Inverse Numerical Method Research Articles

Measurement of the Curie temperature based on temperature dependent thermal properties

A temperature gradient evaluation method for swift determination of the Curie temperature TC based on thermal conductivity and thermal diffusivity as functions of temperature is presented. In an imposed one-dimensional temperature gradient, temperature profiles along the axis of a cylindrical sample are recorded in steady-state and transient states using a photon detector. Transient temperature profiles are evaluated by an inverse numerical method, yielding the temperature dependent thermal diffusivity with a distinct change in slope at TC. The slope of the steady-state temperature profile adjusts according to the local thermal conductivity and changes abruptly at TC. The high-resolution determination of the temperature dependent thermal properties allows the identification of TC by two independent evaluations during a single experimental run, solely relying on data of thermal conductivity and thermal diffusivity. The obtained TC excellently agrees with literature values gained by conventional methods.

A control method for hydraulic manipulators in automatic emulsion filling

Abstract For autonomous operation of hydraulic manipulators, environmental perception and autonomous control are two research priorities. In this paper, our research focuses on emulsion explosive self-filling, including self-identification of boreholes and autonomous control of manipulators. In an effort to achieve that purpose, we establish the kinematics model of the 5-DOF hydraulic manipulator which is transformed from a crane. Vision and laser range sensors are employed to measure the positions and orientations of boreholes. Additionally, a novel inverse kinematics numerical method of the 5-DOF manipulator is presented that only needs information of Z-axis direction vector and the position of end effector. Several experiments are performed to verify the feasibility of the control method for unmanned filling of emulsion explosives by the hydraulic manipulator.

A novel inverse numerical modeling method for the estimation of water and salt mass transfer coefficients during ultrasonic assisted-osmotic dehydration of cucumber cubes

The objective of this paper was to study the moisture and salt diffusivity during ultrasonic assisted-osmotic dehydration of cucumbers. Experimental measurements of moisture and salt concentration versus time were carried out and an inverse numerical method was performed by coupling a CFD package (OpenFOAM) with a parameter estimation software (DAKOTA) to determine mass transfer coefficients. A good agreement between experimental and numerical results was observed. Mass transfer coefficients were from 3.5 × 10−9 to 7 × 10−9 m/s for water and from 4.8 × 10−9 m/s to 7.4 × 10−9 m/s for salt at different conditions (diffusion coefficients of around 3.5 × 10−12–11.5 × 10−12 m2/s for water and 5 × 10−12 m/s–12 × 10−12 m2/s for salt). Ultrasound irradiation could increase the mass transfer coefficient. The values obtained by this method were closer to the actual data. The inverse simulation method can be an accurate technique to study the mass transfer phenomena during food processing.

Determination of parameters for Cauchy's problem for systems of ODEs with application to biological modelling

An inverse numerical method that estimate parameters of dynamic mathematical models given some information about unknown trajectories at some time is applied to examples taken from Biology and Ecology. The method consisting of determining an over-determined system of algebraic equations using experimental data. The solution of the over-determined system is then obtained using, for example the least-squares method. To illustrate the effectiveness of the method an analysis of examples and corresponding numerical example are presented.

A hybrid inverse method for small scale parameter estimation of FG nanobeams

As a first attempt, an inverse hybrid numerical method for small scale parameter estimation of functionally graded (FG) nanobeams using measured frequencies is presented. The governing equations are obtained with the Eringen's nonlocal elasticity assumptions and the first-order shear deformation theory (FSDT). The equations are discretized by using the differential quadrature method (DQM). The discretized equations are transferred from temporal domain to frequency domain and frequencies of the nanobeam are obtained. By applying random error to these frequencies, measured frequencies are generated. The measured frequencies are considered as input data and inversely, the small scale parameter of the beam is obtained by minimizing a defined functional. The functional is defined as root mean square error between the measured frequencies and calculated frequencies by the DQM. Then, the conjugate gradient (CG) optimization method is employed to minimize the functional and the small scale parameter is obtained. Efficiency, convergence and accuracy of the presented hybrid method for small scale parameter estimation of the beams for different applied random error, boundary conditions, length-to-thickness ratio and volume fraction coefficients are demonstrated.

Mathematical modeling of the processes of estimating reserves of iron ore raw materials in conditions of uncertainty

Summary. This article proposed to estimate the technological parameters of mining and metallurgical industry (iron ore stocks), given the fuzzy set values in conditions of uncertainty using the balance sheet and industrial methods of calculation of reserves of ore. Due to the fact that the modeling of the processes of extraction of ore is associated with parameters of the equations that contain variables with different nature of uncertainty, it is better to provide all the information on a single formal language of fuzzy set theory. Thus, the proposed model calculation and evaluation of reserves of iron ore by different methods in conditions of uncertainty geological information on the basis of the theory of fuzzy sets. In this case the undefined values are interpreted as intentionally fuzzy, since this approach largely corresponds to the real industrial situation than the interpretation of such quantities in terms of random. Taken into account the fact that the application of the probabilistic approach leads to the identification of uncertainty with randomness, but in practice, the basic nature of uncertainty in the calculation of reserves of iron ore is unclear. Under the proposed approach, each fuzzy parameter is a corresponding membership function, to determine which proposed using a General algorithm, as the result of algebraic operations on arbitrary membership function of the inverse numerical method. Because of the existence of many models describing the same production process in different methods (for example, the balance model or industrial model) and under different assumptions proposed to coordinate such models on the basis of the model of aggregation of heterogeneous information. For matching this kind of information, its generalization and adjustment of the outcome parameters, it is expedient to use the apparatus of fuzzy set theory that allows to obtain quantitative characteristics of imprecisely specified parameters and make the most informed decisions.

Mathematical modeling of the processes of estimating reserves of iron ore raw materials in conditions of uncertainty

Summary. This article proposed to estimate the technological parameters of mining and metallurgical industry (iron ore stocks), given the fuzzy set values in conditions of uncertainty using the balance sheet and industrial methods of calculation of reserves of ore. Due to the fact that the modeling of the processes of extraction of ore is associated with parameters of the equations that contain variables with different nature of uncertainty, it is better to provide all the information on a single formal language of fuzzy set theory. Thus, the proposed model calculation and evaluation of reserves of iron ore by different methods in conditions of uncertainty geological information on the basis of the theory of fuzzy sets. In this case the undefined values are interpreted as intentionally "fuzzy", since this approach largely corresponds to the real industrial situation than the interpretation of such quantities in terms of random. Taken into account the fact that the application of the probabilistic approach leads to the identification of uncertainty with randomness, but in practice, the basic nature of uncertainty in the calculation of reserves of iron ore is unclear. Under the proposed approach, each fuzzy parameter is a corresponding membership function, to determine which proposed using a General algorithm, as the result of algebraic operations on arbitrary membership function of the inverse numerical method. Because of the existence of many models describing the same production process in different methods (for example, the balance model or industrial model) and under different assumptions proposed to coordinate such models on the basis of the model of aggregation of heterogeneous information. For matching this kind of information, its generalization and adjustment of the outcome parameters, it is expedient to use the apparatus of fuzzy set theory that allows to obtain quantitative characteristics of imprecisely specified parameters and make the most informed decisions.

Prediction of damage in small curvature bending processes of high strength steels using continuum damage mechanics model in 3D simulation

Sheet metal bending of modern lightweight materials like high-strength low-alloyed steels (HSLA) is one major challenge in metal forming, because conventional methods of predicting failure in numerical simulation, like the forming limit diagram (FLD), can generally not be applied to bending processes. Furthermore, the damage and failure behaviour of HSLA steels are changing as the fracture mechanisms are mainly depending on the microstructure, which is very fine-grained in HSLA steels composed with different alloying elements compared to established mild steels. Especially for high gradients of strain and stress over the sheet thickness, as they occur in small curvature bending processes, other damage models than the FLD have to be utilised. Within this paper a finite element (FE) 3D model of small curvature bending processes is created. The model includes continuum damage mechanics model in order to predict and study occurring failure by means of ductile coherence loss of the material and crack formation with respect to influencing process parameters. Damage parameters are determined by inverse numerical identification method. The FE-model is strain based validated considering the deformation field at the outer bending edge of the specimen by using an optical strain measurement system. The Lemaitre based damage model is calibrated against the experimental results within metallographic analysis adapting the identified damage parameters to the bending process und thus adjusting the crack occurrence in experiment and simulation. Using this model the bendability of common HSLA steel, used for structural components, is evaluated with respect to occurring damage and failure by numerical analysis.

Experimental measurements within a phase change metallurgical reactor

The measurement of solidification front evolution is essential for the optimization and control of many important metallurgical processes. However, this measurement is tedious, imprecise, and time consuming. More generally, industry needs reliable instruments for the thermal characterization of phase change reactors. This paper enables researchers with means and instruments to study the thermal behavior of processes involving the transformation of phase change materials up to 1000 °C. In this work, an original experimental setup is described to analyze the behavior of two high temperature phase change materials: zinc and molten salts. In particular, it is possible to evaluate the 2D solid solidification front evolution with time. The measurements done with zinc show the presence of two thermal regimes. A solidification rate of 20 mm h(-1) is measured with two different approaches: thermocouples and a mechanical probe. Finally, an infrared camera is also used to make the link between the external thermal behavior and the solidification front evolution inside the reactor. When implemented within an inverse numerical method, the use of this instrument as a new external sensor looks promising.

Characterization of Controls on High-Resolution Stratigraphic Architecture in Wave-Dominated Shoreface-Shelf Parasequences Using Inverse Numerical Modeling

Abstract A new inverse numerical modeling method is used to constrain the environmental parameters (e.g., relative-sea-level, sediment-supply, and wave climate histories) that control stratigraphic architecture in wave-dominated shallow-marine deposits. The method links a “process-response” forward stratigraphic model that simulates wave and storm processes (BARSIM) to a combination of inverse methods formulated in a Bayesian framework that allows full characterization of uncertainties. This method is applied for the first time to a real geologic dataset, collected at outcrop from two shoreface–shelf parasequences in the Aberdeen Member, Blackhawk Formation of the Book Cliffs, east-central Utah, USA. The environmental parameters that controlled the observed stratigraphic architecture are quantified, and key aspects of stratigraphic architecture are successfully predicted from limited data. Stratigraphic architecture at parasequence-stacking and intra-parasequence scales was driven principally by relative sea level (varying by up to about 55 m) and sediment supply (varying by up to 70 m2/yr), whose interplay determines the shoreline trajectory. Within zones of distinctive shoreline trajectory, variations in wave climate (of up to about 3 m in fairweather-wave height) controlled superimposed variations in sandstone and shale content (e.g., the development of upward-coarsening and upward-fining bedsets). The modeling results closely match the observed stratigraphic architecture, but their quality is limited by: (1) the formulation and assumptions of the forward-modeling algorithms, and (2) the observed data distribution and quality, which provide poor age constraint.

A novel model for diffusion based release kinetics using an inverse numerical method

We developed and analyzed an inverse numerical model based on Fick's second law on the dynamics of drug release. In contrast to previous models which required two state descriptions of diffusion for long- and short-term release processes, our model is valid for the entire release process. The proposed model may be used for identifying and reducing experimental errors associated with measurements of diffusion based release kinetics. Knowing the initial and boundary conditions, and assuming Fick's second law to be appropriate, we use the methods of Lagrange multiplier along with least-square algorithms to define a cost function which is discretized using finite difference methods and is optimized so as to minimize errors. Our model can describe diffusion based release kinetics for static and dynamic conditions as accurately as finite element methods, but results are obtained in a fraction of CPU time. Our method can be widely used for drug release procedures and for tissue engineering/repair applications where oxygenation of cells residing within a matrix is important.

An Inverse Method to Obtain Porosity, Fibre Diameter and Density of Fibrous Sound Absorbing Materials

Characterization of sound absorbing materials is essential to predict its acoustic behaviour. The most commonly used models to do so consider the flow resistiv- ity, porosity, and average fibre diameter as parameters to determine the acoustic impedance and sound absorbing coefficient. Besides direct experimental techniques, numerical approaches appear to be an alternative to estimate the material’s pa- rameters. In this work an inverse numerical method to obtain some parameters of a fibrous material is presented. Using measurements of the normal incidence sound absorption coefficient and then using the model proposed by Voronina, subsequent application of basic minimization techniques allows one to obtain the porosity, aver- age fibre diameter and density of a sound absorbing material. The numerical results agree fairly well with the experimental data.

An inverse method to characterize fibrous sound absorbing materials.

Characterization of sound absorbing materials is needed to predict its behavior. The most commonly used models to do so consider the flow resistivity, porosity, and average fiber diameter as parameters to determine the acoustic impedance and sound absorbing coefficient. Besides direct experimental techniques, numerical approaches appear to be an alternative to estimate the material’s parameters. In this work an inverse numerical method to obtain the porosity, the fiber density, and the fiber average diameter of a fibrous material is described. Using normal incidence measurements of the sound absorption coefficient and then using the model proposed by Voronina, subsequent application of basic optimization techniques allows one to characterize a sound absorbing material. The numerical results agree fairly well with the experimental data.

Development of a simple and robust inverse method for determination of thermal diffusivity of solid foods

Thermal properties are essential requirements for mathematical modeling and simulation of various thermal processing operations. Knowledge of accurate values of thermal properties will result in accurate prediction of temperature profiles needed for process selection, design and optimization. The aim of this work was to develop a simple, accurate and robust method for determination of thermal diffusivity of solid foods. An inverse numerical method was developed to estimate thermal diffusivity from transient temperature measurements at any position in a food sample using sequential parameter estimation technique. The developed algorithm was validated using computer generated temperatures in addition to actual experimental temperatures data. The estimated thermal diffusivity from the computer generated data is in excellent agreement with the true value, and the estimated thermal diffusivity from the experimental measurements is in good agreement with literature data. The method presented here was demonstrated to be simple accurate and robust.

An inverse procedure for determination of material constants of a periodic multilayer using Floquet wave homogenization

Abstract An inverse numerical method for periodic composite characterization is reported. The method utilizes the velocity data based on Floquet wave homogenization. The optimization procedure is performed on the basis of the gradient method. An efficient polynomial function is derived from Christoffel equation. The numerical procedure leads to an analytical form of the minimized function which is related to the whole Floquet data. The set of input data is collected from different azimuthal plane orientations inside the homogenization domain. The output results mainly include the effective elastic constants of the multidirectional composite and the reliability factor. The initialization of the elastic stiffness matrix is obtained by averaging the rigidity tensor corresponding to each layer orientation. This procedure is examined for [0/90] and [0/60/−60] composites; some of the obtained elastic constants are significantly dependent on the frequency. The agreement between the adopted Floquet velocities and the calculated ones is good; the reliability factor does not exceed 1%. Slight deviations are pointed out in the vicinity of the homogenization limits.

Controlled interface acceleration in unidirectional solidification

This paper develops a new experimental/numerical technique for controlling phase interface motion, acceleration and temperature gradients during pure material solidification. The required time-dependent boundary conditions are predicted with an inverse numerical method, in order to produce the desired interfacial motion. The experimental study with freezing of water is performed in a rectangular test cell. Three cases of different interface accelerations are considered. It was observed that an accelerating interface required higher interfacial temperature gradients over time, while these gradients become nearly constant when the phase interface moves at a uniform velocity (zero acceleration). It is noted how the interfacial acceleration and temperature gradients affect the structural characteristics of the solidified microstructures.

Comparison between adsorption isotherm determination techniques and overloaded band profiles on four batches of monolithic columns

The adsorption isotherms of 4- tert.-butyl phenol were measured on four different monolithic columns, using three different techniques, classical frontal analysis (FA), the perturbation on a plateau method (PP) and the recently introduced numerical procedure known as the inverse numerical method (IN). This last approach requires only the recording of a few overloaded profiles and has the potential advantage of affording a dramatic decrease of the amounts of compounds, solvent, and time needed to determine accurate estimates of the coefficients of the isotherm. The reproducibility of the adsorption data measured on the four columns is discussed with reference to the specific techniques used for obtaining these data and to the most suitable equation used for modeling them. The data obtained for the different columns were highly consistent. The inverse numerical approach was confirmed to provide a powerful, accurate, and economic method for measuring single component adsorption data.

Mantle Source Characteristics of Alkali Basalts and Basanites in an Extensional Intracontinental Plate Setting, Western Anatolia, Turkey: Implications for Multi-stage Melting

The alkaline volcanic province of Western Anatolia is characterized by intra-continental plate alkali olivine basalts and basanites extruded along localized extensional basins during Late Miocene (<11 Ma) to Quaternary (>0.13 Ma) time. The rocks are characterized by low 87Sr/86Sr (0.70311-0.70325) and high 143Nd/144Nd (0.51293-0.51298) ratios; they have OIB-like trace-element patterns characterized by enrichment in LILE, HFSE, and L-MREE, and a slight depletion in HREE relative to N-MORB. Trace-element modeling indicates that the mafic magmas formed by variable degrees (˜2% -10%) of partial melting of an isotopically homogenous garnet-bearing mantle source. The degree of melting decreased progressively from early-formed alkali olivine basalts to later basanites. Major- and trace-element systematics reveal two distinct depth ranges of melt segregation from the source mantle: (1) garnet and spinel + garnet stability zone for the Late Miocene rocks; and (2) spinel and spinel + garnet stability zone for the Quaternary rocks. Source concentrations, calculated using an inverse numerical method, show that the mantle from which the alkaline magmas were generated was enriched in all incompatible elements (e.g., LILE, HFSE, and LMREE) relative to depleted MORB mantle (DMM) and primitive mantle (PM) compositions. The isotopically depleted nature of the alkaline rocks relative to bulk silicate earth (BSE) further indicates that this enrichment is a recent event related to small-degree, multi-stage melting processes that involve local metasomatism of the mantle.

An efficient algorithm to estimate material parameters of biphasic mixtures

The paper describes an inverse numerical experimental method to determine material parameters for biological tissues. Measured field quantities are compared to calculated field quantities. The field equations are solved with the finite element method, using an assumed constitutive model and estimations of the material parameters. The parameter estimates are improved iteratively by means of an algorithm that calls the finite element program as a subroutine. The paper is focused on biological materials that can be described as biphasic mixtures. An efficient recursive algorithm is presented. All parameters are determined on the basis of displacements and pressures measured at different positions within the material at subsequent points in time. A pseudo-analytical approach is used to determine the sensitivity matrix. The algorithm has been tested in a simulation of an experiment on a mixture of a solid and a fluid. It appears that for this example an iterative loop to determine the material parameters requires no more than 30 per cent more CPU-time than one straightforward analysis of the problem. Copyright © 1999 John Wiley & Sons, Ltd.

Partial melting below Tubuai (Austral Islands, French Polynesia)

Process identification diagrams based on trace element data show that mafic lavas from Tubuai, including alkali basalts, basanites, analcitites and nephelinites, result from different degrees of partial melting of an isotopically homogeneous mantle source. Our fractionation-corrected data are consistent with a batch melting model or a dynamic melting model involving a threshold value for melt separation close to 1% and degrees of melting ranging from 5–8% (alkali basalts) to 1.5–3% (nephelinites). The relative source concentration pattern, calculated using an inverse numerical method, shows an enrichment in highly incompatible elements. We propose that the Tubuai lava suite was derived from a two-stage partial melting process. Melting first affected the plume material located within the transition zone between garnet and spinel domains, producing alkali basalts and basanites. Then, the melting zone migrated upwards to the base of the overlying spinel-bearing lithospheric mantle, producing highly silica-undersaturated lavas. The lower lithosphere had previously been enriched by intrusion of pyroxenite veins representing plume-derived melts which percolated away from the main magma conduits.