Inverse Analysis Method Research Articles

Synthesis, crystal structure, and DFT study of 1-cyclopropyl-3-(3-((1-(2-methoxyphenyl)-5-oxo-[1, 2, 4]triazolo[4,3-a]quinazolin-4(5H)-yl)methyl)phenylurea

A new triazoline-quinazolinone compound, 1-cyclopropyl-3-(3-((1-(2- methoxyphenyl)-5-oxo-[1, 2, 4]triazolo[4,3-a]quinazoline-4(5H)-yl)methyl)phenylurea, was attained by nine steps and selected the method of inverse synthetic analysis. Meanwhile, the structure of the title compound was not only certified by MS, 1H NMR, FT-IR, and 13C NMR spectroscopy, but the compound’s single crystal was measured by X-ray diffraction. The optimized molecular crystal structure was ulteriorly determined using density functional theory (DFT), and it was compared with the value of X-ray diffraction. Furthermore, through more deeply studies by means of the molecular electrostatic potential and frontier molecular orbitals (FMOs) of compound 1, more physicochemical properties were investigated.

Efficient Inverse Method for Structural Identification Considering Modeling and Response Uncertainties

The inverse problem analysis method provides an effective way for the structural parameter identification. However, uncertainties wildly exist in the practical engineering inverse problems. Due to the coupling of multi-source uncertainties in the measured responses and the modeling parameters, the traditional inverse method under the deterministic framework faces the challenges in solving mechanism and computing cost. In this paper, an uncertain inverse method based on convex model and dimension reduction decomposition is proposed to realize the interval identification of unknown structural parameters according to the uncertain measured responses and modeling parameters. Firstly, the polygonal convex set model is established to quantify the epistemic uncertainties of modeling parameters. Afterwards, a space collocation method based on dimension reduction decomposition is proposed to transform the inverse problem considering multi-source uncertainties into a few interval inverse problems considering response uncertainty. The transformed interval inverse problem involves the two-layer solving process including interval propagation and optimization updating. In order to solve the interval inverse problems considering response uncertainty, an efficient interval inverse method based on the high dimensional model representation and affine algorithm is further developed. Through the coupling of the above two strategies, the proposed uncertain inverse method avoids the time-consuming multi-layer nested calculation procedure, and then effectively realizes the uncertainty identification of unknown structural parameters. Finally, two engineering examples are provided to verify the effectiveness of the proposed uncertain inverse method.

Experimental Research on Vortex-Induced Force Characteristics of Flexible Riser with Buoyancy Module and Strakes

In this paper, the vortex-induced force characteristics of a flexible riser with buoyancy modules and strakes were experimentally investigated. The strain information caused by vortex-induced vibration (VIV) at different cross-sections on the flexible cylinder was measured in the model test. Combined with the modal superposition method and inverse analysis method for vortex-induced force, the vortex-induced forces on the flexible cylinder were inverted, including the excitation force in phase with velocity and added mass force in phase with acceleration. Then, the excitation coefficients and added mass coefficients at each time step were identified via a least-squares method. The results show that the added mass coefficient and excitation coefficient of the flexible riser covering buoyancy modules present a “sawtooth” distribution along the length of the pipe, while the total mass (sum of structural mass and added mass) is consistent along the pipe. The strake has little effect on the added mass coefficient of the buoyancy module and the bare pipe section, but when it covers the bare pipe section, the excitation coefficient of the bare pipe section decreases to a negative value, showing a damping effect. In addition, when the bare pipe section of the flexible riser is completely covered with helical strakes, only the vortex-shedding frequency component of the buoyancy modules remains in the VIV response of the pipe. The reason for this phenomenon is that helical strakes completely suppress the vortex shedding of the bare pipe section, resulting in the reduction in the VIV excitation energy of the original bare pipe section to 0.

Application of the Maximum Sensitivity Principle in the Optimization of Measuring Point Arrangement in Transversely Isotropic Rock Mass Engineering

The inverse analysis method based on in situ measurement information provides a new approach to determine the mechanical parameters of rock mass. The accurate on-site monitoring data is the prerequisite and basis for the success of displacement back analysis. To improve the accuracy of requirement parameters, a reasonable layout program should be developed to optimize the layout of the measuring position. In order to study the optimal arrangement of measuring points in anisotropic rock mass, the layout optimization of measuring points around a tunnel in the transversely isotropic rock mass is studied according to the maximum sensitivity criteria. The influence of the spatial location of the measuring points on the measurement of the tunnel deformation is obtained. The results indicate that the measuring point should be arranged close to the extreme point in the direction of the larger principal stress.

Study on fracture behaviour of basalt fibre reinforced asphalt concrete with plastic coupled cohesive model and enhanced virtual crack closure technique model

ABSTRACT In this study, the plastic coupled cohesive model and enhanced virtual crack closure technique (VCCT) are used to investigate the fracture behaviour of the basalt fibre reinforced asphalt concrete (BFRAC). In the plastic coupled cohesive model, the separation and traction response along the cohesive zone advance ahead of a crack tip is governed by an exponential cohesive law. The double-K fracture theory is integrated into the enhanced VCCT model. It is shown that the simulated load-cracking mouth opening displacement (P-CMOD) curves from both the plastic coupled cohesive model and the enhanced VCCT model compares favourably with the measured curves from the single-edge notched beam. The parameters used in the plastic coupled cohesive model cannot directly be obtained from the standard test, and the inverse analysis method is always necessary for identifying the fracture parameters. On the contrary, the fracture parameters in the enhanced VCCT method can be directly calculated from the P-CMOD curves based on the double-K fracture theory and the finite plastic fracture theory (Hutchinson, Rice, Rosengren singular crack tip fields, abbreviated as HRR field). Meanwhile, compared with the plastic coupled cohesive model, the enhanced VCCT model coupled with the Ramberg–Osgood elasto-plastic harden model is promising for investigating the physical mechanism underlying the nonlinear fracture of BFRAC. This paper proposed two concrete and valuable models in the finite element method for simulating the fracture behaviour of the huge structure with asphalt and asphalt concrete.

The Inversion Analysis and Material Parameter Optimization of a High Earth-Rockfill Dam during Construction Periods

Inversion analysis is usually an efficient solution to process the monitoring data of earth-rockfill dams. However, it is still difficult to obtain calculation results that are consistent with monitoring data due to different construction statuses. To deal with this situation and to introduce a new solution to improve calculation accuracy, the general method of inversion analysis based on back-propagation neural networks and the original step-by-step inversion method assuming that the parameters of the constitutive model vary with construction periods are introduced and verified in this work. Then, both methods are applied in the inversion analysis of a high gravelly soil core rock-fill dam during construction periods. Moreover, the relationship between the inversed material parameters and the stress values of the core wall is discussed. The material parameters are further optimized to obtain more accurate displacement values. The results show that the step-by-step inversion method has a higher accuracy in vertical compression values compared with the conventional inversion method, the trend of material parameter K is more significant than other parameters, and the proposed variable parameter constitutive model has an accuracy between the step-by-step and conventional inversion methods. Conclusions can be drawn that the original step-by-step inversion method has more advantages than the conventional method and the variable parameter constitutive model proposed in this paper might be more suitable for the analysis of a high earth-rockfill dam during construction periods.

Inverse analysis of critical current density in a bulk high-temperature superconducting undulator

In order to optimize the design of undulators using high-temperature superconductor (HTS) bulks we have developed a method to estimate the critical current density (${J}_{c}$) of each bulk from the overall measured magnetic field of an undulator. The vertical magnetic field was measured along the electron-beam axis in a HTS bulk-based undulator consisting of twenty Gd-Ba-Cu-O (GdBCO) bulks inserted in a 12-T solenoid. The ${J}_{c}$ values of the bulks were estimated by an inverse analysis approach in which the magnetic field was calculated by the forward simulation of the shielding currents in each HTS bulk with a given ${J}_{c}$. Subsequently the ${J}_{c}$ values were iteratively updated using the precalculated response matrix of the undulator magnetic field to ${J}_{c}$. We demonstrate that it is possible to determine the ${J}_{c}$ of each HTS bulk with sufficient accuracy for practical application within around 10 iterations. The precalculated response matrix, created in advance, enables the inverse analysis to be performed within a practically short time, on the order of several hours. The measurement error, which destroys the uniqueness of the solution, was investigated and the points to be noted for future magnetic field measurements were clarified. The results show that this inverse-analysis method allows the estimation of the ${J}_{c}$ of each bulk comprising an HTS bulk undulator.

Experimental and Numerical Analysis on the Damage and Failure Characteristics of Bituminous Coal under Multilevel Cyclic Loads

The coal mining process is often accompanied by periodic disturbance of the surrounding rock mass around the coal mining face. Therefore, it is of great theoretical and engineering value to investigate the damage pattern of bituminous coal under cyclic loading and unloading conditions and analyze its damage precursors. The experiments of uniaxial multistage cyclic loading and unloading of bituminous coal were carried out, and the loading and unloading response ratios were extracted using the elastic modulus variation to describe the damage characteristics and damage precursors of bituminous coal. Based on the accumulated acoustic emission ringing counts, the response ratios were defined, and the internal damage evolution characteristics and damage laws during the damage of bituminous coal were analyzed. The CT scan images of the internal structure of the coal sample before and after the experiment were used to analyze the damage characteristics of the coal sample and the influence of the number of simulation units on the results using the inverse modeling simulation analysis method. The research shows that the response ratio of bituminous coal under uniaxial cyclic loading has three stages of variation, and it is characterized by periodic “W”-type variation at each level of stress. In addition, the inverse modeling and simulation can better characterize the damage evolution of the coal specimen.

Stress measurement and correction with contour method for additively manufactured round-rod specimen

The contour method (CM) was applied to obtain residual stress field in the round-rod titanium alloy specimen fabricated by laser power bed fusion additive manufacturing. In order to improve the accuracy of CM, two methods were investigated. One employed a steel block glued to the specimen to shift the surface stress uncertainties. The other is to reconstruct the stress based on the eigenstrain inverse analysis method. Results show that both methods can improve the measurement accuracy on the surface layer stress to a certain extent. Attaching steel block would affect the cutting process and cause new test errors. The stress reconstruction method requires surface stress results and eigenstrain basis function with an order of at least 10.

An Inverse Analysis for Establishing the Temperature-Dependent Thermal Conductivity of a Melt-Cast Explosive across the Whole Solidification Process.

Thermal conductivity is one of the most important thermophysical properties of a melt-cast explosive. However, the temperature-dependent thermal conductivity of such explosives cannot be easily measured across the whole solidification process (including the liquid, semi-solid, and solid states). This study used an inverse analysis method to estimate the temperature-dependent thermal conductivity of a 2,4-dinitroanisole/cyclotetramethylenetetranitramine (DNAN/HMX) melt-cast explosive in a continuous way. The method that was used is described here in detail, and it is verified by comparing the estimated thermal conductivity with a prespecified value using simulated measurement temperatures, thereby demonstrating its effectiveness. Combining this method with experimentally measured temperatures, the temperature-dependent thermal conductivity of the DNAN/HMX melt-cast explosive was obtained. Some measured thermal conductivity values for this explosive in the solid state were used for further validation.

Illegal connection detection in a viscoelastic pipeline using inverse transient analysis in the time domain

Abstract Illegal connection (IC) in water supply systems and water network wastes water as well as energy and reduces water quality, which has negative technical and economic effects on water management. Transient-based defect detection is a powerful method applied in water pipelines. This paper investigates the efficiency of the transient-based inverse transient analysis (ITA) method in estimating the characteristics of ICs in the viscoelastic water supply system in the time domain. To better evaluate this method, an experimental transient model was developed using polyethylene pipelines (with a length of 158 meters and a nominal diameter of 2 inches). In the first step, the hydraulic transient solver was calibrated in the calibration approach of dynamic parameters of pressure wave speed and pipe wall viscoelasticity. Then, the sensitivity of the ITA method to the spatial step of the method of characteristics and signal sample size was assessed. Finally, the efficiency of the ITA method was evaluated for several experiments with different transient intensities and a noisy signal. The results indicated that the accuracy for locating the IC was higher than the accuracy for the IC's length.

Multi-parameter inverse analysis of concrete dams using kernel extreme learning machines-based response surface model

Inverse analysis by finite element model (FEM) based on measured displacement data is a popular approach for parameter identification of concrete dams. FEM-based inverse analysis method is economical and effective, but with some limitations such as complex computation and time-consuming. This paper presents a kernel extreme learning machine (KELM)-based response surface model (RSM) for parameter inverse analysis of concrete dams. The FEM is replaced by KELM-based RSM to explore the relationships between material parameters and displacement response of dam-foundation systems. Sample data of KELM-based RSM are generated by the efficient sampling technique Latin hypercube sampling. Subsequently, a novel optimization algorithm Jaya is adopted to minimize the objective function for material parameters identification. The effectiveness and practicability of the proposed approach are verified by two cases and two real concrete gravity dams in operation with sufficient monitoring data. Comparative studies with direct finite element method and several optimization algorithms were also performed to demonstrate the superiority of the proposed approach over commonly used techniques. Results show that the proposed KELM-based RSM is a simple and efficient way to achieve high accuracy in parameter inverse analysis of concrete dams at a low computation cost.

Flexural behavior prediction of a layered composite member with 3D textile reinforced concrete

Currently, three-dimensional (3D) textiles are perceived as an attractive construction material that offers a new direction for textile reinforced concrete (TRC) research. In this paper, the textile reinforced layer was strategically applied on the tensile side of a flexural member by taking advantage of the structures of 3D textiles. To simulate the flexural response of layered 3D TRC, an inverse analysis method and closed-form moment–curvature equations were utilized. Simultaneously, bending specimens were fabricated using four different 3D textiles as an experimental method. The composite specimens exhibited significant ductility through deflection hardening. The analytical simulation of layered 3D TRC was compared to the flexural experimental results, and good agreement was found. Furthermore, the applicability of precast 3D TRC was presented using the spacer yarns of the textiles as anchors between the layers.

Flow-induced vibration analysis of two unequal-diameter flexible cylinders in staggered configuration from a hydrodynamic force perspective

This paper presents an experimental study on the hydrodynamic features of two unequal-diameter flexible cylinders in staggered arrangement subject to flow-induced vibration (FIV). Five position angles (α = 15°, 30°, 45°, 60°, and 75°) are defined between the tandem (α = 0°) and side-by-side (α = 90°) cases with the centre-to-centre spacing being fixed at P = 6.0d, where d is the diameter of the small cylinder. The time-varying strains obtained from the experimental tests are converted into displacements, and then the hydrodynamic force coefficients of the two cylinders are derived using an inverse analysis method. It is found that the variation trends of the cross-flow (CF) hydrodynamic coefficients with the reduced velocity do not demonstrate qualitative differences from those of their isolated counterparts except in the mode transition regions. The downstream cylinder experiences stronger influence from the upstream cylinder on its CF hydrodynamic characteristics especially at small α. The more frequent mode transitions in the in-line (IL) direction lead to the multi-frequency responses associated with changes in the IL hydrodynamic coefficients. The typical wake-induced flutter (WIF) phenomenon is observed when Vrs = 5.01, 8.77 and 16.28–25.05 for the downstream small cylinder in Case I and α = 75°. The influence of the characteristics of the WIF phenomenon on the hydrodynamic force is evident because of the nonexistence of the high-frequency components in the oscillations.

A New Approach to Symmetry Reliability: Combination of Forward and Inverse Reliability Principle and Its Application to Frame Structures and Bamboo Bridges

Reliability theory is the core basis of engineering design, mainly including forward reliability theory and inverse reliability theory. Forward reliability theory is used to obtain the reliability index using the known design parameters, that is, it is a mapping function that translates the design parameters to the reliability index. Inverse reliability theory is used to obtain the design parameters using the known reliability index, that is, it is a mapping function that translates the reliability index to the design parameters. In other words, forward reliability theory and inverse reliability theory together constitute a method of dual mapping, which is the specific application of symmetry theory in the reliability field. In this paper, a new inverse reliability analysis method is proposed, which can satisfy the requirements of the target reliability index while obtaining the design parameters, without additional calculation and verification of reliability. The method simplifies the reliability inverse problem to the problem of the nonlinear equation, which is solved by identifying the design parameters, and finally obtains the design parameters by iterating the reliability index for each design parameter to gradually approach the target reliability index. For high-dimension and complex problems, the Levenberg–Marquardt method is introduced to avoid the problem of sensitivity to initial values and iterative divergence when identifying the design parameters. The implicit limit state function problem is solved by the interactive operation between ANSYS software and MATLAB software using finite element theory. The accuracy of the proposed method in this paper is verified by several numerical examples, the applicability of the implicit limit state function is verified by a single-story frame structure, and the engineering applicability of the proposed method is demonstrated with a bamboo bridge.

Extended GTN model for predicting ductile fracture under a broad range of stress states

Continuous damage accumulation resulting from void nucleation, growth, and coalescence leads to the final ductile fracture. The Gurson–Tvergaard–Needleman (GTN) model and its extensions, which model these mechanisms, are famous coupled constitutive models for predicting material failure. In this study, the GTN model was extended by incorporating two different damage variables: void volume fraction and shear damage; this was done to describe damage accumulation and ductile fracture under a wide range of stress states from compression-dominated to tension-dominated ones. The shear damage was composed of the shear void nucleation related to secondary voids and shear deformation damage. In addition, the shear void nucleation and void closure effect resulting from compression deformation were introduced to model the change in void volume under different loading conditions. The Lode angle dependence function was updated to express the various stress states and competition mechanism between two damage variables. Furthermore, the effective damage and its incremental form was used to define the extent of damage accumulation and fracture initiation. Subsequently, the proposed model was implemented in finite element software through user subroutines, and three distinct experiments related to high, low, and negative stress triaxiality were performed to calibrate the model parameters by the inverse analysis method for 1045 steel and 2024-T351 aluminum alloy. The experimental results under proportional and path-changing loading conditions were used to analyze the damage evolution and validate the proposed model. The good agreement between the numerical prediction and experimental results for the displacement and location at fracture, indicates good predictive ability of formulated model under arbitrary loading conditions.

Initial solution estimation of one-step inverse isogeometric analysis for sheet metal forming with complex topologies

The one-step inverse isogeometric analysis method has been successfully applied in sheet metal forming with simple geometries. Generally, actual stamping parts frequently contain numerous trimmed NURBS-based CAD surfaces. The key step in sheet metal forming is to unfold the undevelopable CAD model onto a planar domain and obtain a good initial solution. In this study, we estimate the initial solution of stamping parts with complex topologies using an energy-based algorithm. The trimmed surface analysis technique and Nitsche’s method are adopted for trimmed and multi-patch isogeometric analysis. A new coordinate transformation system is used to avoid special treatment for negative angle and vertical wall problems, which are common in metal sheet forming. We demonstrate our algorithm with three examples and compare the results with one-step inverse isogeometric analysis of simple geometry or the traditional finite element method. These examples illustrate the performance of the new method and its applicability for the integration of design and analysis in sheet metal forming with complex topologies.

Recovering Heat Source from Fourth-Order Inverse Problems by Weighted Gradient Collocation

The weighted gradient reproducing kernel collocation method is introduced to recover the heat source described by Poisson’s equation. As it is commonly known that there is no unique solution to the inverse heat source problem, the weak solution based on a priori assumptions is considered herein. In view of the fourth-order partial differential equation (PDE) in the mathematical model, the high-order gradient reproducing kernel approximation is introduced to efficiently untangle the problem without calculating the high-order derivatives of reproducing kernel shape functions. The weights of the weighted collocation method for high-order inverse analysis are first determined. In the benchmark analysis, the unclear illustration in the literature is clarified, and the correct interpretation of numerical results is given particularly. Two mathematical formulations with four examples are provided to demonstrate the viability of the method, including the extreme cases of the limited accessible boundary.

Effect of steel fiber-volume fraction and distribution on flexural behavior of Ultra-high performance fiber reinforced concrete by digital image correlation technique

This paper investigated the effect of steel fiber-volume fraction (0.5%, 1.0%, 1.5%, and 2.0%) and distribution on the flexural behavior of ultra-high performance fiber reinforced concrete (UHPFRC). Digital image correlation (DIC) was used to obtain the crack propagation behavior of UHPFRC under bending load. With increasing fiber-volume fraction, the crack-propagation path becomes more zigzagged. Based on the flexural response of UHPFRC and fiber distribution on the crack plane, a correlation between fiber distribution characteristics and flexural behavior was discussed. The fibers number per unit area for S0.5, S1.0, S1.5, and S2.0 were 7, 14, 21, and 31, respectively. The fiber pull-out length in cracked zone with different fiber-volume fractions was about 3.56 mm. The fiber orientation factor (ηθ) of S0.5, S1.0, S1.5, and S2.0 were 0.80, 0.79, 0.69 and 0.61 respectively. A quadratic relationship between the ηθ and the fiber pull-out number is proposed. The flexural-tensile strength ratio (β) is about 2.52 for UHPFRC exhibiting deflection hardening behavior. Finally, the post-cracking tensile behavior of UHPFRC was analyzed based on the matrix softening and fiber bridging curve models by the inverse analysis method. The tension softening curves obtained from the tri-linear softening curve analysis exhibited good agreement with the experimental results.

An Inverse Analysis Method Applied to Optimization of Specimen’s Shape for Performing Hot Rapid Crushing Tests from Homogeneous Initial Temperature Field

Specific experimental tests with loadings conditions close to those of industrial fast forming processes as rapid forging, rapid stamping or high speed machining, characterized by large plastic strains, localized deformations and important gradients of strain rates, strain and temperature, requires to analyses material flow behavior at different initial temperatures. One of the more important conditions to obtain intrinsic rheological constitutive equations is to have a quasi-homogenous initial temperature distribution and especially to keep constant the material microstructure during the specimens heating. The rapid induction heating seems to be one of the most reliable processes. This scientific study proposes an inverse analysis technique based on numerical finite element modelling to define on the thermal point of view, optimal specimen shapes for performing hot rapid crushing tests from homogenous initial temperature field.