Robust Inverse Method Research Articles

Data-driven inverse design of the perforated auxetic phononic crystals for elastic wave manipulation

Abstract In addition to the distinctive features of tunable Poisson’s ratio from positive to negative and low stress concentration, the perforated auxetic metamaterials by peanut-shaped cuts have exhibited excellent phononic crystal (PNC) behavior as well for elastic wave manipulation. Thus they have attracted much attention in vibration suppression for dynamic applications. However, traditional structural designs of the auxetic PNCs considerably depend on designers’ experience or inspiration to fulfill the desired multi-objective bandgap properties through extensive trial and error. Hence, developing a more efficient and robust inverse design method remains challenging to accelerate the creation of auxetic PNCs and improve their performance. To shorten this gap, a new machine learning (ML) framework consisting of double back propagation neural network (BPNN) modules is developed in this work to produce desired configurations of the auxetic PNCs matching the customized bandgap. The first inverse BPNN module is trained to establish a logical mapping from the bandgap properties to the structural parameters, and then the second forward BPNN module is introduced to give the new property prediction by using the design configurations generated from the former. The error between the new predictions and the desired target properties is minimized through a limited number of iterations to produce the final optimal objective configurations. The results indicate that the perforated auxetic metamaterials behave relatively wide complete bandgap and the present ML model is effective in designing them with specific bandgaps within or beyond the given dataset. The study provides a powerful tool for designing and optimizing the perforated auxetic metamaterials in dynamic environment.

Robust treatment planning for small animal radio-neuromodulation using focused kV x-ray beams.

In preclinical radio-neuromodulation research, small animal experiments are pivotal for unraveling radiobiological mechanism, investigating prescription and planning techniques, and assessing treatment effects and toxicities. However, the target size inside a rat brain is typically in the order of sub-millimeters. The small target inside the visual cortex neural region in rat brain with a diameter of around 1mm was focused in this work to observe the physiological change of this region. Delivering uniform doses to the small target while sparing health tissues is challenging. Focused kV x-ray technique based on modern x-ray polycapillary focusing lens is a promising modality for small animal radio-neuromodulation. The current manual planning method could lead to sub-optimal plans, and the positioning uncertainties due to mechanical accuracy limitations, animal immobilization, and robotic arm motion are not considered. This work aims to design a robust inverse planning method to optimize the intensities of focused kV x-ray beams located in beam trajectories to irradiate small mm-sized targets in rat brains for radio-neuromodulation. Focused kV x-ray beams were generated through polycapillary x-ray focusing lenses on achieving small (≤0.3mm) focus perpendicular to the beam. The beam trajectories were manually designed in 3D space in scanning-while-rotating mode. Geant4 Monte Carlo (MC) simulation generated a dose calculation matrix for each focused kV x-ray beam located in beam trajectories. In the proposed robust inverse planning method, an objective function combining a voxel-wise stochastic programming approach and L1 norm regularization was established to overcome the positioning uncertainties and obtain a high-quality plan. The fast iterative shrinkage thresholding algorithm (FISTA) was utilized to solve the objective function and obtain the optimal intensities. Four cases were employed to validate the feasibility and effectiveness of the proposed method. The manual and non-robust inverse planning methods were also implemented for comparison. The proposed robust inverse planning method achieved superior dose homogeneity and higher robustness against positioning uncertainties. On average, the clinical target volume (CTV) homogeneity index (HI) of robust inverse plan improved to 13.3 from 22.9 in non-robust inverse plan and 53.8 in manual plan if positioning uncertainties were also present. The average bandwidth at D90 was reduced by 6.5Gy in the robust inverse plan, compared to 9.6Gy in non-robust inverse plan and 12.5Gy in manual plan. The average bandwidth at D80 was reduced by 3.4Gy in robust inverse plan, compared to 5.5Gy in non-robust inverse plan and 8.5Gy in manual plan. Moreover, the dose delivery time of manual plan was reduced by an average reduction of 54.7% with robust inverse plan and 29.0% with non-robust inverse plan. Compared to manual and non-robust inverse planning methods, the robust inverse planning method improved the dose homogeneity and delivery efficiency and was resistant to the uncertainties, which are crucial for radio-neuromodulation utilizing focused kV x-rays.

Inverse design of compact nonvolatile reconfigurable silicon photonic devices with phase-change materials

Abstract In the development of silicon photonics, the continued downsizing of photonic integrated circuits will further increase the integration density, which augments the functionality of photonic chips. Compared with the traditional design method, inverse design presents a novel approach for achieving compact photonic devices. However, achieving compact, reconfigurable photonic devices with the inverse design that employs the traditional modulation method exemplified by the thermo-optic effect poses a significant challenge due to the weak modulation capability. Low-loss phase change materials (PCMs) exemplified by Sb2Se3 are a promising candidate for solving this problem benefiting from their high refractive index contrast. In this work, we first developed a robust inverse design method to realize reconfigurable silicon and phase-change materials hybrid photonic devices including mode converter and optical switch. The mode converter exhibits a broadband operation of >100 nm. The optical switch shows an extinction ratio of >25 dB and a multilevel switching of 41 (>5 bits) by simply changing the crystallinity of Sb2Se3. Here, we experimentally demonstrated a Sb2Se3/Si hybrid integrated optical switch for the first time, wherein routing can be switched by the phase transition of the whole Sb2Se3. Our work provides an effective solution for the design of photonic devices that is insensitive to fabrication errors, thereby paving the way for high integration density in future photonic chips.

Characterization of wave propagation in complex composite structures (CCS) using a robust inverse analysis method

This paper presents the application of wave propagation characterization for complex composite structures through the Algebraic K-space Identification technique in the Cartesian coordinate system (AKSI-C). The proposed method is a novel development since the developed methodology uses adequate partial differential algebraic operations to provide a robust and low-cost framework for identifying wave propagation parameters of the structures with multidimensional signals for the first time. Additionally, the proposed method has been experimentally applied to identify the complex wave propagation phenomenon of different complex composite structures: (i) honeycomb sandwich composite structure: variability of orthotropic behavior and damping properties with frequency and direction is identified by wavenumber space, 3D dispersion curves, and damping loss factor surface. Then, the contribution of individual layer properties on the changes in dynamic behavior is studied by estimating transition frequency; (ii) locally resonant meta-structure: the effect of the local resonator-induced band gap on the wave attenuation is investigated; (iii) periodic rib-stiffened composite plates: the inner resonance phenomena and their remarkable elastic wave manipulation ability are explored by designing 3D-printed resonators and identifying the mixed-resonance-induced band gap. The proposed method has been compared with other inverse methods to assess its reliability under complex conditions.

Compact Mid‐Infrared Chalcogenide Glass Photonic Devices Based on Robust‐Inverse Design

AbstractMid‐infrared (mid‐IR) on‐chip photonic devices have attracted increasing attention because of their potential applications in chemical and biological sensing and optical communications. In particular, chalcogenide glasses (ChGs) have long been regarded as promising materials for mid‐IR integrated photonics, owing to their broad infrared transparency, high nonlinearity, and excellent processing capabilities. Here, an inverse design approach is introduced to ChG photonic device design with a new robust inverse design method. A high‐performance mid‐IR inverse design polarization beam splitter, waveguide polarizer, mode converter, and wavelength demultiplexer are demonstrated for the first time. They all have a footprint of only several micrometers. The robust inverse design method could improve the robustness of device performance against fabrication variations and would be a general approach for designing and optimizing miniaturized chalcogenide photonic devices.

An Automated Machine Learning Engine with Inverse Analysis for Seismic Design of Dams

This paper proposes a systematic approach for the seismic design of 2D concrete dams. As opposed to the traditional design method which does not optimize the dam cross-section, the proposed design engine offers the optimal one based on the predefined constraints. A large database of about 24,000 simulations is generated based on transient simulation of the dam-foundation-water system. The database includes over 150 various dam shapes, water levels, and material properties, as well as 160 different ground motion records. Automated machine learning (AutoML) is used to generate a surrogate model of dam response as a function of thirty variables. The accuracy of single- and multi-output surrogate models are compared, and the efficiency of the design engine for various settings is discussed. Next, a simple yet robust inverse analysis method is coupled with a multi-output surrogate model to design a hypothetical dam in the United States. Having the seismic hazard scenario, geological survey data, and also the concrete mix, the dam shape is estimated and compared to direct finite element simulation. The results show promising accuracy from the AutoML regression. Furthermore, the design shape from the inverse analysis is in good agreement with the design objectives and also the finite element simulations.

Inverse design of aerodynamic configuration using generative topographic mapping

The inverse design method of aerodynamic configuration is hard to give a reasonable pressure distribution, and strongly rely on experience of designers. The method has been difficult to adapt to the needs of modern aircraft design. Aiming at the shortcoming of the method, an efficient and robust aerodynamic configuration inverse design method is developed, employing knowledge of machine learning methods and optimization methods. The present method establishes the mapping between the high dimensional data obtained from aerodynamic shape and pressure distribution and the variables in the latent space. Then, the global optimization is carried out in the latent space by using the genetic algorithm. The optimum pressure distribution and the corresponding shape can be obtained. Through the the GTM model with high precision, there is not necessary for the flow solver in the whole iterative process, thus the design efficiency can be enhanced. Besides, by taking the advantage of optimization method, the target pressure distribution can be given in a very flexible way, and does not need to be physically meaningful. This feature can reduce reliance on the design experience. Airfoils in low speed and transonic flow and a three-dimensional laminar nacelle design cases are carried out. It is shown that the method robustly and efficiently converges to the target pressure, and has good engineering application potential.

Application of inverse heat conduction calculation method for fast-transient flow boiling heat transfer analysis

ABSTRACT A noise robust inverse heat conduction calculation method is applied for the study of fast-transient heat transfer phenomena. This method is useful when the surface of interest is physically inaccessible. A typical finite difference method was modified with a spatial node marching scheme to perform inverse calculations. The Gaussian low-pass frequency filter was adopted to avoid noise induced oscillations during the calculations. Numerical validation of the method, including sensitivity analysis, was performed using a direct one-dimensional heat conduction problem. The developed method predicts the wall temperature and the heat flux with good accuracy, although the inputs to the calculation contain noises. The developed method is demonstrated experimentally using a fast-transient flow boiling test facility. Applying a pulse power on a metallic tube, the resulting temperature response of the tube outer wall was measured with the power transient information simultaneously. The temperature and the heat flux variations on the tube’s inner wall were calculated inversely from the measured data. Finally, its potential to fast-transient boiling heat transfer research was emphasized by showing the clearly different transient boiling heat transfer characteristics according to the applied power.

Temperature dependent radiative properties of semi-transparent fiberglass-epoxy composite materials from 20 °C to 200 °C

The radiative properties of polymer-reinforced composite materials such as laminates may change according to the temperature. The knowledge of the relationship between radiative properties and temperature becomes crucial when designing structural components subjected to thermal stresses, induced for example by a laser irradiation. This study deals with the analysis of the absorption and scattering properties of fiberglass-epoxy composites from room temperature to 200 °C. From the point of view of thermal radiation, the two-phase system (polymer matrix and fibers reinforcements) is treated as an equivalent homogeneous medium characterized by volumetric radiative properties, namely the absorption coefficient, the scattering coefficient, and the scattering phase function. The light interaction with the rough boundaries of the sample is modeled by boundary scattering coefficients. The aim is to determine these volumetric and boundary scattering properties as function of the temperature. We use a robust inverse method based on a Gauss-Newton algorithm to solve the nonlinear least squares problem. It minimizes the sum of the squared difference between the theoretical and experimental data of bidirectional and normal-hemispherical reflectances and transmittances. Scattering measurements are carried out using a visible and near-infrared spectrometer (400 to 2500 nm spectral range) equipped with a goniometric system and a heated sample holder. Theoretical results are retrieved by employing the Monte Carlo method for solving the Radiative Transfer Equation (RTE). We report that reflectance are insensitive to the temperature rise below 150 °C, and increase above this temperature up to 200 °C. Transmittances increase with temperature, reach a maximum around 105–125 °C near the glass transition temperature of the resin (assessed by a differential scanning calorimetry analysis), and decrease until 200 °C. Upon others, this study reveals that radiative properties are strongly temperature-dependent above 100 °C, first because of the dependence of the resin refractive index to the temperature, but also due to the onset of the polymer chemical degradation. The mismatch between the glass fibers and the polymer refractive indexes is at its lowest near the glass transition temperature of the resin, and explains the peak of transmittances and the trough on the extinction coefficient and the scattering albedo. The onset of the resin chemical degradation above 150 °C increases the absorption coefficient. The asymmetry parameter of the Henyey Greenstein phase function decrease notably from 0.94 to 0.3 above 150 °C, due to the enhancement of backscattered light within the sample.

Improved singular robust inverse solutions of redundant serial manipulators

To address the Jacobian matrix approximation error, which usually exists in the iterative solving process of the classic singular robust inverse method, the correction coefficient α is introduced, and the improved singular robust inverse method is the result. On this basis, the constant improved singular robust method and the intelligent improved singular robust inverse method are proposed. In addition, a new scheme, combining particle swarm optimization and artificial neural network training, is applied to obtain real-time parameters. The stability of the proposed methods is verified according to the Lyapunov stability criteria, and the effectiveness is verified in the application examples of spatial linear and curve trajectories with a seven-axis manipulator. The simulation results show that the improved singular robust inverse method has better optimization performance and stability. In the allowable range, the terminal error is smallest, and there is no lasting oscillation or large amplitude. The least singular value is largest, and the joint angular velocity is smallest, exactly as expected. The derivative of the Lyapunov function is negative definite. Comparing the two extended methods, the constant improved singular robust method performs better in terms of joint angular velocity and least singular value optimization, and the intelligent improved singular robust inverse method can achieve a smaller terminal error. There is little difference between their overall optimization effects. However, the adaptability of the real-time parameters makes the intelligent improved singular robust inverse method the first choice for kinematic control of redundant serial manipulators.

Elasto-plastic damage modeling and characterization of 3D needle-punched Cf/SiCm composite materials

In this paper, we present a material constitutive model for three-dimensional (3D) needle-punched carbon/silicon carbide (Cf/SiCm) with a complex meso-scale structure and characterize the material properties through an experimental-numerical hybrid inverse identification analysis. Variations of the material properties induced by the needle-punching process and complex geometrical features could pose challenges when estimating the properties of constituents. In this case, a robust inverse identification method is suitable for characterization. Six groups of experimental tests were performed to determine the comprehensive material behavior of the needle-punched composite and finite element (FE) models were developed reflecting the mesoscale structural characteristics. For the material model, the Drucker-Prager plasticity theory was employed to consider the effect of hydrostatic pressure on the material properties of Cf/SiCm, and a cohesive zone was combined with the proposed model to address the delamination effect in the interface layers. An analytical homogenization method was utilized to determine the effective properties through bridging from the micro-to the meso-scale in the composite analysis. Based on the experimental results, multiple inverse analyses were carried out to identify the material properties and parameters. Simulations of test group with the determined material parameters were found to be in good agreement with the experimental results, and the effects of these parameters on the overall composite properties are discussed.

Extended singular robust inverse solution of redundant serial manipulators

We propose the use of a damping matrix β to replace the unified damping coefficient λ in the singular robust inverse method, allowing for adjustment of the manipulator’s singularity for different joints separately. In addition, the correction coefficient matrix α is employed to eliminate the Jacobian matrix approximation error, which usually exists in the iterative control solving process; the extended singular robust inverse method is thereby proposed. This article contains analyses of the singularities caused by three methods and how they result in larger values of the manipulator terminal error and joint angular velocity; additionally, the semi-empirical selection principles of β and α are given. The stability of the proposed method is investigated with the Lyapunov stability criteria, and its effectiveness is verified for spatial linear and curve trajectories with 7-axis and 10-axis redundant serial manipulators. The simulation results show that the proposed method exhibits improved optimization performance and stability, and the terminal error is stable and within the allowable range. The least singular value is larger and the joint angular velocity is the lowest, which is the expected outcome. Furthermore, the simulation results for the 10-axis manipulator also indicate the generality of the proposed method.

Upgrade and development of elastic surface inverse design method for axial compressor cascade with sharp-edged blades

The aim of an inverse design method is to calculate the geometry corresponding to a target pressure distribution along the walls. Elastic Surface Algorithm (ESA), as one of the newest residual-corrective inverse design method, was proposed for external flows in 2014. In this method, the airfoil walls were considered as a flexible elastic beam that deforms due to the difference between the target and current pressure distribution at each shape modification step. Nevertheless, the previous version of ESA is subjected to oscillation, instability, and divergence for a cascade of sharp-edged blades due to the steep pressure gradient at the leading edge. This study upgrades the ESA for the shape design of sharp-edged blades with steep gradients of pressure near the stagnation point. The basis of this upgrade was to use the deflection curve of Timoshenko beam which is continuous and differentiable at all the nodes. The upgraded ESA against the original ESA used only the physical characteristics of Timoshenko beam instead of applying a geometric filtration for the removal of fractures in the intermediate profiles at large deformations. To increase the beam deformation at each shape modification, the upgraded ESA removed the constraint of node displacement along the spine direction, which is normal to the chord line, so that the nodes of Timoshenko beam could freely move based on the large deformation equations. In addition, the optimal values of elastic modulus, thickness, and width of the beam were obtained to increase the convergence rate of the ESA. The upgraded ESA was finally verified for a DCA blade cascade in subsonic and transonic flow regimes under different angles of attack and different initially-guessed geometries. The results showed the upgraded ESA to be a robust, flexible, and fast-converging inverse design method for sharp-edged blades with steep pressure gradients.

Silicon Quantum Dot-Based Fluorescent Probe: Synthesis Characterization and Recognition of Thiocyanate in Human Blood.

Allylamine-functionalized silicon quantum dots (ASQDs) of high photostability are synthesized by a robust inverse micelle method to use the material as a fluorescent probe for selective recognition of thiocyanate (a biomarker of a smoker and a nonsmoker). The synthesized ASQDs were characterized by absorption, emission, and Fourier transform infrared spectroscopy. Surface morphology is studied by transmission electron microscopy and dynamic light scattering. The synthesized material exhibits desirable fluorescence behavior with a high quantum yield. A selective and accurate (up to 10–10 M) method of sensing of thiocyanate anion is developed based on fluorescence amplification and quenching of ASQDs. The sensing mechanism is investigated and interpreted with a crystal clear mechanistic approach through the modified Stern–Volmer plot. The developed material and the method is applied to recognize the anion in the human blood sample for identification of the degree of smoking. The material deserves high potentiality in the field of bio-medical science.

Identification of composite uncertain material parameters from experimental modal data

Stochastic analysis of structures using probability methods requires the statistical knowledge of uncertain material parameters. This is often quite easier to identify these statistics indirectly from structure response by solving an inverse stochastic problem. In this paper, a robust and efficient inverse stochastic method based on the non-sampling generalized polynomial chaos method is presented for identifying uncertain elastic parameters from experimental modal data. A data set on natural frequencies is collected from experimental modal analysis for sample orthotropic plates. The Pearson model is used to identify the distribution functions of the measured natural frequencies. This realization is then employed to construct the random orthogonal basis for each vibration mode. The uncertain parameters are represented by polynomial chaos expansions with unknown coefficients and the same random orthogonal basis as the vibration modes. The coefficients are identified via a stochastic inverse problem. The results show good agreement with experimental data.

On Construction of Uncertain Material Parameter using Generalized Polynomial Chaos Expansion from Experimental Data

The knowledge of uncertain parameter distributions is often required to investigate any typical stochastic problem. It may be possible to directly measure uncertain parameters but this is often quite easier to identifying these parameters from system outputs by solving an inverse problem. In this paper, a robust and efficient inverse method based of the non–sampling technique, i.e. generalized polynomial chaos expansion, is presented to identifying uncertain elastic parameters from experimental modal data. We review the general polynomial chaos theory and relating issues for uncertain parameter identification. An application is presented in which the elastic parameters of orthotropic plates are identified from the modal data. The distribution functions of uncertain parameters are derived from experimental eigen–frequencies via an inverse stochastic problem. The Pearson model is used to identify the type of density functions. This realization then is employed to construct random orthogonal basis for each uncertain parameter.

A Robust Inverse Method Based on Least Square Support Vector Regression for Johnson-cook Material Parameters

The purpose of this study is to propose a robust inverse method for estimating Johnson–Cook material parameters. The method is shown through illustrative examples for two different advanced high strength steel (AHSS) materials (DP980 and TRIP780) using set of data from impact experiments with different velocities. Compared with widely mixed numerical experimental methods, the suggested inverse method has the capability to guarantee the robustness of the obtained parameters by considering uncertainties. The inverse problem is converted into multi-objective optimization problems. Furthermore, in order to improve the performance in efficiency and accuracy, metamodeling techniques and global optimization method are integrated. The final results demonstrate that the experimental and simulation curves are well matched based on identified by the suggested robust inverse method.

Modified Singular-Direction Avoidance Steering for Control Moment Gyros

T HE geometric singularity problem is one of the most serious difficulties when using single-gimbal control moment gyros (SGCMGs) as spacecraft attitude control devices. Singularities preclude SGCMGs from generating torque in a certain direction, called the singular direction, and lead to loss of three-axis control of the spacecraft. Operating near these singularities may result in unreasonably high gimbal-rate commands and undesirable system response if one wishes to generate torque in the singular direction. This paper presents a simple modified singular-direction avoidance steering (SDA) method while achieving similar performance with current, more complicated, methods. Various approaches have been explored so far to solve the singularity problem [1–10]. These approaches include null motion [3], preferred gimbal-angle setting [4], constrained steering laws [5], offline planning [6], the singular robust inverse (SRI) method, etc. The most feasible and successfully applied technique is the SRI method, such as singularity robust (SR) steering law [7], generalized SR steering law (GSR) [8], offdiagonal SR steering law (o-DSR) [9], and SDA steering law [10], etc. These techniques lead to a practical solution to avoid or escape from singularities by allowing torque error, and they do not require any extra time-consuming planning process, initial gimbal-angle configuration, or constrained workspace. Though transient CMG torque errors are inevitable while escaping or passing through elliptic singularities, the resulting attitude transient dynamics are often acceptable, because precision pointing is not required during large-angle slew maneuvers [9]. In this Technical Note, the so-called SDA steering law proposed by Ford and Hall [10] is further examined. It is confirmed that the SDA steering law cannot escape the singular points effectively, since the gimbal-rate command along the singular direction is zero at singular points [9]. Based on the principle of singular-value decomposition (SVD), the SDA steering logic is augmented with a geometric principal rotation of singular vectors. This rotation introduces additional torque direction error to prevent zero gimbal-rate output when commanded torque is nonzero. Moreover, the singularity avoidance parameter is modified to allow gimbal movement in the null direction as the singularity approaches. The numerical simulations are adopted to evaluate the effectiveness of the proposed steering law. This modified SDA steering has a clearer geometric meaning, yet it shares a similar ability to escape any singularitieswith the existing methods.

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.

Photothermal radiometric determination of thermal diffusivity depth profiles in a dental resin

The depth of curing due to photopolymerization in a commercial dental resin is studied using photothermal radiometry. The sample consists of a thick layer of resin on which a thin metallic layer is deposited guaranteeing full opacity of the sample. In this case, purely thermal-wave inverse problem techniques without the interference of optical profiles can be used. Thermal profiles are obtained by heating the coating with a modulated laser beam and performing a modulation frequency scan. Before each frequency scan, photopolymerization was induced using a high power blue LED. However due to the fact that dental resins are highly light dispersive materials, the polymerization process depends strongly on the optical absorption coefficient inducing a depth dependent thermal diffusion in the sample. It is shown that using a robust depth profilometric inverse method one can reconstruct the thermal diffusivity profile of the photopolymerized resin.