B-spline Model Research Articles

Cluster analysis of longitudinal profiles with subgroups

In this paper, we cluster profiles of longitudinal data using a penalized regression method. Specifically, we allow heterogeneous variation of longitudinal patterns for each subject, and utilize a pairwise-grouping penalization on coefficients of the nonparametric B-spline models to form subgroups. Consequently, we identify clusters based on different patterns of the predicted longitudinal curves. One advantage of the proposed method is that there is no need to pre-specify the number of clusters; instead the number of clusters is selected automatically through a model selection criterion. Our method is also applicable for unbalanced data where different subjects could have measurements at different time points. To implement the proposed method, we develop an alternating direction method of multipliers (ADMM) algorithm which has the desirable convergence property. In theory, we establish the consistency properties for approximated nonparametric function estimation and subgrouping memberships. In addition, we show that our method outperforms the existing competitive approaches in our simulation studies and real data example.

Comparison of B-Spline Model and Iterated Conditional Modes (ICM) For Data With Measurement Error (ME)

Direct observation results are often used to review the estimation model. However, actual data observation findings still need to be re-examined, because of measurement error factors (ME). In the regression modeling if X is a random variable with Measurement Error then the complicated calculation will not loose from application of Computer and Technology. As is the case for a review of the following model estimation, given data (Xi, Yi), then the regression model isYi = g(Xi) + ϵiwhere Xi is the element i from the predictor variables X and Yi is the element i of the response variable Y. The variable X is the predictor variables From the findings specific observations usually are constants, but generally found X which is a random variable variable or where Fixed value is not constant. In this case is called the regression model Regression Model with the measurement Errors. Purpose of this research are estimated nonparametric model approach with B-Spline Method to review regression with Measurement Errors are ignored and methods Iterative Conditional Mode (ICM) for review Model regression with measurement error.

Minimum Entropy Active Fault Tolerant Control of the Non-Gaussian Stochastic Distribution System Subjected to Mean Constraint

Stochastic distribution control (SDC) systems are a group of systems where the outputs considered is the measured probability density function (PDF) of the system output whilst subjected to a normal crisp input. The purpose of the active fault tolerant control of such systems is to use the fault estimation information and other measured information to make the output PDF still track the given distribution when the objective PDF is known. However, if the target PDF is unavailable, the PDF tracking operation will be impossible. Minimum entropy control of the system output can be considered as an alternative strategy. The mean represents the center location of the stochastic variable, and it is reasonable that the minimum entropy fault tolerant controller can be designed subjected to mean constraint. In this paper, using the rational square-root B-spline model for the shape control of the system output probability density function (PDF), a nonlinear adaptive observer based fault diagnosis algorithm is proposed to diagnose the fault. Through the controller reconfiguration, the system entropy subjected to mean restriction can still be minimized when fault occurs. An illustrative example is utilized to demonstrate the use of the minimum entropy fault tolerant control algorithms.

Single-Carrier Frequency-Domain Equalization With Hybrid Decision Feedback Equalizer for Hammerstein Channels Containing Nonlinear Transmit Amplifier

We propose a nonlinear hybrid decision feedback equalizer (NHDFE) for single-carrier (SC) block transmission systems with nonlinear transmit high power amplifier (HPA), which significantly outperforms our previous nonlinear SC frequency-domain equalization (NFDE) design. To obtain the coefficients of the channel impulse response (CIR) as well as to estimate the nonlinear mapping and the inverse nonlinear mapping of the HPA, we adopt a complex-valued (CV) B-spline neural network approach. Specifically, we use a CV B-spline neural network to model the nonlinear HPA, and we develop an efficient alternating least squares scheme for estimating the parameters of the Hammerstein channel, including both the CIR coefficients and the parameters of the CV B-spline model. We also adopt another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can be estimated using the least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. The effectiveness of our NHDFE design is demonstrated in a simulation study, which shows that the NHDFE achieves a signal-to-noise ratio gain of 4dB over the NFDE at the bit error rate level of $10^{-4}$ .

A new paradigm of fuzzy control point in space curve

The control point is the most important element in the production of spline curve or surface model. This is because any changes of control points in the spline model affect the shape of the resulting curve or surface. Wahab and colleagues have introduced fuzzy control points to solve the problem of uncertainty prevailing in the spline modeling. However, based on this concept, this paper will discusses a new type of fuzzy control point that can generates a spline space curve model in 3-dimensional. This is because the generated control point is a 3-dimensional that satisfies the basic concepts of fuzzy set was introduced by Zadeh. However, this paper only taking a B-Spline model as a numerical example in the discussed model.

Decomposition of LiDAR waveforms by B-spline-based modeling

Waveform decomposition is a widely used technique for extracting echoes from full-waveform LiDAR data. Most previous studies recommended the Gaussian decomposition approach, which employs the Gaussian function in laser pulse modeling. As the Gaussian-shape assumption is not always satisfied for real LiDAR waveforms, some other probability distributions (e.g., the lognormal distribution, the generalized normal distribution, and the Burr distribution) have also been introduced by researchers to fit sharply-peaked and/or heavy-tailed pulses. However, these models cannot be universally used, because they are only suitable for processing the LiDAR waveforms in particular shapes. In this paper, we present a new waveform decomposition algorithm based on the B-spline modeling technique. LiDAR waveforms are not assumed to have a priori shapes but rather are modeled by B-splines, and the shape of a received waveform is treated as the mixture of finite transmitted pulses after translation and scaling transformation. The performance of the new model was tested using two full-waveform data sets acquired by a Riegl LMS-Q680i laser scanner and an Optech Aquarius laser bathymeter, comparing with three classical waveform decomposition approaches: the Gaussian, generalized normal, and lognormal distribution-based models. The experimental results show that the B-spline model performed the best in terms of waveform fitting accuracy, while the generalized normal model yielded the worst performance in the two test data sets. Riegl waveforms have nearly Gaussian pulse shapes and were well fitted by the Gaussian mixture model, while the B-spline-based modeling algorithm produced a slightly better result by further reducing 6.4% of fitting residuals, largely benefiting from alleviating the adverse impact of the ringing effect. The pulse shapes of Optech waveforms, on the other hand, are noticeably right-skewed. The Gaussian modeling results deviated significantly from original signals, and the extracted echo parameters were clearly inaccurate and unreliable. The B-spline-based method performed significantly better than the Gaussian and lognormal models by reducing 45.5% and 11.5% of their fitting errors, respectively. Much more precise echo properties can accordingly be retrieved with a high probability. Benefiting from the flexibility of B-splines on fitting arbitrary curves, the new method has the potentiality for accurately modeling various full-waveform LiDAR data, whether they are nearly Gaussian or non-Gaussian in shape.

Spatial Interpolated Lookup Tables (LUTs) Models for Ergodic Capacity of MIMO FSO Systems

We propose low complexity, adaptive multivariate precomputed B-spline and Barycentric Lagrange interpolation-based lookup table ( $ {B}^{2}$ LUT) models for the estimation of channel capacity of multiple-input-multiple-output free-space optical communication systems over generalized Malaga $( {\mathcal{ M}})$ -distributed atmospheric turbulence channels. The models require low memory for efficient operation and exploit precomputed weights to achieve fast and stable operation. The models can significantly reduce the size of lookup table, thereby reducing the computational cost. Similarly, the models can enhance the speed by up to 15 orders of magnitude and beyond without loss of fidelity compared with the current analytical models.

Spline Parameterization of Complex Planar Domains for Isogeometric Analysis

Abstract Isogeometric Analysis (IGA) involves unification of modelling and analysis by adopting the same basis functions (splines), for both. Hence, spline based parametric model is the starting step for IGA. Representing a complex domain, using parametric geometric model is a challenging task. Parameterization problem can be defined as, finding an optimal set of control points of a B-spline model for exact domain modelling. Also, the quality of parameterization, too has significant effect on IGA. Finding the B-spline control points for any given domain, which gives accurate results is still an open issue. In this paper, a new planar B-spline parameterization technique, based on domain mapping method is proposed. First step of the methodology is to map an input (non-convex) domain onto a unit circle (convex) with the use of harmonic functions. The unique properties of harmonic functions: global minima and mean value property, ensures the mapping is bi-jective and with no self-intersections. Next step is to map the unit circle to unit square to make it apt for B-spline modelling. Square domain is re-parameterized by using conventional centripetal method. Once the domain is properly parameterized, the required control points are computed by solving the B-spline tensor product equation. The proposed methodology is validated by applying the developed B-spline model for a static structural analysis of a plate, using isogeometric analysis. Different domains are modelled to show effectiveness of the given technique. It is observed that the proposed method is versatile and computationally efficient.

Near real-time estimation of ionosphere vertical total electron content from GNSS satellites using B-splines in a Kalman filter

Abstract. Although the number of terrestrial global navigation satellite system (GNSS) receivers supported by the International GNSS Service (IGS) is rapidly growing, the worldwide rather inhomogeneously distributed observation sites do not allow the generation of high-resolution global ionosphere products. Conversely, with the regionally enormous increase in highly precise GNSS data, the demands on (near) real-time ionosphere products, necessary in many applications such as navigation, are growing very fast. Consequently, many analysis centers accepted the responsibility of generating such products. In this regard, the primary objective of our work is to develop a near real-time processing framework for the estimation of the vertical total electron content (VTEC) of the ionosphere using proper models that are capable of a global representation adapted to the real data distribution. The global VTEC representation developed in this work is based on a series expansion in terms of compactly supported B-spline functions, which allow for an appropriate handling of the heterogeneous data distribution, including data gaps. The corresponding series coefficients and additional parameters such as differential code biases of the GNSS satellites and receivers constitute the set of unknown parameters. The Kalman filter (KF), as a popular recursive estimator, allows processing of the data immediately after acquisition and paves the way of sequential (near) real-time estimation of the unknown parameters. To exploit the advantages of the chosen data representation and the estimation procedure, the B-spline model is incorporated into the KF under the consideration of necessary constraints. Based on a preprocessing strategy, the developed approach utilizes hourly batches of GPS and GLONASS observations provided by the IGS data centers with a latency of 1 h in its current realization. Two methods for validation of the results are performed, namely the self consistency analysis and a comparison with Jason-2 altimetry data. The highly promising validation results allow the conclusion that under the investigated conditions our derived near real-time product is of the same accuracy level as the so-called final post-processed products provided by the IGS with a latency of several days or even weeks.

Choosing the optimal number of B-spline control points (Part 2: Approximation of surfaces and applications)

Abstract Freeform surfaces like B-splines have proven to be a suitable tool to model laser scanner point clouds and to form the basis for an areal data analysis, for example an areal deformation analysis. A variety of parameters determine the B-spline's appearance, the B-spline's complexity being mostly determined by the number of control points. Usually, this parameter type is chosen by intuitive trial-and-error-procedures. In [10] the problem of finding an alternative to these trial-and-error-procedures was addressed for the case of B-spline curves: The task of choosing the optimal number of control points was interpreted as a model selection problem. Two model selection criteria, the Akaike and the Bayesian Information Criterion, were used to identify the B-spline curve with the optimal number of control points from a set of candidate B-spline models. In order to overcome the drawbacks of the information criteria, an alternative approach based on statistical learning theory was developed. The criteria were evaluated by means of simulated data sets. The present paper continues these investigations. If necessary, the methods proposed in [10] are extended to areal approaches so that they can be used to determine the optimal number of B-spline surface control points. Furthermore, the methods are evaluated by means of real laser scanner data sets rather than by simulated ones. The application of those methods to B-spline surfaces reveals the datum problem of those surfaces, meaning that location and number of control points of two B-splines surfaces are only comparable if they are based on the same parameterization. First investigations to solve this problem are presented.

On identification of Hammerstein and Wiener model with application to virtualised software system

ABSTRACTThis paper proposes a system identification method for estimating virtualised software system dynamics within the framework of a Hammerstein–Wiener model. Building on the authors’ previous work in identification and control of the software systems, the approach utilises frequency sampling filter structure to describe the linear dynamics and B-spline curve functions for the inverse static output nonlinearity. Furthermore, the issue on parameter selection for B-spline model approximation of scatter data is addressed by using a data clustering method. An experimental test-bed of virtualised software system is established to generate real observational data which are used to confirm the performance of the proposed approach. The identification results have shown that the model efficacy is increased with the proposed approach because the dimension of the nonlinear model can be significantly reduced while maintaining the desired accuracy.

Comparative Performance of Complex-Valued B-Spline and Polynomial Models Applied to Iterative Frequency-Domain Decision Feedback Equalization of Hammerstein Channels.

Complex-valued (CV) B-spline neural network approach offers a highly effective means for identifying and inverting practical Hammerstein systems. Compared with its conventional CV polynomial-based counterpart, a CV B-spline neural network has superior performance in identifying and inverting CV Hammerstein systems, while imposing a similar complexity. This paper reviews the optimality of the CV B-spline neural network approach. Advantages of B-spline neural network approach as compared with the polynomial based modeling approach are extensively discussed, and the effectiveness of the CV neural network-based approach is demonstrated in a real-world application. More specifically, we evaluate the comparative performance of the CV B-spline and polynomial-based approaches for the nonlinear iterative frequency-domain decision feedback equalization (NIFDDFE) of single-carrier Hammerstein channels. Our results confirm the superior performance of the CV B-spline-based NIFDDFE over its CV polynomial-based counterpart.

On the surface quality of additive manufactured parts

This paper presents the development, implementation and application of a methodology to predict and control the surface quality of the additive manufacturing products based on an accurate representation of the cusps’ geometric model. A non-uniform rational B-spline (NURBS) model representing the geometry of cusps generated by layer-based manufacturing is employed, and its parameters are extracted by running experimental study of the fabricated test specimens. The significant difference of the results obtained using the developed models with what is used in common practice is discussed and demonstrated. Using the developed model, a unified solution to estimate the surface roughness based on the local surface gradient on the part and the selected fabrication layer thickness is presented. The results show that the developed methodology effectively estimates the local surface roughness of the fabricated products.

Hyperpolarizabilities of alkaline-earth metal ions Be+, Mg+, and Ca+

The knowledge of the hyperpolarizabilities of atoms and ions is helpful for the analysis of the high order effects of the frequency shifts in precision spectroscopy experiments. Liu et al. [Phys. Rev. Lett. 114, 223001 (2015)] proposed to establish all-optical trapped ion clocks using laser at the magic wavelength for clock transition. To evaluate the high-order frequency shifts in this new scheme of optical clocks, hyperpolarizabilities are needed, but absent. Using the finite field method based on the B-spline basis set and model potentials, we calculated the electric-field-dependent energy shifts of the ground and low-lying excited states in Be+, Mg+, and Ca+ in the field strength range of 0.0-6×10−5 a.u.. The scalar and tensor polarizabilities (α 0, α 2) and hyperpolarizabilities (γ 0, γ 2, γ 4) were deduced. The results of the hyperpolarizabilities for Be+ showed good agreement with the values in literature, implying that the present method can be applied for the effective estimation of the atomic hyperpolarizabilities, which are rarely reported but needed in experiments. The feasibility of optical trapping of Ca+ is discussed, and the contributions of hyperpolarizabilities to the transition frequency shift for Ca+ in the optical dipole trap are estimated using quasi-electrostatic approximation.

Time series modeling of pathogen-specific disease probabilities with subsampled data.

Many diseases arise due to exposure to one of multiple possible pathogens. We consider the situation in which disease counts are available over time from a study region, along with a measure of clinical disease severity, for example, mild or severe. In addition, we suppose a subset of the cases are lab tested in order to determine the pathogen responsible for disease. In such a context, we focus interest on modeling the probabilities of disease incidence given pathogen type. The time course of these probabilities is of great interest as is the association with time-varying covariates such as meteorological variables. In this set up, a natural Bayesian approach would be based on imputation of the unsampled pathogen information using Markov Chain Monte Carlo but this is computationally challenging. We describe a practical approach to inference that is easy to implement. We use an empirical Bayes procedure in a first step to estimate summary statistics. We then treat these summary statistics as the observed data and develop a Bayesian generalized additive model. We analyze data on hand, foot, and mouth disease (HFMD) in China in which there are two pathogens of primary interest, enterovirus 71 (EV71) and Coxackie A16 (CA16). We find that both EV71 and CA16 are associated with temperature, relative humidity, and wind speed, with reasonably similar functional forms for both pathogens. The important issue of confounding by time is modeled using a penalized B-spline model with a random effects representation. The level of smoothing is addressed by a careful choice of the prior on the tuning variance.

Estimation of the water–oil–gas relative permeability curve from immiscible WAG coreflood experiments using the cubic B-spline model

Immiscible water-alternating-gas (WAG) flooding is an EOR technique that has proven successful for water drive reservoirs due to its ability to improve displacement and sweep efficiency. Nevertheless, considering the complicated phase behavior and various multiphase flow characteristics, gas tends to break through early in production wells in heterogeneous formations because of overriding, fingering, and channeling, which may result in unfavorable recovery performance. On the basis of phase behavior studies, minimum miscibility pressure measurements, and immiscible WAG coreflood experiments, the cubic B-spline model (CBM) was employed to describe the three-phase relative permeability curve. Using the Levenberg–Marquardt algorithm to adjust the vector of unknown model parameters of the CBM sequentially, optimization of production performance including pressure drop, water cut, and the cumulative gas–oil ratio was performed. A novel numerical inversion method was established for estimation of the water–oil–gas relative permeability curve during the immiscible WAG process. Based on the quantitative characterization of major recovery mechanisms, the proposed method was validated by interpreting coreflood data of the immiscible WAG experiment. The proposed method is reliable and can meet engineering requirements. It provides a basic calculation theory for implicit estimation of oil–water–gas relative permeability curve.

Atmospheric Predictors for Annual Maximum Precipitation in North Africa

AbstractThe high precipitation variability over North Africa presents a major challenge for the population and the infrastructure in the region. The last decades have seen many flood events caused by extreme precipitation in this area. There is a strong need to identify the most relevant atmospheric predictors to model these extreme events. In the present work, the effect of 14 different predictors calculated from NCEP–NCAR reanalysis, with daily to seasonal time steps, on the maximum annual precipitation (MAP) is evaluated at six coastal stations located in North Africa (Larache, Tangier, Melilla, Algiers, Tunis, and Gabès). The generalized extreme value (GEV) B-spline model was used to detect this influence. This model considers all continuous dependence forms (linear, quadratic, etc.) between the covariates and the variable of interest, thus providing a very flexible framework to evaluate the covariate effects on the GEV model parameters. Results show that no single set of covariates is valid for all stations. Overall, a strong dependence between the NCEP–NCAR predictors and MAP is detected, particularly with predictors describing large-scale circulation (geopotential height) or moisture (humidity). This study can therefore provide insights for developing extreme precipitation downscaling models that are tailored for North African conditions.

Approximation of Vehicle Trajectory with B-Spline Curve

In this contribution, we present the description of a B-spline curve. We deal with creation of its basis function as well as with creation of the curve itself from entered control points. Following the literature, we formed an algorithm for B-spline modelling and we used it for the planar and spatial curve. The planar curve is made of chosen points. The spatial curve approximates the trajectory of a real vehicle, which trajectory was obtained by the set of measured points. The modelled curve very exactly describes the polygon created from the linked control points. With the lowering degree of the curve, this one is more clamping to the given polygon and for the extreme case it is transformed to the polygon itself. The advantage of the B-spline curve use is, for example in comparison with a Bézier curve, high adaptability, which is expressed in its parameters - besides entered control points, these are knots generated on the curve and degree of the curve.

Noble Metal Alloys for Plasmonics

The fixed optical properties of noble metals currently limit their use in photonic devices that operate at optical frequencies. To achieve metals with tunable optical response, we present noble metal alloyed thin-films formed by the binary mixture of Ag, Au, and Cu. As the dielectric functions (e) of the alloys cannot be modeled as the linear combination of the pure metals, we combined transmission and reflection measurements of the alloyed thin films with a B-spline model that takes into account the Kromers–Kronig relation and experimentally determined the dielectric functions. We found that in some cases a mixture can provide a material with higher surface plasmon polariton quality factor than the corresponding pure metals. We independently measured the surface plasmon polariton coupling angle for all alloys using the Kretschmann configuration and found excellent agreement between the two methods when determining e. Our approach paves the way to implement metallic thin films and nanostructures with on-d...

Bi-cubic B-spline fitting-based local volatility model with mean reversion process

This paper studies the traditional local volatility model and proposes: A novel local volatility model with mean-reversion process. The larger is the gap between local volatility and its mean level, the higher will be the rate at which local volatility will revert to the mean. Then, a B-spline method with proper knot control is applied to interpolate the local volatility matrix. The bi-cubic B-spline is used to recover the local volatility surface from this local volatility matrix. Finally, empirical tests show that the proposed mean-reversion local volatility model offers better prediction performance than the traditional local volatility model.