quasi-Newton Iterative Method Research Articles

Calculation of ship floating state by quasi-Newton iteration method for onboard loading computer

ABSTRACT Calculating the floating state of a ship is the basic function of onboard loading computer, which is crucial for ship safety. Aiming at the deficiencies in the existing algorithms, we used the quasi-Newton iteration method to calculate the floating state of a ship. Firstly, the section model database of ship's hull was established by cutting the stereolithographic (STL) 3D model which is created by ship design software. Then, Sutherland–Hodgma polygon clipping algorithm and Shoelace Formula were used to calculate the Jacobian matrix. Finally, We selected a 108,000 DWT bulk carrier, ADMIRAL SCHMIDT, as an example to verify the correctness of the algorithm. We performed 100,000 random loading numerical tests, the average number of iterations was 2–3, and the number of convergence failures was zero. We calculated 24 typical standard loading conditions. We found the maximum average absolute error of the draught and trim were 0.0081 and −0.0283 m, respectively. The calculation error was far less than the requirements of the classification society. The results showed that the Quasi-Newton iteration method is simple to implement and easy to program, and has high robustness and accuracy and appropriate convergence. The method is suitable for the real-time calculation of a ship's floating state and has considerable engineering application value.

A Multi-medium and Multi-mechanism model for CO2 injection and storage in fractured shale gas reservoirs

Under the background of “dual-carbon”, it is strategically significant to use shale gas reservoirs for CO2 injection and storage. Injection of CO2 into shale formations can improve natural gas recovery and achieve effective storage of CO2. However, due to the complex characteristics of shale reservoirs, like complex fractures and a variety of flow mechanisms, few work has been done to comprehensively consider those complex characteristics for accurate reservoir simulation of CO2 injection and storage. Therefore, to improve this situation, this paper establishes a fully coupled model of the matrix, natural fracture and hydraulic fracture, which considers multiple mechanisms, including adsorption/desorption, diffusion, stress sensitivity of fracture and stimulated reservoir volume (SRV). The embedded discrete fracture model (EDFM) is applied to describe the transfer flow between matrix-fracture, fracture-fracture and fracture-well. The finite volume and quasi-Newton iterative methods are used to solve the model. The model's reliability and practicability are verified by matching the production history of commercial software in shale gas reservoirs. The effects of various factors on the production curve and CO2 storage characteristics are analyzed, including adsorption/desorption, diffusion, stress sensitivity, well production pressure, CO2 injection rate, CO2 injection opportunity and fracture parameters. The results show that the model is reliable and practical and can be used to study the dynamic performances of enhanced shale gas recovery and CO2 storage.

Real-time modeling of transient behavior of the primary coolant system in pool-type sodium cooled fast reactor

In the paper, a real-time simulation code THCSA-RT is developed to analyze the primary coolant system of pool-type sodium cooled fast reactor which includes reactor core, hot and cold sodium pools, pumps, and intermediate heat exchangers. Different numerical methods including Gear multi-value method and Quasi-Newton iteration method are used to solve the mass and energy equations set and the momentum equations set, respectively. Several typical design basis conditions of CEFR such as planned shutdown condition and RIA are analyzed, and the calculation results agree well with those of the final safety analysis report calculated by DINROS. The simulation time is presented to prove the effectiveness of the new numerical methods developed in the present work, and the new numerical methods could be applied in the similar system analysis codes as well. The newly developed code THCSA-RT could be used in the system real-time simulation of pool-type sodium cooled fast reactor and has been adopted in the development of CEFR full scope simulator.

Realization of Accurate Modeling and Simulation of Oilfield Water Mixing Gathering and Transportation System

In order to solve the shortcomings that the simulation accuracy of oilfield water mixing gathering and transportation system is not high, the dual-process of mixing water and returning to the station cannot be realized at the same time, the system is accurately modeled, and the data structure and computer model suitable for calculation are established by reading static data. The design modeling software realizes the logical and data interface and realizes the display of the physical model on the computer. Based on the quasi-Newton loop iteration method, an online algorithm is proposed. Using the flow rate of each node of the system as the constraint condition, the water mixing process node and pipeline parameters are calculated. According to the calculation results and the oil well produced fluid parameters, the principle of mixed calorimetry is applied to construct the initial value and iterative formula of the return flow simulation. The temperature at the return station is consistent with the inlet temperature of the heating furnace at the joint station. It can dynamically reflect the production and operation status of the water mixing system, and provide a scientific basis for the control and operation of the water mixing system.

Inverse scattering problem for detecting a defect in a magnetoelastic layer

ABSTRACT This work is devoted to studying a direct and inverse scattering problem for a magnetoelastic layer having a defect, in the frame of the electromagnetic theory. In terms of the displacement field over the defect's contour, a coupled system of boundary integral equations is formulated, for magnetically permeable and impermeable defects. To identify the position and size of the defect, an efficient numerical algorithm is developed by using the quasi-Newton iterative method. In order to check the influence of the magnetic field upon the scattering waves from the layer, a series of numerical examples is presented with different noise levels. The results showed that the magnetic field has a sensitive effect on the identification process when the external magnetic field increases, especially for the materials having a high magnetic permeability factor . Also, a special inverse problem for predicting the external applied magnetic field, upon a copper layer having a defect with various sizes, has been performed.

Microwave Correlation Forward-Looking Super-Resolution Imaging Based on Compressed Sensing

Forward-looking correlated imaging plays an increasingly important role in modern radar imaging systems. It overcomes disadvantages of traditional side or squint synthetic aperture radar (SAR) which is dependent on specific relative motion between the radar and target scene. A new microwave forward-looking correlated 3-D imaging method based on random radiation field combined with sparse reconstruction is proposed in this article. Firstly, phased array radar (PAR) is adopted to form different and random antenna patterns. Then, combined with the compressed sensing (CS) theory, the target image can be recovered with very few samples which can break through Rayleigh resolution limitation. Furthermore, the proposed method can achieve resolution at least 5.5 times higher than real aperture imaging. To raise computation efficiency of sparse reconstruction, an improved quasi-Newton iteration method based on graphics processing unit (GPU) platform is developed. Meanwhile, a GPU-based (NVIDIA Tesla K40c) accelerated computing method can significantly reduce the processing time compared with the time given by a personal computer (PC). Both simulation and field experiment verify the validity of the proposed method.

Robust radiobiological optimization of ion beam therapy utilizing Monte Carlo and microdosimetric kinetic model

To develop a Monte Carlo (MC)-based and robust ion beam therapy optimization system that separates the optimization algorithm from the relative biological effectiveness (RBE) modeling. Robustly optimized dose distributions were calculated and compared across three ion therapy beams (proton, helium, carbon). The effect of different averaging techniques in calculating RBE in mixed beams was also investigated. Ion particles were transported in TOPAS MC. The microdosimetric-kinetic model (MKM) parameter, saturation corrected specific energy (), was calculated with a customized MKM implementation in TOPAS MC. Intensity modulated ion therapy robust optimization was performed by a quasi-Newton iterative method based on dose-volume objective function. The robust optimization took setup and range uncertainties into account. In the present work, the biological dose for each individual spot was calculated, and then summed together to calculate total biological dose. In other published works, radiosensitive parameters, such as , were first averaged over all beam spots within a mixed-beam field, after which biological dose was calculated using the averaged radiosensitive parameters. The difference between the two mixed-beam biological dose calculations was quantified. Robust plans were achieved with the three particle types. The effect of averaging depended on particle type. The difference between biological doses calculated with individual and averaged may be greater than 3% for a carbon beam. MC based radiobiological and robust optimization was made flexible to incorporate dose-volume histogram constraints and to be independent of RBE models. Iterative optimization with RBE models was feasible. Evaluation of the RBE calculation for mixed beam could be necessary if better accuracy was demanded.

A Mathematical Model of Lubricant Film Flow Velocity on a Belt Type Oil Skimmer in a Part of Wastewater Treatment Process Using a Finite Difference Method with Quasi-Newton Iterative Technique

Oil skimmer is a useful tool in recovering all types of floating waste oils, greases and fats from water surfaces. Lubricant film flow velocity approximation is an important problem of oil skimmer belt speed adjustment. The adjustment belt speed level is up to several physical parameters of oil types. A thin lubricant film flow velocity on a moving belt oil skimmer can be modeled in a form of a nonlinear differential equation as a boundary value problem. The model is providing the lubricant film flow velocity in each thickness layers. In this research, a centered in space finite difference method and a Quasi-Newton iterative method are proposed to approximate the solutions of the nonlinear thin lubricant film flow velocity model. Their numerical simulations of a thin lubricant film flow velocity on a moving oil skimmer belt with varied physical parameters are investigated. The proposed numerical techniques give good agreement approximated solutions in several moving belts speed levels with the external force factor. These are then useful to achieve the optimum belt oil skimmer speed for each lubricant type.

Development of a multi-continuum quadruple porosity model to estimate CO2 storage capacity and CO2 enhanced shale gas recovery

Geologic storage of CO2 in shale formation not only enhances natural gas recovery, but also sequestrates CO2 effectively. According to this technology, a multi-continuum quadruple porosity binary component gas model is developed to investigate carbon dioxide storage capacity and CO2 enhanced shale gas recovery, which is based on multiple flow mechanisms, including dissolution, adsorption/desorption, viscous flow, diffusion, slip flow and stress sensitivity of hydraulic fractures. This fully coupled model is divided into quadruple media, including organic matters, organic pore system, matrix system and natural fracture system. The matrix-fracture transfer flow is simulated by modified multiple interacting continua (MINC) method. Embedded discreate fracture model (EDFM) is introduced to describe the gas flow in hydraulic fractures and the transfer flow between hydraulic fractures and natural fractures. Finite difference method (FDM) and quasi-Newton iterative method are applied to solve this model. The reliability and practicability of this model is validated by matching the production history of a fractured horizontal well in shale gas reservoir. The effects of relevant parameters on production curves are analyzed, including adsorption parameters, dissolution parameters, well production pressure, injection pressure, volumetric fraction of kerogen and injection opportunity. The result shows that the model in this work is reliable and practicable, and the model presented here can be used to investigate the injectivity of CO2 and CO2 enhanced shale gas recovery.

Efficient and Robust Inverse Simulation Techniques Using Pseudo-Spectral Integrator with Applications to Rotorcraft Aggressive Maneuver Analyses

This paper intends to propose new inverse simulation techniques to cope with the numerical stability and accuracy problems frequently encountered with the integration inverse simulation methods widely used today. To achieve this, the pseudo-spectral method is adopted as a time integrator of the aircraft motion equations. In addition, the quasi-Newton and fixed-point iterative methods are applied to solve the resultant nonlinear algebraic equations in an efficient manner. These algorithms are integrated into a moving horizon framework to guarantee fast numerical convergence. The proposed methods are applied to the analyses of rotorcraft aggressive maneuvers such as popup, pirouette, and depart/abort mission-task-elements defined in the rotorcraft handling qualities requirements, ADS-33E-PRF. Numerical properties of the proposed methods are thoroughly investigated to clarify the effect of the numbers of quadrature nodes and time-horizon segments, and the level of maneuver aggressiveness on the robustness and efficiency of the analyses. Numerical efficiency and robustness of the present method are identified using specially designed performance measures such as the number of iterations to obtain a converged solution, functional residuals at the final solutions, and the variation of the adaptive relaxation factor. The results show that the present approach can provide extremely fast solutions of the inverse simulation problems and presents strong robustness to the level of maneuver aggressiveness, long-term simulation, and solution control parameters. Therefore, it is worthwhile to use the present techniques as one of the inverse simulation methods.

Modeling Time-Varying Effects With Large-Scale Survival Data: An Efficient Quasi-Newton Approach

ABSTRACTNonproportional hazards models often arise in biomedical studies, as evidenced by a recent national kidney transplant study. During the follow-up, the effects of baseline risk factors, such as patients’ comorbidity conditions collected at transplantation, may vary over time. To model such dynamic changes of covariate effects, time-varying survival models have emerged as powerful tools. However, traditional methods of fitting time-varying effects survival model rely on an expansion of the original dataset in a repeated measurement format, which, even with a moderate sample size, leads to an extremely large working dataset. Consequently, the computational burden increases quickly as the sample size grows, and analyses of a large dataset such as our motivating example defy any existing statistical methods and software. We propose a novel application of quasi-Newton iteration method to model time-varying effects in survival analysis. We show that the algorithm converges superlinearly and is computationally efficient for large-scale datasets. We apply the proposed methods, via a stratified procedure, to analyze the national kidney transplant data and study the impact of potential risk factors on post-transplant survival. Supplementary materials for this article are available online.

A Refinement of Quasi-Newton Iterative Method for Non-Linear Multivariable Optimization Problems

The Newton’s method and some of its modifications were reviewed. A new modification of the Newton’s method, which is of the Quasi-Newton principle is constructed and presented. Some standard test problems were solved using the Newton’ method, one of the existing modifications of the Newton’s method (David Fletcher Powell) and the refined method. From the results obtained, the newly modified method compared favourably with the existing ones and proved superior to the David Fletcher Powell method.

Robust blind separation for MIMO systems against channel mismatch using second-order cone programming

To improve the deteriorated capacity gain and source recovery performance due to channel mismatch problem, this paper reports a research about blind separation method against channel mismatch in multiple-input multiple-output (MIMO) systems. The channel mismatch problem can be described as a channel with bounded fluctuant errors due to channel distortion or channel estimation errors. The problem of blind signal separation/extraction with channel mismatch is formulated as a cost function of blind source separation (BSS) subject to the second-order cone constraint, which can be called as second-order cone programing optimization problem. Then the resulting cost function is solved by approximate negentropy maximization using quasi-Newton iterative methods for blind separation/extraction source signals. Theoretical analysis demonstrates that the proposed algorithm has low computational complexity and improved performance advantages. Simulation results verify that the capacity gain and bit error rate (BER) performance of the proposed blind separation method is superior to those of the existing methods in MIMO systems with channel mismatch problem.

Second-Order Cone Programming Based Robust Blind Multiuser Detector for CDMA Systems

In this paper, we propose a robust blind multiuser detector for code-division multiple access (CDMA) systems against signature waveform mismatch (SWM) derived from the influences of time asynchronization or channel distortion. This blind detection method with SWM problem is formulated as blind source separation (BSS) model subject to the second-order cone (SOC) constraint. The resulting blind separation based on SOC programming problem is solved by approximate negentropy maximization using quasiNewton iterative methods. Theoretical analysis and simulation results show that the performance of the proposed blind detector is superior to those of the existing methods.

SAR Image Despeckling by the Use of Variational Methods With Adaptive Nonlocal Functionals

In this paper, we focus on the despeckling of synthetic aperture radar (SAR) images by variational methods which introduce nonlocal regularization functionals. To achieve this goal, two models are investigated from different aspects. The first model is derived for the logarithmically transformed (homomorphic) domain of the SAR data, and the other is derived for the original (nonhomomorphic) domain. The statistical properties of the speckle and the log-transformed speckle are analyzed, and the similarity measurements between pixels in the homomorphic domain and nonhomomorphic domain are then derived for constructing the corresponding nonlocal regularization functionals. Meanwhile, in the proposed models, we develop a strategy to adaptively choose the regularization parameters based on both the local heterogeneity information and the noise level of the images, aiming at getting a better balance between the goodness of fit of the original data and the amount of smoothing. A quasi-Newton iteration method is employed to quickly minimize the proposed adaptive nonlocal functionals. Experiments conducted on both simulated images and real SAR images confirm the good performances of the proposed methods, both in reducing speckle and preserving image quality.

The steady flying of a plasmonic flying head over a photoresist-coated surface in a near-field photolithography system

The near-field photolithography technique (NFPT) offers a new approach of nanolithography for a dramatic increase in the resolution with high throughput and low cost. The NFPT utilizes the same flight principle as that of the magnetic head of hard-disk drives but replacing the magnetic head with a plasmonic flying head. The plasmonic flying head, which can focus the incident laser beam to a spot size of sub-20 nm with an enhanced field intensity by exciting surface plasmon polaritons, takes off and then flies steadily above the revolving disk coated by a photoresist film to be patterned with a narrow gap of tens of nanometers. As a key foundation of the NFPT, the take off and flight stability of the plasmonic flying head affects the pattern density and the fabrication efficiency. This work proposed and investigated a molecular glass photoresist, named FPT-8Boc, for the large-scale consistent fabrication with the NFPT. To overcome the take-off problem of the head over the soft photoresist film, a transition zone is intentionally formed by washing off the coated photoresist in the outer area of the disk using a solvent. The simulation results by COMSOL Multiphysics software and quasi-Newton iteration method review that the matched transition zone height with spreading length can guarantee the flight stability of the plasmonic flying head on the soft photoresist. Using this method, a preliminary photolithography result with a 31 nm line width has been achieved.

A Self-Tuning PID Control System Based on Control Performance Assessment

A Quasi-Newton iterative method is developed for the calculation of the best achievable PID control performance and the corresponding optimal PID setting based on the control parameters and input-output data. At the basis of the proposed method, a self-tuning PID control system is proposed for the time-variant dynamic process. When controllers performance deteriorates below the general performance, controller parameters are directly adjusted with the Quasi-Newton iterative method. When below the poor performance, it can be indirectly adjusted with the identification of the closed-loop impulse response matrix. A data-driven solution is developed for calculation of the closed-loop impulse response matrix. Based on the acquired state information, system is assessed and adjusted cyclically so that a self-tuning PID control system is finally realized. Simulation results show the practicality and utility of this method.

A regularized three-dimensional magnetotelluric inversion with a minimum gradient support constraint

SUMMARY Most 3-D magnetotelluric (MT) inversions are classified as a regularized inversion with a smoothness constraint. These inverse algorithms provide smooth solutions but cannot clearly image sharp geo-electrical interfaces. In this paper, we introduce the minimum gradient support (MGS) functional to regularize the 3-D MT inverse problem. This functional has a property whereby the functional seeks a structure with minimum volume containing large conductivity gradients. Therefore, the MGS functional can be used to search for a model with a sharp boundary. We apply the MGS functional to 3-D MT inversion to obtain a clear and accurate image of geo-electrical interfaces. In addition, the modified scattering equation approach introduced in the modified iterative dissipative method (MIDM) is applied to forward calculation, which is based on integral equation (IE) formulation and allows us to efficiently reduce the time required for forward calculation with high accuracy. The quasi-Newton iterative method is used to optimize the objective functional. It is a kind of iterative method with simplified calculation of the inverse Hessian matrix using Broyden–Fletcher–Goldfarb–Shanno (BFGS) update. The convergence of this iterative method is guaranteed with inexact line searches. We also modify the adaptive approach for optimum selection of the regularization parameter so as to fit the inverse algorithm of this study. Three synthetic models are investigated, and the obtained results are compared with those obtained by a smoothing inversion. Based on the comparison, we confirm that the MGS inversion can provide higher resolution when geo-electrical interfaces are sharp. This property will help us to determine reliable electrical structures by the MT exploration method.

Surface Topology Optimization of Air Bearing Slider for Wear Durability in Magnetic Hard Disk Drives

In order to protect the slider and disk from excessive wear, a numerical scheme is proposed for transient dynamics at slider/disk interface with the emphasis on the slider wear mechanism and the surface topology optimization of sub-ambient pressure slider. For each transient flying height and slider attitude, the modified Reynolds lubrication equation is solved by the control volume method to obtain the simultaneous pressure distribution in the slider surface. Then the dynamic flying attitude of the slider subject to the calculated pressure distribution can be solved by the Quasi-Newton iteration method at each time step. On the basis of above work, the optimization of the slider surface topology is implemented, and it’s concluded that slider crown has the most significant impact on the dynamic flying attitude and stability. Finally, a sub-ambient pressure slider is designed, which can effectively avoid the slider wear and severe fault of hard disk drive.

HDI-01 A MESH-FREE METHOD FOR NUMERCIAL SIMULATION OF HDD SLIDER AIR BEARINGS

In this paper, a mesh-free numerical method (least square finite difference scheme) is presented to solve the slider air bearing problems of hard disk drives. For each specified attitude, the air bearing pressure is obtained by solving the generalized Reynolds equation using the mesh-free method. The method with second order accuracy directly approximates the derivatives in the differential equations. The discretized nonlinear systems of equations are solved by Successive Over-Relaxation (SOR) implementation. Finally, the steady-state flying attitude of a slider subject to pro-applied suspension force and torques is obtained by a Quasi-Newton iteration method.