Initial Guess Research Articles

Advanced numerical scheme and its convergence analysis for a class of two-point singular boundary value problems

In the past decades, many applications related to applied physics, physiology and astrophysics have been modelled using a class of two-point singular boundary value problems (SBVPs). In this article, a novel approach based on the shooting projection method and the Legendre wavelet operational matrix formulation for approximating a class of two-point SBVPs with Dirichlet and Neumann–Robin boundary conditions is proposed. For the new approach, an initial guess is postulated in contrast to the boundary conditions in the first step. The second step deals with the usage of the Legendre wavelet operational matrix method to solve the initial value problem (IVP). Further, the resulting solution of the IVP is utilized at the second endpoint of the domain of a differential equation in a shooting projection method to improve the initial condition. These two steps are repeated until the desired accuracy of the solution is achieved. To support the mathematical formulation, a detailed convergence analysis of the new approach is conducted. The new approach is tested against some existing methods such as various types of the variational iteration method, considering several numerical examples to which it provides high-quality solutions.

Efficient solution of bimaterial Riemann problems for compressible multi-material flow simulations

When solving compressible multi-material flow problems, an unresolved challenge is the computation of advective fluxes across material interfaces that separate drastically different thermodynamic states and relations. A popular idea in this regard is to locally construct bimaterial Riemann problems, and to apply their exact solutions in flux computation. For general equations of state, however, finding the exact solution of a Riemann problem is expensive as it requires nested loops. Multiplied by the large number of Riemann problems constructed during a simulation, the computational cost often becomes prohibitive. The work presented in this paper aims to accelerate the solution of bimaterial Riemann problems without introducing approximations or offline precomputation tasks. The basic idea is to exploit some special properties of the Riemann problem equations, and to recycle previous solutions as much as possible. Following this idea, four acceleration methods are developed, including (1) a change of integration variable through rarefaction fans, (2) storing and reusing integration trajectory data, (3) step size adaptation, and (4) constructing an R-tree on the fly to generate initial guesses. The performance of these acceleration methods is assessed using four example problems in underwater explosion, laser-induced cavitation, and hypervelocity impact. These problems exhibit strong shock waves, large interface deformation, contact of multiple (>2) interfaces, and interaction between gases and condensed matters. For all the problems, the acceleration methods are able to significantly reduce the computational cost without affecting solver robustness or solution accuracy. In different cases, the solution of bimaterial Riemann problems is accelerated by 37 to 87 times. As a result, the total cost of advective flux computation, which includes the exact Riemann problem solution at material interfaces and the numerical flux calculation over the entire computational domain, is accelerated by 18 to 81 times.

AMagPoseNet: Real-Time Six-DoF Magnet Pose Estimation by Dual-Domain Few-Shot Learning From Prior Model

Traditional magnetic tracking approaches based on mathematical models and optimization algorithms are computationally intensive, depend on initial guesses, and do not guarantee convergence to a global optimum. Although fully-supervised data-driven deep learning can solve the above issues, the demand for a comprehensive dataset hampers its applicability in magnetic tracking. Thus, we propose an annular magnet pose estimation network (called AMagPoseNet) based on dual-domain few-shot learning from a prior mathematical model, which consists of two sub-networks: PoseNet and CaliNet. PoseNet learns to estimate the magnet pose from the prior mathematical model, and CaliNet is designed to narrow the gap between the mathematical model domain (MMD) and the real-world domain (RWD). Experimental results reveal that AMagPoseNet outperforms the optimization-based method regarding localization accuracy (1.87 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 1.14 mm, 1.89 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm 0.81^{\circ }$</tex-math></inline-formula> ), robustness (non-dependence on initial guesses), and computational latency (2.08 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 0.02 ms). In addition, the six degrees of freedom (6-DoF) pose of the magnet could be estimated when discriminative magnetic field features are provided. With the assistance of the mathematical model, AMagPoseNet requires only a few real-world samples and has excellent performance, showing great potential for practical biomedical and industrial applications.

Helical Three Dimensional Reconstruction Using Bayesian Optimization for Cryogenic Electron Microscopy.

Three-dimensional (3D) reconstruction for cryogenic electron microscopy (cryo-EM) often falls into an ill-posed problem owing to several uncertainties in observations, including noise. To reduce excessive degree of freedom and avoid overfitting, the structural symmetry is often used as a powerful constraint. In the case of the helix, the entire 3D structure is determined by the subunit 3D structure and two helical parameters. There is no analytical method to simultaneously obtain both of the subunit structure and helical parameters. A common approach is to employ an iterative reconstruction in which the two optimizations are performed alternately. However, iterative reconstruction does not necessarily converge when a heuristic objective function is used for each optimization step. Also, the obtained 3D reconstruction highly depends on the initial guess of the 3D structure and the helical parameters. Herein, we propose a method for estimating the 3D structure and helical parameters that also performs an iterative optimization; however, the objective function for each step is derived from a single objective function to make the algorithm convergent and less sensitive to the initial guess. Finally, we evaluated the effectiveness of the proposed method by testing it on cryo-EM images, which were challenging to reconstruct using conventional methods.

Could initial guess of the ligament parameters during estimation procedures affect post-operative predictions of knee laxity following total knee arthroplasty?

Could initial guess of the ligament parameters during estimation procedures affect post-operative predictions of knee laxity following total knee arthroplasty?

Hydraulic Tomography Estimates Improved by Zonal Information From the Clustering of Geophysical Survey Data

AbstractHydraulic tomography (HT) has been demonstrated as a robust approach to characterize subsurface heterogeneity through the inverse modeling of multiple pumping data. However, smooth or even erroneous tomograms can result when insufficient observations are involved in the inversion. In this study, the feasibility of integrating geophysical survey data into HT analysis is investigated. First, k‐means clustering is utilized to extract zonal information from borehole geophysical logs, and a new type of spatial constraints containing geological knowledge is proposed to obtain improved hydrostratigraphic boundaries along boreholes. Next, zonation models are constructed by applying clustering‐based zone geometry and populating zonal estimates of hydraulic conductivity (K) from analyzing pumping data. Afterwards, zonation models are treated as the initial guess of spatial variability in the geostatistical inversion of HT analysis. Additionally, local K measurements can be utilized to further improve HT estimates. Comparative cases of HT analyses are designed for a numerical sandbox experiment to highlight the HT performance integrated with geophysical surveys, in which the geostatistical inversion is initialized with: (a) a homogeneous K field; (b) zonation models built by the clustering of disparate geophysical surveys with/without spatial constraints; and (c) zonation improved by incorporating local K measurements. Based on ln K field comparisons and validation through predictions of drawdowns and tracer plume migration from independent tests not used in the calibration effort, we find that integration of geophysical surveys into HT analysis by clustering with spatial constraints is demonstrated as an effective approach, and local K measurements can further improve HT estimates.

Astrodynamics-Informed Kinodynamic Sampling-Based Motion Planning for Relative Spacecraft Motion

This paper presents a sampling-based spacecraft relative motion planning algorithm to reconfigure a spacecraft from a given initial state to a desired final state, subject to kinodynamic (simultaneous kinematic and dynamics) constraints. We leverage theoretical advancement in the field of sampling-based motion planning in robotics and extend their application to achieve motion planning in astrodynamics. We present an astrodynamics-informed kinodynamic motion planning (AIKMP) algorithm that takes advantage of a spacecraft’s natural motion to compute a safe, fuel-efficient motion plan for spacecraft reconfiguration in a cluttered environment. This algorithm is developed in the relative orbital element space of the deputy spacecraft around a chief spacecraft that provides very useful geometric insight to relative spacecraft motion, as well as helps in generating an overall smooth final transfer trajectory without demanding additional postprocessing of the transfer solution. Through several example scenarios, we demonstrate that the AIKMP algorithm is regularly able to compute safe and fuel-efficient solutions to relative transfer problems. We also show that this algorithm iteratively improves on its computed solutions and thus holds the capability of finding near-optimal transfer solutions given a sufficient number of algorithm iterations—without requiring an initial guess of the solution.

An efficient gradient-enhanced kriging modeling method assisted by fast kriging for high-dimension problems

PurposeThe modeling cost of the gradient-enhanced kriging (GEK) method is prohibitive for high-dimensional problems. This study aims to develop an efficient modeling strategy for the GEK method.Design/methodology/approachA two-step tuning strategy is proposed for the construction of the GEK model. First, an auxiliary kriging is built efficiently. Then, the hyperparameter of the kriging model is served as a good initial guess to that of the GEK model, and a local optimal search is further used to explore the search space of hyperparameter to guarantee the accuracy of the GEK model. In the construction of the auxiliary kriging, the maximal information coefficient is adopted to estimate the relative magnitude of the hyperparameter, which is used to transform the high-dimension maximum likelihood estimation problem into a one-dimensional optimization. The tuning problem of the auxiliary kriging becomes independent of the dimension. Therefore, the modeling efficiency can be improved significantly.FindingsThe performance of the proposed method is studied with analytic problems ranging from 10D to 50D and an 18D aerodynamic airfoil example. It is further compared with two efficient GEK modeling methods. The empirical experiments show that the proposed model can significantly improve the modeling efficiency without sacrificing accuracy compared with other efficient modeling methods.Originality/valueThis paper developed an efficient modeling strategy for GEK and demonstrated the effectiveness of the proposed method in modeling high-dimension problems.

Model-free MIMO control tuning of a chiller process using reinforcement learning

The performance of HVAC equipment, including chillers, is continuing to be pushed to theoretical limits, which impacts the necessity for advanced control logic to operate them efficiently and robustly. At the same time, their architectures are becoming more complex; many systems have multiple compressors, expansion devices, evaporators, circuits, or other elements that challenge control design and resulting performance. In order to maintain respectful controlled speed of response, stability, and robustness, controllers are becoming more complex, including the move from thermostatic control, to proportional integrator (PI), and to multiple-input multiple-output (MIMO) controllers. Model-based control design works well for their synthesis, while having accurate models for numerous product variants is unrealistic, often leading to very conservative designs. To address this, we propose and demonstrate a learning-based control tuner that supports the design of MIMO decoupling PI controllers using online information to adapt controller coefficients from an initial guess during commissioning or operation. The approach is tested on a physics-based model of a water-cooled screw chiller. The method is able to find a controller that performs better than a nominal controller (two single PI controllers) in terms of decreasing deviations from the operating point during disturbances while still following reference changes.

Duty-cycle-aware low-thrust trajectory optimization using embedded homotopy

In space mission design, an important operational constraint is planned periodic coast arcs during which various mission-critical tasks such as navigation or ground communications are performed. These constraints, typically implemented as thruster duty cycles, can be characterized as discrete coast arcs enforced periodically during intervals of deterministic thrusting. A typical approach to incorporate duty cycles is by enforcing maximum thrust levels that are less than a nominal value. This work presents an embedded homotopy indirect optimization method for a smooth enforcement of discrete duty-cycle constraints for low-thrust trajectory optimization. The complexity of enforcing such discrete constraints is two-fold: (1) a precise event-detection strategy is needed to determine the beginning of deterministic thrust arcs, which must be successively updated along the trajectory and (2) a smooth modeling of the discrete coast events occurring on the order of 10s or even 100s depending on the duration of deterministic thrust arcs. Duty cycle constraints are enforced at the level of the Hamiltonian using a Composite Smooth Control (CSC) method, producing high-resolution optimal control solutions conscious of planned duty cycle coast arcs. Numerical solutions are presented for the heliocentric transfer phases of three space missions. The results are then validated against the Evolutionary Mission Trajectory Generator (EMTG), one of NASA’s global trajectory optimization tools used for interplanetary mission design and capable of the explicit enforcement of periodic duty cycle coasting. The proposed indirect method is suitable for obtaining high-resolution trajectory solutions with realistically enforced thruster duty cycle, which could then be used as high-quality initial guesses in flight-fidelity mission planning tools. The proposed smooth modeling of discrete coast arcs can also be customized to enforce periodic and non-periodic thrust shutdown constraints.

A two-level strategy for aeroelastic optimization of a 3D wing with constant and variable stiffness skins

In this work, optimization strategies employing a standard heuristic free-derivative algorithm combined with a first-order gradient approach are used to maximize the flutter or divergence airspeed, using the fibre material orientations as design variables. The aeroelastic stability analysis calculations are performed by a classical PK method. The finite element method is used to obtain the structural modes and frequencies and the unsteady aerodynamic influence coefficient matrices are obtained with a doublet-lattice model. Numerical studies are performed with a complex 3D model that includes curved surfaces and internal elements such as spars and ribs. The main goal of the article is to use the heuristic part with a small number of parameters, to reduce the design space and provide an efficient initial guess for the gradient search, so that the optimization complexity is substantially reduced. Results for constant and variable stiffness composite wings are presented for laminates with different numbers of plies. It is shown by several examples that the pres.

Physical Cyclic Animations

We address the problem of synthesizing physical animations that can loop seamlessly. We formulate a variational approach by deriving a physical law in a periodic time domain. The trajectory of the animation is represented as a parametric closed curve, and the physical law corresponds to minimizing the bending energy of the curve. Compared to traditional keyframe animation approaches, our formulation is constraint-free, which allows us to apply a standard Gauss--Newton solver. We further propose a fast projection method to efficiently generate an initial guess close to the desired animation. Our method can handle a variety of physical cyclic animations, including clothes, soft bodies with collisions, and N-body systems.

Preference-Based Multi-Robot Planning for Nuclear Power Plant Online Monitoring and Diagnostics

Current preventative maintenance paradigms in nuclear power plants carry several costly risks and challenges associated with component downtime and the need for human data collection. Preventative maintenance may be enabled by an online monitoring system that accurately assesses component condition and identifies potential faults. We present an approach for autonomous online monitoring and multiagent planning for robotic data collection. Under the occurrence of a fault, we utilize a machine learning model to form an initial guess of its nature, which we then refine by selectively measuring certain variables to gain additional information via a situation-aware variable selection model. To generate a multi-robot plan to conduct these measurements, we develop a preference-based planning framework within a linear temporal logic–based planning approach that prioritizes collecting data from the most important features. Finally, we demonstrate our approach on a case study using a simulated nuclear power plant circulating water system, showing fault diagnostic performance as well as simulated robot data collection.

A new hybrid rate optimization method to enhance oil recovery from Brugge field using streamline-driven injection efficiencies

BackgroundOptimization of waterflooding projects traditionally focuses on optimizing rate control of injector/producer wells to enhance recovered oil from reservoirs. In such projects, a complex, constrained, multi-variable problem is optimized to enhance the oil recovery performance of reservoirs. MethodsStreamline-based rate optimization has been applied as a robust method to find the optimal water injection strategy. The present study aims to optimize injector/producer wells rates using streamline-driven injection efficiencies. A heuristic algorithm (the so-called weights algorithm) was used in previous works. This study proposes a new hybrid particle swarm optimization (PSO)-weights method. The weights algorithm oil recovery results are dependent on the initial guesses to start searching the domain. PSO global search ability provides a proper set of initial guesses for the weights algorithm. Significant findingsThe hybrid method is implemented to optimize two reservoir models. First, the PSO-weights algorithm is applied on a 2-D homogenous model with 13 wells; after optimization, injectors/producers’ computed rate converged to known optimal rates. Second, the proposed algorithm has been tested to optimize the Brugge field and successfully afforded it quickly. The field oil production rate (FOPR) and the total field oil production (FOPT) results indicate an improvement in oil production. In addition, less trapped oil in saturation contours in different reservoir layers is reported.

Accelerating and enabling convergence of nonlinear solvers for Navier–Stokes equations by continuous data assimilation

This paper considers improving the Picard and Newton iterative solvers for the Navier–Stokes equations in the setting where data measurements or solution observations are available. We construct adapted iterations that use continuous data assimilation (CDA) style nudging to incorporate the known solution data into the solvers. For CDA-Picard, we prove the method has an improved convergence rate compared to usual Picard, and the rate improves as more measurement data is incorporated. We also prove that CDA-Picard is contractive for larger Reynolds numbers than usual Picard, and the more measurement data that is incorporated the larger the Reynolds number can be with CDA-Picard still being contractive. For CDA-Newton, we prove that the domain of convergence, with respect to both the initial guess and the Reynolds number, increases as the amount of measurement data is increased. Additionally, for both methods we show that CDA can be implemented as direct enforcement of measurement data into the solution. Numerical results for common benchmark Navier–Stokes tests illustrate the theory.

Redesign of high-precision reference orbit for interferometric SAR satellite with injection error

A two-step optimization algorithm is proposed to redesign a precision reference repeating sun-synchronous orbit for interferometric synthetic aperture radar satellites with injection error. This purpose is to design a new reference orbit for the satellite that deviates from the original preset orbit. Manoeuvring satellites to this new orbit consumes less propellant than manoeuvring to the original orbit. In addition, the repeatability of the orbit is a guarantee for obtaining good interference images, which puts higher requirements on the revisit accuracy of the redesign reference orbit. In the first step, the initial guess for reference orbital elements is designed by considering the global coverage of the Earth and the propellant consumption, taking into account the J2 and J4 perturbations. A search table of feasible solutions in the neighbourhood of the injection orbit is established. This approach, which is based on a search table, transforms the optimization of continuous variables in infinite space into the traversal of discrete variables in finite space, thus greatly reducing the optimization time. In the second step, the revisit accuracy of the satellite’s full-dimensional state vector is optimized under the orbit propagation of a high-order gravity field. Unlike traditional methods that only optimize the revisit error of position, this paper also optimizes that of velocity. A new optimization method for full-dimensional revisit error of state vector is proposed, which combines nested differential correction with non-dominated sorting genetic algorithm-II. Compared with the traditional genetic algorithms, the proposed nested differential correction method provides the non-dominated sorting genetic algorithm-II with more accurate initial values, which reduces the iterations. Finally, the simulation results show that the total velocity change from the actual injection orbit to the redesigned reference orbit is halved compared to the original preset orbit. Moreover, the revisit errors of position and velocity are within 1m and 1m/s, respectively.

Pynta─An Automated Workflow for Calculation of Surface and Gas-Surface Kinetics.

Many important industrial processes rely on heterogeneous catalytic systems. However, given all possible catalysts and conditions of interest, it is impractical to optimize most systems experimentally. Automatically generated microkinetic models can be used to efficiently consider many catalysts and conditions. However, these microkinetic models require accurate estimation of many thermochemical and kinetic parameters. Manually calculating these parameters is tedious and error prone, involving many interconnected computations. We present Pynta, a workflow software for automating the calculation of surface and gas-surface reactions. Pynta takes the reactants, products, and atom maps for the reactions of interest, generates sets of initial guesses for all species and saddle points, runs all optimizations, frequency, and IRC calculations, and computes the associated thermochemistry and rate coefficients. It is able to consider all unique adsorption configurations for both adsorbates and saddle points, allowing it to handle high index surfaces and bidentate species. Pynta implements a new saddle point guess generation method called harmonically forced saddle point searching (HFSP). HFSP defines harmonic potentials based on the optimized adsorbate geometries and which bonds are breaking and forming that allow initial placements to be optimized using the GFN1-xTB semiempirical method to create reliable saddle point guesses. This method is reaction class agnostic and fast, allowing Pynta to consider all possible adsorbate site placements efficiently. We demonstrate Pynta on 11 diverse reactions involving monodenate, bidentate, and gas-phase species, many distinct reaction classes, and both a low and a high index facet of Cu. Our results suggest that it is very important to consider reactions between adsorbates adsorbed in all unique configurations for interadsorbate group transfers and reactions on high index surfaces.

Broyden's method assisted differential evolution (BMADE) based selective harmonic elimination in a cascaded H‐bridge multilevel inverter

AbstractThis paper implements Broyden's Method Assisted Differential Evolution (BMADE) algorithm for eliminating third and fifth harmonics in the output voltage of 7‐level cascaded H‐Bridge multilevel inverter (CHB‐MLI) using selective harmonic elimination technique. Calculations of switching angles are done for various modulation index values (M). Initial guess for Broyden's method is calculated by Differential Evolution (DE). Exact value of switching angles is then calculated by Broyden's method using initial guess obtained from DE. Code of BMADE algorithm for obtaining the required switching angles is written in MATLAB. Results obtained with BMADE algorithm are compared with various other techniques that is, Genetic Algorithm (GA), DE, and Whale Optimization Algorithm (WOA). BMADE is able to successfully eliminate third and fifth order harmonics in the output voltage. Along with removing the desired harmonics, BMADE also provides lower THD than GA, DE, and WOA for certain range of M. The results also showed that BMADE is faster than GA, DE, and WOA as the execution time of BMADE is lesser than GA, DE, and WOA. Moreover, laboratory experiments are used to test the simulation's findings. The experimental results support the simulation results.

One-dimensional magnetotelluric (MT) data inversion modeling using convolutional neural network

The magnetotelluric method is a geophysical method commonly used to map subsurface resistivity. The subsurface’s true resistivity is generated by inversion of the magnetotelluric data. Inversions carried out using conventional methods such as linear and global approaches have several limitations including the need for an initial model, models trapped in local minima, a large number of iterations and long computation time. To overcome the drawbacks, this paper proposes to invert one-dimensional magnetotelluric data using one of the deep learning methods, the convolutional neural network, which is heavily inspired by the human nervous system. This method starts by training the network with large amounts of data. The trained network is then used for inversion by receiving input in the form of apparent resistivity data and generating true resistivity and thickness values instantly. This method has been tested on synthetic data with curves of type A, H, K, and Q. The inversion results show that the convolutional neural network could approach the true resistivity and thickness values with a fairly small error and extremely fast computation time without initial model guess and iteration.

Identifying Parameters of Reactor Operation Digital Twin by Using Swarm and Evolutionary Algorithms

Digital twin (DT) technology is currently gaining popularity in a variety of industrial applications. Recently, the China Institute of Nuclear Power proposed a data driven by nuclear reactor digital twin. The digital twin solves the forward problem for physical field simulation and the inverse problem for parameter identification. The inverse problem can be viewed as a black-box optimization problem where the input parameters are identified by the Latin hypercube sampling (LHS) method based on a given partial observation. While LHS is relatively naive, in this paper, we proposed to apply swarm and evolutionary algorithms to solve the inverse problem. Specifically, we present an experimental comparative study for LHS and four popular SEAs, Particle Swarm Optimizer (PSO), Differential Evolution (DE), Evolutionary Strategy (ES), and evolution strategy with covariance matrix adaptation (CMA-ES). The results show that, for this inverse problem, SEAs are more accurate and efficient than LHS. We also investigate the comparative optimization algorithm’s searching capability under the conditions of noisy observations and no initial input parameter guesses. The experimental results show that DE and CMA-ES have strong robustness and high searching ability.