潮流信号处理与预报在很多方面具有非常重要的意义和价值。本文引入信号稀疏表示理论,构建一种稀疏AR模型,寻找各潮流数据间的历史关联性,并进行预报分析。首先由实测潮流信号进行常规AR建模,获得一组过完备稀疏基;其次随机从该过完备稀疏基抽取部分建立欠定方程组,利用稀疏优化算法获得最稀疏的AR系数;多次重复上一步,获得稀疏AR系数的平均以增强稀疏AR模型的稳定性;最后利用这些稀疏AR系数来重构或预测潮流信号。文章针对实测潮流信号,特别是存在多峰值有回流现象的潮流信号,进行了稀疏AR建模与预测的多次实验。实验结果与传统的潮流信号调和预报方法相对比,发现基于稀疏AR模型的潮流预报对于潮流存在多变的现象时,具有明显优越性,从回报结果来看,稀疏AR模型的潮流预报均方差明显小于传统潮流调和分析预报方法。
Abstract
The processing and prediction of tidal current signal are significant and valuable in various aspects. This study introduced a signal sparse representation theory, constructed a sparse AR model in order to find out the connection among the tidal currents, and to carry out the forecast analysis. Firstly, we established the conventional AR model by measuring current signal, so we could get a set of complete sparse matrix. Secondly, we randomly extracted parts of this to create underdetermined system of equations. We acquired the sparse AR coefficients by using sparse optimization algorithm. After repeating above steps for many times, the stability increased and reached to average sparse AR coefficients. Finally, the last step was to reconstruct or predict the tidal current signal by using the last sparse AR coefficients. By using the measured observations of tidal current, especially the observations with many peaks or rotary current phenomenon. Many experiments had been done to establish the sparse AR model and prediction. Comparing this AR model with flow harmonic method, the sparse AR model is much better than the traditional tidal harmonic method especially in analysing the region with changeable tidal current. Moreover, the variance of the sparse AR model is less than that of the traditional tidal harmonic analysis.
关键词
稀疏AR模型 /
潮流预报 /
稀疏优化 /
OMP算法
Key words
AR model /
tidal current forecast /
sparse optimization /
Orthogonal Matching Pursuit algorithms
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参考文献
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基金
2012年中央分成海域使用金支出项目(环保类,国海办字[2013]551号);国家自然科学基金项目资助(61071198)
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