CN102254081B - Random probability model-based statistical positioning method for sudden river water pollution - Google Patents

Abstract

The invention provides a positioning algorithm of a sudden river water pollution source based on a random probability model, which is characterized by comprising the following steps: establishing a sudden river water pollution propagation model based on random probability; establishing a random probability model for observing the pollution concentration of the burst river water; and carrying out statistical positioning on the sudden river water pollution source.

Description

The statistics localization method of the burst river water contamination based on stochastic probability model

Technical field

The present invention relates to a kind of statistics localization method of the burst river water contamination based on stochastic probability model, belong to mass transfer indirect problem technical field.

Background technology

Sudden earth's surface, subterranean river water pollution accident frequently occur and cause serious social danger, are the focal issues that countries in the world are very paid close attention to.As 1986, more than 30 of the littoral chemical plant emission in the Rhine was planted organism inflow river and is caused water to pollute, and causes a large amount of hydrobionts dead, affects 4 the national number million peoples' in two sides life and production; The Song Hua River nitrobenzene water pollution accident of 2005 causes Harbin City to cut off the water three days, has also caused the concern of Sino-Russian two countries government.In addition,, once subterranean river is polluted, consequence is more fearful.Administer contaminated subterranean river and need the more financial cost of cost and time cost.At the beginning of 2009, the survey showed that, and Southwestern China karst region water environmental problems presents pollution source variation to survey of land and resources project " the great the problems of geo-environment in karst mountainous area in Southwest Chain and countermeasure ", 3066 of karst regions subterranean stream faces the challenge of urban life, industry and agriculture multiple contaminates, is just being subject to becoming the actual threat of blowdown sewer.Subterranean river is imbedded in underground certain depth, anoxic, low, the unglazed photograph of temperature, flow slowly, water alternate cycle is long, once be polluted, the interaction process between pollutant, water and medium is very complicated.Even if afford to bear economically pollution treatment cost, removing pollution source also needs the cycle of growing very much, and more than ten years, decades are centuries even.The extent of injury that China's subterranean river pollutes is on the rise, carry out sudden water pollution accident emergency disposal, and the generation of prevention of water contamination accident from source, be that we tackle the top priority of sudden river water contamination event at present, quick and precisely locating pollution source is keys of prevention of water contamination accident.The feature of sudden river water contamination accident: often there is very large uncertainty, comprise the uncertainty in time of origin and place, the uncertainty of the intensity of pollution source.

It is more passive that existing water pollutes location, early warning and prevention method, and many methods still rest on theoretical research stage.

The provincial boundaries that the laying principle of national water quality of river Sampling network is important river, important inflow stream (river) mouthful and estuary, important Hu Ku lake body and go out ingoing river, river, national boundaries and entry and exit river, large-scale project etc.

Water quality of river automatic monitoring system is comprised of central station and automatic water quality monitoring substation at present, realizes water quality Real-Time Monitoring, and Monitoring Data timing automatic is extracted, and can confirm whether this water quality of river is polluted by data analysis.

Except automatic Sampling network, water quality of river detects and generally also comprises video monitoring, emergency monitoring and pollution prewarning is passed through to sampling, further confirms pollution condition.

Traditional river water contamination localization method as shown in Figure 1, the number that detects website due to water quality of river is limited, distribution density is not high, water quality detection system can only provide near sensor points or around in waters pollutant levels measure sequence, can not accurately locate the position of burst pollution, the harmfulness that prediction is polluted.For the burst pollution of some river, earth's surface water, if observation pollution concentration increases significantly, accurately location can only adopt the method for human assistance search, and speed is slow, and efficiency is low, and the location of polluting for subterranean stream flowing water is more difficult.

Traditional burst river water contamination concentration diffusion propagation model meets formula:

$\frac{\∂c}{\∂t}+\▿\left(\mathrm{uc}\right)+\▿[d\·\mathrm{grad}(C/\mathrm{\ρ})]+s---\left(1\right)$

In formula, c is pollution concentration, mg/m ³; D is coefficient of diffusion, mg/ (ms); U is water flow velocity, m/s; S is pollution source (functions of position and emission intensity), mg/ (m ³s); T is the time, s; ρ is water-mass density, mg/m ³.

Suppose that it is passive that pollution is distributed, pollutant flow velocity is identical with the flow velocity of river water, supposes generation physics useless, chemical conversion in dispersion of pollutants process simultaneously.

(1) diffusion term in formula adopts Using Second-Order Central Difference to carry out discretize,

$\▿[d\·\mathrm{grad}(C/\mathrm{\ρ})]=d_{n+1}\frac{c_{n+1}^m-c_n^m}{{\mathrm{\Δx}}^2}-d_n\frac{c_n^m-c_{n-1}^m}{{\mathrm{\Δx}}^2}$

D _n, d _n+1be coefficient of diffusion, equal the d/ ρ in formula (1).

Convective term adopts Upwind Schemes discrete

$\▿\left(\mathrm{uc}\right)=u_n\frac{c_n^E-c_n^W}{\mathrm{\Δx}}$

Wherein $c_n^E=\left\{\begin{array}{cc}{c}_n& \mathrm{if}{u}_n>0\\ c_{n-1}& \mathrm{if}{u}_n<0\end{array}\right.,c_n^W=\left\{\begin{array}{cc}{c}_{n-1}& \mathrm{if}{u}_n>0\\ c_n& \mathrm{if}{u}_n<0\end{array}\right.,$ U in formula _nthe flow velocity of river water, identical with the u in formula (1).

Pollution concentration adopts central difference to the derivative of time, obtains

$c_n^{m+1}=\left\{\begin{array}{cc}{c}_n^m+(-P_{n1}-P_{n2}-P_{n3})c_n^{m+1}+P_{n2}{c}_{n+1}^{m+1}+(P_{n3}+P_{n1})c_{n-1}^{m+1}+f_n\mathrm{\&Delta;t}& \mathrm{if}{u}_n>0\\ c_n^m+(P_{n1}-P_{n2}-P_{n3})c_n^{m+1}+(P_{n2}-P_{n1})c_{n+1}^{m+1}+P_{n3}{c}_{n-1}^{m+1}+f_n\mathrm{\&Delta;t}& \mathrm{if}{u}_n<0\end{array}\right.$

$P_{n1}=\frac{u_n\mathrm{\&Delta;t}}{\mathrm{\&Delta;x}},P_{n2}=\frac{d_{n+1}\mathrm{\&Delta;t}}{{\mathrm{\&Delta;x}}^2\mathrm{\&rho;}},P_{n3}=\frac{d_n\mathrm{\&Delta;t}}{{\mathrm{\&Delta;x}}^2\mathrm{\&rho;}}$

U in formula _nthe flow velocity of river water, identical with the u in formula (1).

The discrete matrix form of pollution spread model:

Ac _j+1＝c _j+s _j (2)

$A=\left[A_{i_1,i_2}\right],1<i_1<N,1<i_2<N$

$c_j={\left[\begin{array}{ccccc}{c}_j^1& \&CenterDot;\&CenterDot;\&CenterDot;& c_j^i& \&CenterDot;\&CenterDot;\&CenterDot;& c_j^N\end{array}\right]}^T$

$s_j=\mathrm{\&Delta;t}{\left[\begin{array}{ccccc}{s}_j^1& \&CenterDot;\&CenterDot;\&CenterDot;& s_j^i& \&CenterDot;\&CenterDot;\&CenterDot;& s_j^N\end{array}\right]}^T$

In formula, Δ t represents time step, and j represents timing node, i representation space node (i=1,2 ..., N).If there is no pollution source in node i position, have as while being internal node (non-entrance and exit)

$A_{i_1,i_2}=\left\{\begin{array}{ccc}1+P_{n1}+P_{n2}+P_{n3}& i_2=i_1& \\ -P_{n3}-P_{n1}& i_2=i_1-1& u_n>0\\ -P_{n2}& i_2=i_1+1& \\ 1-P_{n1}+P_{n2}+P_{n3}& i_2=i_1& \\ -P_{n3}& i_2=i_1-1& u_n<0\\ -P_{n2}+P_{n1}& i_2=i_1+1& \end{array}\right.$

In known speed and the isoparametric situation of coefficient of diffusion, during handy (2) formula forward calculating concentration sequence, need known pollution source position, intensity, distribute three parameters of initial time.But be to predict this three parameters during location, contamination source simultaneously.The current method for location, contamination source, current territory mainly comprises analytic approach, optimization and probabilistic method.

The analytic solution that analytic approach depends on velocity field distribution and pollution concentration oppositely realize pollution spread identification.Optimization method is all pollution source of hypothesis possible pollution source position, intensity, distributes initial time three parameter combinations, (2) formula of utilization, under this three parametric assumption, obtain all possible corresponding pollution concentration field, then optimize and obtain same observation data and mate pollution concentration field most, thereby determine pollution source position and intensity.Probabilistic method is also to use forward model (2) formula, with probability, represents all situations that pollution source may occur.Due to possible pollution source position, emission intensity with distribute historical combined situation huge amount, above-mentioned two kinds of method calculated amount are very large.

Burst pollution source often has and continues to distribute (non-transient) and intensity time-varying characteristics in practice, and sensor, because the precision of observation data is also subject to noise effect, has uncertain characteristic (but meeting normal distribution) in addition.Due to above-mentioned two main causes, existing method is subject to many limitations in actual applications.

Summary of the invention

In order to seek a kind of method that better overcomes the problems referred to above, this invention has been set up a kind of new pollution spread statistical model on the basis of traditional communication model (2), new burst pollution source localization method is proposed on this basis, by matched sensors observation data sequence and position, suppose the feature of the sensor place concentration hypothetical sequence of acquisition more, realize pollution source position, location, reconstruct is polluted and is distributed history.With based on the many hypothesis of multiparameter (emission intensity, emissioning time and source position) forward optimizing localization method, compare, the method has that calculated amount is little, complexity is low, can realize the source item identification that continues to distribute, and to features such as observation noise strong robustnesses.

The invention provides a kind of statistical modeling and statistical analysis technique, can realize the accurate location of burst river water contamination, further can estimate pollution intensity, the extent of injury that prediction is polluted.

The present invention adopts stochastic probability model to replace deterministic models, has accurately characterized burst river water contamination and has propagated the uncertainty in indirect problem, has improved the precision of location, burst river water contamination source.

According to an aspect of the present invention, provide a kind of localization method of the river water contamination source that happens suddenly, its feature comprises:

Propose to adopt stochastic probability model to replace deterministic models.

The proposition river water contamination identification that will happen suddenly estimates that by statistical model foundation, location and intensity three parts form.

Propose to adopt position probability distribution figure to represent positioning result, adopt the method that multivariate statistics test of hypothesis is combined with statistical estimate to solve burst river water contamination orientation problem, the design and calculation method that comprises location probability compute location method, the design and calculation method of polynary test of hypothesis, thus the burst river water contamination locating information that precision is higher obtained.

Accompanying drawing explanation

Fig. 1 has shown traditional burst pollution positioning flow.

Fig. 2 has shown according to composition and the each several part mutual relationship of the localization method in a burst river water contamination source based on probability model and statistic algorithm of the present invention.

Fig. 3 has shown the main flow of burst stream pollution location.

Fig. 4 has shown the hypothesis calculation of parameter flow process of multielement positional hypothesis.

Fig. 5 has shown an example of the spatial model of burst river water contamination.

Fig. 6 has shown an example of pollution concentration measurement sequence.

Fig. 7 has shown an example of positioning result.

Embodiment

The object of the invention is to be to provide a kind of statistics localization method of the burst river water contamination based on stochastic probability model, to solve the ill-posed problem in existing burst river water contamination location, improve the accuracy of correct location, burst pollution source, for decision center provides pollution evolution and fast early warning information accurately.

According to one embodiment of present invention, provide the statistics localization method in the burst river water contamination source based on stochastic probability model, to solve the ill-posed problem of traditional pollution location; Wherein, on the basis that uses distribution parameter propagation equation to analyze burst river water contamination, consider that systematic uncertainty and sensor observation are uncertain, set up stochastic system model and observation model; For the ill-posedness of contaminated solution location, the concept that proposes employing location probability represents positioning result, proposes to combine to adopt the method for statistical test and statistical estimate to realize pollution location, makes the result of location more accurate.

The statistics localization method in a kind of burst river water contamination source based on stochastic probability model according to an embodiment of the invention has solved the ill-posed problem of polluting location, the propagation equation that the method is polluted one dimension according to the uncertainty of systematic uncertainty and observation is analyzed, and has set up the probabilistic model of burst river water contamination.For solving the ill-posed problem of burst river water contamination, use probability to represent positioning result, combine statistics and detect and statistical estimate, obtain positioning result accurately.

Fig. 5 has shown can apply one embodiment of the present of invention, the space layout in one section of river of the river water contamination that happens suddenly.In Fig. 5, segmented section is counted 21, space step delta x.According to the order that is from upstream to downstream, last does not find the monitoring station of polluting the upstream that the 1st node is river; The 21st node found the monitoring station of polluting for first.Suppose that each node flow velocity u coefficient of diffusion d is all identical.The concentration c of upstream ₀=0, do not pollute.If sensor is fixed on the 20th Nodes.

Fig. 2 has shown method of the present invention, and it comprises:

(1) adopt convective-diffusive equation to propagate and carry out modeling burst river water contamination thing, the feature of propagating according to river water contamination, grid division is carried out in one section of space of adjacent upstream to the basin, sensor place of finding to pollute, set up propagation equation, state is the concentration of each grid node, and parameter is size of mesh opening, coefficient of diffusion and flow velocity; Analyze grid and divide error, the error of each parameter and time variation, set up the statistical model of dispersion of pollutants.(Fig. 2 (201))

(2), according to sensor measurement precision, set up the statistical model of pollution concentration observation.(Fig. 2 (202))

(3) perception in burst pollution source, the conspicuousness changing according to pollution concentration detects to realize burst pollution perception.(Fig. 2 (203))

(4) location, burst pollution source, adopts polynary hypothesis to detect to calculate the probability that pollution source may appear at each position.(Fig. 2 (204))

Burst river water contamination location

According to one embodiment of present invention, a kind of associating statistical test based on stochastic probability model and the one dimension pollution source localization method of statistical estimate are proposed.First carry out grid division, the propagation equation of foundation based on distribution parameter, by this equation, obtain the relation between source item, grid CONCENTRATION DISTRIBUTION, coefficient of diffusion and velocity field, then according to the uncertainty of system, in above-mentioned model, add random entry to represent uncertainty, thereby set up system model more accurately.Because the observation data of sensor comprises measuring error, therefore set up the observation model with random entry.After pollution existence being detected, by matched sensors concentration observation sequence and position, suppose the feature of the sensor place hypothesis concentration sequence of acquisition more, realize the reconstruct of source item position, and tentatively determine source emission intensity.For showing better the impact of observation noise on location, the present invention builds pollution source location probability to represent positioning result.

The concrete application of the burst river water contamination source location algorithm below in conjunction with drawings and Examples introduction based on stochastic probability model.

Exemplary example is the one-dimensional space as shown in Figure 5,21 of nodes, and space step delta x is 0.5km.The 1st node is entrance, and the 21st node, for outlet, supposed the identical u=2m/s of each node wind speed, the identical d=0.2mg/ of coefficient of diffusion (ms), and upstream is without the pollutant levels c in burst pollution area ₀=0mg/m ³.

1) adopt the propagation model based on random chance to represent burst pollution

(1) set up the burst river water contamination propagation model (Fig. 2 (201)) based on random chance

Inlet boundary condition

$c_{j+1}^i=c_0=0---\left(3\right)$

Export boundary condition

$c_{j+1}^i=c_j^{i-1}---\left(4\right)$

C in formula ₀for entrance concentration value; C is concentration; Subscript i represents space lattice node; Subscript j represents timing node.

The uncertainty of propagation model is caused by factors such as discretization error, the fluctuations of convection current coefficient of diffusion.Consider these uncertainties and error, in formula (2), increase the statistical model that an additive noise term obtains pollution spread:

Ac _j+1＝c _j+s _j+ΔtW _j (5)

In formula $W_j={\left[\begin{array}{ccccc}{w}_j^1& \&CenterDot;\&CenterDot;\&CenterDot;& w_j^i& \&CenterDot;\&CenterDot;\&CenterDot;& w_j^N\end{array}\right]}^T,$ (mg/ (ms)) represents various disturbances and error, supposes that it is the white Gaussian noise of zero-mean, and variance is:

$\mathrm{cov}\left(w_j^i\right)=q_w---\left(6\right)$

Q in formula _wrepresent probabilistic intensity.Model structure, model discretize and model coefficient are more accurate, q _wbe worth less, otherwise, q _wbe worth larger.

(2) set up the stochastic probability model (Fig. 2 (202)) of burst river water contamination concentration observation

Pollution source location also needs the time series of the pollutant levels observation data of sensor, and the in the situation that of single-sensor, observation model is:

$z_j=c_j^i+v_j---\left(7\right)$

In formula, subscript i represents sensor place node location, and subscript j represents j sampling time point, v _jthat variance is r (r=cov (v _j)) uncorrelated Gaussian sequence, r determines by the measuring accuracy of sensor, sensor observation is more accurate, r is less; Otherwise when sensor observes inaccurate, r is larger.This variance r that in Fig. 3 (305), compute location probability is used.

If coefficient of diffusion d and water flow velocity u are known, known pollution source position p, pollution source emission intensity s and distribute initial time t in Fig. 3 (303) and Fig. 4 (402,404), adopt above formula and the formula (2) can calculating concentration sequence

2) the statistics location in burst river water contamination source

First according to the pollution concentration observation sequence of sensor, detect whether there is burst pollution, if burst pollution detected, according to polluting perception t constantly _p, utilize concentration sequence, be each node location p _icalculate an optimum burst pollution and distribute initial time t _iwith emission intensity s _i, then utilize a plurality of hypothesis on location p _i, t _i, s _ithe concentration sequence of forward calculating sensor point concentration distance D _iwith location probability p _ri.

This invention has been constructed the probability of burst pollution source at each possible position, shown in (8):

$p_{\mathrm{ri}}=\frac{e^{-D_i^2}/r}{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}{e}^{-D_k^2/r}}---\left(8\right)$

In formula, molecule is likelihood function, and denominator is to realize normalization.D _ifor concentration difference distance, be distance (Fig. 4 (405)) between hypothesis concentration and measurement concentration,

$D_i=\underset{j=\max t_i}{\overset{t_p+M}{\mathrm{\&Sigma;}}}|c_j^i-z_j|---\left(9\right)$

The statistics positioning step in-burst river water contamination source

(1) first detect and pollute, obtain polluting perception (Fig. 2 (203)) constantly.According to the distribution character of sensor observational error, can adopt statistics river burst water to be detected and pollute, determine and pollute perception t constantly _p, Fig. 3 (303,304), Fig. 4 (401,402,403,404,405) will use perception t constantly _p.

(2) set up a plurality of hypothesis on location, each hypothesis on location is found to optimum initial distributing constantly and emission intensity.As Fig. 3 (301), suppose that the position of river burst water pollution is at node p _ii ∈ [1 ..., N], polluting perception t constantly _pa front time period searches for, and obtains one and pollutes the initial t constantly that distributes _iwith pollution source emission intensity s _i(Fig. 3 (302)), calculation procedure as shown in Figure 4, is searched for the optimum initial bicirculating step constantly of distributing in detail:

1. first the moment to be searched is made as [t ₁, t ₂, t ₃]=[t _p, t _p, t _p]-[3,2,1] (Fig. 4 (401)), i.e. nearest 3 moment forward from perception constantly, first interior circulation calculates these 3 not hypothesis concentration in the same time while calculating hypothesis concentration, can use formula (2), formula (7), systematic parameter and hypothesis parameter.Suppose that parameter comprises assumed position p _k, suppose to distribute initial time t _k, suppose emission intensity s _k, t _kand s _kaccording to p _kcalculate, systematic parameter comprises coefficient of diffusion d, water flow velocity u.Then calculating concentration distance D _i, namely suppose concentration with measurement concentration z _jpoor.The concentration distance of three adjacent moment of interior cycle calculations, optimum initial time t is found in outer circulation _kwith source emission intensity s _k, outer circulation at every turn by search time integral body move forward a measuring period, until find optimum initial time D ₁>D ₂<D ₃(Fig. 4 (406)), find corresponding assumed position p _iand a group of hypothesis parameter, i.e. position p measuring distance minimum value between concentration _i, initial time t _iwith source emission intensity s _i.

2. establishing pollution source emission intensity is unit strength s _k=1, utilize p _k, t _k, s _kand d, u, calculates according to formula (2) and formula (7) (Fig. 4 (402))

3. calculate optimum burst pollution hypothesis intensity (Fig. 4 (403))

$s_k=\frac{\underset{j=t_k}{\overset{t_p+M}{\mathrm{\&Sigma;}}}{z}_j}{\underset{j=t_k}{\overset{t_p+M}{\mathrm{\&Sigma;}}}{c}_j^k}---\left(10\right)$

Because there is linear relationship between burst pollution source emission intensity and measurement concentration sequence, so can adopt above formula to calculate burst pollution emission intensity.

4. known coefficient of diffusion d and water flow velocity u, utilize and hypothesis on location p _kcorresponding optimum pollutes and distributes initial time t _k, optimum emission intensity s _k, according to formula (2) and formula (7), calculate hypothesis concentration (Fig. 4 (404))

5. utilize (9) formula to calculate hypothesis concentration and measure distance (Fig. 4 (405)) between concentration.

Each 1 concentration distance corresponding to the moment of 3 adjacent hypothesis in the moment of calculating of interior circulation, interior circulation finishes to obtain 3 hypothesis distances, if relatively obtain Cmin distance D ₁>D ₂<D ₃, finish outer circulation, otherwise, by initial unified 1 the moment [t of translation forward of group (3 moment) constantly that distributes of hypothesis ₁, t ₂, t ₃]=[t ₁, t ₂, t ₃]-[1,1,1], continue optimizing (Fig. 4 (408)).

6. obtain and position p _ipollute the initial t constantly that distributes _iwith pollution source emission intensity s _i(Fig. 4 (407)).

(3), as shown in Fig. 3 (303), calculate and each hypothesis on location p _i, t _i, s _icorresponding hypothesis concentration computing method and Fig. 4 (402,404) are similar.

(4), as shown in Fig. 3 (304), utilize formula (9) to calculate and each hypothesis on location p _i, t _i, s _icorresponding concentration distance D _i, computing method and Fig. 4 (405) are similar.

(5), as shown in Fig. 3 (305), utilize formula (8) to calculate burst pollution source at the probability of each possible position.

In sum, adopt the burst river water contamination concentration observation statistical model of setting up according to embodiments of the invention, the pollution concentration that can obtain as shown in the example of Fig. 6 is measured sequence, wherein in Fig. 6, shows sensor observation concentration over time.Observe according to an embodiment of the invention uncertainty that statistical model comprised propagation model and the uncertainty of sensor measurement, the accuracy that has improved model.In addition, use the statistics localization method in the river water contamination source that happens suddenly according to an embodiment of the invention, can obtain positioning result as shown in Figure 7.In Fig. 7, positioning result shows, each node location is all possible pollution source position, and pollution source have certain probability that exists in each position, and probability the highest position in location is at 2km, so the maximum probability of burst pollution source in position.

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

(1) can realize the location in full-automatic accurate burst fast river water contamination source, reduce manual search scope, by less detection website, realize river water contamination on a large scale and locate;

(2) provide a kind of statistics localization method and calculation procedure of the river water contamination that happens suddenly, can easily and accurately realize the location in burst river water contamination source, overcome complicacy and the ill-posedness of existing various theoretical localization methods;

(3) owing to having adopted stochastic probability model to set up pollution spread model and pollution concentration measurement model, can adopt probability to represent positioning result, overcome the deficiency that existing various theoretical localization method only has a single position to separate, result and reality are more identical, more meet the inherent characteristic of the river water contamination that happens suddenly;

(4) for steady working condition, can calculate in advance and store the characteristic curve of pollution concentration, location algorithm is realized simple, with low cost.

Claims (1)

1. the burst river water contamination source localization method based on stochastic probability model, is characterized in that comprising:

(1) set up the burst river water contamination propagation model based on random chance;

Described burst river water contamination propagation model comprises N the node that one dimension is arranged, and the 1st node is entrance, and N node is outlet,

Described burst river water contamination propagation model has the form of discrete matrix:

Ac _j+1＝c _j+s _j (2)

$c_j={\left[\begin{array}{ccccc}{c}_j^1& \&CenterDot;\&CenterDot;\&CenterDot;& c_j^i& \&CenterDot;\&CenterDot;\&CenterDot;& c_j^N\end{array}\right]}^T$

$s_j=\mathrm{\&Delta;t}{\left[\begin{array}{ccccc}{s}_j^1& \&CenterDot;\&CenterDot;\&CenterDot;& s_j^i& \&CenterDot;\&CenterDot;\&CenterDot;& s_j^N\end{array}\right]}^T$

In formula, Δ t represents time step, and j represents timing node, i representation space node, and i=1,2 ..., N, A represents the diagonal matrix after discrete, and s represents pollution source emission intensity, and c is concentration;

Inlet boundary condition is:

$c_{j+1}^i=c_0=0---\left(3\right)$

Export boundary condition is

$c_{j+1}^i=c_j^{i-1}---\left(4\right)$

C in formula ₀for entrance concentration value;

Further comprise:

In formula (2) thus in supplement the statistical model that necessary indeterminate obtains pollution spread:

Ac _j+1＝c _j+s _j+ΔtW _j (5)

In formula, $W_j={\left[\begin{array}{ccccc}{w}_j^1& \&CenterDot;\&CenterDot;\&CenterDot;& w_j^i& \&CenterDot;\&CenterDot;\&CenterDot;& w_j^N\end{array}\right]}^T,$ represent various disturbances and error, unit be mg/ (ms),

Suppose for the white Gaussian noise of zero-mean, variance is:

$\mathrm{cov}\left(w_j^i\right)=q_w---\left(6\right)$

In formula, q _wrepresent probabilistic intensity, wherein model structure, model discretize and model coefficient are more accurate, q _wbe worth less, otherwise, q _wbe worth larger;

(2) set up the stochastic probability model of burst river water contamination concentration observation;

Observation model in single-sensor situation is:

$z_j=c_j^i+v_j---\left(7\right)$

In formula, subscript i represents sensor place space nodes, and subscript j represents j sampling time point, z _jthe time series of pollutant levels observation data, v _jthat variance is the uncorrelated Gaussian sequence of r, r=cov (v _j), be the concentration sequence of utilizing formula (2) forward to calculate, and r determines by the measuring accuracy of sensor, sensor observation is more accurate, and r is less; Otherwise when sensor observation is more inaccurate, r is larger,

(3) location is added up in burst river water contamination source:

Utilize a plurality of hypothesis parameters: node location p _i, node p _ithe corresponding initial time t that distributes _iwith node p _icorresponding pollution source emission intensity s _i, the concentration sequence of forward calculating sensor point concentration difference distance D _iwith location probability p _ri,

The probability of structure burst pollution source in each node, shown in (8):

$p_{\mathrm{ri}}=\frac{e^{-D_i^2}/r}{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}{e}^{-D_k^2/r}}---\left(8\right)$

In formula, molecule is likelihood function, and denominator has been realized normalization; D _ifor concentration difference distance, be to calculate gained concentration with measurement concentration z _jbetween distance,

$D_i=\underset{j=\max t_i}{\overset{t_p+M}{\mathrm{\&Sigma;}}}|c_j^i-z_j|---\left(9\right)$

T in formula _pit is the pollution source perception moment.