Initial Guess Research Articles

English

In next-generation high throughput satellite (NGHTS), precoding (a preprocessing technique at the gateway (GW) can mitigate the interbeam interference with no additional resource at the user terminal. However, the calculation of precoding requires matrix inversion, which involves huge complexity in terms of hardware resources with real-time calculation for near error-free results. This paper proposes a novel approach for precoding matrix calculation using the Neumann series. In this way, the algorithm does not directly compute the matrix inversion. Hence the computational complexity is highly reduced. The proposed method uses the 4th-order iterative series with the initial guess as an inverse of the diagonal matrix of the input to construct the Neumann series. This leads to fast convergence of the matrix inversion process with fewer resources. The algorithm is claimed to be generic as it is seamlessly applied to any linear precoding scheme. The paper examines the resource complexity, convergence probability and Bit Error Rate (BER) performance for the proposed method with Zero Forcing (ZF) and Regularized Zero Forcing (RZF) based linear precoding scheme. Experiment results demonstrate that the proposed algorithm accomplishes superior performance with fewer resources compared to the Neumann series and Joint iterative Newton/Chebyshev-based Neumann series methods.

Shaping low-thrust multi-target visit trajectories via theory of functional connections

This paper proposes a shaping method via theory of functional connections (TFC) to solve the coplanar low-thrust multi-target visit problems under the J2 perturbation. Three types of targets are considered including ground targets, space targets, and hybrid ground-space targets. The visit constraints for the ground and space targets under the linear J2-perturbed model are transformed into those under the two-body model with a correction term, which avoids directly solving the transfer trajectories with the J2 effect. Then, a unified shaping method via the TFC is proposed for the three types of targets. The multi-target visit problem is transformed into a nonlinear programming problem that analytically satisfies the initial conditions and the multi-target visit constraints. Several numerical examples show that the proposed method can realize rapid optimization for the whole transfer trajectories. Furthermore, the solved trajectories are successfully applied to the initial guess estimation of the Gauss pseudospectral method for further optimization.

Mixed-integer trajectory optimization with no-fly zone constraints for a hypersonic vehicle

This paper focuses on mixed-integer trajectory optimization of no-fly zones avoidance for a hypersonic vehicle. When there are multiple no-fly zones, the trajectory optimization problem has many local optimal solutions, and the performance of the solution depends on the selection of an initial guess. Essentially, the selection of the initial guess can be abstracted as a discrete path decision. To deal with this issue, this paper first integrates the discrete path decision and continuous trajectory optimization for no-fly zones avoidance and models these as a mixed-integer optimal control problem (MIOCP). As the corner stone, a creative directed graph is established to model the path decision problem, which is then formulated by integer constraints. Combined with the minimum effort optimal control problem (Problem 1), we form the MIOCP (Problem 2), thus integrating the path decision and trajectory optimization to improve global performance. Additionally, to solve the MIOCP, an effective iterative mixed-integer convex programming (IMICP) algorithm is customized by adding two ad-hoc techniques, relaxation and a proximity term, thus remedying the artificial infeasibility. Simulation results show that this approach is practically independent of the initial guess and has better performance than existing methods.

Numerical solution of spacecraft pursuit-Evasion-Capture game based on progressive shooting method

The time optimal pursuit-evasion-capture (PEC) game problem for two spacecraft with continuous constant thrust is studied, which is a typical and considerable game scenario in practice. Progressive Shooting Method (PSM) is proposed to solve the PEC game in this paper. The method solves the problem in two stages. First-shooting settles a simplified problem by substituting CW dynamics to simple dynamics, while second-shooting settles the original problem with the results of first-shooting. For first-shooting, an analytic initial guess construction method based on prior information is proposed, in which vague adjoint variables are expressed by quantities with clear physical meanings. Through qualitative analysis for the optimal trajectory, the quantities are approximately estimated and then analytic expressions of an initial guess are constructed. The proposed method provides an instructive way to deal with the difficulty that an initial guess is hard to provide for an optimal control problem based on indirect-method. Numerical results show that a PEC game can be solved by the proposed method with well convergence and high computational efficiency.

Robust Launch Vehicle Trajectory Optimization with Stage Impact and Heat Flux Constraints

A fast trajectory optimization/guidance algorithm in the presence of path constraints for a multistage launch vehicle is presented in this work. The optimization problem is to maximize the payload to be injected into a geostationary transfer orbit with constraints on argument of perigee, second-stage impact point longitude, and heat flux constraint on the third stage that flies a low-altitude trajectory. These constraints constitute a unique set of equality and inequality constraints as they are contradictory in nature. Most of the gradient-based trajectory optimization schemes require an initial guess close enough to the optimal value for assured convergence. In addition, the rate of convergence deteriorates in the presence of inequality constraints. These issues are addressed by providing a solution to the optimization problem with low sensitivity to the initial guess profiles. A self-starting optimization scheme that can generate initial guess profiles automatically from boundary conditions is the major contribution of this work. The proposed method presented in this paper also gives a methodology for real-time implementation of the optimization scheme in the onboard computer. The sensitivity to initial guess in a gradient-based optimization procedure, in the presence of inequality constraints, is clearly brought out as part of this work by studying the convergence from random sets of initial guess profiles. The real-time implementation of the algorithm is validated with various initial conditions in deterministic as well as Monte Carlo sense to establish the robustness of the algorithm.

Determining Lennard-Jones Parameters Using Multiscale Target Data through Presampling-Enhanced, Surrogate-Assisted Global Optimization.

Force field-based models are a Newtonian mechanics approximation of reality and are inherently noisy. Coupling models from different molecular scale domains (including single, gas-phase molecules up to multimolecule, condensed phase ensembles) is difficult, which is also the case for finding solutions that transfer well between the scales. In this contribution, we introduce a surrogate-assisted algorithm to optimize Lennard-Jones parameters for target data from different scale domains to overcome the difficulties named above. Specifically, our approach combines a surrogate-assisted global evolutionary optimization method with a presampling phase that takes advantage of one scale domain being less computationally expensive to evaluate. The algorithm's components were evaluated individually, elucidating their individual merits. Our findings show that the process of parametrizing force fields can significantly benefit from both the presampling method, which alleviates the need to have a good initial guess for the parameters, and the surrogate model, which improves efficiency.

Numerical Stabilization for Flutter Analysis Procedure

Severe mode switching is often observed when the PK-method is used in the flutter analysis of complex aircraft configurations, in particular when nearly 100 vibrational modes are considered. In the commonly used commercial software NASTRAN, the resulting eigenroots are sorted in an ascending order of frequency. Therefore, the appearance of massive mode-switching instances cannot be avoided in the PK-method flutter analyses, especially for engineering applications with real-world complex configurations. In this study, as a post-processing procedure, an extensive sorting capability was developed in order to compensate for NASTRAN’s lack of a mode-tracking procedure in between the airspeed steps. The capability was developed based on both the complex eigenvalues and their corresponding eigenvectors. In addition, numerical techniques commonly used in computational fluid dynamics (CFD) were introduced to improve the convergence of the traditional PK-method. A hybrid approach was applied to the initial guess of the reduced frequency, followed by a deferred correction scheme for the PK-iteration process. Additionally, mode matching was specifically addressed when locking eigenroots onto the aerodynamics within the PK iterations. In addition to the PK iterations, a damping iteration or modified g-method was implemented by extending the PK-method solver. The combination of these special techniques effectively improved the numerical stability of the iterations in the stability eigensolution process and significantly reduced the appearance of the misleading mode switching, minimizing risks in aircraft flight.

Accelerated coupled cluster calculations with Procrustes orbital interpolation.

The coupled cluster method is considered a gold standard in quantum chemistry, reliably giving energies that are exact within chemical accuracy (1.6 mhartree). However, even in the coupled cluster single-double (CCSD) approximation, where the cluster operator is truncated to include only single and double excitations, the method scales as O(N6) in the number of electrons, and the cluster operator needs to be solved for iteratively, increasing the computation time. Inspired by eigenvector continuation, we present here an algorithm making use of the Gaussian processes that provides an improved initial guess for the coupled cluster amplitudes. The cluster operator is written as a linear combination of sample cluster operators that are obtained at particular sample geometries. By reusing the cluster operators from previous calculations in that way, it is possible to obtain a start guess for the amplitudes that surpasses both MP2 guesses and "previous geometry"-guesses in terms of the number of necessary iterations. As this improved guess is very close to the exact cluster operator, it can be used directly to calculate the CCSD energy to chemical accuracy, giving approximate CCSD energies scaling as O(N5).

A simple frequency formulation for fractal–fractional non-linear oscillators: A promising tool and its future challenge

This paper proposes a simple frequency formula developed from He’s frequency formulation for fractal systems. In this approach, the initial guess can be judiciously chosen. Even the simplest initial guess leads to a highly accurate approximate solution. A detailed theoretical development is elucidated, and the solving process is given step by step. The simple calculation and reliable results have been merged into an effective tool for deeply studying fractal vibration systems, and the present approach offers a completely new angle for the fast insight into the physical properties of a non-linear vibration system in a fractal space.

Analytical high-dimensional operators in canonical polyadic finite basis representation (CP-FBR).

In the present work, we introduce a simple means of obtaining an analytical (i.e., grid-free) canonical polyadic (CP) representation of a multidimensional function that is expressed in terms of a set of discrete data. For this, we make use of an initial CP guess, even not fully converged, and a set of auxiliary basis functions [finite basis representation (FBR)]. The resulting CP-FBR expression constitutes the CP counterpart of our previous Tucker sum-of-products-FBR approach. However, as is well-known, CP expressions are much more compact. This has obvious advantages in high-dimensional quantum dynamics. The power of CP-FBR lies in the fact that it requires a grid much coarser than the one needed for the dynamics. In a subsequent step, the basis functions can be interpolated to any desired density of grid points. This is useful, for instance, when different initial conditions (e.g., energy content) of a system are to be considered. We show the application of the method to bound systems of increased dimensionality: H2 (3D), HONO (6D), and CH4 (9D).

Convergence analysis of a block preconditioned steepest descent eigensolver with implicit deflation

AbstractGradient‐type iterative methods for solving Hermitian eigenvalue problems can be accelerated by using preconditioning and deflation techniques. A preconditioned steepest descent iteration with implicit deflation (PSD‐id) is one of such methods. The convergence behavior of the PSD‐id is recently investigated based on the pioneering work of Samokish on the preconditioned steepest descent method (PSD). The resulting non‐asymptotic estimates indicate a superlinear convergence of the PSD‐id under strong assumptions on the initial guess. The present paper utilizes an alternative convergence analysis of the PSD by Neymeyr under much weaker assumptions. We embed Neymeyr's approach into the analysis of the PSD‐id using a restricted formulation of the PSD‐id. More importantly, we extend the new convergence analysis of the PSD‐id to a practically preferred block version of the PSD‐id, or BPSD‐id, and show the cluster robustness of the BPSD‐id. Numerical examples are provided to validate the theoretical estimates.

Reconstructing urban wind flows for urban air mobility using reduced-order data assimilation

Advancements in uncrewed aircrafts and communications technologies have led to a wave of interest and investment in unmanned aircraft systems (UASs) and urban air mobility (UAM) vehicles over the past decade. To support this emerging aviation application, concepts for UAS/UAM traffic management (UTM) systems have been explored. Accurately characterizing and predicting the microscale weather conditions, winds in particular, will be critical to safe and efficient operations of the small UASs/UAM aircrafts within the UTM. This study implements a reduced order data assimilation approach to reduce discrepancies between the predicted urban wind speed with computational fluid dynamics (CFD) Reynolds-averaged Navier Stokes (RANS) model with real-world, limited and sparse observations. The developed data assimilation system is UrbanDA. These observations are simulated using a large eddy simulation (LES). The data assimilation approach is based on the time-independent variational framework and uses space reduction to reduce the memory cost of the process. This approach leads to error reduction throughout the simulated domain and the reconstructed field is different than the initial guess by ingesting wind speeds at sensor locations and hence taking into account flow unsteadiness in a time when only the mean flow quantities are resolved. Different locations where wind sensors can be installed are discussed in terms of their impact on the resulting wind field. It is shown that near-wall locations, near turbulence generation areas with high wind speeds have the highest impact. Approximating the model error with its principal mode provides a better agreement with the truth and the hazardous areas for UAS navigation increases by more than 10% as wind hazards resulting from buildings wakes are better simulated through this process.

Bayesian estimation of fertility rates under imperfect age reporting

This article outlines the application of the Bayesian method of parameter estimation to situations where the probability of age misreporting is high, leading to transfers of an individual from one age group to another. An essential requirement for Bayesian estimation is prior distribution, derived for both perfect and imperfect age reporting. As an alternative to the Bayesian methodology, a classical estimator based on the maximum likelihood principle has also been discussed. Here, the age misreporting probability matrix has been constructed using a performance indicator, which incorporates the relative performance of estimators based on age when reported correctly instead of misreporting. The initial guess of performance indicators can either be empirically or theoretically derived. The method has been illustrated by using data on Empowered Action Group (EAG) states of India from National Family Health Survey-3 (2005–2006) to estimate the total marital fertility rates. The present study reveals through both a simulation and real-life set-up that the Bayesian estimation method has been more promising and reliable in estimating fertility rates, even in situations where age misreporting is higher than in case of classical maximum likelihood estimates.

Optical Metrology of Critical Dimensions in Large-Area Nanostructure Arrays With Complex Patterns

AbstractIt was recently demonstrated that scatterometry-based metrology has the capability to perform high-throughput metrology on large-area nanopatterned surfaces. However, the way this approach is currently pursued requires an a priori generated library of reflectance spectra to be simulated for an exhaustive set of possible underlying critical dimensions (CDs) characterizing the measured nanopatterns. Generating this library is time consuming and can be infeasible for complex patterns characterized by a large number of CDs. This article addresses the aforementioned drawback of optical inspection of CDs of nanopatterned surfaces through the use of an inverse problem-based optimization methodology coupled with a recently introduced approach for efficient organization of the library of previously simulated reflectance spectra. Specifically, for each physically measured reflectance spectrum, the best matching simulated spectrum is sought in the initial incomplete library in order to serve as the initial guess for the inverse problem optimization process. Through that optimization process, further refinements of the best matching simulated spectra are conducted to obtain sufficiently accurate estimates of the CDs characterizing the inspected nanopattern geometries. Capabilities of the newly proposed approach are evaluated through inspection of semiconductor wafer samples with hourglass patterns characterized by eight CDs. It was observed that one can obtain significantly faster measurements of CDs compared to inspection times associated with scanning electron microscopy, while at the same time not deteriorating the corresponding Gage Repeatability and Reproducibility. In conclusion, this method enables real-time, accurate, and repeatable metrology of CDs of large-area nanostructured surfaces with complex nanopatterns.

Mechanistic-mathematical modeling of intracranial pressure (ICP) profiles over a single heart cycle. The fundament of the ICP curve form

The intracranial pressure (ICP) curve with its different peaks has been comprehensively studied, but the exact physiological mechanisms behind its morphology has not been revealed. If the pathophysiology behind deviations from the normal ICP curve form could be identified, it could be vital information to diagnose and treat each single patient. A mathematical model of the hydrodynamics in the intracranial cavity over single heart cycles was developed. A Windkessel model approach was generalized but the unsteady Bernoulli equation was utilized for blood flow and CSF flow. This is a modification of earlier models using the extended and simplified classical Windkessel analogies to a model that is based on mechanisms rooted in the laws of physics. The improved model was calibrated with patient data for cerebral arterial inflow, venous outflow, cerebrospinal fluid (CSF), and ICP over one heart cycle from 10 neuro-intensive care unit patients. A priori model parameter values were obtained by considering patient data and values taken from earlier studies. These values were used as an initial guess for an iterated constrained-ODE (ordinary differential equation) optimization problem with cerebral arterial inflow data as input into the system of ODEs. The optimization routine found patient-specific model parameter values that produced model ICP curves that showed excellent agreement with clinical measurements while model venous and CSF flow were within a physiologically acceptable range. The improved model and the automated optimization routine gave better model calibration results compared to previous studies. Moreover, patient-specific values of physiologically important parameters like intracranial compliance, arterial and venous elastance, and venous outflow resistance were determined. The model was used to simulate intracranial hydrodynamics and to explain the underlying mechanisms of the ICP curve morphology. Sensitivity analysis showed that the order of the three main peaks of the ICP curve was affected by a decrease in arterial elastance, a large increase in resistance to arteriovenous flow, an increase in venous elastance, or a decrease in resistance to CSF flow in the foramen magnum; and the frequency of oscillations were notably affected by intracranial elastance. In particular, certain pathological peak patterns were caused by these changes in physiological parameters. To the best of our knowledge, there are no other mechanism-based models associating the pathological peak patterns to variation of the physiological parameters.

A non-gradient-based reliability method using a new six-item instruction for updating design point

Reliability analysis of structures without spending too much computational cost is still a challenge. In this paper, an efficient non-gradient-based reliability method is proposed for analyzing the structures in which limit state functions are not explicitly known. Starting from an initial guess of design point, the proposed method updates this estimation of design point to approach the real one. A new comprehensive six-item instruction, represented for updating the estimations of the design point, is the main component of the proposed method in finding the solution. Due to including various conditions in the proposed instruction, the improvement of MPP candidates does not stop easily. To investigate the performance of this reliability method, at first, it is implemented in a number of mathematical problems of the literature. Then, structural problems, including a five-story steel building with implicit limit state functions and uncertain data are analyzed to show the applicability of the proposed method in real structures. The results of the mathematical and structural problems clearly show the efficiency and applicability of the proposed method.

Numerical solution of an extra-wide angle parabolic equation through diagonalization of a 1-D indefinite Schrödinger operator with a piecewise constant potential

We present a numerical method for computing the solution of a partial differential equation (PDE) for modeling acoustic pressure, known as an extra-wide angle parabolic equation, that features the square root of a differential operator. The differential operator is the negative of an indefinite Schrödinger operator with a piecewise constant potential. This work primarily deals with the 3-piece case; however, a generalization is made the case of an arbitrary number of pieces. Through restriction to a judiciously chosen lower-dimensional subspace, approximate eigenfunctions are used to obtain estimates for the eigenvalues of the operator. Then, the estimated eigenvalues are used as initial guesses for the Secant Method to find the exact eigenvalues, up to roundoff error. An eigenfunction expansion of the solution is then constructed. The computational expense of obtaining each eigenpair is independent of the grid size. The accuracy, efficiency, and scalability of this method is shown through numerical experiments and comparisons with other methods.

An Efficient Spectral Trust-Region Deflation Method for Multiple Solutions

It is quite common that a nonlinear partial differential equation (PDE) admits multiple distinct solutions and each solution may carry a unique physical meaning. One typical approach for finding multiple solutions is to use the Newton method with different initial guesses that ideally fall into the basins of attraction confining the solutions. In this paper, we propose a fast and accurate numerical method for multiple solutions comprised of three ingredients: (i) a well-designed spectral-Galerkin discretization of the underlying PDE leading to a nonlinear algebraic system (NLAS) with multiple solutions; (ii) an effective deflation technique to eliminate a known (founded) solution from the other unknown solutions leading to deflated NLAS; and (iii) a viable nonlinear least-squares and trust-region (LSTR) method for solving the NLAS and the deflated NLAS to find the multiple solutions sequentially one by one. We demonstrate through ample examples of differential equations and comparison with relevant existing approaches that the spectral LSTR-Deflation method has the merits: (i) it is quite flexible in choosing initial values, even starting from the same initial guess for finding all multiple solutions; (ii) it guarantees high-order accuracy; and (iii) it is quite fast to locate multiple distinct solutions and explore new solutions which are not reported in literature.

Parameter Estimation of the Randles Equivalent Electrical Circuit Using Only Real Part of the Impedance

Electrical impedance spectroscopy (EIS) has been widely used in the modeling and analysis of various electrochemical and energy storage systems. Parameter estimation of the equivalent electrical circuit is usually performed with personal computer (PC)-based software platforms that are not commonly available onsite. Such an approach introduces a lag between measurement and maintenance actions. In this article, we present a method for in situ parameter estimation of the Randles circuit ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\textit {RC}}$ </tex-math></inline-formula> equivalent model). Our method overcomes the shortcoming of the iterative and PC-based estimation approaches since there is no need for an initial guess provided by the user. The low complexity of our approach enables the implementation on cost-effective microcontroller-based portable systems. The proposed method has been validated with simulations and with experimentally obtained data. In the simulation part, we used both the noiseless and noisy data, while in the experimental part, we used impedance data obtained from a dummy circuit created with discrete components, as well as bioimpedance of apple slices. The obtained results are compared with desktop-based Multiple Electrochemical Impedance Spectra Parameterization (MEISP) software. Finally, reliable and accurate estimations with a board based on the ATmega2560 microcontroller confirmed the hypothesis of suitability for implementation on embedded hardware.

Deep feature based cross-slide registration.

Registration of multiple sections in a tissue block is an important pre-requisite task before any cross-slide image analysis. Non-rigid registration methods are capable of finding correspondence by locally transforming a moving image. These methods often rely on an initial guess to roughly align an image pair linearly and globally. This is essential to prevent convergence to a non-optimal minimum. We explore a deep feature based registration (DFBR) method which utilises data-driven descriptors to estimate the global transformation. A multi-stage strategy is adopted for improving the quality of registration. A visualisation tool is developed to view registered pairs of WSIs at different magnifications. With the help of this tool, one can apply a transformation on the fly without the need to generate a transformed moving WSI in a pyramidal form. We compare the performance on our dataset of data-driven descriptors with that of hand-crafted descriptors. Our approach can align the images with only small registration errors. The efficacy of our proposed method is evaluated for a subsequent non-rigid registration step. To this end, the first two steps of the ANHIR winner's framework are replaced with DFBR to register image pairs provided by the challenge. The modified framework produce comparable results to those of the challenge winning team.