Inverse Method Research Articles

Inverse design method for tailoring the deflection of beams with functionally graded metamaterials

Abstract Functionally graded metamaterials represent a cutting-edge approach to designing structures with cellular materials. By manipulating parameters in specific regions, a customized mechanical response is achieved, optimizing material utilization. Despite various proposed methods to generate functionally graded structures, the challenge of high computational costs persists. This study introduces a novel and computationally efficient inverse design method for beams featuring segment-wise graded metamaterials. Using a semi-analytical approach based on Castigliano’s second theorem, this method significantly reduces computational demands. The approach leverages prior experimental and computational characterizations of the transverse deflection in rectangular, reentrant, and hexagonal honeycombs. Validation through finite element models and experimental tests on additively manufactured beams confirms the adequate performance of the method. The proposed framework successfully generates beams with targeted deflections, demonstrating the method’s capability for inverse design under specific loading and boundary conditions. This approach not only optimizes material utilization but also broadens the application scope of functionally graded metamaterials in structural design.

A new understanding of the alkali-silica reaction expansion in concrete using a hybrid ensemble model

Alkali-Silica Reaction (ASR) is a critical issue affecting the durability of concrete structures, leading to significant long-term maintenance costs and safety concerns. This study addresses the need for accurate prediction of ASR-induced expansion in concrete, leveraging advanced machine learning techniques. Two hybrid ensemble methods, the inverse variance method and the artificial neural network-based ensemble method, were proposed to integrate the individual models to enhance the predictive capabilities. A comprehensive experimental database comprising over 1997 sets of ASR expansion data was collected from relevant literature with the environmental conditions, specimen geometry and material composition as the input variables and specimen strain as the output variable. The findings indicate that the predictive performance of individual models falls short of the performance of the hybrid ensemble machine learning model, with the inverse variance-based ensemble model exhibiting the highest performance (R = 97.2 %, RMSE = 0.066 mm). The Shapley Additive Explanations analysis reveals that the most influential factors include reaction days, alkali content, aggregate particle size, and silica content, contributing to up to 35 % of the variation in ASR expansion. This work offers valuable insights for the efficient assessment of durability of concrete structures concerning ASR expansion.

Effect of collagen supplementation on knee osteoarthritis: an updated systematic review and meta-analysis of randomised controlled trials.

To perform a systematic review and meta-analysis to assess the clinical efficacy of collagen-based supplements on knee osteoarthritis (OA) symptoms. Until October 2023, we conducted searches on the MEDLINE, EMBASE, Web of Science, and Scopus databases to identify randomised controlled trials (RCTs) that reported the effects of oral collagen-based supplements on knee OA. Quantitative data from outcomes were pooled using a random- or fixed-effects model (depending on inter-study variability) and the generic inverse variance method. The Cochrane Risk of Bias 2.0 tool was employed to assess the risk of bias. This systematic review incorporated information of 870 participants included from 11 RCTs, with 451 allocated to the collagen supplementation group and 419 to the placebo group. The meta-analysis revealed an overall significant improvement of both function [MD, -6.46 (95% CI -9.52, -3.40); I2=75%; p=0.00001] and pain scores [MD, -13.63 (95% CI -20.67, -6.58); I2=88%; p=0.00001], favouring collagen supplementation. The results of this meta-analysis suggest that oral collagen administration relieves OA symptoms. Our findings revealed noteworthy improvements, statistically and clinically, in both functional and pain scores.

EDAC-modified chitosan/imidazolium-polysulfone composite beads for removal of Cr(VI) from aqueous solution

To enhance the stability and adsorption performance of chitosan in Cr(VI)-contaminated acidic wastewater, a novel EDAC-modified-EDTA-crosslinked chitosan derivative (CSEC) was synthesized via a one-pot method with chitosan, 1-Ethyl-3-(3-dimethylaminopropyl) carbodiimide hydrochloride (EDAC), and Na2EDTA as raw materials. To further improve the mechanical strength and separation performance of CSEC, a novel composite bead (CSEP) of CSEC and imidazolium-functionalized polysulfone (IMPSF) was prepared through a phase inversion method. The chemical composition and microstructure of CSEC and CSEP were characterized by FESEM, FTIR, NMR and XPS techniques. The maximum adsorption capacities of CSEC and CSEP for Cr(VI) were 145.96 and 135.82 mg g−1 at pH 3, respectively, and the equilibrium time for Cr(VI) adsorption by CSEC and CSEP was 5 min and 8 h, respectively. The adsorption process of Cr(VI) by both CSEC and CSEP was exothermic and spontaneous. Compared to CSEC, CSEP has significantly enhanced resistance to interference from coexisting anions. The removal mechanism of Cr(VI) by CSEP might involve redox reaction as well as electrostatic attraction between Cr(VI) oxyanions and various nitrogen cations, including protonated amino groups, guanidinium groups, protonated tertiary amine groups, and imidazolium cations. The CSEP beads have potential application value in the treatment of acidic wastewater containing Cr(VI).

Research on Ground-Based Remote-Sensing Inversion Method for Soil Salinity Information Based on Crack Characteristics and Spectral Response

Research on Ground-Based Remote-Sensing Inversion Method for Soil Salinity Information Based on Crack Characteristics and Spectral Response

Inverse Heat Transfer Method to Control the Cancerous Tissue Temperature During Hyperthermia

Inverse Heat Transfer Method to Control the Cancerous Tissue Temperature During Hyperthermia

Genetic prediction of blood metabolites mediating the relationship between gut microbiota and Alzheimer's disease: a Mendelian randomization study.

Observational studies have suggested an association between gut microbiota and Alzheimer's disease (AD); however, the causal relationship remains unclear, and the role of blood metabolites in this association remains elusive. To elucidate the causal relationship between gut microbiota and AD and to investigate whether blood metabolites serve as potential mediators. Univariable Mendelian randomization (UVMR) analysis was employed to assess the causal relationship between gut microbiota and AD, while multivariable MR (MVMR) was utilized to mitigate confounding factors. Subsequently, a two-step mediation MR approach was employed to explore the role of blood metabolites as potential mediators. We primarily utilized the inverse variance-weighted method to evaluate the causal relationship between exposure and outcome, and sensitivity analyses including Contamination mixture, Maximum-likelihood, Debiased inverse-variance weighted, MR-Egger, Bayesian Weighted Mendelian randomization, and MR pleiotropy residual sum and outlier were conducted to address pleiotropy. After adjustment for reverse causality and MVMR correction, class Actinobacteria (OR: 1.03, 95% CI: 1.01-1.06, p = 0.006), family Lactobacillaceae (OR: 1.03, 95% CI: 1.00-1.05, p = 0.017), genus Lachnoclostridium (OR: 1.03, 95% CI: 1.00-1.06, p = 0.019), genus Ruminiclostridium9 (OR: 0.97, 95% CI: 0.94-1.00, p = 0.027) and genus Ruminiclostridium6 (OR: 1.03, 95% CI: 1.01-1.05, p = 0.009) exhibited causal effects on AD. Moreover, 1-ribosyl-imidazoleacetate levels (-6.62%), Metabolonic lactone sulfate levels (2.90%), and Nonadecanoate (19:0) levels (-12.17%) mediated the total genetic predictive effects of class Actinobacteria on AD risk. Similarly, 2-stearoyl-GPE (18:0) levels (-9.87%), Octadecanedioylcarnitine (C18-DC) levels (4.44%), 1-(1-enyl-stearoyl)-2-oleoyl-GPE (p-18:0/18:1) levels (38.66%), and X-23639 levels (13.28%) respectively mediated the total genetic predictive effects of family Lactobacillaceae on AD risk. Furthermore, Hexadecanedioate (C16-DC) levels (5.45%) mediated the total genetic predictive effects of genus Ruminiclostridium 6 on AD risk; Indole-3-carboxylate levels (13.91%), X-13431 levels (7.08%), Alpha-ketoglutarate to succinate ratio (-13.91%), 3-phosphoglycerate to glycerate ratio (15.27%), and Succinate to proline ratio (-14.64%) respectively mediated the total genetic predictive effects of genus Ruminiclostridium 9 on AD risk. Our mediation MR analysis provides genetic evidence suggesting the potential mediating role of blood metabolites in the causal relationship between gut microbiota and AD. Further large-scale randomized controlled trials are warranted to validate the role of blood metabolites in the specific mechanisms by which gut microbiota influence AD.

Inversion method of NHV based on novel model parameter space acquisition strategy and its application in the Tonghai basin site in Yunnan, China

The imaging of subsurface soil velocity structures from ambient noise inversion is a difficult problem. Few recording points and a simplified 1-D layered profile lead to important non-uniqueness. From our point of view, improving the reliability of processing methods of the observed data to obtain noise horizontal-to-vertical spectral ratio (NHV) curves and setting a complete model parameter space are important tasks to reduce the non-uniqueness of inversion. In this study, using a local site near the border of the Tonghai Basin, China, as a case study, we first demonstrate how to identify and mitigate the influence of industrial sources using surface observations to obtain more reliable NHV curves. Then, a new strategy to determine model parameter space is proposed, that is, stratifying soil layers based on the number of NHV peaks and determining the shear wave velocities, thicknesses, and their ranges based on the empirical relationship between sedimentary thickness and resonant frequency (h-fr). Subsequently, combining the model parameter space acquisition strategy with the NHV inversion, a novel NHV inversion approach is developed and applied to obtain the 2-D VS profile of the investigated Tonghai site. The inverted 2-D VS profile aligns favorably with the frequency-depth conversion results of the measured NHV curves (NHV-profiling) and the measured borehole profiles, affirming the reliability of the proposed NHV inversion method. Finally, by comparing the empirical transfer functions from the strong-motion recordings, we validated the applicability of the inverted models for characterizing site effects. The model parameter space acquisition strategy proposed in this paper and the analysis procedure of the observed data are also applicable to other study areas, which can provide a referable approach to quickly and effectively acquire the soil layer velocity structure of the site.

A rapid imaging approach for transient electromagnetic data based on gradient features

ABSTRACT Data processing techniques in transient electromagnetic (TEM) methods face numerous challenges, such as the problem of 3-D imaging and the demand for new data processing techniques arising from the development of small-loop TEM devices. We have developed an imaging algorithm based on gradient features derived from TEM data to address these challenges. We found that normalising the gradient field of TEM responses under appropriate background conditions enables imaging of the target. Numerical experiments conducted under theoretical models have validated the feasibility of this approach and highlighted the significance of background fields. We further designed more complex models and achieved 3-D imaging of synthetic data within seconds, demonstrating the method's high efficiency and applicability to high-dimensional data. Subsequently, we applied the algorithm to challenging small-loop TEM data and demonstrated its superior performance compared to the inversion method, which presents a novel approach for processing data from small-loop TEM devices. This study demonstrates that the algorithm possesses characteristics of high efficiency and wide applicability, suitable for TEM data from various dimensions and types of devices. Furthermore, it holds promising potential in assisting the enhancement of the efficiency of the three-dimensional inversion of TEM data.

Association between rheumatoid arthritis and chronic respiratory diseases in a Japanese population: A Mendelian randomization study.

Past observational studies have documented an association between rheumatoid arthritis (RA) and chronic respiratory diseases. Undertaking the approach of Mendelian randomization (MR) analysis, this research aims to delve deeper into the probability of a causal connection between RA and chronic respiratory diseases. Collated genome-wide association study data covering RA with 4199 cases against 208,254 controls, asthma comprising 8216 cases versus 201,592 controls, and chronic obstructive pulmonary disease (COPD) detailing 3315 cases in contrast to 201,592 controls were derived from the repository of the Japanese Biobank. A selection of 10 RA-related, 8 asthma-related, and 4 COPD-related single nucleotide polymorphisms notable for their statistical significance (P < 5 × 10-8) were identified as instrumental variables. The primary analytical technique was the inverse variance-weighted (IVW) method, alongside the MR-Egger protocol, weighted median, and weighted mode to reinforce the validity and solidity of the principal results. For scrutinizing possible implications of horizontal pleiotropy, we harnessed the MR-Egger intercept examination and the Mendelian Randomization Pleiotropy REsidual Sum and Outlier test. Employing the inverse variance-weighted technique, we established a positive correlation between genetic predispositions for RA and actual occurrences of asthma (odds ratios [OR] = 1.14; 95% confidence intervals [CI]: 1.04-1.24; P = .003). This correlation remained strong when testing the results utilizing various methods, including the MR-Egger method (OR = 1.32; 95% CI: 1.09-1.60; P = .023), the weighted median (OR = 1.16; 95% CI: 1.06-1.26; P < .001), and the weighted mode (OR = 1.21; 95% CI: 1.11-1.32; P = .002). Furthermore, our findings from the inverse variance-weighted method also demonstrated a positive association between genetically predicted RA and COPD (OR = 1.12; 95% CI: 1.02-1.29; P = .021). However, no such link was discerned in supplementary analyses. In a shifted perspective-the reverse MR analysis-no correlation was identified between genetically predicted instances of asthma (IVW, P = .717) or COPD (IVW, P = .177) and RA. The findings confirm a causal correlation between genetically predicted RA and an elevated risk of either asthma or COPD. In contrast, our results offer no support to the presumed causal relationship between genetic susceptibility to either asthma or COPD and the subsequent development of RA.

Advanced photocatalytic membrane GO-NiFe@SiO2/PVDF for efficient decontamination of synthetic dyes in batik wastewater with superior antifouling features

A novel composite membrane, GO-NiFe@SiO2/polyvinylidene fluoride (PVDF), was prepared via the sol-gel method for nanocomposite synthesis and phase inversion method for membrane fabrication. The investigation encompassed the structural features and properties of the nanocomposite membranes, including photocatalytic activity under UV type C, antifouling capability, and self-cleaning behavior. The degradation of dyes in real Batik wastewater followed pseudo-first-order kinetics, with the GO-NiFe@SiO2/PVDF 1 wt% nanocomposite membranes exhibiting a highest dyes removal efficiency up to 90.50 % within 8 h, compared to the pristine PVDF membrane (60.95 %). The XRD pattern analysis indicates that the incorporation of GO-NiFe@SiO2 into the PVDF membrane induced a transformation in the semi-crystalline phase of PVDF, shifting from the alpha-phase to the beta-phase, consequently facilitating the development of electrostatic charge on the membrane surface. The pore-size distribution analysis revealed that all prepared membranes fall within the range of nanofiltration and tight ultrafiltration (NF-TUF). Additionally, the photocatalytic membrane demonstrated enhanced permeation flux of 30.46 L.m−2.h−1 and flux recovery rate up to 92.57 % under simulated UV light irradiation, showcasing improved antifouling capability. Moreover, the membrane exhibited outstanding cycle test with 6 consecutive cleaning every 3 h, self-cleaning efficiency, with 61.32 % cleaning efficiency under UV irradiation. The incorporation of GO-NiFe@SiO2 enhanced the physicochemical properties of the photocatalytic membrane, including hydrophilicity, surface topologies, and mechanical strength, thereby improving photocatalytic anti-fouling performance and expanding the potential applications of membrane filtration technology.

Modeling spatial variability of mechanical parameters of layered rock masses and its application in slope optimization at the open-pit mine

Mining engineering with layered structures often obtains extensive geological data to ensure reliability of mining operations. Effectively utilizing these data to characterize the spatial distribution of mechanical parameters in layered rock mass is crucial for slope stability analysis. This study focuses on the Heishan open-pit mine as a case study, leveraging the distinctive characteristics of mining engineering geological data. A three-dimensional fracture network was then generated based on the distribution of fractures in the rocks, and the representative elementary volume of the rock mass was determined by calculating the volumetric joint count (Jv). Statistical characteristics of various geological data are analyzed, and a geological statistical method combining the Kriging method and inverse distance power method is applied to establish a spatial distribution block model for geological strength index (GSI) and rock mechanical properties. Subsequently, a spatial variability model of the mechanical parameters of the layered rock mass was generated based on the Hoek–Brown criterion. Furthermore, the heterogeneous mechanical model is implemented in numerical software for stability analysis and slope angle optimization. The findings indicate that each engineering zone of layered slopes exhibits unique mechanical parameters while demonstrating significant layered distribution patterns at a macro level. Considering spatial variability, the mechanical model significantly impacts slope stability and slope angle optimization outcomes. Our research methodology facilitates accurate quantification of the heterogeneity of mechanical parameters in layered slopes without incurring excessive additional survey costs, enabling more rational explanations of slope landslides and the provision of suitable slope angle optimization designs.

Kinematic and dynamic fault slip analyses: Implications from the surface rupture of the 2023 Elbistan (Kahramanmaraş) (Mw7.6) earthquake, Türkiye

On 6 February 2023, the Elbistan (Kahramanmaraş) (Mw7.6) earthquake produced a strike-slip type coseismic surface rupture zone, involving the sinistral slip of the Doğanşehir Fault (DF) and Çardak Fault (ÇF). Fault slickenlines and seismic slickenlines were included in the inversion as part of the dynamic analysis. The inversion of fault slickenlines collected from nine outcrops along the surface rupture following the earthquake, many of which developed during the event and are referred to as coseismic slickenlines, reveals a strike-slip stress regime (σ2 = σv) characterized by a NE-SW (mean azimuth: N045°E) σ1 (maximum) axis. Relict slip planes adjacent to main slip surfaces were found to host slickenlines that appear much older than the most recent earthquake, referred to as paleoslip slickenlines. Inversion of the paleoslip slickenline collected from four outcrops reveals an extensional stress regime (σ1 = σv) characterized by a NE-SW σ3 (min) axis, consistent with previously published studies. To define a significant stress tensor concerning present-day faulting within the investigated area, the inversion method was applied to the seismic slickenlines of shallow earthquakes in the surface rupture area. The inversion of sixty selected nodal planes reveals a strike-slip stress regime (σ2 = σv) characterized by an NNE–SSW (N10°E) σ1 (max) axis. Besides, the moment tensor summation analysis using displacement vectors inferred from visible field markers offset during the earthquake was applied to the seismic slickenlines as part of the kinematic analysis. The shortening and extension results for the moment tensor summation are 044/36 and 307/11 indicating NE-SW compression. Results of the moment tensor summation (weighted by fault displacement) agree broadly with the inversion of seismic slickenlines results, indicating an NE orientation for shortening and an SE orientation for extension.

Data-driven inverse design of the perforated auxetic phononic crystals for elastic wave manipulation

Abstract In addition to the distinctive features of tunable Poisson’s ratio from positive to negative and low stress concentration, the perforated auxetic metamaterials by peanut-shaped cuts have exhibited excellent phononic crystal (PNC) behavior as well for elastic wave manipulation. Thus they have attracted much attention in vibration suppression for dynamic applications. However, traditional structural designs of the auxetic PNCs considerably depend on designers’ experience or inspiration to fulfill the desired multi-objective bandgap properties through extensive trial and error. Hence, developing a more efficient and robust inverse design method remains challenging to accelerate the creation of auxetic PNCs and improve their performance. To shorten this gap, a new machine learning (ML) framework consisting of double back propagation neural network (BPNN) modules is developed in this work to produce desired configurations of the auxetic PNCs matching the customized bandgap. The first inverse BPNN module is trained to establish a logical mapping from the bandgap properties to the structural parameters, and then the second forward BPNN module is introduced to give the new property prediction by using the design configurations generated from the former. The error between the new predictions and the desired target properties is minimized through a limited number of iterations to produce the final optimal objective configurations. The results indicate that the perforated auxetic metamaterials behave relatively wide complete bandgap and the present ML model is effective in designing them with specific bandgaps within or beyond the given dataset. The study provides a powerful tool for designing and optimizing the perforated auxetic metamaterials in dynamic environment.

Natural gas leakage: Forward and inverse method of leakage field based on multipath concentration monitoring

Natural gas leakage can easily lead to safety accidents and environmental pollution, affecting normal safe production and sustainable energy development. Among them, the leakage accident caused by the integrity failure of the process equipment is particularly noteworthy. To improve the efficiency of methane leakage monitoring and the accuracy of leakage source location, the forward prediction model of leakage concentration field, the optimization model of monitoring equipment layout, and the inversion model of leakage source location were established. To evaluate the model’s applicability, an open-air oil–gas joint station was selected for experimental simulation. The monitoring data of the open circuit laser methane sensor and the forward simulation results of the leakage concentration field were compared. It was found that at 30 % methane concentration, the monitoring distance was 0–6 m, with high monitoring accuracy. Then, by eliminating redundant monitoring sensors, three leakage field concentration monitoring paths are formed. A representative leakage source scenario set is selected for inversion localization. In the simulation of the single-point leakage experiment, the leakage location error is 1.824 m, and the average relative error is 3.6 %. Through error analysis, the results show that the inversion positioning model can also have a good adaptability to the parameter estimation of the leakage source when there are only 3 sets of observation data.

Inversion of gas hydrate saturation and solid frame permeability in a gas hydrate-bearing sediment by Stoneley wave attenuation

Natural gas hydrate is a potential novel energy resource that is widely distributed globally. Acoustic logging can effectively provide information on the surrounding reservoir and plays an important guiding role in gas hydrate exploration and development. Natural gas hydrate-bearing sediments are composed of a solid frame with natural gas hydrates and water-filled pores. The borehole mode wave characteristics of two-phase porous media cannot be used to evaluate the parameters of such a multiphase porous medium. We explore factors that influence the monopole Stoneley wave in a borehole embedded in a multiphase porous medium containing two solids and one fluid and analyze the influence of each factor on monopole Stoneley wave attenuation systematically. The sensitivity analysis results indicate that the Stoneley wave attenuation is highly sensitive to solid frame permeability and gas hydrate saturation. Building upon this foundation, a method to invert for gas hydrate saturation and solid frame permeability is first developed using Stoneley wave attenuation. Synthetic logging data are used to demonstrate the feasibility of this method for inverting for gas hydrate-bearing sediment properties. Even in the presence of considerable noise added to the receiver signal arrays, the inversion method is stable, and reliably evaluates gas hydrate saturation and solid frame permeability.

Comparison of machine learning and electrical resistivity arrays to inverse modeling for locating and characterizing subsurface targets

This study evaluates the performance of multiple machine learning (ML) algorithms and electrical resistivity (ER) arrays for inversion with comparison to a conventional Gauss-Newton numerical inversion method. Four different ML models and four arrays were used for the estimation of only six variables for locating and characterizing hypothetical subsurface targets. The combination of dipole-dipole with Multilayer Perceptron Neural Network (MLP-NN) had the highest accuracy. Evaluation showed that both MLP-NN and Gauss-Newton methods performed well for estimating the matrix resistivity while target resistivity accuracy was lower, and MLP-NN produced sharper contrast at target boundaries for the field and hypothetical data. Both methods exhibited comparable target characterization performance, whereas MLP-NN had increased accuracy compared to Gauss-Newton in prediction of target width and height, which was attributed to numerical smoothing present in the Gauss-Newton approach. MLP-NN was also applied to a field dataset acquired at U.S. DOE Hanford site.

Applicability of the inverse dispersion method to measure emissions from animal housings

Abstract. Emissions from agricultural sources substantially contribute to global warming. The inverse dispersion method (IDM) has been successfully used for emission measurements from various agricultural sources. The IDM has also been validated in multiple studies with artificial gas releases mostly in open fields. Release experiments from buildings have rarely been conducted and were partly affected by additional nearby sources of the target gas. Specific release studies for naturally ventilated animal housings are lacking. In this study, a known and predefined amount of methane (CH4) was released from an artificial source inside a barn that mimicked a naturally ventilated dairy housing, and IDM recovery rates, using a backward Lagrangian stochastic (bLS) model, were determined. For concentration measurements, open-path devices (OPs) with a path length of 110 m were placed in a downwind direction of the barn at fetches of 2.0h, 5.3h, 8.6h, and 12h (h equals the height of the highest obstacle), and a 3D ultrasonic anemometer (UA) was placed in the middle of the first three OP paths. Upwind of the barn, an additional OP and a UA were installed. The median IDM recovery rates determined with the UA placed upwind of the barn and the downwind OP ranged between 0.55–0.75. It is concluded that, for the present study case, the effect of the building and a tree in the main wind axis led to a systematic underestimation of the IDM-derived emission rate probably due to deviations in the wind field and turbulent dispersion from the underlying assumptions of the used dispersion model.

Analysis on dual Fano resonance in a coupled-resonator waveguide

Dual Fano resonance was demonstrated in a compact coupling system without additional large footprint tunable devices consisting of a grating-coupled waveguide and a micro-racetrack resonator on thin film lithium niobate. A multimode interference model was proposed for the dual Fano resonance system. The inverse design method was used to realize model fitting, validate our model, and analyze our model. Based on the parameters obtained by the inverse design, we further analyzed the influence of different parameters. Our research also shows that through the interaction of two Fano resonance modes, tunable line shape and enhanced extinction ratio can be realized in the transmission spectrum, which has potential applications in optical sensing.

Tensile constitutive relationship of UHPFRC from crack hinge based inverse analysis of notched beams

The structural applications of ultra-high performance fiber reinforced concrete (UHPFRC) in the construction industry can be promoted if proper constitutive models can be established for design. The various tension test methods for UHPFRC are being adopted to develop a complete stress-crack width or strain response for design. This study aims to understand the fracture behavior of UHPFRC by testing notched beams under a three-point bending configuration. This testing method helps in quality control checks and obtaining complete tension stress-crack opening behavior that can be used for design. The tensile stress-crack width response of UHPFRC is obtained using the load-CMOD response. The variables considered in this study are the volume fraction of fibers (1 % and 2 %), types of steel fibers (straight, combination of straight and hooked ended), and different cross-section dimensions (100×100×500 mm and 75×75×500 mm). A crack hinge-based inverse analysis method is used for UHPFRC to obtain the complete tensile stress-crack opening response. Stress-strain relations from inverse analysis and direct tension stress-crack opening results are compared and found to be similar. A data-driven tension stress-crack opening response UHPFRC is verified by simulating the girder's response using nonlinear finite element analysis (NFEA). Thus, the proposed inverse analysis can be used to obtain the multi-linear tensile stress-crack opening response which is adequate for capturing the structural response.