CN108734596A - A kind of time series interpolating method of aquaculture water quality monitoring missing data - Google Patents

A kind of time series interpolating method of aquaculture water quality monitoring missing data Download PDF

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CN108734596A
CN108734596A CN201810311429.0A CN201810311429A CN108734596A CN 108734596 A CN108734596 A CN 108734596A CN 201810311429 A CN201810311429 A CN 201810311429A CN 108734596 A CN108734596 A CN 108734596A
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time series
principal component
water quality
sequence
monitoring data
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华旭峰
王文清
孙学亮
田云臣
马国强
单慧勇
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Tianjin Agricultural University
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Abstract

The present invention relates to the time series interpolating methods that a kind of aquaculture water quality monitors missing data, including step to have：The first step：Choose the identical water quality monitoring time series containing missing data of two groups of length；Second step：Establish delay matrix and calculating matrix inner product；Third walks：Time series Toeplitz of the construction with missing data postpones autocorrelation matrix；4th step：Singular value decomposition is made to autocorrelation matrix, obtains feature vector；5th step：Calculate principal component vector；6th step：Time series is reconstructed using each principal component, obtains interpolation sequence.The present invention decomposes the time series containing missing values, reconstructs to obtain the time series after interpolation, the interpolating method can hold the transition information of time series comprehensively, achieve good comprehensive interpolation effect, the continuity that ensure that data time series, to realize that the prediction of water monitoring data time series provides effective means.

Description

A kind of time series interpolating method of aquaculture water quality monitoring missing data
Technical field
The invention belongs to aquaculture water quality monitoring technical fields, especially set and a kind of aquaculture water quality monitors missing number According to time series interpolating method.
Background technology
Aquatic environment monitoring technology is used widely in intensive aquaculture industry, and it is strong to be greatly promoted aquatic products The development of health aquaculture.Aquatic environment information monitoring is the key link for realizing high intensity aquaculture, by monitoring water body temperature Degree, pH, dissolved oxygen etc. have aquatic products growing environment the water quality factor of significant impact, and best growth ring is provided for aquatic products Border.Using automatic on-line monitoring system, water quality monitoring sensor automatic collection aquatic environment data are carried out, realizes and covers extensively Lid, automatic measurement, real-time Transmission represent the developing direction of aquaculture water quality environmental monitoring；But there is measurements at this stage The disadvantage that precision is low, data easily lack becomes the bottleneck of such method development, hinders the extensive use in aquaculture.
It is insufficient due to sampling in aquaculture water quality environmental monitoring, system mistake is monitored, or other Reason frequently can lead to error or the missing of monitoring data.In this case, it is handled in progress aquatic environment big data With analysis when, it is common practice to by with missing or mistake observation data collective delete, although do so ensure that it is used The reliability of data, but cause the loss of a large amount of useful information.It realizes to the pre- of water monitoring data time series Survey, it is necessary to the continuity for ensureing time series, for this problem, need combine water monitoring data the characteristics of and difference Missing degree, be specially designed for the interpolating method of aquaculture water quality environmental monitoring data.
Invention content
It is an object of the invention to overcome the deficiencies in the prior art, and provide a kind of aquaculture water quality monitoring missing data Time series interpolating method,
The present invention solves its technical problem and following technical scheme is taken to realize：
A kind of time series interpolating method of aquaculture water quality monitoring missing data, including steps are as follows：
The first step：Choose the identical water quality monitoring time series containing missing data of two groups of length, time series vector Respectively A=(a1,a2,…aN), B=(b1,b2,…bN), sequence length N is established corresponding with nested dimension M, M < N/2 Delay matrix is respectively：
Second step：The missing data component set of above-mentioned two groups of water monitoring data time serieses is：And haveCalculating matrix inner product
Third walks：Time series Toeplitz delay autocorrelation matrix S of the construction with missing data
4th step：Singular value decomposition, S=E λ E are made to autocorrelation matrix ST, obtain eigenvalue λkAnd corresponding feature vector Ek, Wherein 1≤k≤M, characteristic value are arranged as λ in descending order1≥λ2≥…λM≥0；
5th step：Calculate principal component vector, wherein i-th of value of k-th of principal component of monitoring data time series A be：
I-th of value of k-th of principal component of monitoring data time series B be：
6th step：Time series is reconstructed using each principal component,
I-th of element representation of sequence of k-th of principal component reconstruct of monitoring data time series A be：Monitoring data I-th of element representation of sequence of k-th of principal component reconstruct of time series B be：
As M≤i≤N-M+1,
As 1≤i≤M-1,
As N-M+2≤i≤N, I-th of the element x of sequence reconstructed using the preceding K principal component of monitoring data time series AiIt is expressed as：
I-th of the element yi of sequence reconstructed using the preceding K principal component of monitoring data time series B is expressed as：
The advantages and positive effects of the present invention are：
1, the present invention decomposes the time series containing missing values, reconstructs to obtain the time series after interpolation, this is inserted Compensating method can hold the transition information of time series comprehensively, achieve good comprehensive interpolation effect.
2, the present invention overcomes in aquaculture water quality environmental monitoring, since sampling is insufficient, system mistake is monitored, or Person is the loss of a large amount of useful informations caused by some other reasons, ensure that the continuity of data time series, is real The prediction of existing water monitoring data time series provides effective means.
Description of the drawings
Fig. 1 is the logical procedure diagram of the method for the present invention.
Specific implementation mode
The embodiment of the present invention is further described below in conjunction with attached drawing, it is emphasized that, following implementation is to say Bright property, without being restrictive, it cannot be used as limitation of the invention in this embodiment.
A kind of time series interpolating method of aquaculture water quality monitoring missing data, as shown in Figure 1, such as including step Under：
The first step：Choose the identical water quality monitoring time series containing missing data of two groups of length, time series vector Respectively A=(a1,a2,…aN), B=(b1,b2,…bN), sequence length N is established corresponding with nested dimension M, M < N/2 Delay matrix is respectively：
Second step：The missing data component set of above-mentioned two groups of water monitoring data time serieses is：And haveCalculating matrix inner product
Third walks：Time series Toeplitz delay autocorrelation matrix S of the construction with missing data
4th step：Singular value decomposition, S=E λ E are made to autocorrelation matrix ST, obtain eigenvalue λkAnd corresponding feature vector Ek, Wherein 1≤k≤M, characteristic value are arranged as λ in descending order1≥λ2≥…λM≥0；
5th step：Calculate principal component vector, wherein i-th of value of k-th of principal component of monitoring data time series A be：
I-th of value of k-th of principal component of monitoring data time series B be：
6th step：Time series is reconstructed using each principal component,
I-th of element representation of sequence of k-th of principal component reconstruct of monitoring data time series A be：Monitoring data I-th of element representation of sequence of k-th of principal component reconstruct of time series B be：
As M≤i≤N-M+1,
As 1≤i≤M-1,
As N-M+2≤i≤N, I-th of the element x of sequence reconstructed using the preceding K principal component of monitoring data time series AiIt is expressed as：
I-th of the element y of sequence reconstructed using the preceding K principal component of monitoring data time series BiIt is expressed as：

Claims (1)

1. a kind of time series interpolating method of aquaculture water quality monitoring missing data, it is characterised in that including steps are as follows：
The first step：Choose the identical water quality monitoring time series containing missing data of two groups of length, time series vector difference For A=(a1,a2,…aN), B=(b1,b2,…bN), sequence length N establishes corresponding time lag with nested dimension M, M < N/2 Matrix is respectively：
Second step：The missing data component set of above-mentioned two groups of water monitoring data time serieses is：And haveCalculating matrix inner product
Third walks：Time series Toeplitz delay autocorrelation matrix S of the construction with missing data
4th step：Singular value decomposition, S=E λ E are made to autocorrelation matrix ST, obtain eigenvalue λkAnd corresponding feature vector Ek, wherein 1≤k≤M, characteristic value are arranged as λ in descending order1≥λ2≥…λM≥0；
5th step：Calculate principal component vector, wherein i-th of value of k-th of principal component of monitoring data time series A be：
I-th of value of k-th of principal component of monitoring data time series B be：
6th step：Time series is reconstructed using each principal component,
I-th of element representation of sequence of k-th of principal component reconstruct of monitoring data time series A be：The monitoring data time I-th of element representation of sequence of k-th of principal component reconstruct of sequence B be：
As M≤i≤N-M+1,
As 1≤i≤M-1,
As N-M+2≤i≤N,It utilizes I-th of element x of sequence of the preceding K principal component reconstruct of monitoring data time series AiIt is expressed as：
I-th of the element y of sequence reconstructed using the preceding K principal component of monitoring data time series BiIt is expressed as：
CN201810311429.0A 2018-04-09 2018-04-09 A kind of time series interpolating method of aquaculture water quality monitoring missing data Pending CN108734596A (en)

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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2002039254A1 (en) * 2000-11-09 2002-05-16 Spss Inc. System and method for building a time series model
CN102446302A (en) * 2011-12-31 2012-05-09 浙江大学 Data preprocessing method of water quality prediction system
CN103577694A (en) * 2013-11-07 2014-02-12 广东海洋大学 Aquaculture water quality short-time combination forecast method on basis of multi-scale analysis
CN107577649A (en) * 2017-09-26 2018-01-12 广州供电局有限公司 The interpolation processing method and device of missing data

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2002039254A1 (en) * 2000-11-09 2002-05-16 Spss Inc. System and method for building a time series model
CN102446302A (en) * 2011-12-31 2012-05-09 浙江大学 Data preprocessing method of water quality prediction system
CN103577694A (en) * 2013-11-07 2014-02-12 广东海洋大学 Aquaculture water quality short-time combination forecast method on basis of multi-scale analysis
CN107577649A (en) * 2017-09-26 2018-01-12 广州供电局有限公司 The interpolation processing method and device of missing data

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
孙东: "赤潮多源监测数据处理与综合预测预报方法研究", 《万方数据》 *

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