CN102306235A - Unilateral-U-detection-based sudden pollution sensing method - Google Patents

Abstract

The invention provides a unilateral-U-detection-based sudden pollution sensing method. The method is characterized by comprising the following steps of: establishing a one-dimensional pollution dissemination statistical model; establishing a sensor pollutant concentration observation model; and performing a pollution sensing step, namely detecting a pollutant concentration observation time sequence of a sensor by using unilateral U detection method.

Description

Cognitive method is polluted in burst based on monolateral U detects

Technical field

The present invention relates to a kind of burst that detects based on monolateral U and pollute cognitive method, belong to the probability statistics technical field.

Background technology

(1) perception is polluted in burst

People's health and lives safety in sudden environmental pollution serious threat.The extremely strong uncertainty that itself has (time of origin, place and source strength uncertain) has brought serious obstruction for rescue and protected working.Perception is polluted in burst, is the prerequisite of pollution source location, and pollution source identification and improvement are had great importance.At present, mainly be to utilize the real-time monitoring of sensor that perception is carried out in the burst pollution.So-called pollution perception be exactly constantly according to sensors observe to Data Detection judge the moment that the burst pollution source exist.Perception refers to pollute the perception moment and pollutes the actual difference constantly that takes place retardation time.Sensor can not perceive burst sensitively and pollute the initial moment, will directly influence the accuracy that pollution source location and intensity are estimated, even the location that makes the mistake.Therefore, the researchist of association area explores the higher pollution cognitive method of reliability always urgently.

(2) Chang Yong pollution cognitive method

At present, pollution cognitive method commonly used is the threshold decision method, and its principle is: certain pollutant levels threshold value is set, when sensors observe concentration surpasses setting value, thinks that then burst occurring pollutes.The method principle is simple; Use morely, but in practical application, exist two problem: a. to require the sensor measurement precision high, and actual concentrations sensor measurement precision receives many factor affecting; The measuring accuracy of real concentration low (it is bigger to measure noise) uses this method to be prone to cause false-alarm when general.As shown in Figure 1, horizontal ordinate is the time, and ordinate is the pollutant levels value; Gas concentration fluctuates between 20～30ppm during pollution-free source; But, possibly surpass assign thresholds 40ppm like observed reading, thereby cause false-alarm in the A moment and the B moment owing to measure noise effect.B. for avoiding false-alarm, need suitably to improve the threshold value of detection alarm, like Fig. 1 threshold value is brought up to 50ppm from 40ppm, though greatly reduce false-alarm probability, this pollutes perception again and lags behind constantly.

Cause the main cause of the problems referred to above to be, polluting cognitive method based on the burst of concentration threshold is the single point in time discriminating data to concentration, under the influence of observation noise, is bound to exist above-mentioned two problems.

(3) the average test of hypothesis of single normal population

Earlier certain overall unknown parameter or overall distribution form are made certain hypothesis, the information that is provided by the sample that is extracted is constructed suitable statistic then, and the hypothesis that is proposed is tested, and judges to make statistics.Be to accept hypothesis or refusal hypothesis, this type statistical Inference is called hypothesis test problem.

The U check of single normal population average is a kind of of parametric assumption check, and its concrete steps are following:

If x ₁, x ₂, Λ x _nBe from normal population N (μ, σ ₀ ²) sample.

A. at first overall average is done hypothesis

H ₀: μ=μ ₀H ₁: μ＞μ ₀Or H ₀: μ≤μ ₀H ₁: μ＞μ ₀(being called right monolateral check).

B. by the sample architecture statistic that extracts

$U=\stackrel{\‾}{X}-{\mathrm{\μ}}_0/({\mathrm{\σ}}_0/\sqrt{n})---\left(1\right)$

Work as H ₀During establishment, U～N (0,1).Wherein,

Be sample average, σ ₀Be population standard deviation, n is a sample size.

C. under given level of significance, confirm H ₀Region of rejection about statistic.

For given level of significance 0＜α＜1, look into the standardized normal distribution table and get z _α, make

$P\{U>z_{\mathrm{\α}}\}=P\{\stackrel{\‾}{X}-{\mathrm{\μ}}_0>z_{\mathrm{\α}}\·\frac{{\mathrm{\σ}}_0}{\sqrt{n}}\}=\mathrm{\α}---\left(2\right)$

Then De region of rejection does $\stackrel{\‾}{X}-{\mathrm{\μ}}_0>z_{\mathrm{\α}}\·\frac{{\mathrm{\σ}}_0}{\sqrt{n}}.$

D. calculate and judge

According to sample value x ₁, x ₂, Λ x _n, calculate When

The time just refuse H ₀And work as The time, just accept H ₀

(4) one-dimensional and unsteady state mass transfer

The one-dimensional and unsteady state mass transfer differential equation is:

$\frac{\∂C}{\∂t}+u\×\frac{\∂C}{\∂x}=D\×\left(\frac{{\∂}^{2}C}{\∂x^2}\right)+S---\left(3\right)$

In the formula, C is pollutant levels, the mg/m of unit ³T is the time, the s of unit; U is a wind speed, the m/s of unit; X is a length, the m of unit; D is a coefficient of diffusion, the m of unit ²/ s; S is the pollutant emission rate, the mg/m of unit ³S.

The first order derivative that concentration is adjusted the distance adopts backward difference, and the second derivative that concentration is adjusted the distance adopts central difference, gets one-dimensional and unsteady state mass transfer implicit difference scheme discrete equation:

$(1+\frac{u\×\mathrm{\Δt}}{\mathrm{\Δx}}+\frac{2\×D\×\mathrm{\Δt}}{\mathrm{\Δ}{x}^2})\×C_i^{k+1}-(\frac{u\×\mathrm{\Δt}}{\mathrm{\Δx}}+\frac{D\×\mathrm{\Δt}}{\mathrm{\Δ}{x}^2})\×C_{i-1}^{k+1}----\left(4\right)$

$\frac{D\&times;\mathrm{\&Delta;t}}{\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="HDA0000073300210000021.png,HDA0000073300210000022.png"\; state="\{\{state\}\}">x</figure-callout>}}^2}\&times;C_{i+1}^{k+1}=C_i^k+S^{k+1}\&times;\mathrm{\&Delta;t}$

Be reduced to:

AC ^k+1＝C ^k+S ^k+1×Δt (5)

Wherein A is the matrix of each item coefficient composition; Δ t is a time step, the s of unit; K represents the time horizon ordinal number.

Summary of the invention

According to an aspect of the present invention, provide a kind of burst that detects based on monolateral U to pollute cognitive method, it is characterized in that comprising: set up one dimension and pollute the statistical model that distributes; Set up sensor pollutant levels observation model; Pollute the perception step, use monolateral U detection method, the pollutant levels observation time sequence of sensor is detected.

According to another aspect of the present invention, a kind of method that burst Pollution is carried out perception is provided, has it is characterized in that:

Set up one dimension and polluted the statistical model that distributes, considered multiple systems uncertain factors such as discretization error;

Set up sensor pollutant levels observation model, the sensor measurement error has been carried out statistical hypothesis, improved model accuracy;

Propose monolateral U detection method,, obtain polluting perception constantly, improve reliability through the pollution perception that happens suddenly of the seasonal effect in time series statistical property of judging the observation of sensor concentration.The time series of so-called concentration observation, after referring to the time disperse, the sequence of the observation concentration value composition of a plurality of time horizons.

Figure of description

Fig. 1 pollutes the cognitive method analysis chart based on the burst of threshold value.

Fig. 2 shows the composition and the implementation step of the inventive method.

The model instance that Fig. 3 pollutes for the one dimension burst, Δ x represents the length of spatial division grid.

The pollutant levels value that Fig. 4 shows the sensor node place is situation of change in time, and horizontal ordinate is represented time s, and ordinate is represented pollutant levels value mg/m ³

Fig. 5 is the pollution perception process flow diagram that detects based on U.

Embodiment

The objective of the invention is to: propose a kind of burst that detects based on U and pollute cognitive method; Solve in the heritage perception method and do the false-alarm problem that check causes to single sample value; Time series to observed reading is carried out detection of dynamic, reduces perception retardation time, thereby improves the reliability of perception.

Technical solution of the present invention is: on the basis of one-dimensional and unsteady state mass transfer discrete equation, set up one dimension and pollute the statistical model that distributes, comprise uncertain factors such as discretization error, wind speed; Set up sensor pollutant levels observation model, in the sensors observe noise is included in, improve the accuracy of simulation result; Use monolateral U detection method, the initial moment that accurate perception pollutant distributes.

Fig. 2 has shown and has comprised according to one embodiment of present invention:

(1) sets up one dimension and pollute the statistical model that distributes

One dimension polluted distribute instance and simplify, carry out the grid dividing on time and the space, confirm discrete steps.Be the basis with one-dimensional and unsteady state mass transfer discrete equation, the uncertain factor in the combination model, the stochastic variable of increase Normal Distribution is set up statistical model.(Fig. 2 (201))

(2) set up sensor pollutant levels observation model

Consider the sensor measurement The noise, set up the pollutant levels observation model.(Fig. 2 (202))

(3) pollute perception

Use monolateral U detection method, the pollutant levels observation time sequence of sensor is detected, obtain detecting period.(Fig. 2 (203))

The hypothesis testing method that the present invention's utilization detects based on monolateral U pollutes instance to one dimension and pollutes perception

The measurement noise obedience average of supposing concentration sensor is zero, and variance is σ ²Gaussian distribution.Do not pollute if burst takes place, actual concentrations is kept true value C ₀Constant.Under noise effect, then the observation concentration of sensor should be the stack of actual concentrations value and noise, and promptly obeying average is C ₀, variance is σ ²Gaussian distribution.And after the burst pollution occurring, actual concentrations is no longer kept C ₀Constantly (compare C ₀Greatly).Therefore, get that one group of observation sequence detects among Fig. 4,, thinking that burst has taken place pollutes if variation has taken place through detecting its statistical property.Take different samples at every turn and detect, till detecting generation burst pollution, and the minimum sample of the time series in last group of sample can be regarded as the pollution perception constantly.

Practical implementation step below in conjunction with one dimension case introduction cognitive method of the present invention.As shown in Figure 3, total length is 10 meters, and space step delta x is 0.5 meter, and the node number is 21, and the control volume of each node as shown in Figure 3.The wind field inlet is at the 1st node place, and outlet is at the 21st node place, and sensor is at the 20th node place.Wind speed is 0.2m/s, and direction as shown in the figure.Coefficient of diffusion is 0.001m ²/ s.Each point primary pollutant concentration is 2mg/m ³

(1) one dimension pollutes the foundation of distributing statistical model

The fluctuation of discretization error, change of wind velocity and convection current coefficient of diffusion all will become the uncertain factor of system, and this also directly causes the inaccurate of solving result.Use statistical model to represent this uncertainty at this, promptly adopted to have suitable distributed random variable and describe the process of distributing of polluting.

Consider these uncertainties and error, indeterminate of increase obtains polluting and distributes statistical model in formula formula (5):

AC ^k+1＝C ^k+S ^k+1×Δt+w ^k×Δt (6)

The matrix that A forms for each item coefficient in the formula; w ^kRepresent various disturbances and error, unit is mg/m ³S supposes that obeying average is 0, and variance is q _wGaussian distribution.q _wRepresent probabilistic intensity, model structure, model discretize and model coefficient are accurate more, q _wBe worth more little, otherwise, q _wBe worth big more.

(2) foundation of sensor concentration observation model

When polluting perception, need the concentration observation sequence of pollutant, therefore be necessary to set up the pollutant levels observation model of sensor.

$X^k=C_j^k+v^k---\left(7\right)$

Wherein, X ^kBe the pollutant levels observed reading of sensor at the k time horizon, mg/m ³J is a sensor place node location; Be the pollutant levels actual value of the sensing station k of place time horizon, mg/m ³v ^kBeing k time horizon sensor measurement noise figure, is that variance is the uncorrelated white Gaussian noise sequence of σ, and σ is by the measuring accuracy decision of sensor.The σ value is more little, and measuring accuracy is high more; Vice versa.

(3) pollute perception

1. make parametric assumption, structure statistic and set the region of rejection

Null hypothesis H ₀: μ≤C ₀, burst does not take place pollute;

Alternative hypothesis H ₁: μ＞C ₀, burst takes place pollute.(μ is a sample average, C ₀Be initial concentration)

Construction Statistics

where

is the concentration of the sample taken from the mean observed, q is the sample size, σ is the standard deviation of the measurement noise, in this case taken as 0.3.

Get apparent the horizontal α of property=0.01, tabling look-up to get z _α=2.33, with this as critical value.

2. statistic being carried out U detects

(a) choose the sample of a constant volume continuously, compute statistics U value.

The amount of trying to please is the continuous sample C of q _k, C _K+1Λ, C _K+q-1(subscript is represented corresponding time horizon ordinal number) calculates statistic

Calculate U during k=1 ₁, get K=K+1, until all observed readings are all counted.(Fig. 5 (501), (502) (503), (504), (511))

(b) get a certain amount of calculating U value and carry out linear fit, obtain new U value.

The amount of trying to please is the continuous sample U of r _j, U _J+1, Λ U _J+r-1Carry out linear fit, obtain one group of new U (j).Calculate U (1) during j=1.(Fig. 5 (505) (506) (507))

(c) to the minimum value U (j) among every group of U (j) _MinWith critical value z _αCompare.If do not satisfy the loop ends condition, then get j=j+1, repeat (b) and (c) go on foot, until satisfying the loop ends condition, i.e. U (j) _Min＞z _α, the pollution perception that the j representative of this moment obtains constantly.(Fig. 5 (508), (509), (510))

The concentration observation data of Fig. 4 for calculating through sensor concentration observation model, the observation noise of having added sensor is more near actual conditions.Adopt cognitive method as above, the pollution perception that obtains is 228s constantly, and the actual initial moment of pollution is 200s, has postponed 28s.The false-alarm problem does not appear in the perception.Compare with the threshold decision method that obtains identical result, the concentration critical value of the method result's correspondence is littler, and this explanation this method need not guarantee reliability through improving threshold value.

The present invention compares with existing pollution cognitive method and has the following advantages:

(1) set up statistical model and sensor concentration observation model that pollution is distributed, improved the accuracy of model, for the reliability of sensing results is carried out place mat.

(2) the burst pollution cognitive method that detects based on U is not only to differentiate to the single point in time data of concentration, but from the concentration observed reading, chooses sample, utilizes one group of concentration observation sequence to carry out dynamic perfromance and detects.This method of inspection will overcome the interference of observation noise preferably, greatly reduce the probability of false-alarm, thereby guarantee the reliability of perception, and follow-up pollution source location and intensity are estimated to have positive meaning.

(3) the applied method of the present invention need be not that cost improves reliability to improve setting threshold, but pollutes perception through setting suitable region of rejection, thereby has improved pollution perception delay problem.

Claims (8)

1. cognitive method is polluted in the burst that detects based on monolateral U, it is characterized in that comprising:

Set up one dimension and pollute the statistical model that distributes; Set up sensor pollutant levels observation model;

Pollute the perception step, use monolateral U detection method, the pollutant levels observation time sequence of sensor is detected.

2. pollute cognitive method according to the burst of claim 1, it is characterized in that said one dimension pollutes the statistical model that distributes and is:

AC ^k+1＝C ^k+S ^k+1×Δt+w ^k×Δt (6)

In the formula:

C is pollutant levels;

T is the time;

S is the pollutant emission rate;

Δ t is a time step;

K represents the time horizon ordinal number;

The matrix that A forms for each item coefficient;

w ^kRepresent various disturbances and error;

q _wRepresent probabilistic intensity.

3. pollute cognitive method according to the burst of claim 1, it is characterized in that said sensor pollutant levels observation model is:

Wherein,

X ^kBe the pollutant levels observed reading of sensor at the k time horizon;

J is a sensor place node location;

k for the first time at the sensor location level pollutant concentrations actual value;

v ^kBe k time horizon sensor measurement noise figure.

4. pollute cognitive method according to the burst of claim 2, it is characterized in that

If w ^kVarious disturbances of representative and error agrees average are that 0 variance is q _wGaussian distribution.

5. pollute cognitive method according to the burst of claim 3, it is characterized in that

K time horizon sensor measurement noise figure v ^kBe that variance is the uncorrelated white Gaussian noise sequence of σ, wherein σ is by the measuring accuracy decision of sensor, and the σ value is more little, and measuring accuracy is high more, and vice versa.

6. pollute cognitive method according to the burst of claim 1, it is characterized in that said pollution perception step comprises:

Make the step of parametric assumption;

The step of structure statistic;

Set the step of region of rejection;

Statistic is carried out the step that U detects.

7. pollute cognitive method according to the burst of claim 6, it is characterized in that

The said step of doing parametric assumption comprises:

Null hypothesis H ₀: μ≤C ₀, burst does not take place pollute;

Alternative hypothesis H ₁: μ＞C ₀, burst takes place pollute, wherein μ is a sample average, C ₀Be initial concentration;

The structure comprises structural statistics statistics?

where?

for the samples taken from the mean observed concentration, q is the sample size, σ is the standard deviation of the measurement noise;

The step of said setting region of rejection comprises gets level of significance α, and definite critical value.

8. pollute cognitive method according to the burst of claim 6, it is characterized in that saidly statistic is carried out the step that U detects comprising:

(a) choose the sample of a constant volume continuously, compute statistics U value, wherein

The amount of trying to please is the continuous sample C of q _k, C _K+1Λ, C _K+q-1, calculate statistic

Wherein subscript is represented corresponding time horizon ordinal number,

Calculate U during k=1 ₁, get K=K+1, until all observed readings are all counted.

(b) get a certain amount of calculating U value and carry out linear fit, obtain new U value, wherein

The amount of trying to please is the continuous sample U of r _j, U _J+1, Λ U _J+r-1Carry out linear fit, obtain one group of new U (j), calculate U (1) during j=1.

(c) to the minimum value U (j) among every group of U (j) _MinWith critical value z _αComparing, if do not satisfy the loop ends condition, then get j=j+1, repeat (b) and (c) go on foot, is U (j) until satisfying the loop ends condition _Min＞z _α, represent the pollution perception moment that obtains with the j of this moment.

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