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The truncation error is an important problem in the dynamic matrix control (DMC) algorithm. Generally, the dynamic information of a plant for the traditional DMC algorithm is determined by the step response. However, the step response of the plant is limited in practice, which leads to the truncation error of the modeling horizon in the feedback correction of DMC algorithm. A truncation error correction method based on cubic spline function is proposed for DMC algorithm, which is realized by designing coefficients and tracking the dynamic response of the system. In the feedback correction of DMC algorithm, the relationship between the correction parameter and the correction difference is constructed by the fitting of cubic spline functions on the intervals. A truncation error correction procedure is presented to calculate the correction parameters by inputting of the correction difference into the relationship. Then, the control increment and predicted model output are computed based on the correction parameters and updated shift matrix. Finally, numerical experiments demonstrate that the control performance of the proposed DMC algorithm has been much improved compared to that of traditional DMC algorithm. [ABSTRACT FROM AUTHOR]

Copyright of Acta Materiae Compositae Sinica is the property of Acta Materiea Compositae Sinica Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We present a new explicit quasi-Lagrangian integration scheme with the three-dimensional cubic spline function transform (transform = fitting + interpolation, referred to as the "spline format") on a spherical quasi-uniform longitude–latitude grid. It is a consistent longitude–latitude grid, and to verify the feasibility, accuracy, convergence, and stability of the spline format interpolation scheme for the upstream point on the longitude–latitude grid, which may map a quasi-uniform longitude–latitude grid, a set of ideal, exact test schemes is adopted, which are recognized and proven to be effective internationally. The equilibrium flow test, cross-polar flow test, and Rossby–Haurwitz wave test are used to illustrate the spline scheme uniformity to the linear scheme and to overcome the over-dense grid in the polar region and the non-singularity of the poles. The cross-polar flow test demonstrates that the geostrophic wind crosses the polar area correctly, including the South Pole and North Pole. A non-hydrostatic, fully compressible dynamic core is used to complete the density flow test, demonstrating the existence of a time-varying reference atmosphere and that the spline format can simulate highly nonlinear fine-scale transient flows. It can be compared for the two results of the density flow test between the solution with the spline format and the benchmark reference solution with the linear format. Based on the findings, the non-hydrostatic dynamic core with the spline format is recommended for adoption. When simulated for the flow over an ideal mountain, through the "topographic gravity wave test", the bicubic surface terrain and terrain-following height coordinates, time-split integration, and vector discrete decomposition can be derived successfully. These may serve as the foundations for a global, unified spline-format numerical model in the future. [ABSTRACT FROM AUTHOR]

The solution to problems of telecommunications and information technologies using spline approximation and spline extrapolation based on real and complex spline functions is considered. The use of spline approximation for solving problems of signal recovery and self-similar traffic, processes of functioning of telecommunication nodes and networks is shown. It is proposed to use spline extrapolation based on various types of real spline functions to solve the problems of predicting the characteristics of self-similar traffic and maintaining QoS characteristics during its maintenance. It has been established that to predict the real-time telemetry traffic of IoT devices, it is advisable to use spline extrapolation based on the cubic Hermite spike, which ensures the required forecasting accuracy and prevents network overloads, especially under conditions of network load limit. To solve the problem of user positioning in the radio access area, the use of complex plane spline functions is considered. The use of the methods of real and complex spline functions allows for obtaining the results of improving the quality of service in a telecommunications network and ensuring the scalability of the obtained solutions. To identify and predict DDoS cyber-attacks, a spline extrapolation method is used. The use of parametric splines in the problems of information technology, namely, the construction of curves and surfaces in 3D modelling, is proposed.

Compared to other information sources, motion cues provide a pilot with anticipatory information about spatial position and movement of aircraft. For motion cueing a flight simulator cockpit is installed on a motion system, movement of which motion cueing. Therefore, motion system is one of the most important components of full flight simulators. The problem of effective use of constructive resources of six-degrees of freedom synergistic motion system has been solved. But the problem of improving the motion cueing remained unsolved, due to the fact that location of motion system center of rotation is significantly different from location of aircraf’s center of gravity, and motion cues differ from real, flight one. The study subject is motion cueing on flight simulators. The problem was solved on the basis of simplified operator for transformation of motion system movements along individual degrees of freedom into jack movements, cubic spline functions to describe the dependence of the centers of rotation along pitch and yaw, and optimization theory using the deformable polyhedron method. The formulated and solved problem of taking into account of location of aircraft’s center of gravity during motion cueing along pitch and yaw increases an efficiency of using of constructive resource of a six-degrees of freedom synergistic motion system, a motion cueing fidelity and training realism on flight simulator.

Metamodel technology provides an efficient method to approximate complex engineering design problems. However, the approximation for high-dimensional problems usually requires a large number of samples for most traditional metamodeling methods, which leads to the difficulty of "curse of dimensionality." To address the aforementioned issue, this paper presents the Net-high dimension model representation (HDMR) method based on the Cut-HDMR framework. Compared with traditional HDMR modeling, the Net-HDMR method incorporates two novel modeling approaches that improve the modeling efficiency of high-dimensional problems. The first approach enhances the modeling accuracy of HDMR by using the net function interpolation method to decompose the component functions into a series of one-dimensional net functions. The second approach adopts the CV-Voronoi sequence sampling method to effectively represent one-dimensional net functions with limited samples. Overall, the proposed method transforms complex high-dimensional problems into fitting finite one-dimensional splines, thereby increasing the modeling efficiency while ensuring approximate accuracy. Six numerical benchmark examples with different dimensions are examined to demonstrate the accuracy and efficiency of the proposed Net-HDMR. An engineering problem of thermal stress and deformation analysis for a jet engine turbine blade was introduced to verify the engineering feasibility of the proposed Net-HDMR. [ABSTRACT FROM AUTHOR]

We present a new explicit quasi-Lagrangian integration scheme with the three-dimensional cubic spline function transform (transform = fitting + interpolation, referred to as the “spline format”) on a spherical quasi-uniform longitude–latitude grid. It is a consistent longitude–latitude grid, and to verify the feasibility, accuracy, convergence, and stability of the spline format interpolation scheme for the upstream point on the longitude–latitude grid, which may map a quasi-uniform longitude–latitude grid, a set of ideal, exact test schemes is adopted, which are recognized and proven to be effective internationally. The equilibrium flow test, cross-polar flow test, and Rossby–Haurwitz wave test are used to illustrate the spline scheme uniformity to the linear scheme and to overcome the over-dense grid in the polar region and the non-singularity of the poles. The cross-polar flow test demonstrates that the geostrophic wind crosses the polar area correctly, including the South Pole and North Pole. A non-hydrostatic, fully compressible dynamic core is used to complete the density flow test, demonstrating the existence of a time-varying reference atmosphere and that the spline format can simulate highly nonlinear fine-scale transient flows. It can be compared for the two results of the density flow test between the solution with the spline format and the benchmark reference solution with the linear format. Based on the findings, the non-hydrostatic dynamic core with the spline format is recommended for adoption. When simulated for the flow over an ideal mountain, through the “topographic gravity wave test”, the bicubic surface terrain and terrain-following height coordinates, time-split integration, and vector discrete decomposition can be derived successfully. These may serve as the foundations for a global, unified spline-format numerical model in the future.

Land Surface Temperature (LST) is an important factor in ground surface energy balance and in universal climatology studies. Elevation, Land Cover (LC), and vegetation index are three factors that influence ground surface variation, and their influences vary depending on geography. This study aimed to: (i) investigate the seasonal patterns and trends of daytime LST, and (ii) examine the influence of elevation, LC, and vegetation index on daytime LST increase in Taiwan from 2000 to 2021. LST, vegetation, and LC data were downloaded from the Moderate Resolution Imaging Spectroradiometer (MODIS) website, and elevation data were downloaded from the United States Geological Survey (USGS) website. The natural cubic spline method was applied to investigate annual seasonal patterns and trends in daytime LST. Linear regression modeling was applied to investigate the influence of elevation, LC, and vegetation index on daytime LST increases. The results showed that the average increase in daytime LST per decade in Taiwan was 0.021 °C. Elevation, LC, and vegetation had significantly affected the daytime LST increase, with R2 of 32.5% and 28.1% for the North and South parts of the country, respectively. The daytime LST increase in the North at elevations higher than 1000 m had an increasing trend, while in the South the increasing trend was found at elevations higher than 350 m above sea level. All types of forest and urban areas in the North had a higher daytime LST increase than the average, while in the South, the areas with water, closed shrubland, and urban parts had a higher daytime LST increase than the average. [ABSTRACT FROM AUTHOR]

Compared to other information sources, motion cues provide a pilot with anticipatory information about spatial position and movement of aircraft. For motion cueing a flight simulator cockpit is installed on a motion system, movement of which motion cueing. Therefore, motion system is one of the most important components of full flight simulators. The problem of effective use of constructive resources of six-degrees of freedom synergistic motion system has been solved. But the problem of improving the motion cueing remained unsolved, due to the fact that location of motion system center of rotation is significantly different from location of aircraf’s center of gravity, and motion cues differ from real, flight one. The study subject is motion cueing on flight simulators. The problem was solved on the basis of simplified operator for transformation of motion system movements along individual degrees of freedom into jack movements, cubic spline functions to describe the dependence of the centers of rotation along pitch and yaw, and optimization theory using the deformable polyhedron method. The formulated and solved problem of taking into account of location of aircraft’s center of gravity during motion cueing along pitch and yaw increases an efficiency of using of constructive resource of a six-degrees of freedom synergistic motion system, a motion cueing fidelity and training realism on flight simulator. [ABSTRACT FROM AUTHOR]

Abstract Background High Blood Urea Nitrogen (BUN) and high Serum Creatinine (SCr) levels are risk factors for Coronary Artery Disease (CAD). However, the relationship between the Blood Urea Nitrogen to Creatinine (BUN/SCr) ratio (UCR) and the risk of CAD in patients living with new-onset diabetes is unclear. This study aimed to examine the relationship between blood UCR and the risk of CAD in patients living with new-onset type 2 diabetes mellitus (T2DM). Methods We analyzed the data from the cohort of 12,299 patients living with type 2 diabetes mellitus. Primary endpoints were the events of CAD. The ANOVA test (continuous indicators) and χ2 test (categorical indicators) were used to assess the differences of baseline characteristics across the groups of UCR. In order to understand the correlation between variables, we performed correlation analysis on variables that have significant differences between CAD group and non-CAD group. Multivariate-adjusted Cox proportional hazard regression models were applied to estimate the association of the blood UCR with the risk of CAD in patients living with T2DM. The Kaplan–Meier survival function plotting and the log-rank test were used to evaluate the event-free survival according to the groups of UCR. The restricted cubic spline model was used to show the adjusted association between blood UCR and risk of CAD in patients living with T2DM. Results During a median follow-up of 2.66 years, 1173 CAD were recorded with an event rate of 28.49 events per 1000 person-years. In multivariate-adjusted Cox regression models, elevated blood urea nitrogen to creatinine ratio (UCR) was associated with higher risk of CAD in patients living with T2DM [hazard ratio (HR), 1.782; 95% confidence interval (CI), 1.237–2.567]. The Kaplan–Meier survival curves indicated that the high group of UCR tended to have a lower event-free survival than the low group and medium group. There was a nonlinear trend toward increasing risk of CAD across the groups of UCR. And cubic spline function graph suggested that the influence of UCR level on HR for CAD increased significantly at UCR levels above 6.67. Conclusions An elevated UCR was significantly associated with an increased risk for CAD in patients living with T2DM.

For building environments, meteorological factors such as daily mean temperature, extreme temperature and seasonal temperature changes, are essential, as they impact building structures significantly. Due to the importance of detailed and accurate temperature data, and taking Beijing, China, as an example, this paper developed a fast and effective interpolation method to extract hourly meteorological data, based on 30 years' raw meteorological data. With the interpolated data, this paper defined the extreme weather for buildings. Moreover, a temperature model based on probability and statistical analysis was constructed, and the general climate standard for days and extreme climate for typical days with different return periods were obtained. Furthermore, meteorological models for standard annual temperature were also achieved, reflecting the daily variation and annual variation of temperature, and can provide continuous-numerical-simulation parameters for analyzing daily and annual temperature. According to the daily temperature difference obeys the Gumble Distribution, the daily temperature difference in different return periods and extreme climates is obtained by analysis. Therefore, annual temperature ranges of different recurrence intervals and extreme climate are also achieved, and the annual temperature ranges can be used to analyze the effect of different recurrence intervals and extreme weather on building structures. [ABSTRACT FROM AUTHOR]

Transport of pollutants in rivers is one of the most important issues in the environment. Many researchers have solved the advection-dispersion equation by various numerical methods, including finite difference and finite element methods. Despite their advantages, these methods also have disadvantages that are often related to netting of the problem domain. Therefore application of mesh-free methods which do not require solution domain network seems necessary. In the present study, the one-dimensional advection-dispersion equation has been solved using the Mesh-free Local Petrov-Galerkin method in the unsteady state. The Murray Burn River data were used to evaluate the performance of the model. The used approximation and weight function were the moving least squares function and the cubic spline function, respectively. In this study, 9 experiments were used to calibrate the model and 2 experiments were used to validate it. For calibration, the discharge coefficient and velocity plotted against the flow rate, and the power regression equation was extracted which had correlation coefficients of 0.925 and 0.988, respectively. In the validation mode, the dispersion coefficient and velocity were optimized by minimizing the mean squared error between computational and observational concentration for each model. The dispersion coefficient in this study was in the range of 0.13-1.1 m2/s for the flow rate of 13-437 L/s. The results indicated the acceptable performance and accuracy of mesh-free method.

Background: High Blood Urea Nitrogen (BUN) and high Serum Creatinine (SCr) levels are risk factors for Coronary Artery Disease (CAD). However, the relationship between the Blood Urea Nitrogen to Creatinine (BUN/SCr) ratio (UCR) and the risk of CAD in patients living with new-onset diabetes is unclear. This study aimed to examine the relationship between blood UCR and the risk of CAD in patients living with new-onset type 2 diabetes mellitus (T2DM). Methods: We analyzed the data from the cohort of 12,299 patients living with type 2 diabetes mellitus. Primary endpoints were the events of CAD. The ANOVA test (continuous indicators) and χ2 test (categorical indicators) were used to assess the differences of baseline characteristics across the groups of UCR. In order to understand the correlation between variables, we performed correlation analysis on variables that have significant differences between CAD group and non-CAD group. Multivariate-adjusted Cox proportional hazard regression models were applied to estimate the association of the blood UCR with the risk of CAD in patients living with T2DM. The Kaplan–Meier survival function plotting and the log-rank test were used to evaluate the event-free survival according to the groups of UCR. The restricted cubic spline model was used to show the adjusted association between blood UCR and risk of CAD in patients living with T2DM. Results: During a median follow-up of 2.66 years, 1173 CAD were recorded with an event rate of 28.49 events per 1000 person-years. In multivariate-adjusted Cox regression models, elevated blood urea nitrogen to creatinine ratio (UCR) was associated with higher risk of CAD in patients living with T2DM [hazard ratio (HR), 1.782; 95% confidence interval (CI), 1.237–2.567]. The Kaplan–Meier survival curves indicated that the high group of UCR tended to have a lower event-free survival than the low group and medium group. There was a nonlinear trend toward increasing risk of CAD across the groups of UCR. And cubic spline function graph suggested that the influence of UCR level on HR for CAD increased significantly at UCR levels above 6.67. Conclusions: An elevated UCR was significantly associated with an increased risk for CAD in patients living with T2DM. [ABSTRACT FROM AUTHOR]

For building environments, meteorological factors such as daily mean temperature, extreme temperature and seasonal temperature changes, are essential, as they impact building structures significantly. Due to the importance of detailed and accurate temperature data, and taking Beijing, China, as an example, this paper developed a fast and effective interpolation method to extract hourly meteorological data, based on 30 years’ raw meteorological data. With the interpolated data, this paper defined the extreme weather for buildings. Moreover, a temperature model based on probability and statistical analysis was constructed, and the general climate standard for days and extreme climate for typical days with different return periods were obtained. Furthermore, meteorological models for standard annual temperature were also achieved, reflecting the daily variation and annual variation of temperature, and can provide continuous-numerical-simulation parameters for analyzing daily and annual temperature. According to the daily temperature difference obeys the Gumble Distribution, the daily temperature difference in different return periods and extreme climates is obtained by analysis. Therefore, annual temperature ranges of different recurrence intervals and extreme climate are also achieved, and the annual temperature ranges can be used to analyze the effect of different recurrence intervals and extreme weather on building structures.

Understanding the changing patterns and trend of vegetation is essential for its socio-environmental values. Normalized difference vegetation index (NDVI), a satellite based data obtained from Moderate Resolutions Imaging Spectro-radiometer (MODIS) were analysed. The data have a characteristic resolution of 250 × 250 m2 and a 16-day composite period. They were ordered separately for each sample plot from east, centre and west of Nepal, for 15 years period, 2000 to 2015. MODIS, Land Surface Temperature (LST) data were used to identify unreliable NDVI values and hence eliminated. Also, the unusually fluctuating NDVI values during the rainy season were removed. A cubic spline function (for seasonal patterns), linear regression model (for NDVI trend) and generalized estimating equations (GEE for comparison of the changing trends) were the models used. The results showed a patterned annual seasonal vegetation and significant trends during the 15 years. Seasonal growth showed a peak in rainy season and trough in the winter season, with slight temporal variation among the areas with a characteristic shift of seasonal greening (start of greening) and browning (end of greening) from east to west of Nepal. The NDVI trend was significantly rising in eastern and western suburban areas while the central urban city had a significant decline. The temporal shift of start and end of the season from east to west can be of value to agriculturalists. [ABSTRACT FROM AUTHOR]

In this article, we present a new two-level implicit cubic spline numerical method of accuracy 2 in time and 4 in spatial direction for the numerical solution of 1D time-dependent quasilinear biharmonic equation subject to appropriate initial and natural boundary conditions prescribed. The easiness of the proposed numerical method lies in their 3-point discretization in which we use two points x ± (h / 2) and a central point 'x' in spatial direction. Using the continuity of the first-order derivative of cubic spline function, we derive the fourth-order accurate numerical method for the time-dependent biharmonic equation on a uniform mesh. The stability consideration of the proposed method is discussed using a model linear problem. The proposed cubic spline method successfully implements on generalized Kuramoto–Sivashinsky and extended Fisher–Kolmogorov equations. From the numerical experiments, we obtain better computational results compared to the results discussed in earlier research work. [ABSTRACT FROM AUTHOR]

In order to implement rapid prediction of edge defects in the cold roll forming process, a new analytical method based on the mean longitudinal strain of the racks is presented. A cubic spline curve with the parameters of the cumulative chord length is applied to fit the corresponding points and center points of different passes, and fitting curves are obtained. As the cold roll forming is micro-tension forming, the tensions between racks are ignored. Then the mean longitudinal strains between racks are obtained. By comparing the mean longitudinal strain between racks and the yield strain of the material, we can judge whether there are defects at the edges. Finally, the reasonableness of this method is illustrated and validated by an example. With this method, the roll forming effect can be quickly predicted, and the position where a greater longitudinal strain occurred can be determined. In order to prevent the defects, the deformation angles need to be modified when the result is beyond the yield strain. To further prove the correctness of the theory, the results of the analytical method are compared with the ones of the non-linear finite element software ABAQUS. The analytical results have the same trend as the finite element results. This method can provide useful guidance to the actual design process.

When using the Fast Fourier Transform(FFT) to perform harmonic analysis on power systems, due to asynchronous sampling and data truncation, fence effect and spectrum leakage will occur, and accurate harmonic parameters cannot be obtained. In order to improve the accuracy of harmonic detection of asynchronous sampling, this paper proposes a Rife-vincent self-convolution window interpolation FFT algorithm based on cubic spline function. The Rife-vincent self-convolution window has low peak value and fast sidelobe attenuation, which can effectively suppress spectral leakage. The cubic spline function is used to approximate the amplitude ratio function, which can effectively suppress the fence effect and avoid solving high-order equations. The calculation accuracy is high. Through MATLAB simulation analysis, it is verified that the Rife-vincent self-convolution window interpolation FFT algorithm based on cubic spline function can effectively suppress spectrum leakage and fence effect and improve harmonic detection accuracy.

Copyright of Journal of Mine Automation is the property of Industry & Mine Automation Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article is focused on the non-smooth problem of the semi-supervised support vector machine optimization model. A smooth semi-supervised support vector machine model was established. A general cubic spline function with 2 times differentiable at zero point was deduced by a general three-moment method and was used to approach the non-smooth part in the semi-supervised support vector machine. A new smooth semi-supervised support vector with 1 time differentiable based on the general cubic spline function was constructed, and thus a lot of fast optimization algorithms could be applied to solve the smooth semi-supervised vector machine model. The approximation accuracy of the general cubic spline function to the symmetric hinge loss function was analyzed, and the convergence accuracy of the new model was proved. Numerical experiments show that the new model has a better classification result.

In this paper, an efficient numerical methods based on cubic polynomial spline func- tions are proposed for the linear fractional boundary value problems (FBVPs) with Caputos left and right fractional operator. In computing the approximation to the solutions of FBVPs, consistency relations have been derived with the help of spline functions. For convergence analysis of this method, it is assumed that the exact solution of FBVP belongs to a class of C6-functions. Numerical examples are considered to illustrate the accuracy and efficiency of this method and compare the results with other methods developed by Akram and Tariq in [18] and Zahra and Elkholy in [28-30]. [ABSTRACT FROM AUTHOR]

Recent advances in Nano-Science and Technology have provided opportunity to develop sensor nodes below 100 nm using various types of novel materials. These nanosensors have great potential in practical applications, such as measuring chemical compounds in concentrations as low as one part per billion, drug delivery, and disease diagnostics. Much research is devoted to designing and fabricating these nanosensors. However, the question of reliability is often ignored during the design process. Our research focuses on the reliability of one particular wireless nanosensor network (WNSN) that is used for monitoring human lung cells. The WNSN is probabilistically modeled and its reliability is analyzed under different scenarios. The main challenge here is how to define the reliability function for this particular WNSN. We attempt to do it by introducing a flexible definition of reliability that makes sense intuitively and allows for assessing the reliability function. Although this paper is motivated by one particular WNSN, our method of assessing reliability can also be used for any nanosensor where our proposed definition of reliability is reasonable. [ABSTRACT FROM PUBLISHER]

Recently, Eslami et al., (2013) proposed a method of constructing pseudo capillary pressure curves by combining with NMR log data and conventional well logs following a two-step approach. Using this method, Eslami et al. declared that the simulated P c curves showed a good agreement with laboratory derived mercury injection capillary pressure (MICP) curves at low mercury saturations (<35%). However, detailed comparison of the constructed pseudo P c curves with the experimented results illustrates that the constructed P c curves are overestimated. The parts for constructed P c curves with mercury injection saturations ( S Hg s) higher than 35% are all under the laboratory experimented results. This means this technique cannot be accurately apply for formation pore structure evaluation, especially for carbonate rocks and tight sandstone reservoirs. In this paper, we point out that the uncertainty Eslami's method is caused by the dimension difference of mercury injection pressure and 8 T 2 porosity bins, and a technique of improving P c curve construction is proposed. The reliability of the improved technique is verified by the application of the same 3 core samples displayed in Eslami's paper. [ABSTRACT FROM AUTHOR]

To calculate grey absolute relational grade (GARG) is based on employing polygonal line to approximate a system's behavior trial. Prom the perspective of interpolation, the polygonal line is piecewise linear interpolation method. It has two main drawbacks, one is that it is not smooth at the node while the real trial of some system is; the other is that the approximation error is big when the real trial has big curvature, since grey system's study object is a system with small sample or poor information, so the polygonal line can't approach the system's real trial. Therefore, a new GARG called cubic spline based grey absolute relational grade (CUSGARG) is put forward to improve the two drawbacks, where the cubic spline function is employed to improve grey absolute relational grade: first of all, the cubic spline function is used to appropriate the system's trial, and then follow the classic method to calculate the GARG. Properties and utility range of the CUSGARG are explored. The CUSGARG can be applied to analyze growth-curve-type system. In addition, the CUSGARG is suitable for unequal interval time series. [ABSTRACT FROM AUTHOR]

In this paper, an improved gray model is proposed to predict Japan's domestic and overseas automobile production. The improved gray model is established by integrating the cubic spline function into gray model to improve its prediction capability. Two cases of Japan's domestic and overseas automobile production are used to validate the proposed model. The prediction results show that the proposed model have good prediction performance. [ABSTRACT FROM AUTHOR]

In order to promote the feasibility of the construction of cubic splines, this paper presented a novel pseudoinverse-based construction method (PCM) to construct the cubic spline function effectively. Without using endpoint-constraint conditions, this method obtained the solution of the second-order derivatives of the cubic spline that was closest to the origin, namely the minimum norm solution. Theoretical analysis and numerical experiments highlight the efficacy of the PCM. For better understanding, it further studied and investigated the characteristics of various construction methods. In this way, it provided guidelines for choosing suitable methods to construct cubic splines in practical applications of engineering calculation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a novel grey prediction model is proposed to enhance the performance of prediction for the amount of fixed-line and cellular phone subscribers in Japan. The cubic spline function is first integrated into grey prediction model to enhance its prediction capability. Then the particle swarm optimization (PSO) algorithm is applied, so that the prediction performance can be improved further. The prediction results using proposed models are very satisfactory. [Copyright &y& Elsevier]

Abstract: The grey dynamic model GM(1,1), which is based on the grey system theory, has recently emerged as a powerful tool for short term load forecasting (STLF) problem. However, GM(1,1) is only a first order single variable grey model, the forecasted accuracy is unsatisfactory when original data show great randomness. In this paper, we propose improved grey dynamic model GM(2,1), a second order single variable grey model, to enhance the forecasted accuracy. Then it is applied to improve STLF performance. We provide a viewpoint that the derivative and background value of GM(2,1) model can be expressed in grey number. Then cubic spline function is presented to calculate the derivative and background value in grey number interval. We call the proposed model as 3spGM(2,1) model. Additionally, Taylor approximation method is applied to 3spGM(2,1) for achieving the high forecasted accuracy. The improved version is defined as T-3spGM(2,1). The power system load data of ordinary and special days are used to validate the proposed model. The experimental results showed that the proposed model has better performance for STLF problem. [Copyright &y& Elsevier]

Hydroxyapatite precipitation process involves the formation in the first phase of a solid-phase with amorphous structure (amorphous calcium phosphate), which in time turns into hydroxyapatite. Polynomial spline interpolation is a numerical method useful in mathematical modeling of this phase transformation process. By this method, experimental data are interpolated to obtain cubic spline polynomial function which can approximate reasonably well the experimental values of the degree of conversion at any pH between 8.5 ÷ 12. A very good agreement between the experimental and numerical results confirms the validity of the numerical procedure. [ABSTRACT FROM AUTHOR]

This research aims to establish a new method to predict the dome thickness of composite pressure vessels. A cubic spline function was presented to calculate the dome thickness. Using this cubic spline function, the dome thickness of an arbitrary composite pressure vessel was forecasted. The predictive results were compared with the existing methods and actual measured thickness. Then, the accuracy of this cubic spline function was discussed for predicting the dome thickness of composite pressure vessels with different polar radii and different fiber band width values. The results showed that dome thickness obtained from the cubic spline function could reflect the actual measured thickness well and it could provide an accurate model for the finite element analysis. [ABSTRACT FROM AUTHOR]

In recent years, the grey dynamic model GM(2, 1), which is based on the grey system theory has been successfully applied in many prediction fields to solve efficiently the predicted problems of uncertainty systems. However, this model has irrational problem concerning the calculation of initial value and derivative. Therefore, the predicted accuracy of GM(2, 1) is unsatisfying when original data show great randomness. In this paper, the new calculation of initial value and derivative are first proposed to enhance the predicted power according to cubic spline function. The newly generated model is defined as 3spGM(2, 1). To further improve predicted accuracy, the Taylor approximation method is then applied to 3spGM(2, 1). We call the improved version as T-3spGM(2, 1). Finally, the effectiveness of proposed model is validated by using fault data sets of electric product. [ABSTRACT FROM AUTHOR]