Extrapolation Algorithm Research Articles

Explicit Numerical Model of Solar Cells to Determine Current and Voltage

This paper deals with the extraction of the physical parameters of solar cells (a single diode model) from the equivalent circuit of the cell. The extraction is carried out by three different numerical methods with a comparison between them. The first and second methods are a difference of the Newton Raphson algorithm (NRM) and Aitken’s extrapolation algorithm (AEM), respectively. The roots of the nonlinear equation of this cell have been described and solved using the three methods. The proposed method is tested to solve the output voltage; current and power of this cell from the roots of this equation with the various values of load resistance RL.

Сходимость метода экстраполяции из прошлого и метода операторной экстраполяции

Одним из популярных направлений современного прикладного нелинейного анализа является исследование вариационных неравенств. Многие актуальные проблемы исследования операций и математической физики можно записать в форме вариационных неравенств. С появлением генерирующих соревновательных нейронных сетей интерес к алгоритмам решения вариационных неравенств возник и в среде специалистов машинного обучения. Данная работа посвящена исследованию трех новых алгоритмов с брегмановской проекцией для решения вариационных неравенств в гильбертовом пространстве. Первый алгоритм — результат модификации двухэтапного брегмановского метода с помощью экономного регулирования величины шага, не требующего знания лепшицевой константы оператора. Второй алгоритм — алгоритм операторной экстраполяции, полученный заменой в методе Малицкого-Тама евклидовой метрики на дивергенцию Брегмана. Привлекательная черта алгоритма — всего одно вычисление на итерационном шаге проекции Брэгмана на допустимое множество. Третий алгоритм — адаптивный вариант второго, где используется правило обновления величины шага, не требующее знания лепшицевых констант и вычислений значений оператора в дополнительных точках. Для вариационных неравенств с псевдомонотонными, лепшицевыми и секвенционно слабо непрерывными операторами, действующими в гильбертовом пространстве, доказаны теоремы о сходимости методов.

A pilot clinical trial of genomic-based therapy assignment with co-expression extrapolation (COXEN) in advanced/metastatic urothelial carcinoma.

452 Background: We investigated the Co-eXpression ExtrapolatioN (COXEN) algorithm to select “next best therapy” for patients with advanced/metastatic urothelial cancer based on gene expression profiles. Methods: This is a single-arm, open label pilot study, that investigates the COXEN algorithm’s ability to use patients’ tumor gene expression models to predict sensitivities to 75 FDA-approved anticancer agents. The COXEN results were reviewed and discussed in a multi-disciplinary molecular tumor board. From that a treatment plan was chosen based on monotherapy clinical efficacy data in urothelial carcinoma, combination safety data (combinations of agents were allowed provided phase I data were available), side effect profile/tolerability, response or resistance to prior therapies, therapy contraindications, and feasibility of therapy. The objective of this study was to determine the feasibility of using COXEN as a clinical decision algorithm to make a real-time treatment decision within 21 days of specimen collection in patients with advanced/metastatic urothelial carcinoma. Results: A total of 8 patients enrolled and underwent tumor biopsy for COXEN analysis. Five out of 8 patients received COXEN therapy within 21 days of biopsy with various regimens including: vorinostat and etoposide; doxorubicin; sunitinib; doxorubicin and paclitaxel; erlotinib and nab-paclitaxel. There were no objective responses. The 5 patients treated with COXEN therapy had a median potential follow up of 36 months, median overall survival of 8.4 months (95% CI: 5.2 months – not estimable), and median progression free survival of 2.2 months (95% CI: 1.4 – 3.9 months). Grade 3 or 4 adverse events included: febrile neutropenia (n=2), hypophosphatemia (n=1) and hyponatremia (n=1). This trial was terminated early due to a lack of treatment responses. Conclusions: The COXEN algorithm is a unique personalized method for selecting therapy for patients with advanced urothelial carcinoma. Although the COXEN method was feasible, it did not demonstrate clinical efficacy in this small cohort of patients. Clinical trial information: NCT02788201.

A fast finite difference/RBF meshless approach for time fractional convection-diffusion equation with non-smooth solution

In this paper, we propose a fast finite difference/RBF meshless method for time fractional convection-diffusion equation with singularity at the initial moment. Firstly, the time fractional derivative term is discretized by classical L1 format on graded meshes, and the spatial derivative term is approximated by meshless method. The meshless method does not need to construct meshes, which is more conducive for dealing with complex regions or complex boundary conditions. In addition, we adopt proper orthogonal decomposition (POD) technology to derive reduced-order RBF meshless extrapolation algorithm, which effectively reduces the amount of calculation and improves the calculation efficiency. Finally, the accuracy and efficiency of the method are verified by numerical examples.

SBAS-Aided GPS Positioning with an Extended Ionosphere Map at the Boundaries of WAAS Service Area

Space-based augmentation system (SBAS) provides correction information for improving the global navigation satellite system (GNSS) positioning accuracy in real-time, which includes satellite orbit/clock and ionospheric delay corrections. At SBAS service area boundaries, the correction is not fully available to GNSS users and only a partial correction is available, mostly satellite orbit/clock information. By using the geospatial correlation property of the ionosphere delay information, the ionosphere correction coverage can be extended by a spatial extrapolation algorithm. This paper proposes extending SBAS ionosphere correction coverage by using a biharmonic spline extrapolation algorithm. The wide area augmentation system (WAAS) ionosphere map is extended and its ionospheric delay error is compared with the GPS Klobuchar model. The mean ionosphere error reduction at low latitude is 52.3%. The positioning accuracy of the extended ionosphere correction method is compared with the accuracy of the conventional SBAS positioning method when only a partial set of SBAS corrections are available. The mean positioning error reduction is 44.8%, and the positioning accuracy improvement is significant at low latitude.

SPECTRAL ANALYSIS AND FORECASTING OF THE 25TH SOLAR CYCLES

In the present work, we propose an extrapolation method, developed on the basis of spectral analysis, digital filtering, and the principle of demodulation of a complex signal, for predicting the beginning of cycle 25 of solar activity. The Wolf number and other measured characteristics of solar activity have a very complex spectral composition. The Sun, by the nature of its radiation, contributes a significant stochastic component to the observational data. The experimental data are known only up to the present, and the prediction is about bridging the gap in our data set. Mathematically, the prediction problem boils down to extrapolation of discontinuous functions, which leads to a Gibbs phenomenon that occurs at the point of discontinuity and makes prediction into the future impossible. To overcome this discontinuity, additional physical models describing a continuous process are most often used. This paper uses only the Wolf series of numbers from 1818 to 2020. The authors developed an original forecasting technique using Fourier series, digital filtering and representation of the complex process as modulated and subsequent demodulation. As a result of decomposing the complex signal by Fourier series into separate components, the spectral ranges characteristic of the Wolf number were singled out. Taylor's series was used for construction of prediction or extrapolation algorithms. The extraction of spectral ranges, characteristic for the investigated process, is carried out by means of sequential digital filtering methods and information compression in accordance with the cut-off frequency of the digital filter. For example, when selecting eleven-year cycles of solar activity, we have to compress the information by a factor of 160. With such a processing scheme, the forecasting starts with the ultralow-frequency component with a period of more than 11 years, successively moving to the ranges of higher frequencies. The use of spectral analysis and Chebyshev filtering showed the possibility to predict the low-frequency component for the full cycle period. The eleven-year component forecast obtained by the authors is in good agreement with the data of the Brussels Royal Center.

Adequacy of safety data for regulatory approval of pediatric indication through extrapolation algorithm.

Adequacy of safety data for regulatory approval of pediatric indication through extrapolation algorithm.

Radar echo extrapolation algorithm based on adversarial long short-term memory network

Radar echo extrapolation algorithm based on adversarial long short-term memory network

Reimbursement Contracts: Application of Civil Law Mechanisms under Pandemic Restrictions

The article contextualizes and assesses the peculiarities of using the mechanism of civil law reimbursement of medical expenses in the context of the global spread of acute respiratory infection COVID-19 caused by coronavirus SARS-CoV-2, as well as the theoretical possibility of such coverage of financial costs and revenues through the enforcement of reimbursement contracts, by analogy with the currently widespread state program «Affordable Medicines of Ukraine». The author analyses the achievements of many domestic and foreign researchers who have covered various aspects of reimbursement in their writings, including the extrapolation algorithms of such traditional institutions of civil law as the fulfilment of obligations for the third parties, compensation, etc. For the completeness of the scientific search, the article also contains an analysis of statistical indicators of the effectiveness of reimbursement contracts in our country, based on information from open official sources of the National Health Service of Ukraine. As a result of the comparison, the author concluded that the well-thought-out organization of high-quality medical care, followed by reimbursement of the full or partial cost of services received or medicines purchased under reimbursement agreements allows to comprehensively and effectively solve most problems in this area in such a way as to protect the interests of patients, doctors, and pharmaceutical companies as the key participants in such legal relations. It is also emphasized that the system of legal regulation and medical provision of access to medicines and procedures in most developed countries is considered as an integral part of public administration, the need to improve which is always an urgent challenge for every law enforcement, especially in the context of the global spread of acute respiratory infection COVID-19 caused by the coronavirus SARS-CoV-2. Particular attention is paid to the fact that the well-thought-out organization of quality medical care, followed by reimbursement of the full or partial cost of services received or drugs purchased in the context of reimbursement agreements allows comprehensive and effective solutions to most problems in this area to protect the interests of patients, doctors and pharmaceutical companies as key participants in such legal relations.

Solution of two-dimensional elasticity problems using a high-accuracy boundary element method

For the two-dimensional elasticity problems, we give a uniqueness and existence analysis via the single-layer potential approach leading to a system of integral equation that contains a weakly singular operator. For its numerical solutions we describe a O(h3) order quadrature method based on the specific integral formula including convergence and stability analysis. Moreover, the asymptotic expansion of errors with odd power O(h3) is got and the accuracy of numerical approximations can be improved to the order of O(h5) by the Richardson extrapolation algorithm (EA) once. The efficiency of the method is illustrated by two numerical examples.

Full-wave-equation depth extrapolation for migration using matrix multiplication

To investigate wavefield depth extrapolation using the full-wave equation, we have derived a new depth extrapolation scheme for migration using functions of the vertical wavenumber. We develop a complete matrix multiplication formulation and approach to calculate the related mathematical functions of the vertical wavenumber and perform depth extrapolation using matrix multiplication only. Because our depth extrapolation algorithm involves only matrix multiplication, it is naturally applicable to parallel computations. Impulse response experiments demonstrate that our proposed migration method can achieve the same accuracy as full-wave-equation migration using the finite-difference method, in terms of phase information, even for media with strong lateral velocity changes. In numerical experiments using a smoothed version of the 2D SEG/EAGE salt model, our migration method provides an equivalent imaging result compared with reverse time migration (RTM) and a more accurate imaging result than migration using one-way propagators. Our method has certain potential advantages over RTM using the same full-wave equation with fewer internal multiple scatterings and fewer data storage requirements. Our adopted method is a stable depth extrapolation scheme because the evanescent waves are well suppressed. The numerical experimental results on the synthetic model demonstrate the importance of suppressing evanescent waves in a full-wave-equation-based depth extrapolation scheme and migration for imaging quality and computation cost.

A Single Machine Equivalent-Based Approach for Online Tracking of Power System Transient Stability

This paper presents a systematic single machine equivalent system based scheme for fast and accurate prediction of impending angular stability using measurements from generator terminals only. In a post-fault scenario, Kalman filter is designed to estimate rotor positions in real-time, based on damper winding observer with measurements gathered from generator terminals. To identify critical machines, short time-ahead prediction of rotor position is made by designing another Kalman filter. A general method is suggested to differentiate between critical and non-critical machines. To further enhance the accuracy of predicted time to instability, an extrapolation algorithm is developed, based on the knowledge of estimated rotor angles and short time-ahead predicted rotor angles. The proposed methods are successfully implemented on WSCC 9-bus, IEEE 39-bus, and NRPG 246-bus test systems.

Learnable Optical Flow Network for Radar Echo Extrapolation

The impact of extreme weather on maintaining flight schedules is becoming more pronounced. Currently, radar echo extrapolation technology is widely used in the nowcasting of severe convection, in which the optical flow method is a representative example of traditional extrapolation algorithms. By training a large number of known samples to find the optimal solution, the deep extrapolation models have gradually become better than the traditional algorithms in recent years. In this study, after examining the optical flow method and other deep learning models, a learnable optical flow deep model with a fully convolutional structure is proposed. Using the convolutional deep learning of optical flow information, this new model can overcome the kernel size limitation of traditional convolutional neural networks, and it can correlate the data history further in time and space. The six-year radar mosaics of Guangdong Province, China, were used as the data set to independently train and verify the new model. The results reveal that the new model outperformed the traditional optical flow method and it is also better than other deep learning models.

Towards Data-Driven Real-Time Hybrid Simulation: Adaptive Modeling of Control Plants

We present a method for control in real-time hybrid simulation (RTHS) that relies exclusively on data processing. Our approach bypasses conventional control techniques, which presume availability of a mathematical model for the description of the control plant (e.g. the transfer system and the experimental substructure) and applies a simple plug 'n play framework for tuning of an adaptive inverse controller for use in a feedforward manner, avoiding thus any feedback loops. Our methodology involves (i) a forward adaptation part, in which a noise-free estimate of the control plant's dynamics is derived; (ii) an inverse adaptation part that performs estimation of the inverse controller; and (iii) the integration of a standard polynomial extrapolation algorithm for the compensation of the delay. One particular advantage of the method is that it requires tuning of a limited set of hyper-parameters (essentially three) for proper adaptation. The efficacy of our framework is assessed via implementation on a virtual RTHS (vRTHS) benchmark problem that was recently made available to the community. The attained results indicate that data-driven RTHS may form a competitive alternative to conventional control.

Lifetime survival and medical costs of lung cancer: a semi-parametric estimation from South Korea

BackgroundIt is essential to have information on the disease burden of lung cancer at an individual level throughout the life; however, few such results have been reported. Thus, this study aimed to assess the lifetime disease burden in patients with lung cancer by assessing various factors, such as survival, years of life lost (YLL) and medical expenditure in South Korea based on real-world data and extrapolation.MethodsNewly diagnosed lung cancer patients (n = 2919) in 2004–2010 were selected and observed until the end of 2015 using nationwide reimbursement claim database. The patients were categorised into the Surgery group, Chemo and/or Radiotherapy group (CTx/RTx), and Surgery+CTx/RTx according to their treatment modality. Age- and sex-matched control subjects were selected from among general population using the life table. The survival and cost data after diagnosis were analysed by a semi-parametric method, the Kaplan–Meier analysis for the first 100 months and rolling extrapolation algorithm for 101–300 months. YLL were derived from the difference in survival between patients and controls.ResultsLifetime estimates (standard error) were 4.5 (0.2) years for patients and 14.5 (0.1) years for controls and the derived YLL duration was 10.0 (0.2) years. Lifetime survival years showed the following trend: Surgery (14.2 years) > Surgery+CTx/RTx (8.5 years) > CTx/RTx group (3.0 years), and YLL were increased as lifetime survival years decreased (2.3, 8.7, 12.2 years, respectively). The mean lifetime medical cost was estimated at 30,857 USD/patient. Patients in the Surgery group paid higher treatment cost in first year after diagnosis, but the overall mean cost per year was lower at 4359 USD compared with 7075USD of Surgery+CTx/RTx or 7626USD of CTx/RTx group.ConclusionsLung cancer has resulted in about 10 years of life lost in overall patients. The losses were associated with treatment modality, and the results indicated that diagnosing lung cancer in patients with low stage disease eligible for surgery is beneficial for reducing disease burden in terms of survival and treatment cost per year throughout the life.

Lifetime risks and health impacts of hemorrhagic and ischemic stroke in South Korea

This study is aimed toward estimating the lifetime risks, life expectancy, expected years of life lost (EYLL), and lifetime costs related to different subtypes of stroke in South Korea. We included 13,994 patients diagnosed with stroke (ICD-10, I60-I63) in the National Health Insurance Service-National Sample Cohort of Korea between 2006 and 2015. Lifetime risks were calculated using the cumulative incidence rate for patients aged 18–84. Lifetime survival data were obtained through the Kaplan–Meier method and extrapolated with a rolling-over extrapolation algorithm. The lifetime costs were estimated by multiplying the average monthly expenditures with the survival probabilities and adding the values over lifetime. The lifetime risks of stroke in Korea have been decreasing consistently over the last decade with the exception of subarachnoid hemorrhage in females, which appears to have slightly increased. The EYLL is higher in hemorrhagic stroke than in ischemic stroke (6–9.7 vs. 4.7). Expected lifetime costs reimbursed by the NHIS would amount to about $71,406 accompanied with $14,921 copayment from the patients for hemorrhagic stroke, and $50,551 and $11,666, respectively, for ischemic stroke. Further studies are warranted to combine survival with quality of life and functional disability to obtain a more detailed outcome assessment of the potential impact of the prevention of stroke.

A new alternating iteration strategy based on the proper orthogonal decomposition for solving large-scaled transient nonlinear heat conduction problems

In this paper, the application of Free Element Method (FREM) is extended to the transient nonlinear heat conduction problems, and the characteristics of anisotropic, heterogeneous, temperature-dependent thermophysical properties and heat generation are also involved. In order to improve the efficiency during the nonlinear iterations, an alternating iteration strategy, FREM-ROM, is proposed, in which the proper orthogonal decomposition (POD) technique is used to establish a sectionalized extrapolation algorithm with lower dimensions and sufficiently high accuracy. This iteration strategy reduces the computational scale by using the Reduced-Order Model (ROM) technique and can guarantee the accuracy by continually correcting the database and POD bases every few time steps during the process of iterations. It also has the potential to be applied to other numerical methods for improved the efficiency. The accuracy and efficiency are examined by two numerical examples, in which the 2D example illustrates the relationship between truncated basis and accuracy in detail, and the heat transfer performance of a large-scale 3D cross-fin heat sink(CFHS) is investigated to highlight the efficiency advantages of solving large-scaled practical problems.

Robust Model Predictive Control for Dynamics Compensation in Real-Time Hybrid Simulation

Hybrid simulation is an efficient method to obtain the response of an emulated system subjected to dynamic excitation by combining loading-rate-sensitive numerical and physical substructures. In such simulations, the interfaces between physical and numerical substructures are usually implemented using transfer systems, i.e., an arrangement of actuators. To guarantee high fidelity of the simulation outcome, conducting hybrid simulation in hard real-time is required. Albeit attractive, real-time hybrid simulation comes with numerous challenges, such as the inherent dynamics of the transfer system used, along with communication interrupts between numerical and physical substructures, that introduce time delays to the overall hybrid model altering the dynamic response of the system under consideration. Hence, implementation of adequate control techniques to compensate for such delays is necessary. In this study, a novel control strategy is proposed for time delay compensation of actuator dynamics in hard real-time hybrid simulation applications. The method is based on designing a transfer system controller consisting of a robust model predictive controller along with a polynomial extrapolation algorithm and a Kalman filter. This paper presents a proposed tracking controller first, followed by two virtual real-time hybrid simulation parametric case studies, which serve to validate the performance and robustness of the novel control strategy. Real-time hybrid simulation using the proposed control scheme is demonstrated to be effective for structural performance assessment.

On the numerical solutions of two-dimensional scattering problems for an open arc

For the scattering problems of acoustic wave for an open arc in two dimensions, we give a uniqueness and existence analysis via the single layer potential approach leading to a system of integral equations that contains a weakly singular operator. For its numerical solutions, we describe an O(h^{3}) order quadrature method based on the specific integral formula including convergence and stability analysis. Moreover, the asymptotic expansion of errors with odd power O(h^{3}) is got and the Richardson extrapolation algorithm (EA) is used to improve the accuracy of numerical solutions. The efficiency of the method is illustrated by a numerical example.

Soft Sensor Modeling of Blast Furnace Wall Temperature Based on Temporal–Spatial Dimensional Finite-Element Extrapolation

The blast furnace (BF) wall temperature field plays a key role in determining whether the operation of the BF is efficient. However, it cannot be measured directly because the BF is an enclosed complex reactor with an extremely harsh environment. To cope with this problem, a soft sensor modeling strategy of the BF wall temperature field based on a novel temporal–spatial dimensional finite-element extrapolation algorithm (TS-FEEA) is designed. A 3-D transient heat conduction model of the BF wall is first established, which considers the layered physical structure of the BF. The large volume of the BF wall causes great calculation burden when solving the 3-D transient heat conduction model of the BF wall, to solve this problem, a TS-FEEA is proposed that realizes a high-speed and accurate model numerical solution. To further improve the 3-D model precision, the measured thermocouple temperatures in the cooling stave are served as the judgment criteria, and a correction strategy for inner wall temperature is finally designed to correct the assumed inner wall temperature through multiple iterations. Simulation results demonstrate the validity of the soft sensor modeling strategy and its applicability in industrial plants. The research achievements provide valuable reference information for the BF operators to judge the furnace conditions and adjust the operation parameters.