Study On Nonnegative Matrix Factorization On Tidal Analysis And Prediction

Tidal harmonic analysis method is one of the most main methods of analysis and prediction of tides and according to the principle of least square method and the harmonic constants of each constituent finally stack together become the observed tidal expression. With the advent of the computer and the improvement of the performance of the calculation, the study of the theory of the harmonic analysis method has been very mature, but in view of the practical problems, still exists many problems: Shallow water port in the presence of shallow water wave, tidal analysis and forecast precision is still very low; When in extreme weather conditions, storm surge and astronomical tide nonlinear coupling leads to astronomical tide tidal harmonic constant calculation error, how to effectively eliminate the storm surge components in urgent need of solution; For tidal harmonic analysis, to calculate the accurate harmonic constants, at least need to collect tidal data of 18.6 years, for many remote owes the developed coastal areas, has not been such a long time of observation data have been collected. In order to solve the above problems existing in the harmonic analysis, this paper introduced the ideas of nonnegative matrix decomposition to the analysis and prediction of tides. On the basis of computational thinking, choose the method based on intelligent computing, the different frequency(energy), the reaction between the sea surface fluctuations will produce the corresponding as theoretical basis, based on a relatively limited observation data, to the Marine environment factors through analyzing the observation data, Empty change at any time according to the elements present different characteristics, the variation regularity of elements in the research of the Marine environment, and then through the use of these elements to model to simulate and predict the ocean environment condition, for the law of motion of the ocean of other research provides a new way for reference. The main research contents and results are as follows:1、Based on the tidal harmonic analysis method, the choice of KM stand hourly measured tidal water level data, used for the middle water level observation data analysis method of least squares, according to the basic flow of middle water level data analysis, singular value out first, and then harmonic analysis made on the tidal data, calculate the hourly tidal level returns and more than high and low tide level calculation, combining with the measured data of tide station has carried on the preliminary analysis and calculation results.2、The introduction of nonnegative matrix decomposition method, nonnegative matrix decomposition does not allow decomposition of matrix elements in the negative, but does not require the decomposition of matrices must be orthonormal, this kind of nonnegative limit captures the essence of intelligent data description, not negative makes explanation for some of the data more reasonable, Such as tidal astronomical tidal constituent can’t be negative, cannot be explained. And decomposition of sparse performance to a certain extent, can restrain the negative influence of the change of the outside world to feature extraction. At the same time for traditional nonnegative matrix decomposition based on multiplicative iterative method(NMF) appeared in the process of solving fanaticism, separation of computation, such as slow convergence speed problem, this paper proposes a nonnegative matrix decomposition based on projection gradient method of fanaticism, separation algorithm(PGNMFB). The algorithm by adding the determinant, sparse constraints and correlation constraints, the optimization problem is transformed into alternating least squares problem, USES the method of projection gradient based on constrained non-negative matrix decomposition fanaticism separation problems. The simulation experimental results show that the algorithm can well balanced reconstruction error, on the basis of maintaining source separation of signal sparse only implements the mixed signal decomposition, Compared with the classical NMF algorithm and NMFDSC algorithm, PGNMFB algorithm’s convergence speed is faster, decomposition time shorter. Separation of signal reconstruction of signal-to-noise ratio(SNR) is higher than the classic NMF algorithm and NMFDSC algorithm.3、In this paper, proposed a deviation from conventional tidal analysis approaches and investigate into the problem from the perspective of “signal unmixing”, where interpreted the observed data as a linear combination of constituents and apply robust unsupervised unmixing algorithm, referred to as the minimum-volume-constrained nonnegative matrix factorization(MVC-NMF), to decompose the observation into a set of source signals(i.e., the harmonics). The unmixing–based tidal analysis is fundamentally different from harmonic-based analyses by not limiting itself to just astronomical tide, and being unsupervised thus not requiring long-term training. Preliminary experiments are conducted to study the feasibility of the proposed approach for tidal analysis.