Construction and research on the navigation condition of oil supply vessels

. Constructing navigation condition of oil supply vessels is of vital importance to both the research on the main engine and the safety of navigation. This paper carries out in-depth research and analysis based on the half-year shipping data derived from Hai Gong You 31, the oil supply vessel of Shanghai Chimbusco Marine Bunker Co., Ltd. After classifying 3946 pieces of shipping data, and there are 119 valid sequences. As for 13 characteristic parameters ,which include time, distance, average acceleration ,etc., they are eigenvalues of kinematics sequences ,and there are principal component analysis and contribution rate analysis relevant to them. Instead of original eigenvalues, three principal components whose contribution ratios are the highest and the accumulative one is around 85% are selected to be analyzed then. By means of between-groups linkage, this paper calculates the distance among clusters ,and the nearest two clusters are regarded as a new cluster. Afterward, calculations and combinations are made over and over till there is only one cluster. Eventually, the navigation condition of oil supply vessels is successfully formed, that is the one with a total length of 9240s.


INTRODUCTION
China joined the World Trade Organization in 2001.
Since then, this country has gradually become a global manufacturing base. Under the background of economic globalization, China's economy grows rapidly, posing considerable challenges to its shipping industry [1][2] . In a sense, a country's development is dependent on this industry. With domestic and international trade expanding, China's shipping industry achieves significant growth.
Meanwhile, the demand for marine fuel oil rises sharply.
To be more specific, statistics reveal that the internal trade

The division of kinematics sequences
In the course of sailing, ships can be in different conditions, including start, acceleration, deceleration ,and idle speed [3] . On the basis of the demand for data processing, this paper divides data into kinematics sequences. More specifically, a kinematics sequence refers to a continuous process that the ship experiences setting sail, acceleration, maintaining a steady speed, decelerating ,and stopping successively. Such classification is beneficial to the analysis of ship's condition. As is reflected in Table 1, after classifying 3946 pieces of data herein, 119 valid segments are gained in total.

Factor Analysis
After dividing data into kinematics sequences, speed and time fail to give a comprehensive description of such sequences. Consequently, it is essential to take advantage of other characteristic parameters [4] . For the purpose of describing the feature of kinematics sequences adequately, this paper concerns 13 characteristic parameters as eigenvalues of them, including running time, the time in steady running speed, acceleration time, etc. Information on each characteristic parameter is indicated in Table 2. Using Java language to design a program in My Eclipse, it is possible to make computations of 119 Taking a segment as an example, relevant results can be seen in Table 3.

Principal component analysis
The analysis reveals that these 13 characteristic parameters are not mutually independent. Instead, there is overlap among the information demonstrated by them. If all these parameters are used to form sailing conditions, the amount of data will be so large that it will be complicated to handle [5] . In order to make the calculation easier, this paper uses the method of principal component analysis to recombine previous indicators with certain correlations into new linear independent indicators through linear transformation, which could condense them into a few principal components with the least loss in information.

Data Processing
Let n be the number of kinematics sequences and p be the number of characteristic parameters, the corresponding matrix is: Now matrix A is called the original matrix, and then this original matrix is standardized to eliminate the differences between indicators [6] . Let: of which: The standardized matrix is expressed as:

Calculation of correlation coefficient matrix
Suppose the correlation coefficient matrix is R , , then: where ij r is the correlation coefficient between

Calculation of the eigenvalue and eigenvector of
In total, p eigenvalues of λ1, λ2…λp which satisfyλ1＞λ 2＞…＞λp＞0 can be calculated, and the corresponding eigenvectors u1, u2 … up can be obtained. All eigenvectors can be constructed into an eigenmatrix U. are linearly independent of each other, their importance is unequal [7] . The eigenvalues obtained in the previous step, λ1, λ2…λp, represent the importance of the first to p th principal components ,respectively. This paper utilizes the contribution rate of each principal component to show its importance, and the former can be calculated as follows: It is universally acknowledged that when the Supposing the cumulative contribution rate is , it can be believed that the first k principal components can replace the original index when ≥ 85% [8] . = ∑ =1 (12)

Calculation of the value of principal components
According to 3.3.1.4, the value of the first k principal components requires computation. The method is as follows: ( )  Table 4 for related figures [9] . As is shown in Table 4, the cumulative contribution rate of the first three principal components is 83.592%, which is close to 85% and can reflect the original working condition adequately. Therefore, this paper chooses these three components to continue handling the data derived from Hai Gong You 31. Table 5 suggests the principlecomponent score matrix of the working condition segment.

Hierarchical Cluster Analysis
When performing hierarchical cluster analysis, this paper concerns each fragment in the whole as a cluster, the nearest two clusters as a new one. Afterward, distance calculation and clusters combination are made over and over till there is only one cluster. It is by means of betweengroups linkage that the distance among clusters is calculated herein [10] .
The program written in My Eclipse is able to compute the overall eigenvalues of not only each category of kinematics sequences but also the whole. The results are shown in Table 6.

The length of the working condition to be
constructed.
Based on the method for determining the length of vehicle working conditions, this paper takes data as well as reality into consideration and then sets 9000 seconds as the length of ship navigation conditions. In other words, the working condition fitted with a certain number of kinematics sequences should fulfill this condition.

Calculation of correlation coefficients
Correlation Where Var(x) and Var(y) are variances of vector X and vector Y respectively, ρ is the correlation coefficient of vector X and vector Y.

Judgment about whether the absolute value of correlation coefficient meets the standard
When constructing ship navigation conditions, it is generally believed that the segments with a relatively high degree of correlation are those with the absolute value of correlation coefficient above 0.8. As a consequence, this paper removes the segments whose absolute value of correlation coefficient is less than 0.8. Then the remaining segments are randomly combined according to the required quantity calculated in the second step, and the characteristic parameter values of these randomly combined long segments are recalculated. In addition, we compute the correlation coefficient between these characteristic parameter values and the overall comprehensive characteristic value of such segments to find the combination with the largest correlation coefficient. Afterward, this combination is used to construct the final working condition [11] .

Construction of ship navigation condition
From the first kind of characteristic value in Table 6, this paper extracts the average velocity, average acceleration, average deceleration, acceleration ratio, deceleration ratio and constant speed ratio, followed by calculating the correlation coefficient between the eigenvalue of every segment and the overall comprehensive eigenvalue with CORREL function in Excel. Eventually, it can be found that the absolute value of each coefficient is greater than 0.9.
In the first kinematics sequence herein, there are three segments with the highest correlation coefficient, whose length reaches 3480s, 2880s and 2880s ,respectively. They are selected to form navigation conditions with a total length of 9240s. The correlation coefficients between eigenvalues of these three segments and the overall eigenvalue are all above 0.99991, revealing that they have a close correlation and can represent the actual sailing condition. Fig.3 exactly shows the constructed condition.