution close to the material behavior represented by the data. The maximum entropy data-driven solver is a generalization of this method, providing increased robustness concerning outliers in the underlying data set. Additionally, a tensor voting enhancement based on incorporating locally linear tangent spaces enables interpolating in regions of sparse sampling. In this contribution, a comparison of neural network-based constitutive models and data-driven computational mechanics is made. General differences between machine learning, distance minimizing, and entropy maximizing data-driven methods are explored. These include the pre-processing of data and the required computational effort for optimization as well as evaluation. Numerical examples with synthetically generated datasets obtained by numerical material tests are employed to demonstrate the capabilities of the investigated methods. An anisotropic nonlinear elastic constitutive law is chosen for the investigation. The resulting constitutive representations are then applied in structural simulations. Thereby, differences in the solution procedure as well as use-case accuracy of the methods are investigated.