Proposed Inverse Procedure Research Articles

Inverse identification of cell-wall material properties of closed-cell aluminum foams based upon Vickers nano-indentation tests

This study aims to develop an inverse approach to identifying the cell-wall material properties of closed-cell aluminum (Al) foams, which is based upon indentation tests, numerical simulation and optimization technique. Vickers nano-indentation tests are conducted on the cell-wall of foams, and the residual surface deformation is measured by a high definition confocal microscopy. To enhance identification efficiency, a combined 2D with 3D micromechanics modeling strategy is proposed here, in which the load-depth curve and residual imprint (pile-up) of the indentation tests are considered. In this study, the cell-wall material properties such as the yield strength and strain-hardening exponent are identified using this proposed inverse approach, while the Young's modulus is obtained directly for the unloading part of the indentation load-depth curves. The identification results indicate that the proposed inverse procedure can provide a well-posed solution to the cell-wall material properties by introducing the pile-up information. Microscopic computed tomography (μCT) technique is also utilized to reconstruct accurate 3D image-based representative volume element (RVE) model of foam structure, through which the numerical simulation is conducted for uniaxial compression. The identified cell-wall material parameters are validated by comparing the numerical simulation with the experimental data in terms of the deformation/failure modes and quantitative results. It is noted that the cell-wall of aluminum foams that are commonly made of melt foaming processes exhibits a quite different stress-strain relation when compared with the raw material of cell-wall. This study is expected to provide an effective approach for identifying the material properties that may be not easily determined through conventional testing methods.

Crustal and upper mantle structures of Makran subduction zone, SE Iran by combined surface wave velocity analysis and gravity modeling

The inversion of Rayleigh wave group velocity dispersion curves is challenging, because it is non-linear and multimodal. In this study, we develop and test a new Rayleigh wave dispersion curve inversion scheme using the Shuffled Complex Evolution (SCE) algorithm. Incorporating this optimization algorithm into the inverse procedure not only can effectively locate the promising areas in the solution space for a global minimum but also avoids its wandering near the global minimum in the final stage of search. In addition, our approach differs from others in the model parameterization: Instead of subdividing the model into a large number of thin layers, we invert for thickness, velocities and densities and their vertical gradients of four layers, sediments, upper-crust, lower-crust and upper mantle. The proposed inverse procedure is applied to non-linear inversion of fundamental mode Rayleigh wave group dispersion curves for shear and compressional wave velocities. At first, to determine the efficiency and stability of the SCE method, two noise-free and two noisy synthetic data sets are inverted. Then real data for Makran region in SE Iran are inverted to examine the usage and robustness of the proposed approach on real surface wave data. In a second step, we applied 3D Gravity Modeling based on surface wave analysis results to obtain the density structure and thickness of each layer. The reason for using both types of data sets, is that gravity anomaly has a bad vertical resolution and surface wave group velocities are good for placing layer limits at depth, but they are not very sensitive to densities. Therefore, using gravity data increases the overall resolution of density distribution. In a final step, we used again the SCE method to invert the fundamental mode Rayleigh wave group dispersion curves based on the gravity results. Gravity results like thicknesses and sediment densities have been used to constrain the limit of search space in the SCE method. Results show a high shear and compressional velocity under the Gulf of Oman which reduce to the North of the Makran region. The Moho depth of the Oman Gulf is about 18–28 km and it increases to 46–48 km under the Taftan-Bazman volcanic-arc. The density image shows an average crustal density with maximum values under the Gulf of Oman decreasing northward to the Makran.

Evaluation of Lightning Current and Return Stroke Velocity Using Measured Far Electric Field Above a Horizontally Stratified Ground

This paper proposed an inverse procedure for evaluating the channel-base current and return stroke velocity using measured far electric fields over a two-layer horizontally stratified ground, where the lightning current along lightning channel adopt the modified transmission line model with linear current decaying with height (MTLL) model. Moreover, the proposed method has been validated using two numbers of measured electric field obtained from triggered lightning, where the velocity is considered to be variable along lightning channel and the average value along lightning channel, respectively. The results show that the evaluated channel-base current is in good agreement with the corresponding measured channel-base current, and the average evaluated return stroke velocity is among 1/3 to 2/3 of the speed of light in free space. Also, we compare the evaluated results using transmission line (TL) model or adopting single-layer soil model. The results both show that the method, which combines the MTLL model and the two-layer stratification soil model, is more suitable to evaluate the channel-base current and return stroke velocity in this paper. The proposed inverse procedure can evaluate the lightning current as well as return stroke velocity, this is useful for studies on lightning characteristics and lightning protection.

An effective inverse procedure for identifying viscoplastic material properties of polymer Nafion

An effective inverse procedure is suggested to identify the viscoplastic material properties of polymer Nafion, by minimizing differences in the force–displacement responses of uniaxial tension test between experimental and simulation results. In this procedure, a two-layer viscoplastic constitutive model is adopted to describe the viscoplastic behavior of Nafion. A response surface method is used as a forward solver to calculate the force–displacement response for given material property varying continuously in a certain range. An intergeneration projection genetic algorithm (IP-GA) is then employed as the inverse operator on the response surface to determine the unknown key constants. The selected viscoplastic constants, A, n and f, are varied iteratively using the proposed inverse procedure until the stopping criterion is satisfied. The identification results for two cases demonstrate the effectiveness of the present inverse procedure, as well as its robustness to the noises effects. It is found that this procedure is a potentially useful tool to effectively help determine the viscoplastic material properties of polymer Nafion.

Differential evolution algorithm for nonlinear inversion of high-frequency Rayleigh wave dispersion curves

Abstract In recent years, Rayleigh waves are gaining popularity to obtain near-surface shear (S)-wave velocity profiles. However, inversion of Rayleigh wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this study, we proposed and tested a new Rayleigh wave dispersion curve inversion scheme based on differential evolution (DE) algorithm. DE is a novel stochastic search approach that possesses several attractive advantages: (1) Capable of handling non-differentiable, non-linear and multimodal objective functions because of its stochastic search strategy; (2) Parallelizability to cope with computation intensive objective functions without being time consuming by using a vector population where the stochastic perturbation of the population vectors can be done independently; (3) Ease of use, i.e. few control variables to steer the minimization/maximization by DE's self-organizing scheme; and (4) Good convergence properties. The proposed inverse procedure was applied to nonlinear inversion of fundamental-mode Rayleigh wave dispersion curves for near-surface S-wave velocity profiles. To evaluate calculation efficiency and stability of DE, we firstly inverted four noise-free and four noisy synthetic data sets. Secondly, we investigated effects of the number of layers on DE algorithm and made an uncertainty appraisal analysis by DE algorithm. Thirdly, we made a comparative analysis with genetic algorithms (GA) by a synthetic data set to further investigate the performance of the proposed inverse procedure. Finally, we inverted a real-world example from a waste disposal site in NE Italy to examine the applicability of DE on Rayleigh wave dispersion curves. Furthermore, we compared the performance of the proposed approach to that of GA to further evaluate scores of the inverse procedure described here. Results from both synthetic and actual field data demonstrate that differential evolution algorithm applied to nonlinear inversion of high-frequency surface wave data should be considered good not only in terms of the accuracy but also in terms of the convergence speed.

Application of particle swarm optimization to interpret Rayleigh wave dispersion curves

Abstract Rayleigh waves have been used increasingly as an appealing tool to obtain near-surface shear (S)-wave velocity profiles. However, inversion of Rayleigh wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this study, we proposed and tested a new Rayleigh wave dispersion curve inversion scheme based on particle swarm optimization (PSO). PSO is a global optimization strategy that simulates the social behavior observed in a flock (swarm) of birds searching for food. A simple search strategy in PSO guides the algorithm toward the best solution through constant updating of the cognitive knowledge and social behavior of the particles in the swarm. To evaluate calculation efficiency and stability of PSO to inversion of surface wave data, we first inverted three noise-free and three noise-corrupted synthetic data sets. Then, we made a comparative analysis with genetic algorithms (GA) and a Monte Carlo (MC) sampler and reconstructed a histogram of model parameters sampled on a low-misfit region less than 15% relative error to further investigate the performance of the proposed inverse procedure. Finally, we inverted a real-world example from a waste disposal site in NE Italy to examine the applicability of PSO on Rayleigh wave dispersion curves. Results from both synthetic and field data demonstrate that particle swarm optimization can be used for quantitative interpretation of Rayleigh wave dispersion curves. PSO seems superior to GA and MC in terms of both reliability and computational efforts. The great advantages of PSO are fast in locating the low misfit region and easy to implement. Also there are only three parameters to tune (inertia weight or constriction factor, local and global acceleration constants). Theoretical results exist to explain how to tune these parameters.

Identification of Interaction Pressure Between Structure and Explosive with Inverse Approach

An inverse approach for the identification of the time-dependent localized interaction pressure between a structure and an explosive has been proposed and developed. In this approach, surface measurements of structural response (displacement and velocity) are integrated with numerical simulations to identify the spatial and time-dependent interaction pressure (i.e. the normal traction) on a structure surface. For verification and validation purposes, numerical simulations are used to (a) generate the time-dependent displacement and velocity fields on the free surface of the specimen at specified time intervals, (b) form a blast wave and compute the resulting interaction traction field between the structure and blast wave on the interaction interface for comparison to inverse predictions. In particular, validation of the proposed approach was performed using numerical simulation results for an underwater explosion, with excellent agreement between the identified interaction traction and the simulation generated interaction traction up to and including the maximum traction condition. To demonstrate the potential of the method, the proposed inverse procedure was employed to estimate the interaction traction field on a thin aluminum specimen subjected to transient pressure loading through detonation of explosive buried in sand.

Insights into performance of pattern search algorithms for high-frequency surface wave analysis

Inversion of high-frequency surface wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this paper, we implemented an investigation to fully exploit and utilize the potentiality of pattern search algorithms and to further enhance their performance for surface wave analysis. We first investigate effects of different inversion strategies, initial mesh size and final mesh size, expansion factor, and contraction factor, as well as inclusion of noise in surface wave data on the performance of the approaches, by three synthetic earth models. Then, a comparative analysis with genetic algorithms is made to further highlight the advantages of the proposed inverse procedure. Finally, the insights issued from this analysis are verified by a real-world example from Henan, China. Results from both synthetic and field data demonstrate: (a) generalized pattern search (GPS) algorithm with the maximal positive basis set 2 N vectors works better than GPS algorithm with the minimal positive basis set N+1 vectors; (b) if one gets a suitable initial mesh size by taking some experimentation, then setting expansion factor Λ=1 (i.e., not allow expansions) and contraction factor θ=1/2 can greatly enhance the performance of pattern search algorithms. This is particularly true as the algorithm converges and final mesh size should go to zero; and (c) pattern search algorithms possess stronger immunity with respect to noise and should be considered good not only in terms of accuracy but also in terms of computation effort, especially when compared to the application of genetic algorithms to Rayleigh wave inversion.

Inverse procedure for calibrating parameters that control land subsidence caused by subsurface fluid withdrawal: 1. Methods

Land subsidence prediction depends on a selected theoretical model and the calibration of its parameter values. An inverse model is developed that calibrates five parameters of a compacting confined aquifer system: K′v (vertical hydraulic conductivity of the aquitards), S′skv (aquitard nonrecoverable skeletal specific storage), S′ske (aquitard recoverable skeletal specific storage), Ssk (skeletal specific storage of the aquifer), and p′max 0 (initial preconsolidation stress within the aquitards). This inverse model combines a procedure for finding an initial set of parameter values and an inverse adjustment procedure. Initial values are estimated by using a new graphic method for the analysis of field data. The follow‐up inverse procedure is a computer algorithm that combines the Newton‐Raphson method with Helm's one‐dimensional finite difference subsidence model (COMPAC). COMPAC offers two options: a constant‐parameter simulation and a stress‐dependent parameter simulation. The classical least squares criterion is employed as the objective function of this inverse procedure. Three characteristics of the objective function are considered. This inverse model is applied to calculations of an idealized compacting confined aquifer system using Helm's model. This investigation shows that the final values for the five parameters lead to simulated compaction error of less than 1%. This contrasts to the initial error of more than 60%. These results indicate that the proposed inverse procedure (model) can be applied to actual field data.

An Inverse Method to Estimate the Source‐Sink Term in the Nitrate Transport Equation

The source‐sink term (SST) in the convection‐dispersion equation (CDE) to simulate nitrate (NO3−–N) transport integrates several NO3−–N transformation processes in soils. The term is affected by considerably complicated micro‐environmental conditions and is difficult to be measured directly. In this study, the average SST distribution was estimated by solving the CDE with an unknown SST iteratively using an inverse method. The required input information for the SST estimation was easily obtained, including soil hydraulic properties, two successively measured NO3−–N concentration distributions, and the boundary and initial conditions. Numerical experiments were designed to examine the accuracy and stability of the inverse approach, considering spatial intervals of measurement data along the soil profile, time intervals between the successive measurements of soil NO3−–N concentration, boundary conditions, layered soils, and measurement errors of NO3−–N concentration. Comparisons with theoretical results showed that the inverse method was reliable for estimating the SST in the CDE. Data from a column experiment with winter wheat (Triticum aestivum L. ) growth were used to demonstrate applications of the inverse method. The root‐nitrate‐uptake (RNU) rate distributions were estimated according to the proposed inverse procedure and the soil NO3−–N transport with RNU in the columns was simulated. The simulated soil NO3−–N concentration distributions were comparable with the measured values. The relative errors between the simulated and measured values of the total N mass extracted by winter wheat were <10%.

An FE‐based sequential inverse algorithm for heat flux calculation during impingement water cooling

PurposeTo develop an effective and reliable procedure for the calculation of heat fluxes from the measured temperatures in experimental tests of impingement water cooling.Design/methodology/approachAn inverse heat transfer analysis procedure is developed and implemented into a 2D finite element program. In this method, the least‐squares technique, sequential function specification and regularization are used. Simplifications in the sensitivity matrix calculation and iterative procedures are introduced. The triangular and impulse‐like profiles of heat fluxes simulating practical conditions of impingement water cooling are used to investigate the accuracy and stability of the proposed inverse procedure. The developed program is then used to determine the heat flux during impingement water cooling.FindingsA hybrid procedure is developed in which inverse calculations are conducted with a computation window. This procedure may be used as a whole time domain method or become a periodically sequential or real sequential method by adjusting the sequential steps.Originality/valueParametric study and application show that the developed method is effective and reliable and that inverse analysis may obtain the heat flux with an acceptable level of accuracy.

Soil water content inverse profiling from single TDR waveforms

An inverse procedure for the estimation of soil water content profiles along TDR probes is presented. A TDR metallic probe is considered as a transmission line, for which relevant partial derivatives equations apply. The direct problem consists in the integration of transmission line equations, providing V( x, t) along the line. To this aim, the unit length parameters of the transmission line must be known. In particular, unit length capacitance C( x) and transverse conductance G( x) depend on water content distribution along the probe θ( x) through relative permittivity ε r( x) and bulk soil electrical conductivity σ( x), respectively. The inverse procedure consists in finding the water content distribution, and the relevant unit length parameters, giving rise to the best fit between the numerically simulated voltage V ( x ¯ , t ) at the beginning of the line and the experimental voltage trace V exp ( x ¯ , t ) measured by a cable tester. In order to reduce the ill-posedness of the inverse problem, unknown water content profiles are expressed by means of a four parameters functional form. The search for the best fitting parameters vector is carried out with a genetic algorithm. The proposed inverse procedure is successfully applied to the determination of vertical water content profiles along a soil sample in the laboratory by means of a single three rods metallic TDR probe. Water content profiles estimated either in steady flow conditions, or during controlled infiltration-evaporation transients are compared with independent water content measurements carried out by means of horizontal TDR probes at various depths, showing in all cases good agreement.

A global system identification approach for the accurate parametric modeling of ultrasonic reflection and transmission experiments

This paper presents a global system identification approach for the parametric modeling of both reflection and transmission experiments performed on a linear homogeneous visco-elastic material at normal incidence. It is shown that this global approach leads to improved estimates of the parameters occuring in the analytical model for the reflection and transmission coefficients of a visco-elastic plate immersed in water. The plane wave propagation model takes into account the absorption and dispersion in the material as well as an analytic diffraction correction for the beam spread. The proposed inverse procedure Is based on a maximum likelihood estimator.

A proposed quasi-Newton method for parameter identification in a flow and transport system

A quasi-Newton algorithm allied with the adjoint state equation method is proposed to solve the inverse problem of parameter estimation. The proposed method utilizes the information from both groundwater flow and solute transport in parameter estimation. It is capable of identifying parameters which control both flow and transport simultaneously. It also avoids the calculation of sensitivity coefficients, which normally requires much computational effort. The BFGS (Broyden, 2 Fletcher, 10 Goldfarb, 13 and Shanno 21) formula is used to approximate the Hessian matrix required in the optimization procedure. The proposed inverse procedure is applied to a two-dimensional flow-transport problem. Two dimensionless numbers, the Peclet number and the Damkoehler number, are used to characterize the behavior of the transport processes. Numerical experiments which were conducted demonstrate the usefulness of the proposed methodology and show good results in practical application.