Initial Guess Research Articles

Estimating Mean Wind Profiles Inside Realistic Urban Canopies

Mean wind profiles within a unit-aspect-ratio street canyon have been estimated by solving the three-dimensional Poisson equation for a set of discrete vortex sheets. The validity of this approach, which assumes inviscid vortex dynamics away from boundaries and a small nonlinear contribution to the growth of turbulent fluctuations, is tested for a series of idealised and realistic flows. In this paper, the effects of urban geometry on accuracy are examined with neutral flow over shallow, deep, asymmetric and realistic canyons, while thermal effects are investigated for a single street canyon and both bottom cooling and heating. The estimated mean profiles of the streamwise and spanwise velocity components show good agreement with reference profiles obtained from the large-eddy simulation: the canyon-averaged errors (e.g., normalised absolute errors around 1%) are of the same order of magnitude as those for the unit-aspect-ratio street canyon. It is argued that the approach generalises to more realistic flows because strong spatial localisation of the vorticity field is preserved. This work may be applied to high-resolution modelling of winds and pollutants, for which mean wind profiles are required, and fast statistical modelling, for which physically-based estimates can serve as initial guesses or substitutes for analytical models.

Atlas of Optimal Low-Thrust Rephasing Solutions in Circular Orbit

In this paper, the time- and propellant-optimal low-thrust rephasing problems in circular orbit are studied to depict their solution spaces in an atlas. The rephasing problem is known as the same-orbit rendezvous from different angular positions. It is generally solved by some optimization methods, but its whole solution space is rarely investigated due to many key parameters. To reduce the number of parameters, a set of linearized equations of motion is developed based on the Sundman transformation, and two reduced shooting functions are formulated using the minimum principle and symmetry properties. Only one key parameter is identified for the time-optimal problem, while two key parameters are obtained for the propellant-optimal one. Numerical investigation of the relationships between these parameters and shooting variables reveals that they can be depicted by some curve (or contour) maps and approximated by piecewise functions (or linear interpolations). For the relatively short- or long-term rephasing cases, some analytical time- and propellant-optimal solutions are proposed and consistent with the numerical solutions. Numerical results demonstrate that the proposed solutions can provide good initial guesses to solve the low-thrust rephasing problems with nonlinear dynamics. Moreover, the approximations of the performance indexes can be used in the preliminary mission design.

Highly Accurate Wavelet Solution for Bending and Free Vibration of Circular Plates Over Extra-Wide Ranges of Deflections

Abstract The wavelet multiresolution interpolation Galerkin method in which both the unknown functions and nonlinear terms are approximated by their respective projections onto the same wavelet space is utilized to implement the spatial discretization of the highly coupled and nonlinear Von Karman equation for thin circular plates with various types of boundary conditions and external loads. Newton’s method and the assumption of a single harmonic response are then used for solving the static bending and free vibration problems, respectively. Highly accurate wavelet solutions for an extremely wide range of deflections are finally obtained by the proposed method. These results for moderately large deflections are in good agreement with existing solutions. Meanwhile, the other results for larger deflections are rarely achieved by using other methods. Comparative studies also demonstrate that the present wavelet method has higher accuracy and lower computational cost than many existing methods for solving geometrically nonlinear problems of thin circular plates. Moreover, the solutions for large deflection problems with concentrated load support the satisfactory capacity for handling singularity of the proposed wavelet method. In addition, a trivial initial guess, such as zero, can always lead to a convergent solution in very few iterations, even when the deflection is as large as over 46 times thickness of plate, showing an excellent convergence and stability of the present wavelet method in solving highly nonlinear problems.

Quantum variational algorithms are swamped with traps

One of the most important properties of classical neural networks is how surprisingly trainable they are, though their training algorithms typically rely on optimizing complicated, nonconvex loss functions. Previous results have shown that unlike the case in classical neural networks, variational quantum models are often not trainable. The most studied phenomenon is the onset of barren plateaus in the training landscape of these quantum models, typically when the models are very deep. This focus on barren plateaus has made the phenomenon almost synonymous with the trainability of quantum models. Here, we show that barren plateaus are only a part of the story. We prove that a wide class of variational quantum models—which are shallow, and exhibit no barren plateaus—have only a superpolynomially small fraction of local minima within any constant energy from the global minimum, rendering these models untrainable if no good initial guess of the optimal parameters is known. We also study the trainability of variational quantum algorithms from a statistical query framework, and show that noisy optimization of a wide variety of quantum models is impossible with a sub-exponential number of queries. Finally, we numerically confirm our results on a variety of problem instances. Though we exclude a wide variety of quantum algorithms here, we give reason for optimism for certain classes of variational algorithms and discuss potential ways forward in showing the practical utility of such algorithms.

M³LVI: a multi-feature, multi-metric, multi-loop, LiDAR-visual-inertial odometry via smoothing and mapping

PurposeThe purpose of this paper is to propose a multi-feature, multi-metric and multi-loop tightly coupled LiDAR-visual-inertial odometry, M3LVI, for high-accuracy and robust state estimation and mapping.Design/methodology/approachM3LVI is built atop a factor graph and composed of two subsystems, a LiDAR-inertial system (LIS) and a visual-inertial system (VIS). LIS implements multi-feature extraction on point cloud, and then multi-metric transformation estimation is implemented to realize LiDAR odometry. LiDAR-enhanced images and IMU pre-integration have been used in VIS to realize visual odometry, providing a reliable initial guess for LIS matching module. Location recognition is performed by a dual loop module combined with Bag of Words and LiDAR-Iris to correct accumulated drift. M³LVI also functions properly when one of the subsystems failed, which greatly increases the robustness in degraded environments.FindingsQuantitative experiments were conducted on the KITTI data set and the campus data set to evaluate the M3LVI. The experimental results show the algorithm has higher pose estimation accuracy than existing methods.Practical implicationsThe proposed method can greatly improve the positioning and mapping accuracy of AGV, and has an important impact on AGV material distribution, which is one of the most important applications of industrial robots.Originality/valueM3LVI divides the original point cloud into six types, and uses multi-metric transformation estimation to estimate the state of robot and adopts factor graph optimization model to optimize the state estimation, which improves the accuracy of pose estimation. When one subsystem fails, the other system can complete the positioning work independently, which greatly increases the robustness in degraded environments.

Optimisation method for automatic selection of rate constants of global reaction mechanisms

Optimisation approach to automate selection of global reaction mechanisms rate constants is proposed and studied. The objective of optimisation is to find reaction rate constants minimising deviation of some flame characteristics (e.g. laminar burning velocity, ignition delay time, etc.) calculated by global mechanism from their reference values known from experiments or computed by detailed mechanisms. Examples of one, two and four step mechanisms optimisation with respect to laminar burning velocity and concentration distributions in counterflow diffusion flame are given. Computer codes implementing optimisation algorithm for these examples are also afforded and can be modified and used for reaction constants selection in various applications. Uniqueness of singlecriteria and multicriteria optimisation solutions is studied numerically by computations with different initial guesses and by direct evaluation of the objective functions. Particularly, it is found that for considered global mechanisms the minimum value of objective function is reached in some subdomain of the parametric space. This means that any values of rate parameters from this subdomain results in almost the same deviations of chosen flame characteristic from its reference value.

Efficient Construction of Canonical Polyadic Approximations of Tensor Networks.

We consider the problem of constructing a canonical polyadic (CP) decomposition for a tensor network, rather than a single tensor. We illustrate how it is possible to reduce the complexity of constructing an approximate CP representation of the network by leveraging its structure in the course of the CP factor optimization. The utility of this technique is demonstrated for the order-4 Coulomb interaction tensor approximated by two order-3 tensors via an approximate generalized square-root (SQ) factorization, such as density fitting or (pivoted) Cholesky. The complexity of constructing a four-way CP decomposition is reduced from (for the nonapproximated Coulomb tensor) to (for the SQ-factorized Coulomb tensor), where n and RCP are the basis and CP ranks, respectively. This reduces the cost of constructing the CP approximation of two-body interaction tensors of relevance to accurate many-body electronic structure by up to 2 orders of magnitude for systems with up to 36 atoms studied here. The full four-way CP approximation of the Coulomb interaction tensor is shown to be more accurate than the known approaches which utilize CP-factorizations of the SQ factors (which are also constructed with an cost), such as the algebraic pseudospectral and tensor hypercontraction approaches. The CP-decomposed SQ factors can also serve as a robust initial guess for the four-way CP factors.

Perception, Path Planning, and Flight Control for a Drone-Enabled Autonomous Pollination System

The decline of natural pollinators necessitates the development of novel pollination technologies. In this work, we propose a drone-enabled autonomous pollination system (APS) that consists of five primary modules: environment sensing, flower perception, path planning, flight control, and pollination mechanisms. These modules are highly dependent upon each other, with each module relying on inputs from the other modules. In this paper, we focus on approaches to the flower perception, path planning, and flight control modules. First, we briefly introduce a flower perception method from our previous work to create a map of flower locations. With a map of flowers, APS path planning is defined as a variant of the Travelling Salesman Problem (TSP). Two path planning approaches are compared based on mixed-integer programming (MIP) and genetic algorithms (GA), respectively. The GA approach is chosen as the superior approach due to the vast computational savings with negligible loss of optimality. To accurately follow the generated path for pollination, we develop a convex optimization approach to the quadrotor flight control problem (QFCP). This approach solves two convex problems. The first problem is a convexified three degree-of-freedom QFCP. The solution to this problem is used as an initial guess to the second convex problem, which is a linearized six degree-of-freedom QFCP. It is found that changing the objective of the second convex problem to minimize the deviation from the initial guess provides improved physical feasibility and solutions similar to a general-purpose optimizer. The path planning and flight control approaches are then tested within a model predictive control (MPC) framework where significant computational savings and embedded adjustments to uncertainty are observed. Coupling the two modules together provides a simple demonstration of how the entire APS will operate in practice.

Modified homotopy perturbation method and its application to analytical solitons of fractional-order Korteweg–de Vries equation

BackgroundExperimentally brought to light by Russell and hypothetically explained by Korteweg–de Vries, the KDV equation has drawn the attention of several mathematicians and physicists because of its extreme substantial structure in describing nonlinear evolution equations governing the propagation of weakly dispersive and nonlinear waves. Due to the prevalent nature and application of solitary waves in nonlinear dynamics, we discuss the soliton solution and application of the fractional-order Korteweg–de Vries (KDV) equation using a new analytical approach named the “Modified initial guess homotopy perturbation.”ResultsWe established the proposed technique by coupling a power series function of arbitrary order with the renown homotopy perturbation method. The convergence of the method is proved using the Banach fixed point theorem. The methodology was demonstrated with a generalized KDV equation, and we applied it to solve linear and nonlinear fractional-order Korteweg–de Vries equations, which are in Caputo sense. The method’s applicability and effectiveness were established as a feasible series of arbitrary orders that accelerate quickly to the exact solution at an integer order and are obtained as solutions. Numerical simulations were conducted to investigate the effect of Caputo fractional-order derivatives in the dispersion and propagation of water waves by varying the order alpha on the [0,1] interval. Comparative analysis of the simulation results, which were presented graphically and discussed, reveals that the degree of freedom of the Caputo fractional-order derivative is vital to controlling the magnitude of environmental hazards associated with water waves when adjusted.ConclusionThe proposed method is recommended for obtaining convergent series solutions to fractional-order partial differential equations. We suggested that applied mathematicians and physicists investigate this work to better understand the impact of the degree of freedom posed by Caputo fractional-order derivatives in wave dispersion and propagation, as physical applications can help divert wave-related environmental hazards.

Theoretical dispersion curves for borehole real-valued wave modes in vertically transverse isotropic formations

The dispersion curves of real-valued modes in a fluid-filled borehole are widely used in acoustic well logging. The accurate dispersion curves are the precondition of theoretical analysis and inversion process. Generally, these curves can be obtained by solving the conventional dispersion equation for isotropic formations and most vertically transverse isotropy (VTI) formations. However, if the real-valued solutions exist when the radial wavenumbers for the formation quasi-P and quasi-S equals to each other, the existed methods based on the conventional dispersion equation could lead to incorrect results for some VTI formations. Few studies have focused on the influence of these real-valued solutions on dispersion curve extraction. To remove these real-valued solutions, we have proposed a modified dispersion equation and its corresponding solving process. When solving the dispersion equation, the Scholte wave velocity of VTI formation at high frequency is used as the initial guess. The two synthetic examples including fast and slow VTI formations validate that these real-valued solutions do not contribute to the wavefield, and the new dispersion curve extraction method is suitable for all kinds of VTI formations. Consequently, the method can provide reliable dispersion curves for both theoretical analysis and anisotropic parameters inversion in VTI formations.

Fourier Transform Infra-Red (FTIR) Spectrum Characterization of Bacillus Mycoides

The presence of Bacillus mycoides and its ability to grow and spread quickly certainly affect the growth of the target pathogen and it can cause invalid detection results. Therefore, the presence of contaminant bacteria needs to be detected to ensure the specificity of the detection results against the target pathogenic bacteria. Various kinds of detection methods are commonly used, such as ELISA (enzyme-linked immunosorbent assay) and PCR (polymerase chain reaction) are time-consuming and not always very specific. Fourier-transform infrared (FTIR) spectroscopy methods were adopted to provide a comprehensive and reliable method for bacterial analysis. In this study, FTIR spectroscopy was used as an initial guess for the identification of bacterial isolates. Our results showed that there are dominant peaks from the FTIR spectrum obtained that were most associated with protein and carbohydrate in the range of wave number 400-4000 cm-1.

Optimal Projected Circular Orbit for Spacecraft Formation Flying Near a Slowly Rotating Asteroid

In spacecraft formation flying missions, the projected circular (relative) orbit (PCO), which appears circular when viewed along the zenith-nadir direction of the nominal chief spacecraft, is suitable for constructing a synthetic aperture radar. In this paper, the analysis of a PCO for spacecraft formation flying near a slowly rotating asteroid is conducted. By matching the in-plane and out-of-plane relative motion frequency, the critical values of the initial phase angle that characterizes the PCO are identified, resulting in the minimum precession of relative orbit. The analysis is then utilized to develop the fuel-optimal control law for establishing a target PCO. In particular, the fuel-optimal problem is addressed with an indirect method, where a homotopy approach is adopted, and the initial (unknown) costate vector is calculated with a scaling technique, so that the sensitivity to the initial guess problem is mitigated.

Optimal design of robotic work-cell through hierarchical manipulability maximization

The increasing requests for flexible robotic applications involving the rapid relocation of the robot manipulator , possibly mounted on a mobile base, imposes tolerance to imprecise positioning. The high manipulability of the nominally designed poses, i.e. , the capacity to change the position and the orientation of a given robot joint configuration’s end-effector, is often considered a proxy for robustness to imprecise positioning. This work presents a method for choosing target end-effector poses to manipulate bulky objects in complex environments. The paper proposes a two-layer optimizer connected in cascade to maximize the manipulability and achieve reasonable computational time. First, using a genetic algorithm (GA) allows a global search for a satisfactory solution to the target poses of the task at the same time. Subsequently, the output of the GA becomes the initial guess for the simulated annealing (SA) algorithm, which locally maximizes each pose’s manipulability separately. The feasibility of the connecting trajectories and collisions are checked in both layers. Experiments show the method’s ability to find excellent solutions within a limited time, considering a complex problem involving manipulating large objects in a cluttered environment. The simulations of three working scenarios allowed testing of the proposed method. The final validation of the algorithm was on two relevant industrial use-cases: the manipulation of sidewalls and the manipulation of cargo panels inside an aircraft fuselage . • Optimal robotic workcell design can be a hard problem in some situations. • A tool is provided to optimize the robot position with respect to target poses. • Cascaded optimization allows for fast solutions search in complex environments. • Global optimization of the whole set of tasks followed by single task refinement.

Numerical Determination of Thermal Conductivity in Heat Equation under Nonlocal Boundary Conditions and Integral as Over specified Condition

In this article, an inverse problem of finding timewise-dependent thermal conductivity has been investigated numerically. Numerical solution of forward (direct) problem has been solved by finite-difference method (FDM). Whilst, the inverse (indirect) problem solved iteratively using Lsqnonlin routine from MATLAB. Initial guess for unknown coefficient expressed by explicit relation based on nonlocal overdetermination conditions and intial input data .The obtained numrical results are presented and discussed in several figures and tables. These results are accurate and stable even in the presense of noisy data.

Extended real-time voltage instability identification method based on synchronized phasor measurements

This paper presents an extended adaptive approach designed to accurately estimate the Thévenin equivalent parameters using phasor measurements at a given bus for measurements lying in any of four quadrants of the PQ-plane. The improvement is achieved by using a new condition to properly update the estimated parameters after an initial guess. Based on an adaptive philosophy, the proposed approach can correctly account for the intrinsic nonlinearities of a power system, can provide a real-time estimation of Thévenin parameters, and does not require network topology knowledge. The method is validated using the Kundur 2-area system, showing estimation improvements compared to the current adaptive approach and the classical recursive least-squares method. The proposed approach is able to estimate both sides of the system with respect to the measurement bus. In addition, a data-driven voltage stability index is developed. To illustrate the performance of the proposed approach in a larger power system, a voltage stability assessment is carried out on the IEEE 39-bus system, considering the action of overexcitation limiters of generators and nonlinear loads. The proposed approach is suitable for applications that require an accurate Thévenin equivalent estimation in real-time, such as for voltage stability assessment. The new approach provides a reliable tool for the system operators to make proper and timely decisions.

Phase retrieval algorithm using edge point referencing.

In the past few decades, extensive research and efforts have been made for developing a phase retrieval iterative algorithm (PRA) for reconstructing a complex object from far-field intensity equivalently from the object autocorrelation. Since most of the existing PRA techniques employ a random initial guess, the reconstruction output sometimes changes in different trials leading to a non-deterministic output. Additionally, the output of such algorithm occasionally either shows non-convergence, needs a longer time to converge, or shows the twin-image problem. Due to these problems, PRA methods are unsuitable for cases where consecutive reconstructed outputs need to be compared. In this Letter, a novel, to the best of our knowledge, method is developed and discussed using edge point referencing (EPR). In the EPR scheme, in addition to illuminating a region of interest (ROI) of the complex object, a small area near the periphery of the complex object within the ROI is illuminated with an additional beam. Such illumination creates an imbalance in the autocorrelation that can be used to improve the initial guess for achieving unique deterministic output free from the aforementioned problems. Furthermore, by introducing the EPR, one can also achieve faster convergence. To support our theory, derivation, simulations, and experiment are performed and presented.

A robust numerical treatment of solid-phase diffusion in pseudo two-dimensional lithium-ion battery models

Solid-phase diffusion in active materials of lithium-ion batteries significantly affects charging and safety-related behavior of lithium-ion batteries. Therefore, it is essential to develop an efficient and robust numerical algorithm for solving solid-phase diffusion equations in physics-based battery models. In this work, we discuss the origins of numerical instabilities that can occur when solving the solid-phase diffusion equations using iterative methods. Then, in order to resolve such issues, we propose a simple numerical treatment to the surface flux term of discretized solid-phase diffusion equations. To demonstrate its numerical robustness, the proposed method is implemented into a pseudo two-dimensional (P2D) physics-based battery model and simulations are conducted at wide ranges of operating conditions. Even with extremely poor initial guesses for the Li+ concentrations of the active materials, computations using the proposed method do not diverge and the their computational speeds are comparable to those with conventional initial guesses. Comprehensive tests of the proposed method are also performed with a dynamic current profile based on US06 driving profile and a multi-stage charging profile with very high initial C-rate (12C).

Application of generalized finite difference method for elastoplastic torsion analysis of prismatic bars

In this paper, the generalized finite difference method (GFDM) is employed for the elastic-plastic torsion analysis of prismatic bars, and the generalized finite difference numerical scheme of the elastic-plastic torsion governing equation is derived. This approach divides the computational domain into a series of overlapping sub-domains and constructs a system of linear equations based on Taylor series expansion and moving least squares. With the help of Picard's iterative method, the elastic solution is utilized as the initial guess to reach the elastic-plastic solution. The plastic nonhomogeneous term is then evaluated via radial basis function (RBF) interpolation. Since the generalized finite difference method does not require intra-domain integration and allows random distribution of nodes, it could simply deal with complex computational domain problems. In numerical experiments, the elastic-plastic torsion examples of square-section bars and linear guide rail reveal that the numerically developed generalized finite difference model is a reliable and effective analysis solution for elastic-plastic torsion problems of prismatic bars.

A novel method to design monolithic catalysts for non-isothermal packed-bed reactors using topology optimisation

This research investigates the application of topology optimisation to the design of monolithic catalysts for packed-bed reactors with endothermic reactions. A reactor model has been developed based on the main assumptions of laminar flow and a first-order reaction. The model includes a catalytic reaction whose rate is determined by a proposed Arrhenius equation along with mass transfer limitations. Using the density-based method, the optimisation problem is formulated as a catalyst distribution problem. The catalyst volume fraction of elements in the discretised design domain determines the geometry of the monolithic structure and consequently the momentum, heat, and mass transfer characteristics of the reactor. By a combination of interpolation functions, continuous material properties and a sufficient penalisation for the intermediate fluid volume fraction values are derived. The Globally Convergent Method of Moving Asymptotes (GCMMA) was employed to solve the optimisation problem. The effects of initial guesses, the energy dissipation constraint, and the Peclet number on the design are investigated in a 2D framework. Then through a 3D optimisation, a complex structure with enhanced mass transfer, thermal, and hydraulic behaviour is developed. Compared to a reference honeycomb geometry with the same catalyst volume fraction, the resulting 3D optimised geometry shows quantitative improvements in terms of the conversion and pressure drop.

Enhancing high-fidelity nonlinear solver with reduced order model

We propose the use of reduced order modeling (ROM) to reduce the computational cost and improve the convergence rate of nonlinear solvers of full order models (FOM) for solving partial differential equations. In this study, a novel ROM-assisted approach is developed to improve the computational efficiency of FOM nonlinear solvers by using ROM’s prediction as an initial guess. We hypothesize that the nonlinear solver will take fewer steps to the converged solutions with an initial guess that is closer to the real solutions. To evaluate our approach, four physical problems with varying degrees of nonlinearity in flow and mechanics have been tested: Richards’ equation of water flow in heterogeneous porous media, a contact problem in a hyperelastic material, two-phase flow in layered porous media, and fracture propagation in a homogeneous material. Overall, our approach maintains the FOM’s accuracy while speeding up nonlinear solver by 18–73% (through suitable ROM-assisted FOMs). More importantly, the proximity of ROM’s prediction to the solution space leads to the improved convergence of FOMs that would have otherwise diverged with default initial guesses. We demonstrate that the ROM’s accuracy can impact the computational efficiency with more accurate ROM solutions, resulting in a better cost reduction. We also illustrate that this approach could be used in many FOM discretizations (e.g., finite volume, finite element, or a combination of those). Since our ROMs are data-driven and non-intrusive, the proposed procedure can easily lend itself to any nonlinear physics-based problem.