A Two-step Inverse Method for Quantitative Damage Evaluation of Plate-like Structures Using Vibration Approach

This study presents a novel two-step approach to assess plate-like structural laminar damages,particularly for delamination damage detection of composite structures.Firstly,a 2-D continuous wavelet transform is employed to identify the damage location and sizes from vibration curvature data.An inverse method is subsequently then used to determine the bending stiffness reduction ratio along a specified direction,enabling the quantification of the delamination severity.The method employed in this study is an extension of the one-dimensional inverse method developed in a previous work of the authors.The applicability of the two-step inverse approach is demonstrated in a simulation analysis and by an experimental study on a cantilever composite plate containing a single delamination.The inverse method is shown to have the capacity to reveal the detailed damage information of delamination within a constrained searching space and can be used to determine the effective flexural stiffness of composite plate structures,even in cases of complex delamination damage.

Inverse Method of Centrifugal Pump Impeller Based on Proper Orthogonal Decomposition (POD) Method

To improve the accuracy and reduce the calcu- lation cost for the inverse problem of centrifugal pump impeller, the new inverse method based on proper orthog- onal decomposition （POD） is proposed. The pump blade shape is parameterized by quartic Bezier curve, and the initial snapshots is generated by introducing the perturbation of the blade shape control parameters. The internal flow field and its hydraulic performance is predicted by CFD method. The snapshots vector includes the blade shape parameter and the distribution of blade load. The POD basis for the snap- shots set are deduced by proper orthogonal decomposition. The sample vector set is expressed in terms of the linear combination of the orthogonal basis. The objective blade shape corresponding to the objective distribution of blade load is obtained by least square fit. The Iterative correction algorithm for the centrifugal pump blade inverse method based on POD is proposed. The objective blade load dis- tributions are corrected according to the difference of the CFD result and the POD result. The two dimensional and three dimensional blade calculation cases show that the proposed centrifugal pump blade inverse method based on POD have good convergence and high accuracy, and thecalculation cost is greatly reduced. After two iterations, the deviation of the blade load and the pump hydraulic perfor- mance are limited within 4.0% and 6.0% individually for most of the flow rate range. This paper provides a promising inverse method for centrifugal pump impeller, which will benefit the hydraulic optimization of centrifugal pump.

Application of inverse method to estimation of boundary conditions during investment casting simulation

Inverse method was used in single crystal superalloy DD6 processing simulation during solidification. Numerical modeling coupled with experiments has been used to estimate the interface heat transfer coefficient （IHTC） between the surface of slab casting and inner mold. Calculated temperature dependent values of IHTC were obtained from a numerical solution. The calculated temperatures agreed well with the measurement of cooling profile.

Calculation of circulation in the South China Sea during summer of 2000 by the modified inverse method

On the basis of hydrographic data obtained in August 2000 cruise, the circulation in the South China Sea (SCS) is computed by the modified inverse method in combination with SSH data from TOPEX/ERS-2 analysis. For study of the dynamical mechanism, which causes the pattern of summer circulation in the SCS, the diagnostic model (Yuan et al. 1982. Acta Oceanologica Sinica,4(1):1-11; Yuan and Su. 1992. Numerical Computation of Physical Oceanography.474-542) is used to simulate numerically the summer circulation in the SCS. The following results have been obtained. (1) The central and southwestern SCSs are dominated mainly by anticy-clonic circulation systems. They are mainly as follows. 1) There is strong anticyclonic eddy southeast of Vietnam (W1). Its horizontal scale is about 300 km, and it extends vertically from the surface to the about 1 000 m level. 2) There are a warm eddy W2 southeast of Zhongsha Islands and the anticyclonic circulation system W3 west off the Luzon Island. 3) There is a stronger cyclonic eddy C1 between the anticyclonic eddies W1 and W2.4) A strong northward coastal jet is present near the coast of Vietnam, and separates from the coast of Vietnam at about 12° N to the northeast.(2)The northern SCS is dominated mainly by a cyclonic circulation system. There is a cyclonic circulation system near and north of Section N2. (3) The southeastern SCS is dominated mainly by the cyclonic circulation system. (4) Comparing the results of circulation in the SCS during the summer of 2000 with those during the summer of 1998, it is found that they agree qualitatively, but there is the some difference between them in quantity.This shows that the circulation in the SCS has obviously seasonal feature. (5) The dynamical mechanism which products the basic pattern of summer circulation is because the following two reasons: 1) the joint effect of the baroclinity and relief (JEBAR) is essential dynamical cause; and 2) it is next important dynamical cause that the interaction between the wind stress and bottom topography under the southerly monsoon. (6) Comparing the hydrographic structure and distribution of stream functions with the SSH data from TOPEX/ERS-2 analysis in the SCS during August of 2000, they agree qualitatively.

Investigation on heat-transfer-coefficient between aluminum alloy and organic/inorganic sand mold based on inverse method

A kind of cylinder sand mold was designed to investigate the heat-transfer-coefficients（HTCs） between aluminum alloy and organic/inorganic binder bonded sand mold during the solidification processes. Temperature during the solidification process was recorded and input into the simulation software. The inverse model of MAGMA was used to calculate the HTC based on the actual temperature. Results show that the temperature of the inorganic sand mold increased faster than the organic sand mold; while the temperature of the casting part with the inorganic sand mold decreased faster. The optimal HTCs between Al and the organic/inorganic sand mold are confirmed to be 300 to 700 and 1000 to 1800 W·m-2·K-1, respectively, along with the change of solid-liquid phase line. The simulated temperature curves show the same trend as the measured ones. The maximum deviation between the two temperature curves are 17.32 °C and 18.77 °C for castings by inorganic and organic sand molds.

Model predictive inverse method for recovering boundary conditions of two-dimensional ablation

A model predictive inverse method (MPIM) is presented to estimate the time- and space-dependent heat flux onthe ablated boundary and the ablation velocity of the two-dimensional ablation system. For the method, first of all, therelationship between the heat flux and the temperatures of the measurement points inside the ablation material is establishedby the predictive model based on an influence relationship matrix. Meanwhile, the estimation task is formulated as aninverse heat transfer problem (IHTP) with consideration of ablation, which is described by an objective function of thetemperatures at the measurement point. Then, the rolling optimization is used to solve the IHTP to online estimate theunknown heat flux on the ablated boundary. Furthermore, the movement law of the ablated boundary is reconstructedaccording to the estimation of the boundary heat flux. The effects of the temperature measurement errors, the numberof future time steps, and the arrangement of the measurement points on the estimation results are analyzed in numericalexperiments. On the basis of the numerical results, the effectiveness of the presented method is clarified.

Estimation of vertical diffusion coefficient based on a onedimensional temperature diffusion equation with an inverse method

Diapycnal mixing is important in oceanic circulation. An inverse method in which a semi-explicit scheme is applied to discretize the one-dimensional temperature diffusion equation is established to estimate the vertical temperature diffusion coefficient based on the observed temperature profiles. The sensitivity of the inverse model in the idealized and actual conditions is tested in detail. It can be found that this inverse model has high feasibility under multiple situations ensuring the stability of the inverse model, and can be considered as an efficient way to estimate the temperature diffusion coefficient in the weak current regions of the ocean. Here, the hydrographic profiles from Argo floats are used to estimate the temporal and spatial distribution of the vertical mixing in the north central Pacific based on this inverse method. It is further found that the vertical mixing in the upper ocean displays a distinct seasonal variation with the amplitude decreasing with depth, and the vertical mixing over rough topography is stronger than that over smooth topography It is suggested that the high-resolution profiles from Argo floats and a more reasonable design of the inverse scheme will serve to understand mixing processes.

An inverse method for characterization of dynamic response of 2D structures under stochastic conditions

The reliable estimation of the wavenumber space(k-space)of the plates remains a longterm concern for acoustic modeling and structural dynamic behavior characterization.Most current analyses of wavenumber identification methods are based on the deterministic hypothesis.To this end,an inverse method is proposed for identifying wave propagation characteristics of twodimensional structures under stochastic conditions,such as wavenumber space,dispersion curves,and band gaps.The proposed method is developed based on an algebraic identification scheme in the polar coordinate system framework,thus named Algebraic K-Space Identification(AKSI)technique.Additionally,a model order estimation strategy and a wavenumber filter are proposed to ensure that AKSI is successfully applied.The main benefit of AKSI is that it is a reliable and fast method under four stochastic conditions:(A)High level of signal noise;(B)Small perturbation caused by uncertainties in measurement points’coordinates;(C)Non-periodic sampling;(D)Unknown structural periodicity.To validate the proposed method,we numerically benchmark AKSI and three other inverse methods to extract dispersion curves on three plates under stochastic conditions.One experiment is then performed on an isotropic steel plate.These investigations demonstrate that AKSI is a good in-situ k-space estimator under stochastic conditions.

A three-dimensional inverse method based on moving no-slip boundary for profiled end wall design

How to utilize existing flow control mechanisms to make profiled end wall design more flexible,efficient,and physical is a meaningful challenge.This study presents a three-dimensional inverse method for profiled end wall design to achieve the application of flow control mechanisms.The predetermined pressure distribution on the end wall is reached by modifying the end wall geometry during flow field calculation.A motion velocity model is derived from the normal momentum equation of the moving no-slip boundary to modify the end wall geometry.A Reynolds-Averaged Navier-Stokes(RANS)solver based on the Semi-Implicit Method for Pressure Linked Equations(SIMPLE)algorithm is adopted to simulate the flow field.Based on the mechanism understanding obtained through numerical optimization results,this study adopts the inverse method to redesign an optimized end wall in a compressor cascade.The results indicate that the redesigned end wall exhibits better loss reduction,reducing the overall total pressure loss by 5.5%,whereas the optimized end wall reduces it by 3%.The inverse method allows the imposition of desired influences on the end wall flow without constructing a database,making it highly flexible,efficient,and physical.

Novel thick-target inverse kinematics method for the astrophysical ^(12)C+^(12)C fusion reaction

The ^(12)C+^(12)C fusion is one of the most important reactions in modern nuclear astrophysics.The trend and magnitude of the reaction rate within the Gamow window strongly influence various astrophysical processes.However,direct measurement of this reaction is extremely difficult,which makes it necessary to develop indirect methods.In this study,the ^(23)Na+p reaction system was used to study the compound nucleus ^(24)Mg.We employed a thick-target inverse kinematics method combined with theγ-charged-particle coincidence technique to measure the proton andα exit channels of ^(24)Mg.Technical details of the ^(23)Na+p thick-target inverse kinematics experiment and analysis are presented herein.

Two 3-D multi-cascade co-design inverse methods based on streamline curvature approach and Clebsch formulation for single-stage centrifugal compressors

Two strategies extended the single-cascade methods from a compressible three-dimensional inverse method for radial and mixed flow turbomachines to two three-dimensional multi-cascade co-design methods for single-stage centrifugal compressors.These two three-dimensional methods and a typical quasi-threedimensional streamline curvature through-flow inverse method were employed to design the same subsonic high-speed single-stage centrifugal compressors.The compressor performances were simulated by a commercial Reynolds averaged Navier-Stokes(RANS) equations solver.The studies show that two three-dimensional codesign methods are reasonable and feasible.It was found that : firstly the blade camber angle designed by the three-dimensional methods was larger than that designed by the quasi-three-dimensional method;and secondly with regard to two three-dimensional methods with different boundary conditions,the co-design result differences between the diffusers were small,but those between the deswirlers were relatively large.

INVERSE METHOD TO DETERMINE SOIL HYDRAULIC PROPERTIES FROM TRANSIENT OUTFLOW EXPERIMENTS

Transient outflow experiments coupling with an inverse method are promisingto derive soil hydraulic information. The water retention curves obtained from one-step andmulti-step outflow experiments were compared with those from the pressure cell method. We found thatin one-step experiments the increment of pressure would reduce the non-uniqueness of inversetechnique and that in multi-step experiment the combination of cumulative outflow with pressure headin the objective function would improve the final estimation and also reduce the non-uniqueness ofinverse problem.

The development and application of an inviscid inverse method

A two-dimensional inviscid inverse method is developed,verified and applied inthis paper.The method solves the Euler equation in absolute reference frame by a cell-centeredfinite volume method,and the hybrid Runge-Kutta method ls used for time integration.Different from the direct method,the inverse method imposes a unique"transpiration"boundary condition on the blade surfaces.The inputs of inverse method are pressure loadingand blade tangential thickness distribution along the blade chord.During the time marchingprocess,the blade shape is periodically updated.When the solution is converged,the bladeshape will be stabled.In the paper,the principle of the inverse method is described in detail.Then the developed inverse method is verified against a consistence test:recover an axialcompressor cascade from a different start.Finally,to demonstrate the powerful capability ofthe method,it is used to redesign the cascade,and final results give an improved aerodynamicperformance.

Inverse methodology as applied to reconstruct local textile features from measured pressure field

One can compute the final deformation of a known geometry under specific boundary conditions using the constitutive laws of mechanics that describe their stress strain behavior.In such cases the initial geometry is known,and all operators mapping the deformation are defined on the reference domain.However,there are situations in which the final configuration of a deformation might be known but not the initial.The inverse formulation allows one to determine the initial geometry of a domain,given its final deformation state,the material behavior law and a set of boundary conditions.In the present work we propose a method to reconstruct the mesoscale geometry of a textile based on its mechanical response during compaction.To do so,stress boundary conditions are acquired by means of a pressuresensitive film.By adopting an appropriate material law,the thickness and width information of the yarns are deduced from the pressure field experienced by the compacted textile.Unlike 3 D scanning techniques such as-CT,the proposed method can be applied on any domain size,allowing long-range variability to be captured.To the best of the authors’knowledge,there are no previous works that use a pressure-sensitive film on a large domain to capture the input data for a shape reconstruction.This example application serves as a demonstration of a methodology which could be applied to other classes of materials.

A MEMBRANE ELEMENT MODEL WITH BENDING MODIFICATION FOR ONE STEP INVERSE METHOD

A membrane element model with bending modification based on element moment equilibrium is proposed for the first time by the authors, who apply the element model in one step inverse method and simulate the forming process of a flower-shaped box using the membrane element model with and without this modification. The numerical results are compared with those of the incremental method to verify the validity of the element model developed in this paper.

Modeling of Diffusion Transport through Oral Biofilms with the Inverse Problem Method

Aim The purpose of this study was to develop a mathe-matical model to quantitatively describe the passive trans-port of macromolecules within dental biofilms. Methodology Fluorescently labeled dextrans with different molecular mass （3 kD,10 kD,40 kD,70 kD,2 000 kD） were used as a series of diffusion probes. Streptococcus mutans,Streptococcus sanguinis,Actinomyces naeslundii and Fusobacterium nucleatum were used as inocula for biofilm formation. The diffusion processes of different probes through the in vitro biofilm were recorded with a confocal laser microscope. Results Mathematical function of biofilm penetration was constructed on the basis of the inverse problem method. Based on this function,not only the relationship between average concentration of steady-state and molecule weights can be analyzed,but also that between penetrative time and molecule weights. Conclusion This can be used to predict the effective concentration and the penetrative time of anti-biofilm medicines that can diffuse through oral biofilm. Further-more,an improved model for large molecule is proposed by considering the exchange time at the upper boundary of the dental biofilm.

Inverse Construction Methods of Heterogeneous NURBS Object Based on Additive Manufacturing

According to the requirement of heterogeneous object modeling in additive manufacturing(AM),the Non-Uniform Rational B-Spline(NURBS)method has been applied to the digital representation of heterogeneous object in this paper.By putting forward the NURBS material data structure and establishing heterogeneous NURBS object model,the accurate mathematical unified representation of analytical and free heterogeneous objects have been realized.With the inverse modeling of heterogeneous NURBS objects,the geometry and material distribution can be better designed to meet the actual needs.Radical Basis Function(RBF)method based on global surface reconstruction and the tensor product surface interpolation method are combined to RBF-NURBS inverse construction method.The geometric and/or material information of regular mesh points is obtained by RBF interpolation of scattered data,and the heterogeneous NURBS surface or object model is obtained by tensor product interpolation.The examples have shown that the heterogeneous objects fitting to scattered data points can be generated effectively by the inverse construction methods in this paper and 3D CAD models for additive manufacturing can be provided.

Nonlinear system compound inverse control method

A compound neural network is utilized to identify the dynamic nonlinear system. This network is composed of two parts： one is a linear neural network, and the other is a recurrent neural network. Based on the inverse theory a compound inverse control method is proposed. The controller has also two parts： a linear controller and a nonlinear neural network controller. The stability condition of the closed-loop neural network-based compound inverse control system is demonstrated .based on the Lyapunov theory. Simulation studies have shown that this scheme is simple and has good control accuracy and robustness.

Shape Sensing of Thin Shell Structure Based on Inverse Finite Element Method

Shape sensing as a crucial component of structural health monitoring plays a vital role in real-time actuation and control of smart structures,and monitoring of structural integrity.As a model-based method,the inverse finite element method(iFEM)has been proved to be a valuable shape sensing tool that is suitable for complex structures.In this paper,we propose a novel approach for the shape sensing of thin shell structures with iFEM.Considering the structural form and stress characteristics of thin-walled structure,the error function consists of membrane and bending section strains only which is consistent with the Kirchhoff–Love shell theory.For numerical implementation,a new four-node quadrilateral inverse-shell element,iDKQ4,is developed by utilizing the kinematics of the classical shell theory.This new element includes hierarchical drilling rotation degrees-of-freedom(DOF)which enhance applicability to complex structures.Firstly,the reconstruction performance is examined numerically using a cantilever plate model.Following the validation cases,the applicability of the iDKQ4 element to more complex structures is demonstrated by the analysis of a thin wallpanel.Finally,the deformation of a typical aerospace thin-wall structure(the composite tank)is reconstructed with sparse strain data with the help of iDKQ4 element.

Sensitivity and inverse analysis methods for parameter intervals

This paper proposes a sensitivity analysis method for engineering parameters using interval analyses.This method substantially extends the application of interval analysis method.In this scheme,parameter intervals and decision-making target intervals are determined using the interval analysis method.As an example,an inverse analysis method for uncertainty is presented.The intervals of unknown parameters can be obtained by sampling measured data.Even for limited measured data,robust results can also be obtained with the inverse analysis method,which can be intuitively evaluated by the uncertainty expressed in terms of an interval.For complex nonlinear problems,an iteratively optimized inverse analysis model is proposed.In a given set of loose parameter intervals,all the unknown parameter intervals that satisfy the measured information can be obtained by an iteratively optimized inverse analysis model.The influences of measured precisions and the number of parameters on the results of the inverse analysis are evaluated.Finally,the uniqueness of the interval inverse analysis method is discussed.