Initial Guess Research Articles

Initial Orbit Determination Based on Intelligent Optimization Algorithm

Classical methods for initial orbit determination (IOD) include Laplace method, Gauss method, and their variations. In addition to this, based on the characteristic of optical observation data nowadays, experts propose some other IOD methods, like Double-r method and admissible region method. One of the ways to determinate the orbit through double-r method is to guess distances of the target from the observer at two epochs—usually at the first and the last one. By doing so, we can solve the Lambert problem, and use its solution as the initial guess of the orbit. Furthermore, we can improve the initial guess by iterations to reduce the root mean square (RMS) of the observations. The admissible method is based on the concept of attributable (longitude, latitude, and their rates). With some conceptions, the admissible region described by the range and range rate from the observer is characterized. Using triangulation we can find the nodal point that makes the RMS minimal. In our work, we apply one intelligent optimization method—the particle swarm optimization method to the two methods, based on simulated and real data, and compare the results with that of modified Laplace method. At last, we briefly discuss the possibility of applying the double-r method to the orbit link problem.

Differential Time of Arrival Based Opportunistic Positioning for Asynchronous Cellular Signals: Model, Algorithms and Experiments

Signal asynchronism significantly challenges opportunistic cellular signal positioning. Existing solutions typically rely on global navigation satellite system (GNSS)-assisted initialization or multiterminal collaboration, resulting in limited application scenarios and high implementation costs. To overcome this, a differential time-of-arrival (DTOA)-based asynchronous cellular signal positioning system is developed. By treating the user equipment at the previous time as a differential reference, a DTOA positioning model is presented to implement asynchronous cellular positioning completely independently. The Taylor-series method, which has Cramer–Rao lower bound accuracy, is considered to solve the DTOA equations. To ensure global convergence, the two-step weighted least squares (TSWLS) method and its bias reduction methods are extended to DTOA positioning to obtain an initial position guess. The linear equations at each step are reconstructed, and TSWLS ambiguity is eliminated. Simulations are conducted to analyze the DTOA positioning geometry and the performance of the proposed algorithms. The proposed system implements preliminary positioning based on DTOA and exploits an extended Kalman filter for real-time positioning. It is validated experimentally, the DTOA and EKF positioning root mean-squared errors in the field test are 4.0 m and 4.2 m, respectively, which are close to the accuracy of a conventional system with GNSS-assisted initialization.

Online Path Decision of No-Fly Zones Avoidance for Hypersonic Vehicles Based on a Graph Attention Network

The path decision problem for a hypersonic vehicle is recently formulated as it helps to decide a good initial guess for trajectory optimization with no-fly zone constraints. This path decision problem is a hybrid problem, discrete variables optimize paths and continuous variables optimize dynamics, which consumes costly computation time and is hard to apply in online scenarios. To reduce the computation, instead of directly solving the hybrid problem, we design a heuristics approach taking advantage of the interpretability and flexibility of a graph attention network (GAT). The path decision is modeled by a directed graph and transformed into a GAT training problem, and the resulting GAT can directly output a path in online use. During this work, there are two innovations: GAT customization and offline training. First, we define the mask to express the graph structure, and model the problem-specific decoder process in the GAT, thus meeting the path decision logic of no-fly zones avoidance and ensuring the solutions are feasible. Second, we numerically integrate dynamics by a path-following guidance law, calculate the total control effort as the cost function, and use this cost to train the GAT based on the widely used REINFORCE, thus conforming to dynamics that are practical for hypersonic vehicles. Simulation results illustrate the high-accuracy path decision, much faster calculation, and generalization on no-fly zone layouts and numbers.

An inverse method for elastic constants identification of two-layer hyperelastic bodies with suction loading

Some soft tissues of the human body and biomaterials are considered as multi-layer structures with layer-specific material properties. Identification of the material parameters of these distinct layers is challenging and has attracted considerable attention in recent decades. In this research, an inverse finite element method, which uses the data obtained from simulated suction experiments, is developed. The method employs a limited number of surface-measured data to recover the layer-specific hyperelastic material parameters of a two-layer structure. The Gauss-Newton method is employed to minimize a cost function, which is defined in terms of the difference between measured and calculated displacements of the surface points. The sensitivity analysis during the optimization process is carried out by the finite difference method. The effects of pipette diameter, noise in experimental data, the initial guess and the hyperelastic material model, on the robustness and efficiency of the inverse method are investigated.

An Optimal Parameter Extraction Procedure for SiC Power MOSFET Model

A simple and efficient parameter extraction method for Silicon Carbide (SiC) power MOSFET model is described. This method uses nonlinear optimization algorithm to find the optimal set of parameters to model. The optimizer algorithm starts with initial guess parameters, extracted from measurement, to provide a set of parameters minimizing errors between model and measurements data in entire operating regions of the device. The starting initial guess parameter values give to the algorithm a closed solution to obtain the optimal set of model parameters with reduced iteratives. The Levenberg-Marquardt (LM) algorithm will be used in this work. The efficiency of the proposed extraction method is proved with the good agreements obtained between the model and the measurements.

Geometric inverse estimation for the inner wall of a furnace under transient heat conduction based on dual reciprocity boundary element method

A boundary shape estimation problem for the furnace’s inner surface is solved using the dual reciprocity boundary element method (DRBEM) and the conjugate gradient method (CGM) under transient heat conduction. The DRBEM is utilized to eliminate the drawbacks of traditional numerical methods and classical boundary element method of discretizing the entire computational domain, with only boundary discretization. The inversion results are obtained by applying the CGM to minimize the objective function, in which the sensitivity coefficients are calculated with the complex variable derivation method (CVDM), making the calculation precise and independent of step size. To verify the accuracy of the DRBEM in solving the transient heat conduction problem, the influencing factors including radial-basis function, the number of internal collocation points, and time step size are investigated. The influences of measurement time interval, future time step, initial guess, measurement error, and the number and position of measurement points on the inversion results are analyzed. Meanwhile, the effectiveness of the proposed approach is tested by numerical examples, and the inversion results show that it is stable, accurate, and efficient for identifying different and complicated unknown boundary shapes of the furnace.

Computational performance of musculoskeletal simulation in OpenSim Moco using parallel computing.

Optimal control musculoskeletal simulation is a valuable approach for studying fundamental and clinical aspects of human movement. However, the high computational demand has long presented a substantial challenge, creating a need to improve simulation performance. The OpenSim Moco software package permits musculoskeletal simulation problems to be solved in parallel on multicore processors using the CasADi optimal control library, potentially reducing the computational demand. However, the computational performance of this framework has not been thoroughly examined. Thus, we aimed to investigate the computational speed-up obtained via multicore parallel computing relative to solving problems serially (i.e., using a single core) in optimal control simulations of human movement in OpenSim Moco. Simulations were solved using up to 18 cores with a variety of temporal mesh interval densities and using two different initial guess strategies. We examined a range of musculoskeletal models and movements that included two- and three-dimensional models, tracking and predictive simulations, and walking and reaching tasks. The maximum overall parallel speed-up was problem specific and ranged from 1.7 to 7.7 times faster than serial, with most of the speed-up achieved by about 6 processor cores. Parallel speed-up was generally greater on finer temporal meshes, while the initial guess strategy had minimal impact on speed-up. Considerable speed-up can be achieved for some optimal control simulation problems in OpenSim Moco by leveraging the multicore processors often available in modern computers. However, since improvements are problem specific, achieving optimal computational performance will require some degree of exploration by the end user.

A Boundary-Type Numerical Procedure to Solve Nonlinear Nonhomogeneous Backward-in-Time Heat Conduction Equations

In this paper, an explicit boundary-type numerical procedure, including a constraint-type fictitious time integration method (FTIM) and a two-point boundary solution of the Lie-group shooting method (LGSM), is constructed to tackle nonlinear nonhomogeneous backward heat conduction problems (BHCPs). Conventional methods cannot effectively overcome numerical instability to solve inverse problems that lack initial conditions and take a long time to calculate, even using different variable transformations and regularization techniques. Therefore, an explicit-type numerical procedure is developed from the FTIM and the LGSM to avoid numerical instability and numerical iterations. First, a two-point boundary solution of the LGSM is introduced into the numerical algorithm. Then, the maximum and minimum values of the initial guess value can be determined linearly from the boundary conditions at the initial and final times. Finally, an explicit-type boundary-type numerical procedure, including a boundary value solution and constraint-type FTIM, can directly avoid the numerical iterative problems of BHCPs. Several nonlinear examples are tested. Based on the numerical results shown, this boundary-type numerical procedure using a two-point solution can directly obtain an approximated solution and can achieve stable convergence to boundary conditions, even if numerical iterations occur. Furthermore, the numerical efficiency and accuracy are better than in the previous literature, even with an increased computational time span without the regularization technique.

The Oblate Lambert Problem: Geometric Formulation and Solution of an Unperturbed, Generalized Lambert Problem Governed by Vinti’s Potential

Numerous methods exist for solving the Lambert problem, the two-point boundary value problem (BVP) governed by two-body dynamics. Many applications would benefit from a solution to a perturbed Lambert problem; a few studies have attempted to solve one. Establishing a larger pool of alternative solution methods gives practitioners greater latitude in choosing the solution that best suits their needs. To that end, a novel Lambert-type BVP is constructed in this work that includes oblateness by way of Vinti’s potential, rendering the problem mathematically unperturbed. This BVP is first defined and then converted to a system of equations that is amenable to an iterative solution. The formulation, which is valid for both the zero- and multiple-revolution problems, couples oblate spheroidal (OS) universal variables and OS equinoctial orbital elements together to sow robustness across all orbital regimes, only excepting orbits that are sufficiently rectilinear. For the first time, the solution space is broadly explored, exposing multiple new insights of significant practical use. Initial guess and root-solve techniques are offered to solve the system of equations. When assessed at Earth for robustness, accuracy, and computational efficiency, the zero-revolution algorithm excels across all three performance metrics, with runtimes averaging only about 15 times slower than a typical two-body Lambert solver. The multiple-revolution algorithm, while not yet evaluated as extensively, also exhibits high levels of performance, the formulation generally characterizing the existence of solutions around oblate bodies more accurately than its Keplerian counterpart.

To guess or not to guess excited state amplitudes during optimization and dynamics.

We report robust initial guesses for the amplitudes and z-vectors in a configuration interaction singles or Tamm-Dancoff approximation calculation that consistently reduce the total number of iterations required for an excited state calculation often by over 50%. The end result of these guesses is that the practicing chemist can expect to generate excited state optimized structures with a total wall time reduced by as much as 30% in the future without any approximations-simply by using information gathered at one geometry and applying it to another geometry.

Reconciling ice dynamics and bed topography with a versatile and fast ice thickness inversion

Abstract. We present a novel thickness inversion approach that leverages satellite products and state-of-the-art ice flow models to produce distributed maps of sub-glacial topography consistent with the dynamic state of a given glacier. While the method can use any complexity of ice flow physics as represented in ice dynamical models, it is computationally cheap and does not require bed observations as input, enabling applications on both local and large scales. Using the mismatch between observed and modelled rates of surface elevation change (dh/dt) as the misfit functional, iterative point-wise updates to an initial guess of bed topography are made, while mismatches between observed and modelled velocities are used to simultaneously infer basal friction. The final product of the inversion is not only a map of ice thickness, but is also a fully spun-up glacier model that can be run forward without requiring any further model relaxation. Here we present the method and use an artificial ice cap built inside a numerical model to test it and conduct sensitivity experiments. Even under a range of perturbations, the method is stable and fast. We also apply the approach to the tidewater glacier Kronebreen on Svalbard and finally benchmark it on glaciers from the Ice Thickness Models Intercomparison eXperiment (ITMIX, Farinotti et al., 2017), where we find excellent performance. Ultimately, our method shown here represents a fast way of inferring ice thickness where the final output forms a consistent picture of model physics, input observations and bed topography.

Composition optimization of PMMA base denture reinforced with different percentages of Nano Hydroxyapatite and alumina particles to obtain highest KIc and KIIc values using hybrid IWO/PSO algorithm

Composition of three-phase dental denture (Polymethyl methacrylate or PMMA + Nano Hydroxyapatite + Nano Alumina) was optimized using hybrid IWO/PSO algorithm to obtain the highest KIc and KIIc. First, initial fracture toughness tests were performed on nine groups of PMMA base dentures with different percentages of ingredients. Symmetric single edge notch beam and asymmetric three-point bend beam with inclined crack were used for KIc and KIIc testing, respectively. The initial design parameters were considered as: {75–100% PMMA, 0–10% Nano Hydroxyapatite and, 0–15% Nano Alumina}. As the initial guess values for starting the hybrid optimization algorithm, B-spline curves (as the cost function) were fitted to the experimental results of both modes I and II. Then the IWO/PSO algorithm was run to find the optimum composition and maximum fracture toughness value of each mode. The best KIc was found for the composition of {78.5% PMMA + 9% Nano Hydroxyapatide + 12.5% Nano Alumina}. Similarly, using the hybrid IWO/PSO algorithm the optimum composition of {83.4% PMMA + 8.7% Nano Hydroxyapatide + 7.9 % Nano Alumina} was obtained to gain the highest KIIc. The experimental fracture toughness values obtained from the proposed compositions via employing the hybrid algorithm were approximately 40% higher than the all tested nine groups of PMMA base dentures under both modes I and II. The fracture toughness ratio KIIc/KIc of the optimum mix-designs predicted by the hybrid algorithm was equal to 0.78 and showed good agreement with the experimental KIIc/KIc ratio. The fracture toughness for any desired mixed mode condition can also be predicted in-terms of the KIc and stress intensity factors and T-stress of the desired mode mixity.

Bi-layer sizing and design optimization method of propulsion system for electric vertical takeoff and landing aircraft

Electric vertical takeoff and landing (eVTOL) aircraft is a promising solution for future urban air mobility, but it suffers from insufficient energy and power density as opposed to fossil fuel-based aircraft. This paper proposes a bi-layer design optimization method for electric propulsion systems. To tackle the issue of high-dimension design parameters and multiple performance constraints, the design process is divided into two parameter optimization problems. In the upper layer, only scalar parameters of components are considered to determine a feasible sizing result subject to energy-flow limits. The outcome of this layer further serves as the initial guess of the lower design layer. The constraints of power conservation and conversion among components are taken into account. The optimization is scheduled in a cascaded paradigm that maximizes the total energy efficiency with minimized total weight. The blade-element momentum method is employed to estimate propeller thrust and torque coefficients. The proposed method is applied to a tilt-wing eVTOL. The sizing results shows that the eVTOL mass is reduced by 11.66% as opposed to the benchmark method. The proposed method provides a generic framework for sizing and design optimization independent of configuration and mission profiles.

3DEG: Data-Driven Descriptor Extraction for Global re-localization in subterranean environments

Localization algorithms that rely on 3D LiDAR scanners often encounter temporary failures due to various factors, such as sensor faults, dust particles, or drifting. These failures can result in a misalignment between the robot’s estimated pose and its actual position in the global map. To address this issue, the process of global re-localization becomes essential, as it involves accurately estimating the robot’s current pose within the given map. In this article, we propose a novel global re-localization framework that addresses the limitations of current algorithms heavily reliant on scan matching and direct point cloud feature extraction. Unlike most methods, our framework eliminates the need for an initial guess and provides multiple top-k candidates for selection, enhancing robustness and flexibility. Furthermore, we introduce an event-based re-localization trigger module, enabling autonomous robotic missions. Focusing on subterranean environments with low features, we leverage range image descriptors derived from 3D LiDAR scans to preserve depth information. Our approach enhances a state-of-the-art data-driven descriptor extraction framework for place recognition and orientation regression by incorporating a junction detection module that utilizes the descriptors for classification purposes. The effectiveness of the proposed approach was evaluated across three distinct real-life subterranean environments.

Motion Primitive Approach to Spacecraft Trajectory Design in a Multi-body System

The increasing number and variety of spacecraft that are expected to operate within cislunar space and other multi-body gravitational environments throughout the solar system necessitates the continued development of strategies for rapid trajectory design and design space exploration. In the field of robotics, similar needs have been addressed using motion primitives that capture the fundamental building blocks of motion and are used to rapidly construct complex paths. Inspired by this concept, this paper leverages motion primitives to construct a framework for rapid and informed spacecraft trajectory design in a multi-body gravitational system. First, motion primitives of fundamental solutions, e.g., selected periodic orbits and their stable and unstable manifolds, are generated via clustering to form a discrete summary of segments of the phase space. Graphs of motion primitives are then constructed and searched to produce primitive sequences that form candidate initial guesses for transfers of distinct geometries. Continuous transfers are computed from each initial guess using multi-objective constrained optimization and collocation. This approach is demonstrated by constructing an array of geometrically distinct transfers between libration point orbits in the Earth-Moon circular restricted three-body problem with impulsive maneuvers.

Physics-informed neural networks to solve lumped kinetic model for chromatography process

Numerical method is widely used for solving the mechanistic models of chromatography process, but it is time-consuming and hard to response in real-time. Physics-informed neural network (PINN) as an emerging technology combines the structure of neural network with physics laws, and is getting noticed for solving physics problems with a balanced accuracy and calculation speed. In this research, a proof-of-concept study was carried out to apply PINN to chromatography process simulation. The PINN model structure was designed for the lumped kinetic model (LKM) with all LKM parameters. The PINN structure, training data and model complexity were optimized, and an optimal mode was obtained by adopting an in-series structure with a nonuniform training data set focusing on the breakthrough transition region. A PINN for LKM (LKM-PINN) consisting of four neural networks, 12 layers and 606 neurons was then used for the simulation of breakthrough curves of chromatography processes. The LKM parameters were estimated with two breakthrough curves and used to infer the breakthrough curves at different residence times, loading concentrations and column sizes. The results were comparable to that obtained with numerical methods. With the same raw data and constraints, the average fitting error for LKM-PINN model was 0.075, which was 0.081 for numerical method. With the same initial guess, the LKM-PINN model took 160 s to complete the fitting, while the numerical method took 7 to 72 min, depending on the fitting settings. The fitting speed of LKM-PINN model was further improved to 30 s with random initial guess. Thus, the LKM-PINN model developed in this study is capable to be applied to real-time simulation for digital twin.

An aneurysm-specific preconditioning technique for the acceleration of Newton-Krylov method with application in the simulation of blood flows.

In this paper, we develop an algorithm to simulate blood flows in aneurysmal arteries and focus on the construction of robust and efficient multilevel preconditioners to speed up the convergence of both linear and nonlinear solvers. The work is motivated by the observation that in the local aneurysmal region, the flow is often quite complicated with one or more vortices, but in the healthy section of the artery, the principal component of blood flows along the centerline of the artery. Based on this observation, we introduce a novel two-level additive Schwarz method with a mixed-dimensional coarse preconditioner. The key components of the preconditioner include (1) a three-dimensional coarse preconditioner covering the aneurysm; (2) a one-dimensional coarse preconditioner covering the central line of the healthy section of the artery; (3) a collection of three-dimensional overlapping subdomain preconditioners covering the fine meshes of the entire artery; (4) extension/restriction operators constructed by radial basis functions. The blood flow is modeled by the unsteady incompressible Navier-Stokes equations with resistance outflow boundary conditions discretized by a stabilized finite element method on fully unstructured meshes and the second-order backward differentiation formula in time. The resulting large nonlinear algebraic systems are solved by a Newton-Krylov algorithm accelerated by the new preconditioner in two ways: (1) the initial guess of Newton is obtained by solving a linear system defined by the coarse preconditioner; (2) the Krylov solver of the Jacobian system is preconditioned by the new preconditioner. Numerical experiments indicate that the proposed preconditioner is highly effective and robust for complex flows in a patient-specific artery with aneurysm, and it significantly reduces the numbers of linear and nonlinear iterations.

Triple-objective MPSO of zeotropic-fluid solar ejector cycle integrated with cold storage tank based on techno-economic criteria

The current study objective is to optimize the integration of a solar ejector cycle with cold storage by applying a multi-objective modified particle swarm optimization technique. Various collector and working fluid's effects are evaluated on dynamic system behavior, which zeotropic fluid and parabolic trough collector have been the most effective choices. Hot and cold storage tanks are applied to overcome the instability of solar energy and ensure sustainable access to produced cold. Design parameter's optimum values are estimated through sensitivity analysis and genetic algorithm optimization which are decreased up to 70% compared to initial guesses. An artificial neural network is employed to train exergo-economic-environmental data which fed into the multi-objective modified particle swarm optimization algorithm. With using of cold storage tank, the system's coefficient of performance is enhanced up to three times compared to the ejector cycle at optimum design variable. By employing of parabolic trough collector, the system has its maximum coefficient of performance and exergy efficiency, as well as the minimum size of the ejector cycle and cold storage tank. The parabolic trough collector, air handling unit, and cold storage tank waste over 80% of the overall system's exergy. The payback period of system is estimated about 3.5 years.

An efficient accurate scheme for solving the three-dimensional Bratu-type problem

In this manuscript, we present an innovative discretization algorithm designed to address the challenges posed by the three-dimensional (3D) Bratu problem, a well-known problem characterized by non-unique solutions. Our algorithm aims to achieve exceptional precision and accuracy in determining all potential solutions, as previous studies in the literature have only managed to produce limited accurate results. Additionally, our computational scheme approximates the critical values of the transition parameter. Moreover, we establish a rigorous proof demonstrating the uniform convergence of the approximation sequence to the exact solution of the original problem, under the condition that the initial guess is sufficiently close to the true solution. This theoretical result further establishes the reliability of our algorithm. To evaluate the effectiveness of our proposed approach, we conduct extensive numerical simulations, which convincingly demonstrate its capability to accurately solve the 3D Bratu problem while effectively determining the critical values of the transition parameter. Furthermore, we investigate the bifurcated behavior of the solution by analyzing the infinity norm for various values of the transition parameter. The outcomes of our study offer a robust and efficient method for tackling the 3D Bratu problem, making a significant contribution to the field of numerical analysis of partial differential equations (PDEs) where non-unique solutions are commonly encountered. Our algorithm's ability to produce accurate results for this challenging problem showcases its potential for broader applications in diverse scientific and engineering domains.

On a principle for mass sensing using self-excited template dynamics of coupled oscillators and root-finding algorithms

In this work, we analyze a mass sensing mechanism that relies on self-excited template dynamics of a simple network of two coupled oscillators, one linear and one nonlinear, to detect changes in the mass of the linear oscillator with tunable sensitivity. The resultant shift in the ratio of oscillation amplitudes is predicted using perturbation analysis and verified against numerical results obtained via parameter continuation. A physical realization of the mass sensing mechanism is proposed, in which the linear oscillator is represented by a periodically excited actuator/microcantilever assembly, the nonlinear oscillator is simulated in silico on a finite interval of time while driven by the periodic steady-state response of the linear oscillator, and a nonlinear root-finding algorithm is used to identify the input to the actuator that reproduces the sought, coupled, self-excited dynamics. The analysis shows that the sensor gain can be adjusted by appropriate tuning of the coupling stiffness without modifications to the physical components. Numerical results for two different actuator models demonstrate rapid convergence of the root-finding algorithm from a trivial initial solution guess over ranges of values of model parameters and added mass ratios.