由三类船舶安全营运问题驱动的统计问题研究

For the shipping safety, the optimal selection of heading angle and speed under heavy waves, the designing of real-time ship vibration warning system, and the fatigue damage detection of the key components of the hull are three types of crucial ship-operation problems. Based on the real vibration and stress data of the ship hull, this project will study three cutting-edged statistical problems, which are driven by the three above-mentioned practical problems, respectively. They are as follows. (1) The spectral estimation for nonstationary multivariate time series. Based on Bayesian methods, the adaptive estimation of the spectral density, which can be efficiently implemented, will be proposed for the nonstationary multivariate time series. (2) The statistical test on comparing marginal spectral densities of nonstationary multivariate time series. For testing that marginal spectral densities are equal or proportional, a test statistic, which can achieve good performance in the asymptotic properties and can describe the difference of marginal spectral densities of nonstationary multivariate time series, will be constructed. (3) The nonparametric inference of the inhomogeneous moving average driven by the Levy process. A nonparametric estimation of the kernel function of the moving average will be given. The nonparametric test of the moving average will be considered by means of two different aspects: power variation and nonparametric estimator of the kernel function. Relying on the real data, the project will also study how to apply the concluded statistical results to solve the problems in aid of safe shipping operations. The concerning time series is multivariate and nonstationary, and the concerning stochastic process is inhomogeneous, non-Markov and even non-martingale. The statistical issues are driven by the practical problems, they are novel and challenging.

大风浪中船舶最佳航向角和航速的选择、船舶振动实时预警系统的设计及船体关键部位构件疲劳损坏情况的检测是三类重要的船舶安全营运问题。本项目基于船体振动和应力实测数据，将研究由上述三类实际问题分别驱动的三类新的统计问题：1）非平稳多变量时间序列的谱密度估计。基于贝叶斯统计提出可高效估计非平稳多变量时间序列谱密度的适定方法。2）非平稳多变量时间序列边际谱密度相等或成比例的检验。就该问题，构造渐近性质优良且可用于刻画多维非平稳时间序列边际谱密度差别的统计量。3）由Levy过程驱动的非时齐滑动平均核函数的非参数推断。给出滑动平均核函数的非参数估计量，通过幂变差和滑动平均核函数估计量两种渠道研究滑动平均的非参数检验。立足实际数据，本项目还研究将统计结论应用于解决三类船舶安全营运问题。时间序列研究对象具有多变量非平稳性，随机过程研究对象具有非时齐非马氏非鞅性。统计问题由实际问题驱动，新颖且具挑战性。

大风浪下船舶安全驾驶是船舶营运中的一类重要课题。本项目基于船体振动和应力实测数据，研究了由船舶安全营运问题驱动的若干新的谱域上的统计问题，主要研究内容及成果分三个方面。第一，平稳谱的统计推断。① 借助谱矩阵的Cholesky分解，提出了一种可自动选择光滑参数并同时估计多组耦合谱的快速非参数谱估计法；② 借助于时间—尺度变换，提出了一种估计不规则间距数据谱密度的迂回方法，所提供的方法不仅使得光滑样条中基函数的选择与抽样设计无关，而且无需根据不同的不规则抽样改变调节参数。③ 将空间对数谱密度表示为一类新型光滑样条基，基于该样条基提出了一种自动实现谱光滑的空间网格数据谱估计法。第二，时变谱的统计分析。① 基于两时间序列在不同频率点的周期图比值，将谱比较问题转化为拟合优度检验问题，构造了适用性广且不依赖于任何参数或非参数估计量的Pearson型及Anerson-Darling型谱比较检验法；② 基于谱比较的思想，提出了检验时间序列二阶非平稳性的一类不依赖于参数或非参数估计量的新检验法。第三，模型性质谱域诊断。① 基于分位数和耦合的概念，提出了平稳随机过程分位数—耦合交叉协方差函数的概念，并探讨了该函数的估计方法及在研究平稳随机过程相依性特征中的应用；② 借助耦合谱，从二维边际分布角度提出了检验成对时间可逆性的新的频率域方法；③ 基于在一组频率点及其旋转点处的空间周期图比值，提供了无调节参数、计算效率高的用于检验不规则间距空间数据各向同质性的检验方法；④ 通过时间序列的正弦与余弦变换将时间序列变换为频率域上的独立随机变量序列，利用正则化累积和提出了不依赖于滞后阶数且计算简单的多维与高维白噪声频率域检验方法。本项目成果对船舶智能安全营运具有重要潜在应用价值。例如，通过经典谱及耦合谱的非参数统计推断，可发现船体不同部位振动或受力的自相依性差异、探讨自相依性与海况、航向、船速等的联系，进而探寻数据分析结论在大风浪下船舶安全驾驶的相应对策等。