Hybrid Inverse Method Research Articles

Inverse aerodynamic design for distributed propulsion wing with expected circulation distribution

Distributed Propulsion Wing (DPW) technology offers significant advantages in terms of flight energy savings, but the strong aerodynamic coupling between the propulsive internal flow and aerodynamic external flow brings significant design challenges. As the primary DPW profile design is of great significance, this paper proposes a hybrid method to solve the inverse problem mainly based on the formula relationship between the required aerodynamic loads and the profile shape, which is more direct and instructive compared with traditional parametric iterative methods. The aerodynamic characteristics are described by the circulation distribution in the Fourier series form, then the mean camber line of the profile is solved through the re-derived airfoil theory considering disk’s influence. Further CFD correction methods are also proposed. To validate the effectiveness and feasibility of the proposed hybrid inverse method, several DPW profile design tests are then conducted. Finally, the relationship between 2D and realistic 3D unit shape is also researched. The results show that the proposed inverse design method has great accuracy and convergence speed in the design tests, and shows good robustness against changes of the design parameters. The 2D profile shape and the actual 3D shape of DPW unit can establish an aerodynamic-propulsion equivalent relationship based on the same internal mass fluxes.

Case study: Hybrid inverse method for aircraft noise abatement isolator: Experimental and vibroacoustic assessment

In the aeronautical industry, the vibrations generated by mechanical systems produce unwanted noise perceived by users, which affects their comfort. Engineers encounter several difficulties in carrying out experimental measurements when studying complex systems. To solve this problem, a solution was proposed for the manufacturers' benefit, allowing them to access the various identified measurement points, describe the systems' vibroacoustic behavior, whether coupled or decoupled, and share the work between several teams and reduce the time spent on measurements. This paper deals with the experimental study performed on an aircraft noise abatement isolator. The component-based transfer path analysis hybrid inverse method is developed to allow the work on the subsystems separately between several teams and characterize them on an external test bench outside real functioning conditions. The studied system consists of a mass coupled by a noise abatement isolator fixed in an aluminum plate backed by a concrete cavity. Several parameters are studied such as the number of transfer paths to be considered to see the effect of neglecting certain transfer paths, the effects of coupling versus decoupling of the connected substructures and the number of indicator points chosen and used in the inversion method. The results are compared to the direct method.

Machine Learning in Model-free Mechanical Property Imaging: Novel Integration of Physics With the Constrained Optimization Process

The Autoprogressive Method (AutoP) is a fundamentally different approach to solving the inverse problem in quasi-static ultrasonic elastography (QUSE). By exploiting the nonlinear adaptability of artificial neural networks and physical constraints imposed through finite element analysis, AutoP is able to build patient specific soft-computational material models from a relatively sparse set of force-displacement measurement data. Physics-guided, data-driven models offer a new path to the discovery of mechanical properties most effective for diagnostic imaging. AutoP was originally applied to modeling mechanical properties of materials in geotechnical and civil engineering applications. The method was later adapted to reconstructing maps of linear-elastic material properties for cancer imaging applications. Previous articles describing AutoP focused on high-level concepts to explain the mechanisms driving the training process. In this review, we focus on AutoP as applied to QUSE to present a more thorough explanation of the ways in which the method fundamentally differs from classic model-based and other machine learning approaches. We build intuition for the method through analogy to conventional optimization methods and explore how maps of stresses and strains are extracted from force-displacement measurements in a model-free way. In addition, we discuss a physics-based regularization term unique to AutoP that illuminates the comparison to typical optimization procedures. The insights gained from our hybrid inverse method will hopefully inspire others to explore combinations of rigorous mathematical techniques and conservation principles with the power of machine learning to solve difficult inverse problems.

A hybrid inverse method for hydraulic tomography in fractured and karstic media

We apply a stochastic Newton (SN) approach to solve a high-dimensional hydraulic inverse problem in highly heterogeneous geological media. By recognizing the connection between the cost function of deterministic optimizations and the posterior probability density of stochastic inversions, the Markov chain Monte Carlo (MCMC) sampler of SN is constructed by two parts: a deterministic part, which corresponds to a Newton step of deterministic optimization, and a stochastic part, which is a Gaussian distribution with the inverse of the local Hessian as the covariance matrix. The hybrid inverse method exploits the efficient tools for fast solution of deterministic inversions to improve the efficiency of the MCMC sampler. To address the ill-posedness of the inverse problem, a priori models, generated by a transition-probability geostatistical method, and conditioned to inter-well connection data, are used as regularization constraints.The effectiveness of the stochastic Newton method is first demonstrated by a synthetic test. The transmissivity field of the synthetic model is highly heterogeneous, and includes sharp variations. The inverse approach was then applied to a field hydraulic tomography investigation in a fractured and karstified aquifer to reconstruct its transmissivity field from a collection of real hydraulic head measurements. From the inversions, a series of transmissivity fields that produce good correlations between the inverted and the measured hydraulic heads were obtained. The inverse approach produced slightly different a posteriori transmissivity patterns for different a priori structure models of transmissivity; however, the trend and location of the high-transmissivity channels are consistent among various realizations. In addition, the uncertainty associated with each realization of the inverted transmissivity fields was quantified.

A hybrid parameter identification method based on Bayesian approach and interval analysis for uncertain structures

The hybrid inverse method based on Bayesian approach and interval analysis is presented for parameter identifications under uncertainty, which can deal with both measurement noise and model uncertainty. The measurement noise from an experiment may be described by a set of random variables, obeying a certain probability distribution. The each uncertain parameter of a structure model may be treated as an interval, and only the bounds of the uncertainty are needed. Because of the existence of the interval parameters, a posterior probability density distribution strip enclosed by two bounding distributions is then formed, rather than a single distribution that we usually obtain through the Bayesian identification for a deterministic structure. Using an interval analysis method, a structure response with small uncertainty levels can be approximated as a linear function of the interval parameters. A monotonicity analysis is adopted for marginal posterior distribution transformation, through which effects of the interval parameters on the posterior distribution strip can be well revealed. Based on the monotonicity analysis, finally, the mean estimates and confidence intervals of the unknown parameters are identified from the posterior distribution strip. Three numerical examples are investigated, and fine numerical results are obtained.

The shape, internal structure and gravity of the fast spinner β Pictoris b

Abstract A young extrasolar gas giant planet, β Pictoris b, recently discovered in the β Pictoris system, spins substantially faster than the giant gas planets Jupiter and Saturn. Based on the newly measured parameters – the rotation period of the planet, its mass and radius – together with an assumption that the gas planet β Pictoris b is in hydrostatic equilibrium and made of a fully compressible barotropic gas with a polytropic index of unity, we are able to compute, via a hybrid inverse method, its non-spherical shape, internal density/pressure distribution and gravitational zonal coefficients up to degree 8. Since the mass Mβ for the planet β Pictoris b is highly uncertain, various models with different values of Mβ are studied in this Letter, providing the upper and lower bounds for its shape parameter as well as its gravitational zonal coefficients. If Mβ is assumed to be 6MJ with MJ being Jupiter's mass, we show that the shape of the planet β Pictoris b is approximately described by an oblate spheroid whose eccentricity at the one-bar surface is $\mathcal {E}_{\beta }=0.369\,28$ with the gravitational coefficient (J2)β = +15 375.972 × 10−6. It follows that our results open the possibility of constraining or inferring the mass Mβ of the planet β Pictoris b if its shape can be measured or constrained. By assuming that the planet β Pictoris b will shrink to the size of Jupiter in the process of cooling down and, hence, rotate much faster, we also calculate the future shape and internal structure of the planet β Pictoris b.

Estimation of Optimal Water Flow Rate of a Steel Roller Shutter with Water Film Cooling System

The hybrid inverse method to estimate the optimal water flow rate and surface temperature on the hot surface of the steel roller shutter with water film cooling system subjected to a fire environment is presented in this paper. The results show that the effect of the down-flowing water film flow rate on the present estimates cannot be negligible. The water-film system combined with the steel roller shutter can effectively improve the heat resistance and the temperature of the shutter slat surface can be controlled to around 100 °C. The optimal water flow rate is 110 L/min for a typical 3m x 3m steel roller shutter with water film cooling system.

A hybrid inverse method for the thermal design of radiative heating systems

This work applies the inverse analysis for the thermal design of a three-dimensional radiative enclosure formed with diffuse-gray surfaces. The objective is to determine the powers and locations of the heaters to attain prescribed uniform temperature and radiative heat flux on the design surface. The solution is based on a hybrid solution that couples two different approaches to solve the inverse problem, optimization and regularization. The determination of the locations of the heaters is treated via optimization with the generalized extremal optimization (GEO), whereas the evaluation of the required heat inputs in the heaters, a problem that embodies the Fredholm equation of first kind, is achieved through the truncated singular value decomposition (TSVD) regularization of the ill-conditioned system of equations. The results illustrate that the hybrid solution is a more flexible and accurate approach than the explicit solution based on regularization, and less time consuming than the implicit solution based solely on optimization.

Direct Extraction of Cohesive Fracture Properties from Digital Image Correlation: A Hybrid Inverse Technique

The accuracy of an adopted cohesive zone model (CZM) can affect the simulated fracture response significantly. The CZM has been usually obtained using global experimental response, e.g., load versus either crack opening displacement or load-line displacement. Apparently, deduction of a local material property from a global response does not provide full confidence of the adopted model. The difficulties are: (1) fundamentally, stress cannot be measured directly and the cohesive stress distribution is non-uniform; (2) accurate measurement of the full crack profile (crack opening displacement at every point) is experimentally difficult to obtain. An attractive feature of digital image correlation (DIC) is that it allows relatively accurate measurement of the whole displacement field on a flat surface. It has been utilized to measure the mode I traction-separation relation. A hybrid inverse method based on combined use of DIC and finite element method is used in this study to compute the cohesive properties of a ductile adhesive, Devcon Plastic Welder II, and a quasi-brittle plastic, G-10/FR4 Garolite. Fracture tests were conducted on single edge-notched beam specimens (SENB) under four-point bending. A full-field DIC algorithm was employed to compute the smooth and continuous displacement field, which is then used as input to a finite element model for inverse analysis through an optimization procedure. The unknown CZM is constructed using a flexible B-spline without any “a priori” assumption on the shape. The inversely computed CZMs for both materials yield consistent results. Finally, the computed CZMs are verified through fracture simulation, which shows good experimental agreement.

Identification of elastic-plastic mechanical properties for bimetallic sheets by hybrid-inverse approach

Analysis, evaluation and interpretation of measured signals become important components in engineering research and practice, especially for material characteristic parameters which can not be obtained directly by experimental measurements. The present paper proposes a hybrid-inverse analysis method for the identification of the nonlinear material parameters of any individual component from the mechanical responses of a global composite. The method couples experimental approach, numerical simulation with inverse search method. The experimental approach is used to provide basic data. Then parameter identification and numerical simulation are utilized to identify elasto-plastic material properties by the experimental data obtained and inverse searching algorithm. A numerical example of a stainless steel clad copper sheet is considered to verify and show the applicability of the proposed hybrid-inverse method. In this example, a set of material parameters in an elasto-plastic constitutive model have been identified by using the obtained experimental data.

A hybrid inverse method for evaluating FC-PBGA material response to thermal cycles

This study proposes a hybrid experimental-analytical inverse method that can be used to evaluate thermomechanical cyclic behavior of flip-chip plastic ball grid array modules and the constituent materials. Treating such a package as an adhesively bonded trilayer plate, the structural formulation follows and modifies an existing analytical model. A phase-shifted shadow moire method is employed to obtain the package thermal warpage variation in responding to a temperature cycle. By correlating the modeling predicted and the experimentally measured package warpage, the application of the method leads to the determination of those uncertain material parameters including temperature dependent modulus of elasticity and coefficient of thermal expansion of the die attachment and the substrate materials. These parameters are difficult to determine otherwise due to the complexity involving the effect of package processing condition and extremely thin thickness of the adhesive layer. As the values of all material parameters are ascertained, shear and peel stresses in the module adhesive layer can also be evaluated based on the analytical model.

Determination of competitive isotherms of enantiomers by a hybrid inverse method using overloaded band profiles and the periodic state of the simulated moving-bed process

A procedure for determination of adsorption isotherms in simulated moving-bed (SMB) chromatography is presented. The parameters of a prescribed adsorption isotherm model and rate constants are derived using a hybrid inverse method, which incorporates overloaded band profiles of the racemic mixture and breakthrough data from a single frontal experiment. The latter are included to reduce the uncertainty on the estimated saturation capacity, due to the dilution of the chromatograms with respect to the injected concentrations. The adsorption isotherm model is coupled with an axially dispersed flow model with finite mass-transfer rate to describe the experimental band profiles. The numerical constants of the isotherm model are tuned so that the calculated and measured band profiles match as much as possible. The accuracy of the isotherm model is then checked against the cyclic steady state (CSS) of the target SMB process, which is readily and cheaply obtained experimentally on a single-column set-up. This experiment is as expensive and time consuming as just a few breakthrough experiments. If necessary, the isotherm parameters are adjusted by applying the inverse method to the experimental CSS concentration profile. The method is successfully applied to determine the adsorption isotherms of Trögers base enantiomers on Chiralpak AD/methanol system. The results indicate that the proposed inverse method offers a reliable and quick approach to determine the competitive adsorption isotherms for a specific SMB separation.

On the measurement of the mechanical properties of acoustic porous materials

This paper discusses the measurements and use of the mechanical properties of porous materials. It starts with a review of the classical methods currently used and concentrates in explaining the assumptions, difficulties and limitations of these methods. Next, it concentrates on two methods: a quasi-static approach accounting for the effect of shape factors on the measured properties and a hybrid inverse method similar to the vibrating beam method used for viscoelastic materials. Through full 3-D numerical simulations, both methods are simulated and their main features, assumptions, and limitations are investigated. In particular, the model uses full poro-elastic modeling and boundary element in order to investigate the effect of acoustic radiation damping and viscous damping. Using various types of materials, comparisons between these two methods and experimental data are also discussed.

Structural Dynamics Optimization Based on a Hybrid Inverse Synthesis Method Using a Quadratic Approximation

This paper lies within the framework of the so-called redesign problem of structures subjected to dynamic constraints. A hybrid synthesis algorithm is developed, combining the truncated modal basis of the initial system and the spatial or material co-ordinates of an added component, which is modelled with shell-type finite elements parameterized with respect to a shape factor. Based upon a quadratic inverse formulation, the proposed technique shows several advantages in comparison to other synthesis methods, such as a refined sensitivity strategy, a powerful modal synthesis approach and a simplified optimization phase. Numerical examples are provided illustrating the capabilities of the novel procedure.

Hybrid Inverse Airfoil Design Method for Complex Three-Dimensional Lifting Surfaces

A method is presented for inverse design of airfoils for complex three-dimensional wings in incompressible e ow. The method allows for prescription of inviscid velocity distributions over different cross sections of the wing in a multipoint fashion. A hybrid approach is used to determine the shapes of the wing cross sections that satisfy the design specie cations. The airfoils forming the cross sections of the wing are generated using an inverse code for isolated airfoil design. A three-dimensional panel method is then used to obtain the velocity distributions over the resulting wing. The isolated airfoil velocity distributions are then used as design variables in a multidimensional Newton iteration method to achieve the design specie cations on the wing. The method is particularly useful for complex geometries such as junctures, where three-dimensional and interference effects have to be accounted for in the design process. Akey feature ofthedesign method is a schemeto avoid using thepanel method for sensitivity computations for the Newton iterations. This scheme not only results in signie cant reductions in computation time but also enables the integration of any readily available three-dimensional analysis code in executable form. Examples are shown to demonstrate the usefulness of the method. Nomenclature Cl = airfoil lift coefe cient, chord D1 c = airfoil/section chord F = vector containing the residuals J = Jacobian matrix n = number of design variables V = airfoil/section velocity nondimensionalized by the freestream velocity v = desired value for the velocity difference over a segment ® = angle of attack, deg 1V = velocity difference over a segment normalized by the freestream velocity ±x = vector containing the corrections to the design variables Subscripts i = index of design variable for the Newton iteration r = property associated with the wing root t = property associated with the wing tip w = property associated with the wing 2D = property associated with an airfoil in isolation 3D = property associated with a cross section of a three-dimensional lifting surface

Dual-Point Design of Transonic Airfoils Using the Hybrid Inverse Optimization Method

A new dual-point design procedure has been developed to improve the aerodynamic performance of transonic airfoils at two design points. A target pressure distribution at each design point was optimized by a genetic algorithm. Single-point design was performed to make an airfoil that produced given target pressures and satisfied specified geometric constraints at each design point. Following this, several intermediate airfoils were made by the hybrid inverse optimization method. A redesigned airfoil of dual-point design was found using the weighted average of intermediate airfoil shapes, based on the linear variation assumption. Two examples of dual-point design to improve the performance at an off-design condition are presented.