The Weighted Basis for PHT-Splines

PHT-splines are defined as polynomial splines over hierarchical T-meshes with very efficient local refinement properties.The original PHT-spline basis functions constructed by the truncation mechanism have a decay phenomenon,resulting in numerical instability.The non-decay basis functions are constructed as the B-splines that are defined on the 2×2 tensor product meshes associated with basis vertices in Kang et al.,but at the cost of losing the partition of unity.In the field of finite element analysis and topology optimization,forming the partition of unity is the default ingredient for constructing basis functions of approximate spaces.In this paper,we will show that the non-decay PHT-spline basis functions proposed by Kang et al.can be appropriately modified to form a partition of unity.Each non-decay basis function is multiplied by a positive weight to form the weighted basis.The weights are solved such that the sum of weighted bases is equal to 1 on the domain.We provide two methods for calculatingweights,based on geometric information of basis functions and the subdivision of PHT-splines.Weights are given in the form of explicit formulas and can be efficiently calculated.We also prove that the weights on the admissible hierarchical T-meshes are positive.

Improvement of Cardiac Function by Dry Weight Optimization Based on Interdialysis Inferior Vena Caval Diameter (1)

In hemodialysis (HD) patients, the diameter of the inferior vena cava (IVC) serves for evaluation of the amount of body fluid.

An Intelligent Early Warning Method of Press-Assembly Quality Based on Outlier Data Detection and Linear Regression

Focusing on controlling the press-assembly quality of high-precision servo mechanism,an intelligent early warning method based on outlier data detection and linear regression is proposed.Linear regression is used to deal with the relationship between assembly quality and press-assembly process,then the mathematical model of displacement-force in press-assembly process is established and a qualified press-assembly force range is defined for assembly quality control.To preprocess the raw dataset of displacement-force in the press-assembly process,an improved local outlier factor based on area density and P weight(LAOPW)is designed to eliminate the outliers which will result in inaccuracy of the mathematical model.A weighted distance based on information entropy is used to measure distance,and the reachable distance is replaced with P weight.Experiments show that the detection efficiency of the algorithm is improved by 5.6 ms compared with the traditional local outlier factor(LOF)algorithm,and the detection accuracy is improved by about 2%compared with the local outlier factor based on area density(LAOF)algorithm.The application of LAOPW algorithm and the linear regression model shows that it can effectively carry out intelligent early warning of press-assembly quality of high precision servo mechanism.

Monoexponential, biexponential and stretched-exponential models based diffusion weighted imaging: a comparative study in the differential diagnosis of benign and malignant breast lesions

Objective To investgate the value of various parameters obtained from monoexponential,biexponential,and stretched exponential diffusion-weighted imaging models in the differential diagnosis of breast lesions.Methods A retrospective study was performed in 54 patients with pathologically confirmed malignant tumors(n=30),benign lesions(n=34)and normal fibroglandular

A simple data assimilation method for improving the MODIS LAI time-series data products based on the object analysis and gradient inverse weighted filter

A simple data assimilation method for improving estimation of moderate resolution imaging spectroradiometer （MODIS） leaf area index （LAI） time-series data products based on the gradient inverse weighted filter and object analysis is proposed. The properties and quality control （QC） of MODIS LAI data products are introduced. Also, the gradient inverse weighted filter and object analysis are analyzed. An experiment based on the simple data assimilation method is performed using MODIS LAI data sets from 2000 to 2005 of Guizhou Province in China.

Spectral clustering based on matrix perturbation theory

This paper exposes some intrlnsic chsracterlstlca of the spectral clustering method by using the tools from the mstrlx perturbation theory. We construct s welght mstrix of s graph and study Its elgenvalues and elgenvectors. It shows that the number of clusters Is equal to the number of elgenvslues that are larger than 1, and the number of polnts In each of the clusters can be spproxlmsted by the associated elgenvslue. It also shows that the elgenvector of the weight rnatrlx can be used dlrectly to perform clusterlng; that Is, the dlrectlonsl angle between the two-row vectors of the mstrlx derlved from the elgenvectors Is s sultable distance measure for clustsrlng. As s result, an unsupervised spectral clusterlng slgorlthm based on welght mstrlx （USCAWM） Is developed. The experlmental results on s number of srtlficisl and real-world data sets show the correctness of the theoretical analysis.

Evolved clustering analysis of 300 MW boiler furnace pressure sequence based on entropy characterization

The furnace process is very important in boiler operation,and furnace pressure works as an important parameter in furnace process.Therefore,there is a need to analyze and monitor the pressure signal in furnace.However,little work has been conducted on the relationship with the pressure sequence and boiler’s load under different working conditions.Since pressure sequence contains complex information,it demands feature extraction methods from multi-aspect consideration.In this paper,fuzzy c-means analysis method based on weighted validity index(VFCM)has been proposed for the working condition classification based on feature extraction.To deal with the fluctuating and time-varying pressure sequence,feature extraction is taken as nonlinear analysis based on entropy theory.Three kinds of entropy values,extracted from pressure sequence in time-frequency domain,are studied as the clustering objects for work condition classification.Weighted validity index,taking the close and separation degree into consideration,is calculated on the base of Silhouette index and Krzanowski-Lai index to obtain the optimal clustering number.Each time FCM runs,the weighted validity index evaluates the clustering result and the optimal clustering number will be obtained when it reaches the maximum value.Four datasets from UCI Machine Learning Repository are presented to certify the effectiveness in VFCM.Pressure sequences got from a 300 MW boiler are then taken for case study.The result of the pressure sequence case study with an error rate of 0.5332%shows the valuable information on boiler’s load and pressure sequence in furnace.The relationship between boiler’s load and entropy values extracted from pressure sequence is proposed.Moreover,the method can be considered to be a reference method for data mining in other fluctuating and time-varying sequences.

Outboard abnormal noise source localization method with curved surface projection based on time delay matching and weighting criterion

An improved localization method consisting of ＂filtering-time delay estimationhyperbolic localization＂ is proposed. Combining the empirical mode decomposition（EMD）and time delay estimation method based on generalized average magnitude difference function,the original signals are decomposed into intrinsic mode function（IMF） components. The energy distribution criterion and spectrum consistency criterion are used to select the IMFs, which can represent the physical characteristics of the source signal. Several sets of signals are applied to estimate the time delay, and then a vector matching criterion is proposed to select the correct time delay estimation. Considering the hydrophones location, a shell model is established and projected to a plane according to the quadrant before the hyperbolic localization. Results of mooring and sailing tests show that the proposed method improves the localization accuracy,and reduces the error caused by time delay estimation.