CN106777985A - A kind of Hydrologic Series nonuniformity diagnostic method based on classification - Google Patents

A kind of Hydrologic Series nonuniformity diagnostic method based on classification Download PDF

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CN106777985A
CN106777985A CN201611177270.5A CN201611177270A CN106777985A CN 106777985 A CN106777985 A CN 106777985A CN 201611177270 A CN201611177270 A CN 201611177270A CN 106777985 A CN106777985 A CN 106777985A
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nonuniformity
time series
sequence
variance
null hypothesis
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CN106777985B (en
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王建华
李海红
翟家齐
赵勇
章数语
何凡
王丽珍
朱永楠
王庆明
顾艳玲
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China Institute of Water Resources and Hydropower Research
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China Institute of Water Resources and Hydropower Research
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Abstract

The present invention relates to a kind of Hydrologic Series nonuniformity diagnostic method based on classification, including step:Collect statistical information;Carry out the nonuniformity diagnosis of Hydrological Time Series variance;Carry out the nonuniformity diagnosis of Hydrological Time Series average;Judge whether Hydrological Time Series are consistent.Method of the present invention is according to the nonconforming definition of the hydrology, and classified the hydrology is non-uniform according to the different of running parameter, then diagnosed using for running parameter selection different statistical methods, avoid the fuzzy disunity for causing statistical methods to diagnose the repetition of object, result due to checked object and inspection purpose, and it is uncertain, therefore the technical method is comparatively more advanced.The present invention is applied to any Hydrological Time Series.The method of the invention technical method is general, it is easy to popularization and application.

Description

A kind of Hydrologic Series nonuniformity diagnostic method based on classification
Technical field
It is that a kind of hydrology that is based on surveys number the present invention relates to a kind of Hydrologic Series nonuniformity diagnostic method based on classification According to Statistical Identifying Method, be it is a kind of based on nonuniformity classification diagnostic method.
Background technology
On the diagnosis of hydrology nonuniformity, current technology mainly has following several.One kind is to Hydrological Time Series trend With the statistical check of catastrophe point, quantitative assessment is carried out according to assay watershed hydrographic features.Such diagnostic method is a lot, generation The table method of inspection has Man-Kendall to check, Hurst coefficients, Pettitt inspections, Spearman rank correlation methods.Second It is then integrated various Statistical Identifying Methods, the multiple statistical inspection of trend and catastrophe point is carried out to single time series, to determine The real change of the hydrology variable, diagnostic system is made a variation as representative with the hydrology, and diagnosis process is divided into:Tentative diagnosis, examine in detail Disconnected, three steps of comprehensive diagnos, in detail tentative diagnosis design process collimation method, moving average method and Hurst Y-factor method Ys, diagnosis then divide It is that trend and jump are diagnosed, is related to 14 kinds of statistical methods, and comprehensive diagnos is then by the result synthesis of trend and jump diagnosis Get up to be analyzed and evaluated.Finally combine actual hydrologic survey to analyze, variant form and conclusion are confirmed, so as to obtain most Whole variation diagnostic result.The third is, based on statistical means such as Spectrum Analysis, the subjective judgement of line period to be entered to time series, Main method has wavelet analysis method, continuous Zymography, period map method etc..More than it is several existing non-uniform to Hydrologic Series All there are some deficiencies in various degree in property diagnostic method.
Individual event inspection to Hydrologic Series, the basic assumption that defect comes from different statistical methods is different, these methods master Will by judge sequence whether occurrence tendency or jump change it is whether consistent to judge sequence, its essence is to Hydrologic Series sample Whether this average there is the hypothesis testing of significant changes.Computational accuracy differs between distinct methods, and assay is inconsistent, verifies Jump it is not unique.Though non-uniform diagnostic system combines statistical methods, it is intended to by the result of various diagnostic methods Reliability to assay is lifted, but calculating process is cumbersome, and the reliability of result of calculation is not also in single inspection Increased significantly on the basis of method.
The deficiency of above method is:The definition of the uniformity according to time series:The average and variance of sequence samples are equal Do not changed with the time, conventional inspection method is only checked to the average of sample, and have ignored the change of variance.This is right Judge the whether consistent most important of time series.
The content of the invention
In order to overcome problem of the prior art, the conformance definition according to time series of the invention, to Hydrological Time Series Nonuniformity be classified, and propose a kind of based on average is non-uniform and the non-uniform two kinds of Hydrologic Series of variance Nonuniformity diagnostic method.Methods described has the ability applied in any Hydrological Time Series, and with can be diagnosed to be Which kind of nonconforming ability is key element belong to.
The object of the present invention is achieved like this:A kind of Hydrologic Series nonuniformity diagnostic method based on classification, it is special Levy and be, comprise the following steps:
The step of collecting statistical information:The time series of the hydrographic features for needing to be analyzed is collected, sample size is at least 30;
The step of carrying out Hydrological Time Series variance nonuniformity and diagnose:Assuming that predictor is constituted by with Regression:
(1)
Wherein
Make the following assumptions:
:,:
Construction augmentation Dickey-fowler(Augmented Dickey-Fuller, ADF)Test statistics:, its In,It is the standard deviation of statistic ρ;
In the case where there is unit root in sequence,Statistic does not meet t- distributions, and with the increase of sample size, τ statistics are received Hold back in the functional of standard Wiener-Hopf equation, and can be drawn with monte carlo method simulation, delayed item is added on the right of model:, to alleviateThe auto-correlation problem of item.ADF inspections are based on least square(OLS)Regression equation assume predictor by Constituted with Regression:
(2)
Wherein:T is the time,.Inspection random processWhether there is unit root, as checkWhether Significantly, less than 0, and null hypothesis be in the presence of a unit root, alternative hypothesis be in the absence of unit root, ifSignificantly, less than 0, then zero Assuming that being rejected.ADF verifies as single side test, when significance is taken asWhen, noteFor the level of signifiance isWhen tantile, ThenWhen, refuse null hypothesis, it is believed that sequence does not exist unit root, otherwise receives null hypothesis, it is believed that sequence has unit root, Variance has significant change.
The step of nonuniformity for carrying out Hydrological Time Series average is diagnosed:To sequence x1, x2 ..., xn, first determine all Allelomorph (xi, xj), (j>I), the xi in<The appearance number (being set to p) of xj;(i, j) subset of order is:(i=1, j= 2,3,4 ..., n), (i=2, j=3,4,5 ..., n) ..., (i=n-1, j=n);If the value advanced in order is all greater than preceding One value, this is a kind of ascendant trend, p be (n-1)+(n-2)+...+1, it is arithmetic series to be, then summation is n (n-1)/2.Such as Fruit order is all turned around, then p=0, as downward trend.It follows that to neutral sequence, the mathematic expectaion of p is
This inspection statistic be:
(3)
Wherein:
Work as n>When 10, U converges on standardized normal distribution;
Null hypothesis is trendless, after given level of signifiance α, critical value U α/2 is found in gaussian distribution table;
WhenWhen, receive null hypothesis, i.e. average and significant changes do not occur;WhenWhen, refuse null hypothesis, i.e., There are significant changes in value;
Judge the whether consistent step of Hydrological Time Series:When average and variance do not exist significant changes, the hydrology time Sequence is consistent;Otherwise it is non-uniform.
The beneficial effect comprise that:Method of the present invention according to the nonconforming definition of the hydrology, and according to The different of running parameter are classified the hydrology is non-uniform, are then examined using for running parameter selection different statistical methods It is disconnected, it is to avoid due to checked object and inspection purpose the fuzzy repetition, the result that cause statistical methods to diagnose object not It is unified and uncertain, therefore the technical method is comparatively more advanced.The present invention is applied to any hydrology time sequence Row.The method of the invention technical method is general, it is easy to popularization and application.
Brief description of the drawings
The invention will be further described with reference to the accompanying drawings and examples.
Fig. 1 is the flow chart of embodiments of the invention methods described.
Specific embodiment
Embodiment:
The present embodiment is a kind of Hydrologic Series nonuniformity diagnostic method based on classification.Consistency concept is to hydrology simple sequence Nonuniformity is classified, and provides reliable diagnosis according to the nonuniformity research that nonuniformity is categorized as hydrology simple sequence Method.
The general principle of the present embodiment is:According to the nonconforming definition of the hydrology:Hydrological Time Series are no longer complies with independence Same distributional assumption, average or variance or both change with the time, it is possible thereby to pass through Check-Out Time sequence average and Whether variance there are significant changes to determine whether time series occurs nonuniformity.Change in Mean show time series with There is a Long-term change trend for determination time, and variance change shows that the dispersion of time series changes.Conversed analysis, with going Stable time series necessarily contains trend components after trend, and stable time series its original after first-order difference Variance necessarily change over time, but the change of its average with otherwise do not know.But processed by both, can be according to average Or nonuniformity is divided into two classes by the change of variance, a class is the nonuniformity of average, and another kind of is the nonuniformity of variance.
According to classification, the non-uniform of average is diagnosed using Kendall ranks related check, using unit root test The non-uniform of variance is diagnosed, exclude two kinds it is non-uniform can confirm that the sequence is consistent, otherwise for non-uniform, and examine Break and the sequence and belong to any non-uniform type.
It is computer program that method described in the present embodiment can be worked out, in operating in PC or other all-purpose computers. The step of the present embodiment methods described, is as follows:
The step of collecting statistical information:The time series of the hydrographic features for needing to be analyzed is collected, sample size is at least 30;
The step of nonuniformity for carrying out Hydrological Time Series variance is diagnosed:The non-uniform of variance is carried out from unit root test Inspection, is used to diagnose whether variance occurs significant changes.Checked using the augmentation Dickey in unit root test-fowler (Augmented Dickey-Fuller, ADF)Carry out the non-uniform diagnosis of variance:
Assuming that predictor is constituted by with Regression:
(4)
Wherein
Make the following assumptions:
:,:
Construction augmentation Dickey-fowler(Augmented Dickey-Fuller, ADF)Test statistics:, its In,It is the standard deviation of statistic ρ;
In the case where there is unit root in sequence,Statistic does not meet t- distributions, and with the increase of sample size, τ statistics are received Hold back in the functional of standard Wiener-Hopf equation, and can be drawn with monte carlo method simulation, delayed item is added on the right of model:, to alleviateThe auto-correlation problem of item.ADF inspections are based on least square(OLS)Regression equation assume predictor by Constituted with Regression:
(5)
Wherein:T is the time,.Inspection random processWhether there is unit root, as checkWhether Significantly, less than 0, and null hypothesis be in the presence of a unit root, alternative hypothesis be in the absence of unit root, ifSignificantly, less than 0, then zero Assuming that being rejected.ADF verifies as single side test, when significance is taken asWhen, noteFor the level of signifiance isWhen tantile, ThenWhen, refuse null hypothesis, it is believed that sequence does not exist unit root, otherwise receives null hypothesis, it is believed that sequence has unit root, Variance has significant change.
The step of nonuniformity for carrying out Hydrological Time Series average is diagnosed:From Kendall rank related checks, with true Determine whether average occurs significant changes:
To sequence x1, x2 ..., xn, all allelomorphs (xi, xj) (j is first determined>I) xi in<The appearance number of xj (is set to p).(i, j) subset of order is:(i=1, j=2,3,4 ..., n), (i=2, j=3,4,5 ..., n) ..., (i=n-1, j=n). If the value advanced in order is all greater than previous value, this is a kind of ascendant trend, p be (n-1)+(n-2)+...+1, be for Arithmetic series, then summation is n (n-1)/2.If order is all turned around, p=0, as downward trend.It follows that to nothing The sequence of trend, the mathematic expectaion of p is
This inspection statistic be:
(6)
Wherein:
Work as n>When 10, U converges on standardized normal distribution.
Null hypothesis is trendless, after given level of signifiance α, critical value U α/2 is found in gaussian distribution table.WhenWhen, receive null hypothesis, i.e. average and significant changes do not occur;WhenWhen, refuse null hypothesis, i.e. average and occur Significant changes.
Judge the whether consistent step of Hydrological Time Series:When there are no significant changes in average and variance, the sequence It is consistent, otherwise for non-uniform.
Two inspections by showing that former sequence is concensus sequence, any one not by being non-uniform sequence, if The test fails for Kendall, and as average is non-uniform, if unit root test does not pass through, as variance is non-uniform, if both Do not pass through, show that former sequence belongs to the non-uniform of average and variance.
The present embodiment application example:
7 Inflow Sequences of the 9 extreme rainfall sequences and Miyun Reservoir of choosing Beijing carry out non-uniform diagnosis, as a result as follows Shown in table.
The extreme interception rainfall index sequence nonuniformity diagnostic result in table 1- Beijing 9
Continuous Drought day Number Continuous rainfall day Number Moistening day accumulation drop Rainfall Rainfall > 10mm Number of days Rainfall > 25mm Number of days Rainfall > 50mm Number of days >95% tantile rainfall is tired out Metering >99% tantile rainfall is tired out Metering Drop within maximum one day Water Drop within maximum five days Water
Difference
Trend
Diagnosis As a result
7 runoff index series nonuniformity diagnostic results of table 2- Miyun Reservoirs
Spring runoff Summer runoff Autumn runoff Winter runoff Non-flood period runoff Flood season runoff Annual flow
Difference
Trend
Diagnostic result
In table:● represent such non-uniform change, zero represents such non-uniform change
Diagnostic result shows have 6 indexs that non-uniform changes, 6 sides of index occur in 9 Extreme Precipitation indexs of Beijing There is non-uniform change in difference, wherein 2 averages of index occur non-uniform change;7 runoff indexs of Miyun remittance are all sent out There is non-uniform change in the non-uniform change of life, 7 averages of index, wherein 3 variances of index also there occurs non-uniform change.
The application effect for reaching is as follows:
1st, ability of the present invention suitable for various time serieses has been embodied.9 Extreme Precipitation indexs and 7 runoff indexs are entered Nonuniformity diagnosis is gone, and has determined which kind of nonuniformity it belongs to;
2nd, calculate easy, it is only necessary to carry out two steps and just can determine whether whether time series is nonuniformity, if so, can simultaneously judge that it belongs to In which kind of time series;
Finally it should be noted that being merely illustrative of the technical solution of the present invention and unrestricted above, although with reference to preferred arrangement side Case has been described in detail to the present invention, it will be understood by those within the art that, can be to technical scheme (The application of such as statistical method, the use of formula, ordinal relation of each step etc.)Modify or equivalent, without Depart from the spirit and scope of technical solution of the present invention.

Claims (1)

1. it is a kind of based on the Hydrologic Series nonuniformity diagnostic method classified, it is characterised in that to comprise the following steps:
The step of collecting statistical information:The time series of the hydrographic features for needing to be analyzed is collected, sample size is at least 30;
The step of nonuniformity for carrying out Hydrological Time Series variance is diagnosed:Assuming that predictor is constituted by with Regression:
(1)
Wherein
Make the following assumptions:
:,:
Construction augmentation Dickey-fowler test statistics:, wherein,It is the standard deviation of statistic ρ;
In the case where there is unit root in sequence,Statistic does not meet t- distributions, and with the increase of sample size, τ statistics are received Hold back in the functional of standard Wiener-Hopf equation, and can be drawn with monte carlo method simulation, delayed item is added on the right of model:, to alleviateThe auto-correlation problem of item;
ADF inspections are based on least square(OLS)Regression equation assumes that predictor is constituted by with Regression:
(2)
Wherein:T is the time,;Inspection random processWhether there is unit root, as checkWhether Significantly, less than 0, and null hypothesis be in the presence of a unit root, alternative hypothesis be in the absence of unit root, ifSignificantly, less than 0, then zero Assuming that being rejected;
ADF verifies as single side test, when significance is taken asWhen, noteFor the level of signifiance isWhen tantile, then When, refuse null hypothesis, it is believed that sequence does not exist unit root, otherwise receives null hypothesis, it is believed that sequence has unit root, and variance has aobvious Write change;
The step of nonuniformity for carrying out Hydrological Time Series average is diagnosed:To sequence x1, x2 ..., xn, all antithesis are first determined Value (xi, xj) (j>I) xi in<The appearance number (being set to p) of xj;(i, j) subset of order is:(i=1, j=2,3, 4 ..., n), (i=2, j=3,4,5 ..., n) ..., (i=n-1, j=n);If the value advanced in order is all greater than previous value, This is a kind of ascendant trend, p be (n-1)+(n-2)+...+1, it is arithmetic series to be, then summation is n (n-1)/2;
If order is all turned around, p=0, as downward trend;
It follows that to neutral sequence, the mathematic expectaion of p is
This inspection statistic be:
(3)
Wherein:
Work as n>When 10, U converges on standardized normal distribution;
Null hypothesis is trendless, after given level of signifiance α, critical value U α/2 is found in gaussian distribution table;
WhenWhen, receive null hypothesis, i.e. average and significant changes do not occur;WhenWhen, refuse null hypothesis, i.e., There are significant changes in value;
Judge the whether consistent step of Hydrological Time Series:When average and variance do not exist significant changes, the hydrology time Sequence is consistent;Otherwise it is non-uniform.
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CN109271664A (en) * 2018-08-03 2019-01-25 华南理工大学 Design storm Safety Analysis Method under the conditions of being assumed based on consistency and nonuniformity
CN110260774A (en) * 2019-07-22 2019-09-20 安徽理工大学 A kind of inspection of GNSS deformation information and method for early warning based on Pettitt algorithm
CN111353127A (en) * 2018-12-24 2020-06-30 顺丰科技有限公司 Single variable point detection method, system, equipment and storage medium
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Cited By (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107330252A (en) * 2017-06-12 2017-11-07 武汉大学 Hydrological Time Series jump variation error comprehensive diagnosis method
CN109271664A (en) * 2018-08-03 2019-01-25 华南理工大学 Design storm Safety Analysis Method under the conditions of being assumed based on consistency and nonuniformity
CN109271664B (en) * 2018-08-03 2022-09-27 华南理工大学 Design rainstorm safety analysis method based on assumed conditions of consistency and non-consistency
CN111353127A (en) * 2018-12-24 2020-06-30 顺丰科技有限公司 Single variable point detection method, system, equipment and storage medium
CN111353127B (en) * 2018-12-24 2024-05-17 顺丰科技有限公司 Single-change-point detection method, system, equipment and storage medium
CN110260774A (en) * 2019-07-22 2019-09-20 安徽理工大学 A kind of inspection of GNSS deformation information and method for early warning based on Pettitt algorithm
CN111488679A (en) * 2020-04-03 2020-08-04 中国能源建设集团江苏省电力设计院有限公司 Method for calculating non-uniform wind speed sequence design wind speed
CN111488679B (en) * 2020-04-03 2022-06-10 中国能源建设集团江苏省电力设计院有限公司 Method for calculating non-uniform wind speed sequence design wind speed
CN112149296A (en) * 2020-09-17 2020-12-29 中国科学院地理科学与资源研究所 Method for judging stability type of hydrological time sequence
CN112149296B (en) * 2020-09-17 2023-06-20 中国科学院地理科学与资源研究所 Method for judging stability type of hydrologic time sequence

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