Initial Guess Research Articles

Rapid generation of time-optimal rendezvous trajectory based on convex optimisation and DNN

Abstract The minimum flight time of spacecraft rendezvous is one of the fundamental indexes for mission design. This paper proposes a rapid trajectory planning method based on convex optimisation and deep neural network (DNN). The time-optimal trajectory planning problem is reconstructed into a double-layer optimisation framework, with the inner being a convex optimisation problem and the outer being a root-finding problem. The thrust properties corresponding to time-optimal control are analysed theoretically. A DNN-based rapid planning method (DNN-RPM) is put forward to improve computational efficiency, in which the trained DNN provides a high-quality initial guess for Newton’s method. The DNN-RPM is extended to search for the optimal entering angle of natural-motion circumnavigation orbit injection problem and the minimum reconfiguration time of spacecraft swarm. Numerical simulations show that the proposed method can improve the computational efficiency while ensuring the calculation accuracy.

Inverse estimation of heat flux and temperature field for a nonlinear heat transfer system using step-renewed two-stage Kalman filter

Inverse estimation of the thermal input and states is a useful tool for the monitoring of a thermal system. Nonlinear heat transfer is a quite common issue in this kind of problem. As the thermal properties are temperature-dependent, it is difficult to inversely estimate the input and temperature field. To deal with this problem, a step-renewed scheme is adopted into the weighted optimal two-stage Kalman filter (WOTSKF), forming step-renewed WOTSKF (SR-WOTSKF). This strategy is a marching method, without solving the Jacobian matrix in extended Kalman filter. The feasibility of dealing with the nonlinear inverse heat transfer problem is implemented by comparing WOTSKF and SR-WOTSKF. Then, the weighting factor, initial guess of the input heat flux and measurement noise are changed to investigate their effects on the simultaneous estimation results of heat flux and temperature field. It is found that when the weighting factor is 0.95, the relative error of the estimated heat flux using SR-WOTSKF is approximately 2.73% which is much lower than that using WOTSKF. Results using SR-WOTSKF demonstrate that the estimation results are independent of the initial guess and the estimated heat flux can track the exact one in a short period. An incorrect initial guess causes the initial estimation error of the temperature and heat flux and it makes no sense to following period. When the standard deviations of the measurement noise are adopted as 0.01, 0.10, 0.50 and 1.00, the mean relative error of the heat flux is 2.73%, 4.79%, 7.71% and 9.43%, demonstrating the strong robustness of SR-WOTSKF to resist the measurement noise.

In situ adaptive tabulation of vapor-liquid equilibrium solutions for multi-component high-pressure transcritical flows with phase change

Vapor-liquid equilibrium (VLE) is a family of first-principled thermodynamic models for transcritical multiphase flows, which can accurately capture the phase transitions at high-pressure conditions that are difficult to deal with using other models. However, VLE-based computational fluid dynamics (CFD) simulation is computationally very expensive for multi-component systems, which severely limits its applications to real-world systems. In this work, we developed a new ISAT-VLE method based on the in situ adaptive tabulation (ISAT) method to improve the computational efficiency of VLE-based CFD simulation with reduced memory usage. We developed several ISAT-VLE solvers for both fully conservative (FC) and double flux (DF) schemes. New methods are proposed to delete redundant records in the ISAT-VLE table and the ISAT-VLE method performance is further improved. To improve the convergence of the VLE solvers, a modified initial guess for equilibrium constant is also introduced. Simulations of high-pressure transcritical two-phase temporal mixing layers and shock-droplet interaction were conducted using the ISAT-VLE CFD solvers. The simulation results show that the new method obtains a speed-up factor approximately from 10 to 60 and the ISAT errors can be controlled within 1%. The shock-droplet interaction results show that the DF scheme can achieve a higher speed-up factor than the FC scheme. The two sets of simulations exhibit the phase separation at high-pressure conditions. It was found that even at supercritical pressures with respect to each component, the droplet surface could still be in a subcritical two-phase state, because the mixture critical pressure is often significantly higher than each component and hence triggers phase separation. In addition, a shock wave could partially or completely convert the droplet surface from a subcritical two-phase state to a single-phase state by raising temperature and pressure.

Single-shot Fourier ptychographic microscopy with isotropic lateral resolution via polarization-multiplexed LED illumination.

Fourier ptychographic microscopy (FPM) has emerged as a new wide-field and high-resolution computational imaging technique in recent years. To ensure data redundancy for a stable convergence solution, conventional FPM requires dozens or hundreds of raw images, increasing the time cost for both data collection and computation. Here, we propose a single-shot Fourier ptychographic microscopy with isotropic lateral resolution via polarization-multiplexed LED illumination, termed SIFPM. Three LED elements covered with 0°/45°/135° polarization films, respectively, are used to provide numerical aperture-matched illumination for the sample simultaneously. Meanwhile, a polarization camera is utilized to record the light field distribution transmitted through the sample. Based on weak object transfer functions, we first obtain the amplitude and phase estimations of the sample by deconvolution, and then we use them as the initial guesses of the FPM algorithm to refine the accuracy of reconstruction. We validate the complex sample imaging performance of the proposed method on quantitative phase target, unstained and stained bio-samples. These results show that SIFPM can realize quantitative imaging for general samples with the resolution of the incoherent diffraction limit, permitting high-speed quantitative characterization for cells and tissues.

Topology optimization of a pseudo 3D microchannel heat sink: influence of the initial guess

Nowadays, the optimization of microchannel heat sinks involves using algorithms, e.g., topology optimization (TO), to find the optimal layout of fluid channels to enhance certain objectives, e.g., heat transfer, pressure drop. The outcome is an unintuitive material distribution in the design space, subject to constraints such as manufacturability, fluid flow requirements, and thermal performance. This approach has been shown to provide significant benefits compared to traditional design methods, leading to increased cooling performance. However, depending on the application, defining an initial (i.e., starting) guess for the optimization problem is not trivial. Initial guess for TO, i.e., starting design for the optimization process, can play a crucial role in determining the final optimized design. Its choice may affect the convergence rate, the performance of the final solution, and the computational effort, as it can be set in a variety of ways, e.g., a random distribution, a preconceived design, or a combination of these two. In this study, we propose a heuristic approach for incorporating a genetic algorithm (GA) as outer algorithm into the TO routine in order to find the initial guess that ensures the lowest thermal resistance while limiting the pumping power. The aim is to correlate initial designs with final objectives and to define new useful insights on microchannel optimization, since TO has proved to be a promising area of research for the development of advanced thermal management systems.

Study of electronic structure and optical transition properties of low-lying excited states of AuB molecules based on configuration interaction method

High-level configuration interaction method including the spin-orbit coupling is used to investigate the low-lying excited electronic states of AuB that is not reported experimentally. The electronic structure in our work is preformed through the three steps stated below. First of all, Hartree-Fock method is performed to compute the singlet-configuration wavefunction as the initial guess. Next, we generate a multi-reference wavefunction by using the state-averaged complete active space self-consistent field (SACASSCF). Finally, the wavefunctions from CASSCF are utilized as reference, the exact energy point values are calculated by the explicitly correlated dynamic multi-reference configuration interaction method (MRCI). The Davidson correction (+Q) is put forward to solve the size-consistence problem caused by the MRCI method. To ensure the accuracy, the spin-orbit effect and correlation for inner shell electrons and valence shell electrons are considered in our calculation. The potential energy curves of 12 Λ-S electronic states are obtained. According to the explicit potential energy curves, we calculate the spectroscopic constants through solving radial Schrödinger equation numerically. We analyze the influence of electronic state configuration on the dipole moment by using the variation of dipole moment with nuclear distance. The spin-orbit matrix elements for parts of low-lying exciting states are computed, and the relation between spin-orbit coupling and predissociation is discussed. The predissociation is analyzed by using the obtained spin-orbit matrix elements of the 4 Λ-S states which spilt into 12 Ω states. It indicates that due to the absence of the intersections between the curves of spin-orbit matrix elements related with the 4 low-lying Λ-S states, the predissociation for these low-lying exciting states will not occur. Finally, the properties of optical transition between the ground Ω state <inline-formula><tex-math id="M3">\begin{document}$ {\rm A}^{1}{{{\Pi}}}_{1} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M3.png"/></alternatives></inline-formula> and first excited Ω state <inline-formula><tex-math id="M4">\begin{document}$ {{\mathrm{X}}}^{1}{{{\Sigma }}}_{{0}^{+}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231347_M4.png"/></alternatives></inline-formula> are discussed in laser-cooling filed by analyzing the Franck-Condon factors and radiative lifetime. And the transition dipole moment is also calculated. But our results reveal that the AuB is not an ideal candidate for laser-cooling. In conclusion, this work is helpful in deepening the understanding of AuB, especially the structures of electronic states, interaction between excited states, and optical transition properties. All the data presented in this paper are openly available at <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://www.doi.org/10.57760/sciencedb.j00213.00009">https://www.doi.org/10.57760/sciencedb.j00213.00009</ext-link>.

Mapping spin contamination-free potential energy surfaces using restricted open-shell methods with Grassmannians.

The Lagrange-based Grassmann interpolation (G-Int) method has been extended for open-shell systems using restricted open-shell (RO) methods. The performance of this method was assessed in constructing potential energy surfaces (PESs) for vanadium(II) oxide, benzyl radical, and methanesulfenyl chloride radical cation. The density matrices generated by G-Int when used as initial guesses for self-consistent field (SCF) calculations, exhibit superior performance compared to other traditional SCF initial guess schemes, such as SADMO, GWH, and CORE. Additionally, the energy obtained from the G-Int scheme satisfies the variational principle and outperforms the direct energy-based Lagrange interpolation approach. In the case of methanesulfenyl chloride radical cation, a unique example with a flat PES at the end region along the H-C-S-Cl dihedral angle, the use of an equally-spaced grid sampling leads to significant oscillations near the end of the interval due to the effects of Runge's phenomenon. Introducing an unequally-spaced grid sampling based on a scaled Gauss-Chebyshev quadrature effectively mitigated the Runge's phenomenon, making it suitable for combining with G-Int in constructing PESs for general applications. Thus, G-Int provides an efficient and robust strategy for building spin contamination-free PESs with consistent accuracy.

Positronium imaging in J-PET with an iterative activity reconstruction and a multistage fitting algorithm

Positronium imaging is a new technique complementary to positron emission tomography (PET) based on the histogramming of time delay between the emission of a de-excitation photon, and a consequent electron-positron annihilation, to estimate the mean lifetime of orthopositronium (o-Ps), which depends on the local size of the voids, concentration of oxygen and bioactive molecules. We improve the resolution and reduce noise in positronium imaging by building time-delay spectra from the PET activity reconstructed by a 3-photon time-of-flight maximum likelihood expectation maximisation. The method was tested on the data measured for four human-tissue samples injected by <sup>22</sup>Na and put in the Jagiellonian PET “Big barrel” scanner. Due to an ill-posed problem of fitting time-delay histograms, a multistage optimisation procedure was explored along with inferential analysis of the solution space. Run in parallel for multiple sets of initial guesses, we compared the second-order Levenberg- Marquardt algorithm (LMA) and the direct search Nelder-Mead simplex (NMS) method. The LMA proved to be faster and more precise, but the NMS was more stable with a higher convergence rate. The estimated mean o-Ps lifetimes in the 1.9 ns – 2.6 ns range were consistent with the reference results, while other fitting parameters allowed differentiation between the two patients who provided the tissue samples.

Topology and anisotropy optimisation of continua using non-uniform rational basis spline entities

This paper presents a novel method to address the challenge of concurrent topology and anisotropy optimisation of variable-stiffness anisotropic structures with variable thickness from additive manufacturing technologies. The proposed methodology relies on the multi-level optimisation strategy based on non-uniform rational basis spline (NURBS) entities, density-based method for topology optimisation and the polar formalism to describe the anisotropy of the continuum. Specifically, NURBS entities are used to describe both the density field and the distribution of the polar parameters and the thickness across the design domain. Furthermore, the properties of NURBS entities are efficiently exploited to derive the gradient of the physical responses involved in the problem formulation. The proposed method is applied to the problem of maximising the structural stiffness, while fulfilling design requirements on the lightness and on the feasibility of the polar parameters. In this context, the problem is formulated in the most general case considering inhomogeneous Neumann–Dirichlet boundary conditions. The effectiveness of the approach is tested on benchmark problems taken from literature subjected to both in-plane and out-of-plane loads. Particularly, a large campaign of sensitivity analyses has been carried out to examine the impact of integer parameters of the NURBS entity, the penalty scheme used for the element stiffness matrix, inhomogeneous Neumann–Dirichlet boundary conditions, optimisation strategy (sequential versus concurrent) and initial guess on the optimised solution.

Multi-Phase Vertical Take-Off and Landing Trajectory Optimization with Feasible Initial Guesses

The advancement of electric vertical take-off and landing (eVTOL) aircraft has expanded the horizon of urban air mobility. However, the challenge of generating precise vertical take-off and landing (VTOL) trajectories that comply with airworthiness requirements remains. This paper presents an approach for optimizing VTOL trajectories considering six degrees of freedom (6DOF) dynamics and operational constraints. Multi-phase optimal control problems are formulated to address specific constraints in various flight stages. The incremental nonlinear dynamic inversion (INDI) controller is employed to execute the flight mission in each phase. Controlled flight simulations yield dynamically feasible trajectories that serve as initial guesses for generating sub-optimal trajectories within individual phases. A feasible and sub-optimal initial guess for the holistic multi-phase problem is established by concatenating these single-phase trajectories. Focusing on a tilt-wing eVTOL aircraft, this paper computes VTOL trajectories leveraging the proposed initial guess generation procedure. These trajectories account for complex flight dynamics, align with various operation constraints, and minimize electric energy consumption.

Improved Initialization of Optimal Path Calculations Using Sequential Traversal over the Image-Dependent Pair Potential Surface.

In reaction path optimization, such as the calculation of a minimum energy path (MEP) between given reactant and product configurations of atoms, it is advantageous to start with an initial guess where the close proximity of atoms is avoided and bonds are not unnecessarily broken only to be reformed later. When the configurations of the atoms are described with Cartesian coordinates, a linear interpolation between the end points can be problematic, and a better option is provided by the so-called image dependent pair potential (IDPP) approach where interpolated pairwise distances are generated to form an objective function that can be used to construct an improved initial path. When started with a linear interpolation, this method can, however, still lead to unnecessary bond breaking in, for example, reactions in which a molecular subgroup undergoes significant rotation. In the method presented here, this problem is addressed by constructing the path gradually, introducing images sequentially starting from the vicinity of the end points while the distance between images in the central region is larger. The distribution of images is controlled by systematically scaling the tightness of springs acting between the images until the desired number of images is obtained, and they are evenly spaced. This procedure generates an initial path on the IDPP surface, a task that requires negligible computational effort, as no evaluation of the energy of the system is needed. The calculation of the MEP, typically using electronic structure calculations, is then subsequently carried out in a way that makes efficient use of parallel computing with the nudged elastic band method. Several examples of reactions are given where the linear interpolation IDPP (LI-IDPP) method yields problematic paths with unnecessary bond breaking in some of the intermediate images, while the sequential IDPP (S-IDPP) method yields paths that are significantly closer to realistic MEPs.

New gas radiation model of high accuracy based on the principle of weighted sum of gray gases

The standard WSGG (Weighted Sum of Gray Gases) model is very fast and simple but can lead to relatively high discrepancies in the computation of the radiative heat transfer. A new model of high accuracy relying on the principle of the WSGG model is proposed. Contrary to the standard WSGG model, the pressure absorption coefficient depends here weakly on the temperature while the weighting factor is not predefined by a mathematical function. Mathematical properties on the model parameters are obtained and we show that all the model parameters can be determined from only one of them. This last is reconstructed with an efficient inverse algorithm from the total radiative heat source data computed with the LBL method using HITEMP 2010. We propose an efficient method to find good initial guesses (of the model parameters) leading to the best accuracy of the model. It is shown, on 17 selected 1D cases representative of the combustion of CO2H2O mixtures, that the maximum relative errors on the radiative heat source for the new model (based on 6 gray gases) does not exceed 3.5% (for these 17 cases) whereas for the standard WSGG model, these errors vary up to 14.5% (five cases have errors higher than 10.0% and nine cases have errors between 5.0% and 10.0%). The accuracy of the total radiative heat flux is also greatly enhanced with the new model. We also show that the present model is robust and can be used in 3D geometry.

Analysis of transverse free vibrations of rotating beams with variable cross-section using the point collocation method

In this article, a study of transverse free vibrations of rotating cantilever beams with variable cross-sectional area is carried out using the point collocation method. The study considers four thickness variation functions, including linear, parabolic, sinusoidal, and exponential types, for the beam’s cross-sectional area changes. The point collocation method uses Gauss-Legendre points to solve the equation of motion and determine the natural frequencies. To enhance the convergence rate, the initial guess function is based on the precise mode shapes of the stationary uniform beam. The effect of section functions and various rotational speeds on the structure’s natural frequencies is investigated. The outcomes of the investigation are compared with 3D finite element simulations and related published results. Through the analysis, the results show that the point collocation method is highly accurate, with a maximum error of 0.0025% compared to 3D finite element simulations. Moreover, the natural frequencies of the rotating cantilever beams decrease as the section functions become steeper. Finally, the increase in rotational speed causes the natural frequencies to increase in a non-linear manner, with the maximum increase rate occurring at a specific rotational speed.

Theory of Functional Connections and Nelder–Mead optimization methods applied in satellite characterization

The growing population of man-made objects with the build up of mega-constellations and the multiplication of space debris not only increases the potential danger to all space vehicles and in-space infrastructures (including space observatories), but also poses a serious threat to astronomy and dark skies. Monitoring of this population requires precise satellite characterization, which is a challenging task that involves analyzing observational data such as position, velocity, and light curves using optimization methods. In this study, the applications of two optimization procedures are proposed and analyzed to determine the parameters associated with the dynamics of a satellite: one based on the Theory of Functional Connections (TFC) and another one based on the Nelder–Mead heuristic optimization algorithm. The TFC performs linear functional interpolation to embed the constraints of the problem into a functional. We propose to use this functional to analytically embed the observational data of a satellite into its equations of dynamics. After that, any solution will always satisfy the observational data. The second proposed procedure takes advantage of the Nelder–Mead algorithm, that does not require the gradient of the objective function, as alternative solution. The accuracy, efficiency, and dependency on the initial guess of each method is investigated, analyzed, and compared for several dynamical models. These methods can be used to obtain the physical parameters of a satellite from available observational data and for space debris characterization contributing to follow-up monitoring activities in space and astronomical observatories.

Influence of Heat Source on Thin Film Flow of Ferrofluid Past an Unsteady Stretching Sheet

In this work, the impact of a heat source on the thin-film ferrofluid flow over an unstable stretching sheet in the presence of an external magnetic field has been examined. The governing partial differential equations are transformed into a system of ordinary differential equations by similarity transformation. The resultant system of ordinary differential equations is solved numerically through shooting technique involving Runge-Kutta-Fehlberg (RKF45) method. To improve the initial guess values, the Newton-Raphson method is used. The significance of magnetization parameter, Prandtl number and heat source parameter on the flow and heat transmission process have been graphically analysed. The decrease in film thickness is observed for growing values of heat source parameter.

Stochastic inversion for equivalent hydraulic fracture characterization using low-frequency distributed acoustic sensing data

Distributed fiber-optic sensing, a game-changing technology, has been successfully applied in monitoring hydraulic fracturing treatments. The cross-well fiber-optic strain/strain-rate responses are directly related to the fracture-propagation process and dynamic fracture geometry. Extracting the insightful information regarding hydraulic fractures requires robust interpretation workflows. In this paper, we aim to develop a stochastic inversion approach to characterize the dynamic equivalent fracture geometry and quantify the associated uncertainties using cross-well low-frequency distributed acoustic sensing (LF-DAS) measurements. A fast analytical forward solver based on the 3D displacement discontinuity method is developed to model the strain. The objective function is the sum-of-squares error between the modeled strain and the measured strain. We focus on an equivalent fracture geometry with a predefined length centered around the monitoring well, which is a reasonable assumption considering the spatial sensitivity of LF-DAS. Therefore, the model parameters reduce to fracture width and height of the equivalent fracture. We adopted the delayed rejection adaptive metropolis (DRAM) algorithm, an efficient Markov-chain Monte Carlo (MCMC)-based method, to perform the optimization. The efficiency and accuracy of the algorithm are tested using a synthetic case that has three monitoring wells at different locations. The mean values of fracture width and height are both close to the true values with negligible standard deviations for all the three monitoring wells. The algorithm performance is not sensitive to the initial guess and the predefined length needs to be large enough. Then, a field case with a single cluster from the HFTS-2 project is presented. The fracture width increases from about 0.5 mm to about 0.9 mm during the pumping stage and gradually decreases during the shut-in period. The fracture height changes during the pumping stage and stabilizes at about 150 m during the shut-in period, the trend of which is consistent with the LF-DAS signals from the offset vertical monitoring well. To the best of our knowledge, this is the first algorithm that can efficiently quantify the fracture width and height simultaneously. The results could provide novel insights on the characteristics of fracture geometry and significantly improve the understanding of complex fracture propagation processes in subsurface reservoirs.

Innovative Optimal Control Path Planning for PMCU in Cruise Ship Construction: A Kinematic and Obstacle Avoidance Model

In cruise ship manufacturing, it is common practice for prefabricated modular cabin units (PMCU) to be assembled in the workshop and transported to a designated installation location on board the ship. This paper proposed a Radau pseudospectral method based on a probabilistic roadmap (PRM) for PMCU path planning in complex deck environments. Firstly, a kinematic model is constructed, and the continuous-time optimal control path planning problem is established. Among them, an area-based obstacle avoidance constraint is applied to the approach. Then, the continuous-time optimal control problem is discretized into a nonlinear programming (NLP) problem using the orthogonal collocation method. For the initial value-sensitive NLP problem solving, a strategy using PRM combined with a heuristic rule is used to obtain a high-quality initial guess. Finally, experiments under two operating scenarios of PMCU pushing demonstrate that the method is capable of generating a better path while ensuring that the whole process is collision-free. The results show that the algorithm proposed in this paper can effectively solve the PMCU pushing path planning problem in the complex deck environment, and the path considering kinematic characteristics can be used for cabin installation, which has strong operability and applicability.

Whip-Bezier: A C1-continuous hardening law for efficient direct and inverse identification

In 3D constitutive models, the hardening law is an essential model ingredient that has a first order effect on the predicted stress–strain response. In most phenomenological plasticity models, the hardening law coincides with the stress–strain curve for monotonic uniaxial loading. When identifying the hardening law for large strains through hybrid experimental–numerical approaches, the numerical properties of the hardening law play an important role. Here, we propose a novel piecewise-defined hardening law based on a composition of quadratic Bezier curve segments. The Whip-Bezier formulation preserves C1 continuity and achieves a parametrization with less parameters than its piecewise-linear counterpart. Both the possibility of identifying the hardening parameters in a decoupled optimization (e.g. from in-plane torsion experiments) and the use of a fully-coupled identification scheme (e.g. from notched tension experiments) are detailed. When contrasted with widely-used analytical expressions, the Whip-Bezier model consistently demonstrates enhanced performance with increasing number of parameters. This improvement comes with minimal statistical variance and reduced dependence on the initial optimization guess. Furthermore, the fitting quality is at least equivalent to that of the Swift-Voce hardening law with the same number of parameters.

Automated parameterization of velocity pulses in near‐fault ground motions

AbstractProper parameterization of near‐fault ground motions is of critical importance in earthquake engineering, and this process is traditionally performed by directly fitting an analytical pulse model to the original motion. Yet such a process is usually limited by the trial‐and‐error procedure, which is strongly dependent on the initial guesses and may converge to local rather than global minimums. In this study, we propose a progressive (step‐by‐step) iterative approach that can achieve a fully automated parameterization of the velocity pulse contained in near‐fault motions. Assuming that a velocity pulse can be characterized by a pulse model with four key parameters, the approach is conducted by iteratively matching the pulse model to the smoothed ground motion, and the parameterized pulse is analytically derived by best fitting to the smoothed motion not only in the time domain but also in the spectral domain. Specifically, the velocity time history of interest is initially smoothed by a moving average filter so that the low‐frequency content can be filtered out of the original motion, from which the pulse amplitude as well as its epoch is accordingly determined. The coherent velocity pulse is then progressively extracted by performing the nonlinear least‐square‐fitting of the pulse model to the filtered low‐frequency content, during which the remaining parameters, that is, the pulse period, the number of cycles and the phase of the pulse, are estimated successively. Finally, the above procedure is applied repeatedly to the original ground motion by changing an empirical factor controlling the extent of smoothing of the motion so that convergence to local minimums that frequently occurs in the trial‐and‐error procedure could be largely avoided, and best match of the spectrum of the extracted pulse to that of the original motion can be acquired. Fitting quality of the velocity pulses is examined by comparing with existing methods. Prospective applications of the proposed procedure include the stochastic simulations of near‐fault ground motions and parametric investigations of the influence of velocity pulses on various engineered structures.

SIMP Phase-field topology optimization framework to maximize fracture resistance in FGMs

In this study, we explore the use of SIMP topology optimization and the phase field approach to fracture to maximize fracture resistance in functionally graded materials (FGMs) in the presence of a second phase. We derive a mathematical formulation using a consistent derivation of the second law of thermodynamics to maximize the external work under the constraints of volume fraction. We also demonstrate that, for every distribution of the density function, the topology optimization problem Γ−Converges. We highlight the significant difference between the fracture resistance in FGMs and homogeneous materials. We investigate the crack propagation path along with the optimum topology for the FGM under different grading profiles, elastic mismatch ratio, strength mismatch ratio, and inclusion mismatch ratio. We present several numerical examples to demonstrate the predictive capability of the presented model. A comparison between the initial design guess and the final optimized design is also provided for each example, to further assess the model capability.