A prediction theory of random level distribution based on a generalized difference type of Fokker-Planck equation and its application to environmental noise and vibration,II: Experimental study

In a companion paper [1], a procedure for solving the short time prediction problem in terms of the transition probability distribution has been theoretically derived, for discrete time-sampled data. Explicit algorithms for estimating the non-stationary moment statistics of arbitrary order also have been derived, based on a generalized difference equation of Fokker-Planck type for the conditional probability distributed function, which is central to the theory. In this paper, evidence for the validity and effectiveness of the proposed method is presented, as obtained not only by means of digital simulation but also by using road traffic noise data obtained experimentally in Hiroshima. For several non-stationary random processes simulated by means of random numbers, the theoretical and experimental conditional probability functions are compared. For non-stationary road traffic noise data the theoretically predicted and experimentally determined confidence intervals are compared; in these comparisons several types of conditional probability function and various values of weighting parameter are used in the algorithm. All of the theoretical results show good agreement with the experimental results.     

Identifying almost invariant sets in stochastic dynamical systems

We consider the approximation of fluctuation induced almost invariant sets arising from stochastic dynamical systems. The dynamical evolution of densities is derived from the stochastic Frobenius-Perron operator. Given a stochastic kernel with a known distribution, approximate almost invariant sets are found by translating the problem into an eigenvalue problem derived from reversible Markov processes. Analytic and computational examples of the methods are used to illustrate the technique, and are shown to reveal the probability transport between almost invariant sets in nonlinear stochastic systems. Both small and large noise cases are considered.     

Multiangle dynamic light scattering analysis using a modified Chahine method

Multiangle dynamic light scattering (MDLS) is used to determine particle size distributions (PSDs). The angular intensity weighting coefficients used in the inversion of the PSD data affect dramatically the PSD recovered. Noise in the weighting factors gives rise to poor PSD results. A modified Chahine method, which is insensitive to the noise of the weighting coefficients, is developed for estimating the PSD from MDLS. The method was evaluated through simulated examples that involved unimodal and bimodal PSDs of different shapes and employed for estimating two bimodal PSDs obtained by mixing two standard polystyrene latexes. For comparison, all examples were also analyzed using a nonnegatively-constrained Tikhonov regularization technique typically used for inverting ill-conditioned linear problems. The PSDs estimated by the proposed modified Chahine method were more accurate than those obtained by the Tikhonov technique.     

基于运动补偿的红外图像噪音时域IIR滤波算法

从模式识别的角度出发将图像分为运动区域和非运动区域,采用基于噪音分布模型的运动检测技术与基于概率松弛法的运动区域标号技术相结合对这两种区域进行具体划分,对分类后的图像采用时域IIR滤波,不同区域采用不同的影响因子,以期达到最终的运动补偿.仿真结果表明该方法有效抑制了噪音,同时并未引起明显的运动模糊,图像的视觉效果得到了极大改善.     

基于运动补偿的红外图像噪音时域ⅡR滤波算法

从模式识别的角度出发将图像分为运动区域和非运动区域,采用基于噪音分布模型的运动检测技术与基于概率松弛法的运动区域标号技术相结合对这两种区域进行具体划分,对分类后的图像采用时域ⅡR滤波,不同区域采用不同的影响因子,以期达到最终的运动补偿.仿真结果表明该方法有效抑制了噪音,同时并未引起明显的运动模糊,图像的视觉效果得到了极大改善.     

Correlation dimension: A pivotal statistic for non-constrained realizations of composite hypotheses in surrogate data analysis

Currently surrogate data analysis can be used to determine if data is consistent with various linear systems, or something else (a nonlinear system). In this paper we propose an extension of these methods in an attempt to make more specific classifications within the class of nonlinear systems.

In the method of surrogate data one estimates the probability distribution of values of a test statistic for a set of experimental data under the assumption that the data is consistent with a given hypothesis. If the probability distribution of the test statistic is different for different dynamical systems consistent with the hypothesis, one must ensure that the surrogate generation technique generates surrogate data that are a good approximation to the data. This is often achieved with a careful choice of surrogate generation method and for noise driven linear surrogates such methods are commonly used.

This paper argues that, in many cases (particularly for nonlinear hypotheses), it is easier to select a test statistic for which the probability distribution of test statistic values is the same for all systems consistent with the hypothesis. For most linear hypotheses one can use a reliable estimator of a dynamic invariant of the underlying class of processes. For more complex, nonlinear hypothesis it requires suitable restatement (or cautious statement) of the hypothesis. Using such statistics one can build nonlinear models of the data and apply the methods of surrogate data to determine if the data is consistent with a simulation from a broad class of models. These ideas are illustrated with estimates of probability distribution functions for correlation dimension estimates of experimental and artificial data, and linear and nonlinear hypotheses.     

Influence of multichannel combination, parallel imaging and other reconstruction techniques on MRI noise characteristics

The statistical properties of background noise such as its standard deviation and mean value are frequently used to estimate the original noise level of the acquired data. This requires the knowledge of the statistical intensity distribution of the background signal, that is, the probability density of the occurrence of a certain signal intensity. The influence of many new MRI techniques and, in particular, of various parallel-imaging methods on the noise statistics has neither been rigorously investigated nor experimentally demonstrated yet. In this study, the statistical distribution of background noise was analyzed for MR acquisitions with a single-channel and a 32-channel coil, with sum-of-squares (SoS) and spatial-matched-filter (SMF) data combination, with and without parallel imaging using k-space and image-domain algorithms, with real-part and conventional magnitude reconstruction and with several reconstruction filters. Depending on the imaging technique, the background noise could be described by a Rayleigh distribution, a noncentral chi-distribution or the positive half of a Gaussian distribution. In particular, the noise characteristics of SoS-reconstructed multichannel acquisitions (with k-space-based parallel imaging or without parallel imaging) differ substantially from those with image-domain parallel imaging or SMF combination. These effects must be taken into account if mean values or standard deviations of background noise are employed for data analysis such as determination of local noise levels. Assuming a Rayleigh distribution as in conventional MR images or a noncentral chi-distribution for all multichannel acquisitions is invalid in general and may lead to erroneous estimates of the signal-to-noise ratio or the contrast-to-noise ratio.     

Particle Sizing by Dynamic Light Scattering: Noise and distortion in correlation data

Two undesirable effects occur in particle sizing by dynamic light scattering; statistical noise, and distortion of correlation data. Statistical noise in the correlation data, caused by estimating the autocorrelation of scattered laser light by a time average, leads to non-physical artifacts in the resulting linewidth distribution. These may be removed by regularization, computer modeling, or other techniques. The regularized kernel function for inverting the Laplace transform is calculated, and used to illustrate the problem of noise. Correct choice of the regularization parameter gives the minimum overall error. It is found that excessive error occurs unless the linewidth distribution is modeled over a finite range. Analytical models for the linewidth with finite range, based on the beta distribution of probability theory, are given. Distortion of correlation data may occur in three ways, through a focused or otherwise nonuniform laser beam in the optical system, by insufficient bit resolution in the quantized detection of scattered laser light, or by calculating a first order field autocorrelation from a second order intensity autocorrelation. Unlike noise, distortion cannot be removed by any known methods, since the exact nature of the distortion is unknown. Several examples illustrate how distortion can lead to artifacts in the linewidth distribution which could easily be misinterpreted as segments of a size distribution, not present in the physical sample.     

Statistical damage identification of structures with frequency changes

Model updating methods based on structural vibration data have being rapidly developed and applied to detect structural damage in civil engineering. But uncertainties existing in the structural model and measured vibration data might lead to unreliable damage detection. In this paper a statistical damage identification algorithm based on frequency changes is developed to account for the effects of random noise in both the vibration data and finite element model. The structural stiffness parameters in the intact state and damaged state are, respectively, derived with a two-stage model updating process. The statistics of the parameters are estimated by the perturbation method and verified by Monte Carlo technique. The probability of damage existence is then estimated based on the probability density functions of the parameters in the two states. A higher probability statistically implies a more likelihood of damage occurrence. The presented technique is applied to detect damages in a numerical cantilever beam and a laboratory tested steel cantilever plate. The effects of using different number of modal frequencies, noise level and damage level on damage identification results are also discussed.     

Wavelet-based density estimation for noise reduction in plasma simulations using particles

For given computational resources, the accuracy of plasma simulations using particles is mainly limited by the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on wavelet analysis is proposed and tested to reduce this noise. The method, known as wavelet-based density estimation (WBDE), was previously introduced in the statistical literature to estimate probability densities given a finite number of independent measurements. Its novel application to plasma simulations can be viewed as a natural extension of the finite size particles (FSP) approach, with the advantage of estimating more accurately distribution functions that have localized sharp features. The proposed method preserves the moments of the particle distribution function to a good level of accuracy, has no constraints on the dimensionality of the system, does not require an a priori selection of a global smoothing scale, and its able to adapt locally to the smoothness of the density based on the given discrete particle data. Moreover, the computational cost of the denoising stage is of the same order as one time step of a FSP simulation. The method is compared with a recently proposed proper orthogonal decomposition based method, and it is tested with three particle data sets involving different levels of collisionality and interaction with external and self-consistent fields.     

基于最大Lyapunov指数不变性的混沌时间序列噪声水平估计

提出了一种基于最大Lyapunov指数不变性的计算混沌时间序列噪声水平的新方法. 首先分析了噪声对相空间中两点距离的影响, 然后基于最大Lyapunov指数在不同维数的嵌入相空间不变的性质, 建立了估计噪声水平的方法. 仿真计算结果表明, 当噪声水平小于10% 时, 估计值与真实值符合良好. 该方法对噪声分布类型不敏感, 是一种有效的混沌时间序列噪声估计方法.     

Improved gamut-constrained illuminant estimation by combining modified category correlation

In this paper we propose a new gamut-constrained illuminant estimation framework using an improved category correlation method. Firstly, we obtain a set of feasible illuminations by the original gamut mapping method. Then, the probability of each feasible illumination as the ground truth illuminant is calculated according to its ability to map the corrected image onto specific colors using the improved category correlation method. Differently from the original category correlation method, to decrease the effect of image noise and the computation complexity, instead of using an entire pixel set for estimating the probability of portable illuminant, superpixel segments of an input image are used in our improved method. And the best illuminant estimate is given on the basis of the measure of the degree to which each feasible illumination is consistent with the image data. Experiment results prove that our improved method shows better current state-of-the-art performance Gamut mapping methods.     

Statistical Approach of Gene Set Analysis with Quantitative Trait Loci for Crop Gene Expression Studies

Genome-wide expression study is a powerful genomic technology to quantify expression dynamics of genes in a genome. In gene expression study, gene set analysis has become the first choice to gain insights into the underlying biology of diseases or stresses in plants. It also reduces the complexity of statistical analysis and enhances the explanatory power of the obtained results from the primary downstream differential expression analysis. The gene set analysis approaches are well developed in microarrays and RNA-seq gene expression data analysis. These approaches mainly focus on analyzing the gene sets with gene ontology or pathway annotation data. However, in plant biology, such methods may not establish any formal relationship between the genotypes and the phenotypes, as most of the traits are quantitative and controlled by polygenes. The existing Quantitative Trait Loci (QTL)-based gene set analysis approaches only focus on the over-representation analysis of the selected genes while ignoring their associated gene scores. Therefore, we developed an innovative statistical approach, GSQSeq, to analyze the gene sets with trait enriched QTL data. This approach considers the associated differential expression scores of genes while analyzing the gene sets. The performance of the developed method was tested on five different crop gene expression datasets obtained from real crop gene expression studies. Our analytical results indicated that the trait-specific analysis of gene sets was more robust and successful through the proposed approach than existing techniques. Further, the developed method provides a valuable platform for integrating the gene expression data with QTL data.     

Analytical results for a non-Markovian process of gene expression with positive and negative feedbacks

Gene expression is a very complex process and involves many small biochemical reaction steps, resulting in a non-Markovian discrete stochastic process due to molecular memory between individual reactions. At present, this process is successfully investigated by generalized chemical master equation models. However, these models do not consider the role of feedback networks in gene expression. How the interaction between feedbacks and molecular memory affects gene expression still remains not well understood. Here, we establish generalized chemical master equation models of gene expression with positive and negative feedbacks. Assuming that the process of producing proteins follows an Erlang probability distribution, we obtain the analytical expression for this model in a steady state, as well as the measure of the noise of protein numbers. We further find that molecular memory competes with the positive feedback in suppressing the noise of the protein number. For our model with a negative feedback, molecular memory can strengthen the intensity of suppressing this noise. These interesting results imply that molecular memory are as important as the feedbacks to affect gene expression.     

Maximum Entropy Analysis of Analytically Simulated Complex Fluorescence Decays

We tested a Maximum Entropy Method developed for oversampled data (SVD-MEM) on complex analytically simulated exponential decay data consisting of both noisy and noiseless multi-exponential fluorescence decay curves. We observed recovery of simulated parameters for three sets of data: a decay containing three exponential functions in both intensity and anisotropy curves, a set of intensity decays composed of 4, 5 and 6 exponential functions, and a decay characterized by a Gaussian lifetime distribution. The SVD-MEM fitting of the noiseless data returned the simulated parameters with the high accuracy. Noise added to the data affected recovery of the parameters in dependence on a data complexity. At selected realistic noise levels we obtained a good recovery of simulated parameters for all tested data sets. Decay parameters recovered from decays containing discrete lifetime components were almost independent of the value of the entropy scaling parameter γ used in the maximization procedure when it changed across the main peak of its posterior probability. A correct recovery of the Gaussian shaped lifetime distribution required selection of the γ-factor which was by several orders of magnitude larger than its most probable value to avoid a band splitting.     

Characterization of a cylindrical rod by inversion of acoustic scattering data

In this paper, a new approach is proposed for nondestructive characterization of immersed and embedded isotropic rod-shaped samples by inversion of acoustic scattering data. The normal mode expansion technique is used for modelling the scattered field and the compression incident and compression scattered waves are considered. Genetic algorithm is the inversion technique used for estimating the elastic wave velocities and density of the rods from their measured backscattered pressure spectrum. The inversion technique is capable of computing the parameter values that best fit a particular set of data. A perturbation study is conducted on the sensitivity of the resonance frequencies to changes in elastic properties and density of the rods. The numerical results indicate that proper selection of resonance frequencies leads to accurate measurement of elastic constants and density. The proposed approach showed very good convergence and the results obtained were found to agree very well with available data.     

基于光谱特征点秩和检验的稻曲病发病程度检测

利用无人机航拍获得稻田高光谱图像并计算特征点的归一化植被指数(NDVI),通过NDVI值秩和检验的方法对稻曲病发病程度进行检测。在中国水稻研究基地选取28块面积相同的相邻水稻试验区,采用4种不同农田管理方式,分别为自然生长和喷洒3种不同农药,每种管理方式有7个不同播种日期,相邻地块前后播种日期相差1周,依次递减,每个区域种植水稻500株左右。在稻曲病发病盛期,先实地调查水稻的发病状况,根据单位面积内稻穗的发病数目得到发病指数。然后用无人机载高光谱相机拍摄试验田得到所有试验区的高光谱图。对各个高光谱图像进行高质量拼接,得到完整的覆盖整个试验区域的高光谱图像。对光谱数据预处理后从中提取最能反映稻曲病发病程度的归一化植被指数,用箱型图清洗数据以去除异常值,对不同水稻试验区的NDVI值进行秩和检验,第一步对总样本进行秩和检验,验证各组样本中是否有显著差异,确定差异性来源于何组样本;第二步对4组样本排列组合共得到11组不同组合方式的待检验样本,对这11组样本数据分别进行秩和检验。每组得到的显著性水平均远<0.01,说明不同组间的样本数据存在极显著差异,反映出此方法用于稻曲病发病程度检测的合理性。为了显示不同发病区域,用不同的颜色对不同的稻曲病发病程度的种植区域进行标注。最后以大田水稻发病指数作为对照组,与秩和检测的结果进行比对,结果表明秩和检验对稻曲病的发病程度检测有可行性。     

A prediction method of the response probability distribution for arbitrary sound insulation systems

This paper describes a practical evaluation method of the response probability distribution for an arbitrary sound insulation system with a random input noise of arbitrary distribution. Here, the response probability distribution is derived in a fairly simple form using the statistical Hermite expansion-type series expression. The effect of the sound insulation system and the input fluctuation on the resultant probability distribution form is hierarchically reflected in various types of statistics such as the mean, variance and each expansion coefficient. Finally, the proposed evaluation method is experimentally confirmed by applying it to the observed data for typical examples of single- and double-wall insulation system, with white noise and music excitations.     

基于拟线性局部加权法的煤样光谱散射校正

利用近红外光谱分析技术的诸多优势,可实现煤质多项指标的快速分析。煤样光谱数据的采集易受到噪声散射的干扰,在建模分析前常用多元散射校正方法对其予以恢复去噪。而传统的多元散射校正方法存在以线性表达式描述非线性关系的局限性,以及盲目追随“理想”光谱而导致的失真问题,为此提出基于拟线性局部加权法的煤样光谱散射校正。该法先选取二次曲线、三次曲线和增长曲线等三种拟线性函数,代替原线性函数;再分别引入均值核函数、高斯核函数、Epanechnikov核函数、二次权重核函数及三次权重核函数等五种核函数,在原评估函数中构造局部加权函数,利用局部加权函数精确表述各波长点处的依赖关系;最后,分析不同模式下校正光谱的准确性,确定拟线性函数与核函数的最佳组合。为验证方法的适用性,对0.2,1和3 mm等三种粒度等级下的煤样光谱数据进行散射校正。结果表明：改进多元散射校正方法在消除光谱中散射干扰的同时,放大了特征谱峰信息,校正光谱与煤样各项指标的相关性得到了显著增强,有效地提高了煤质近红外光谱分析模型的预测精度和稳定性。