CN102680657A - Wireless sensor-based detecting and positioning method for pollution source close to impervious boundary - Google Patents

Abstract

The invention relates to a method for detecting and locating a pollution source near an impermeable boundary based on a wireless sensor. Randomly distribute n sensor nodes near the impermeable boundary to be tested. The sensor nodes are connected to the terminal nodes by radio frequency, the terminal nodes are wirelessly connected to the gateway, and the gateway is connected to the PC through a serial line. The PC is equipped with management software, the sensor detects the existence of the pollution source through the detection module in the management software, saves the nodes that detect the existence of the pollution source, and the node that detects the existence of the pollution source passes through the steady state concentration difference threshold in the analysis module of the pollution source diffusion stage After comparing δ _c , enter the positioning module 1 or positioning module 2 to obtain the position coordinates of the pollution source detected by the node; finally, calculate the average value of the position coordinates of the pollution sources detected by all nodes as the positioning coordinates of the pollution source. The invention has the characteristics of strong operability, high precision, low cost and conforming to actual sewage discharge conditions.

Description

Based on surveying and localization method of wireless senser near the impervious boundary pollution source

Technical field

The present invention relates to survey and field of locating technology near the impervious boundary pollution source, specifically is a kind of surveying and localization method near the impervious boundary pollution source based on wireless senser.

Background technology

In recent years, water environment protection has received various circles of society and has paid close attention to more widely, and the detection of pollution source and the location technology critical role in environmental protection highlights in the water environment.Generally; Water pollution is from the bank discharging near the waste water of bank factory, waste residue, therefore, near the pollution source lakeside promptly near the detection of impervious boundary pollution source and location technology for the searching pollution source; Protection and improve environment ensures that the human body safe drinking water has significance.

At present, the orientation problem of pollution source is primarily aimed at the gaseous contamination source, but the diffusion mechanism in Pollutant Source in Aquatic Environment and gaseous contamination source is not quite similar.In gas, the diffusion of pollution source does not receive boundary constraint.Actual water body receives the influence on water-bed and bank, is not unlimited, so the diffusion of pollution source receives edge effect.Therefore the method that is used for gas-monitoring and location is not suitable for the detection and the location of pollution source of water body.The detection of existing pollution source of water body and localization method mainly contain remote sensing technology, underwater robot location technology, manual detection location technology in addition, but there are a lot of shortcomings in said method, such as involve great expense, operability is not strong, the cycle is long etc.

Generally speaking, there are many drawbacks in present detection and location technology, lack feasibility, and seeking a kind of bank detection that tallies with the actual situation is problem demanding prompt solution with localization method.

Summary of the invention

The present invention is intended to overcome the prior art defective, and purpose provides a kind of meet actual river blowdown situation, workable, degree of accuracy is high and with low cost surveying and localization method near the impervious boundary pollution source based on wireless senser.

In order to realize the foregoing invention purpose, the technical scheme that the present invention adopts is following steps:

Step 1, dispose wireless sensor node near the impervious boundary to be measured

Near impervious boundary (promptly in the lake water in a bank or the dykes and dams 1m scope) stochastic distribution n sensor node, the sensor node coordinate is (x to be measured _i, y _i) (i=1,2,3....n>=3), sensor node is connected with terminal node with the mode of radio frequency, terminal node and gateway wireless connections, and gateway is connected with PC through Serial Port Line; Software management system is housed in the PC, and software management system comprises pollution source detecting module, pollution source diffusion phase analysis module, first locating module and second locating module.

Step 2, near the detection of impervious boundary pollution entering the water

Set: water depth is f, and water body initial ion concentration is Cc, has one section to stretch into the unknown blow-off pipe of middle of a lake length l near the impervious boundary; Known: the rate of release of this blow-off pipe is Q, and the concentration of pollution source is C ₀With the impervious boundary is the Y axle, stretches into blow-off pipe that direction is the X axle in the lake, is that initial point is set up rectangular coordinate system M with the intersection point of blow-off pipe and Y axle.

Sensor node (x _i, y _i) to detect the water body ion concentration be C _i(t), if C _i(t)-Cc>=10mg/l, then sensor node (x _i, y _i) detect existence near the impervious boundary pollution source.

The steady state (SS) of step 3, pollution source diffusion is judged

Sensor node (x _i, y _i) detecting the existence of pollution source constantly at t, the water body ion concentration is C _i(t), sensor node (x _i, y _i) when time interval Δ t, to record ion concentration be C _i(t+ Δ t).

Suppose that be isotropic near the impervious boundary pollution source when spreading, promptly the coefficient of diffusion of pollution source on x axle and y axle is D _x=D _y=D, δ _cFor pollution source spread the concentration difference threshold values that reaches steady state (SS),

${\mathrm{\δ}}_c=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(C(x_i,y_i,t_a+\mathrm{\ΔT})-C(x_i,y_i,t_a))/n---\left(1\right)$

In the formula (1):

t _aFor pollution source begin to diffuse to time of steady state (SS), t _aUsually got 100 days;

Δ T is the time interval that pollution source diffuse to detect ion concentration after the steady state (SS), and Δ T got 1 day usually.

$C(x_i,y_i,t_a)=\frac{{\mathrm{QC}}_0}{2\sqrt{\mathrm{\πD}}f}[\frac{1}{r_i}\mathrm{erfc}\left(\frac{r_i}{2\sqrt{{\mathrm{Dt}}_a}}\right)+\frac{1}{\stackrel{\‾}{r_i}}\mathrm{erfc}\left(\frac{\stackrel{\‾}{r_i}}{2\sqrt{{\mathrm{Dt}}_a}}\right)]---\left(2\right)$

$C(x_i,y_i,t_a+\mathrm{\ΔT})=\frac{{\mathrm{QC}}_0}{2\sqrt{\mathrm{\πD}}f}[\frac{1}{r_i}\mathrm{erfc}\left(\frac{r_i}{2\sqrt{D(t_a+\mathrm{\ΔT})}}\right)+\frac{1}{\stackrel{\‾}{r_i}}\mathrm{erfc}\left(\frac{\stackrel{\‾}{r_i}}{2\sqrt{D(t_a+\mathrm{\ΔT})}}\right)]---\left(3\right)$

In formula (2) and the formula (3):

erfc(x)＝1-erf(x) （4）

$\stackrel{\‾}{r_i}=\sqrt{{(x_i-L)}^2+{y_i}^2}---\left(5\right)$

$r_i=\sqrt{{(x_i-L)}^2+{y_i}^2}---\left(6\right)$

In formula (5) and the formula (6):

10m≤L≤40m。

If at time interval Δ t inner sensor node (x _i, y _i) the ion concentration difference that records is greater than δ _c, then the pollution source diffusion does not reach steady state (SS); If at time interval Δ t inner sensor node (x _i, y _i) the ion concentration difference that records is less than or equal to δ _c, then the pollution source diffusion reaches steady state (SS).

Step 4, near the location of impervious boundary pollution source

(1) when spreading, pollution source do not reach steady state (SS), i.e. C _i(t+ Δ t)-C _i(t)＞δ _cThe time, through sensor node (x _i, y _i) length l of the blow-off pipe of locating constantly at t is separating of formula (7):

$\left\{\begin{array}{c}{C}_i(t+\mathrm{\Δt})-C_i\left(t\right)=\frac{{\mathrm{QC}}_0}{2f\sqrt{\mathrm{\πD}}}(\frac{1}{2\sqrt{\mathrm{Dt}}}-\frac{1}{2\sqrt{D(t+\mathrm{\Δt})}})\\ C_i\left(t\right)=\frac{{\mathrm{QC}}_0}{2f\sqrt{\mathrm{\πD}}}(\frac{1}{r_i}-\frac{1}{2\sqrt{\mathrm{Dt}}})\end{array}\right.---\left(7\right)$

In the formula (7):

$r_i=\sqrt{{(x_i-l)}^2+{y_i}^2}.$

(2) when spreading, pollution source reach steady state (SS), i.e. C _i(t+ Δ t)-C _i(t)≤δ _cThe time, through sensor node (x _i, y _i) length l of the blow-off pipe of locating constantly at t is separating of formula (8):

$\left\{\begin{array}{c}{C}_i(t+\mathrm{\Δt})-C_i\left(t\right)=\frac{{\mathrm{QC}}_0}{2f\sqrt{\mathrm{\πD}}}(\frac{1}{\sqrt{\mathrm{Dt}}}-\frac{1}{\sqrt{D(t+\mathrm{\Δt})}})\\ C_i\left(t\right)=\frac{{\mathrm{QC}}_0}{2f\sqrt{\mathrm{\πD}}}(\frac{1}{r_i}+\frac{1}{\stackrel{\‾}{r_i}}-\frac{1}{\sqrt{\mathrm{Dt}}})\end{array}\right.---\left(8\right)$

In the formula (8):

$\stackrel{\‾}{r_i}=\sqrt{{(x_i+l)}^2+{y_i}^2};$

$r_i=\sqrt{{(x_i-l)}^2+{y_i}^2}.$

(3) in actual measurement, use n sensor node (x near the impervious boundary stochastic distribution _i, y _i) in detect k the node (x that pollution source exist _j, y _j) (j=1,2,3....k, 3≤k≤n) position works as C _j(t+ Δ t)-C _j(t)>=δ _cThe time, find the solution l according to formula (7) _jValue; Work as C _j(t+ Δ t)-C _j(t)＜δ _cThe time, find the solution l according to formula (8) _jValue, the l that t is located constantly _jAverage

Length as blow-off pipe is

Then the position coordinates of pollution source does

The main flow of said software management system is:

S-101, initialization;

S-102, reception data;

Do S-103, data finish receiving?

S-104, if accept completion, carry out S-105; If do not accept completion, carry out S-102;

S-105, call the pollution source detecting module;

S-106, detect the existence of pollution source?

S-107, be to carry out S-108; , do not carry out S-102;

The related data that S-108, preservation detect the node of pollution source existence arrives database;

Whether the data recording of same node is greater than 2 times in S-109, the database

S-110, be to carry out S-113; , do not carry out S-111;

Does the time interval of writing down same node in S-111, current time and the database for the first time equal Δ t?

S-112, be to carry out S-102; , do not carry out S-111;

S-113, call pollution source diffusion phase analysis module;

S-114、C _i(t+Δt)-C _i(t)＞δ _c?

S-115, be, data are saved to not steady state (SS) data set, call first locating module; Not, data are saved to the steady state (SS) data set, call second locating module;

S-116, the value in the database is averaged, this mean value is preserved as last positioning result;

S-117, demonstration pollution source position coordinateses

Described detecting module main flow is:

S-201, device initialize;

S-202, accept new data message?

S-203, be to carry out S-204; , do not carry out S-202;

The data that S-204, extraction PC are accepted;

S-205, calculating are also judged C _i(t)-Cc>=10mg/l?

S-206, be to preserve the position (x of this node _i, y _i) and C _i(t) to database; , do not carry out S-202;

S-207, end.

Described analysis module main flow is:

S-301, device initialize;

The data message of same node in S-302, the extraction database;

S-303, judgement C _i(t+ Δ t)-C _i(t)＞δ _c

S-304, be, data are saved to not steady state (SS) data set, call first locating module; Not, data are saved to the steady state (SS) data set, call second locating module.

The described first locating module main flow is:

S-401, device initialize;

S-402, extract the data message of same node in the steady state (SS) data set not;

S-403, call the value that formula (7) is calculated l;

S-404, the value of positioning result l is saved in database;

S-405, end.

The described second locating module main flow is:

S-501, device initialize;

The data message of same node in S-502, the extraction steady state (SS) data set;

S-503, call the value that formula (8) is calculated l;

S-504, the value of positioning result l is saved in database;

S-505, end.

Owing to adopt technique scheme, the present invention meets the water pollution of actual lake water from the factory's discharging characteristics near bank or dykes and dams (being the impervious boundary), therefore has actual using value.In actual mechanical process, only need be with n sensor node stochastic distribution in the scope of offshore limit 1m, sensor node is connected with 1 terminal node with RF-wise, terminal node and 1 gateway wireless connections, gateway is connected with PC through Serial Port Line; In PC,, then can confirm the pollution source position coordinates, so easy to operate, simple according to setting up one dimension time continuous random diffusion model near the diffusion phase at impervious boundary pollution source place.

In addition, because the present invention adopts wireless senser, node is densely distributed, has increased the monitored area that covers, and is easy to the perception monitoring objective, and is with low cost; Sensor node distributes and does not receive the restriction in geographic position; In some special applications; When detecting target and be motion state or the mankind and can't directly monitor; The node of sensor can be accomplished the monitoring task well, and it is not strong to have overcome technological in the past operability, the shortcoming that involve great expense, the cycle is long.Especially the localization method that adopts uses Newton iteration method, is optimized, so possess very high precision.

Therefore, the present invention have workable, degree of accuracy is high, with low cost and meet the characteristics of actual blowdown situation.

Description of drawings

Fig. 1 is the main flow chart of management software in the PC;

Fig. 2 is the main flow chart of detecting module among Fig. 1;

Fig. 3 is the main flow chart of phase analysis module among Fig. 1;

Fig. 4 is the main flow chart of locating module 1 among Fig. 1;

Fig. 5 is the main flow chart of locating module 2 among Fig. 1.

Embodiment

Below in conjunction with accompanying drawing and embodiment the present invention being done further description, is not the restriction to its protection domain.

Embodiment 1

A kind of based on the surveying and localization method of wireless senser near the impervious boundary pollution source, the steps include:

Step 1, dispose wireless sensor node near the impervious boundary to be measured

Near impervious boundary (promptly in the lake water in bank or the dykes and dams 1m scope) 10 sensor nodes of stochastic distribution, the sensor node coordinate is (x to be measured _i, y _i) (i=1,2,3....10), sensor node (x _i, y _i) (i=1,2,3....10) mode with radio frequency is connected with terminal node, terminal node and gateway wireless connections, gateway is connected with PC through Serial Port Line; Software management system is housed in the PC, and software management system comprises pollution source detecting module, pollution source diffusion phase analysis module, first locating module and second locating module.

Step 2, near the detection of impervious boundary pollution entering the water

Set: water depth is f=5m, and water body initial ion concentration is Cc=0.1mg/L, has one section to stretch into the unknown blow-off pipe of middle of a lake length l near the impervious boundary; Known: the rate of release of these pollution source is Q=1.5m ³/ L, the concentration of pollution source is C ₀=5000mg/L; With the impervious boundary is the Y axle, stretches into blow-off pipe that direction is the X axle in the lake, is that initial point is set up rectangular coordinate system M with the intersection point of blow-off pipe and Y axle.

10 sensor node (x _i, y _i) (i=1,2,5 sensor node (x are arranged in 3....10) _i, y _i) (i=1,3,6,8,10) to detect the water body ion concentration be C _i(t), the water body ion concentration C that is detected _i(t) shown in table 1.1, i.e. C _i(t)-0.1mg/l>=10mg/l, then sensor node (x _i, y _i) (i=1,3,6,8,10) detect the existence near the impervious boundary pollution source.

Table 1.1 sensor node (x _i, y _i) (i=1,3,6,8,10) detect the water body ion concentration constantly at t

The steady state (SS) of step 3, pollution source diffusion is judged

Of step 2, sensor node (x _i, y _i) (i=1,3,6,8,10) detect the existence of pollution source constantly at t, the water body ion concentration is C _i(t), sensor node (x _i, y _i) (i=1,3,6,8,10) when time interval Δ t=540s, to record the water body ion concentration be C _i(t+540), the water body ion concentration C that is detected _i(t+540) shown in table 1.2:

Table 1.2 sensor node (x _i, y _i) (i=1,3,6,8,10) record the water body ion concentration when time interval Δ t=540s

Suppose that be isotropic near the impervious boundary pollution source when spreading, promptly the coefficient of diffusion of pollution source on x axle and y axle is D _x=D _y=0.1m ²/ s, δ _cFor the pollution source diffusion reaches stable concentration difference threshold values;

${\mathrm{\δ}}_c=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(C(x_i,y_i,t_a+\mathrm{\ΔT})-C(x_i,y_i,t_a))/n---\left(1\right)$

In the formula (1)

t _aFor pollution source begin to diffuse to time of steady state (SS), t _aUsually got 100 days;

Δ T is the time interval that pollution source diffuse to detect ion concentration after the steady state (SS), and Δ T got 1 day usually;

$C(x_1,y_1,t_a)=\frac{{\mathrm{QC}}_0}{2\sqrt{\mathrm{\πD}}f}[\frac{1}{r_1}\mathrm{erfc}\left(\frac{r_1}{2\sqrt{{\mathrm{Dt}}_a}}\right)+\frac{1}{\stackrel{\‾}{r_1}}\mathrm{erfc}\left(\frac{\stackrel{\‾}{r_1}}{2\sqrt{{\mathrm{Dt}}_a}}\right)]=248.8502\mathrm{mg}/l---\left(2\right)$

$C(x_1,y_1,t_a+\mathrm{\ΔT})=\frac{{\mathrm{QC}}_0}{2\sqrt{\mathrm{\πD}}f}[\frac{1}{r_1}\mathrm{erfc}\left(\frac{r_1}{2\sqrt{D(t_a+\mathrm{\ΔT})}}\right)+\frac{1}{\stackrel{\‾}{r_1}}\mathrm{erfc}\left(\frac{\stackrel{\‾}{r_1}}{2\sqrt{D(t_a+\mathrm{\ΔT})}}\right)]=248.8903\mathrm{mg}/l---\left(3\right)$

δ _c1＝C(x ₁,y ₁,t _a+ΔT)-C(x ₁,y ₁,t _a)＝0.0401m

In formula (2) and the formula (3):

erfc(x)＝1-erf(x) （4）

$\stackrel{\‾}{r_1}=\sqrt{{(x_1-L)}^2+{y_1}^2}=10.0209m---\left(5\right)$

$r_1=\sqrt{{(x_1-L)}^2+{y_1}^2}=9.9624m---\left(6\right)$

In formula (5) and the formula (6):

10m?≤L≤40m

In the present embodiment:

L＝10m；

In like manner can get δ _Ci(i=1,2,3....10), δ _CiShown in table 1.3:

Table 1.3 δ _Ci(i=1,2, value 3....10)

Can get by table 1.3:

${\mathrm{\δ}}_c=\underset{i=1}{\overset{10}{\mathrm{\Σ}}}(C(x_i,y_i,t_a+\mathrm{\ΔT})-C(x_i,y_i,t_a))/10=\underset{i=1}{\overset{10}{\mathrm{\Σ}}}{\mathrm{\δ}}_{c_i}=0.0401\mathrm{mg}/l$

When time interval Δ t=540s, sensor node (x _i, y _i) (i=1,3,6,8,10) ion concentration difference C of recording _i(t+540)-C _i(t) shown in table 1.4:

Table 1.4 sensor node (x _i, y _i) (i=1,3,6,8,10) ion concentration of recording is poor

Can find out from table 1.4, at time interval Δ t=540s inner sensor node (x _i, y _i) (i=1,3,6,8,10) ion concentration difference of recording is greater than δ _c=00401mg/l, then the pollution source diffusion does not reach steady state (SS).

Step 4, near the location of impervious boundary pollution source

In the present embodiment, get 10 sensor node (x near the impervious boundary stochastic distribution _i, y _i) (i=1,2, detect 5 node (x that pollution source exist in 3....10) _i, y _i) (i=1,3,6,8,10) position other 5 node (x _i, y _i) (i=2,4,5,7,9) because C _i(t)-01mg/l＜10mg/l do not detect the existence of pollution source, so do not participate in the location.

The pollution source diffusion does not reach steady state (SS), promptly works as C ₁(t+540)-C ₁(t)＞during 00401mg/l, through sensor node (x ₁, y ₁) length l of the blow-off pipe of locating constantly at t is separating of formula (7):

$\left\{\begin{array}{c}106.263-25.523=\frac{1.5*5000}{2*5\sqrt{\mathrm{\π}*0.1}}(\frac{1}{2\sqrt{0.1*t}}-\frac{1}{2\sqrt{0.1*(t+540)}})\\ 25.523=\frac{1.5*5000}{2*5\sqrt{\mathrm{\π}*0.1}}(\frac{1}{r1}-\frac{1}{2\sqrt{0.1*t}})\end{array}\right.---\left(7\right)$

In the formula (7):

$r_1=\sqrt{{(x_1-l)}^2+{y_1}^2}=9.2195\mathrm{mg}/l;$

Find the solution: l ₁=7.9356m.

In like manner can get: l ₂=7.4059m;

l ₃＝7.522m；

l ₄＝7.2618m；

l ₅＝7.4902m。

The l that t is located constantly _jAverage Length as blow-off pipe:

$\stackrel{\‾}{l}=\underset{j=1}{\overset{5}{\mathrm{\Σ}}}{l}_j/5=7.5231m;$

Then the position coordinates of pollution source is (7.5231,0).

The main flow of the said software management system of present embodiment is:

S-101, initialization;

S-102, reception data;

Do S-103, data finish receiving?

S-104, if accept completion, carry out S-105; If do not accept completion, carry out S-102;

S-105, call the pollution source detecting module;

S-106, detect the existence of pollution source?

S-107, be to carry out S-108; , do not carry out S-102;

The related data that S-108, preservation detect the node of pollution source existence arrives database;

Whether the data recording of same node is greater than 2 times in S-109, the database

S-110, be to carry out S-113; , do not carry out S-111;

Does the time interval of writing down same node in S-111, current time and the database for the first time equal Δ t?

S-112, be to carry out S-102; , do not carry out S-111;

S-113, call pollution source diffusion phase analysis module;

S-114、C _i(t+Δt)-C _i(t)＞δ _c?

S-115, be, data are saved to not steady state (SS) data set, call first locating module; Not, data are saved to the steady state (SS) data set, call second locating module;

S-116, the value in the database is averaged, this mean value is preserved as last positioning result;

S-117, demonstration pollution source position coordinateses

The described detecting module main flow of present embodiment is:

S-201, device initialize;

S-202, accept new data message?

S-203, be to carry out S-204; , do not carry out S-202;

The data that S-204, extraction PC are accepted;

S-205, calculating are also judged C _i(t)-Cc>=10mg/l?

S-206, be to preserve the position (x of this node _i, y _i) and C _i(t) to database; , do not carry out S-202;

S-207, end.

The described analysis module main flow of present embodiment is:

S-301, device initialize;

The data message of same node in S-302, the extraction database;

S-303, judgement C _i(t+ Δ t)-C _i(t)＞δ _c

S-304, be, data are saved to not steady state (SS) data set, call first locating module; Not, data are saved to the steady state (SS) data set, call second locating module;

The described first locating module main flow of present embodiment is:

S-401, device initialize;

S-402, extract the data message of same node in the steady state (SS) data set not;

S-403, call the value that formula (7) is calculated l;

S-404, the value of positioning result l is saved in database;

S-405, end.

The described second locating module main flow of present embodiment is:

S-501, device initialize;

The data message of same node in S-502, the extraction steady state (SS) data set;

S-503, call the value that formula (8) is calculated l;

S-504, the value of positioning result l is saved in database;

S-505, end.

Embodiment 2

A kind of based on the surveying and localization method of wireless senser near the impervious boundary pollution source, the steps include:

Step 1, dispose wireless sensor node near the impervious boundary

With embodiment 1.

Step 2, near the detection of impervious boundary pollution entering the water

Except that following technical parameter, all the other are with embodiment 1.

10 sensor node (x _i, y _i) (i=1,2,5 sensor node (x are arranged in 3....10) _i, y _i) (i=1,5,6,7,10) to detect the water body ion concentration be C _i(t), the water body ion concentration C that is detected _i(t) shown in table 2.1, i.e. C _i(t)-0.1mg/l>=10mg/l, then sensor node (x _i, y _i) (i=1,2,3....10) detect existence near the impervious boundary pollution source.

Table 2.1 sensor node (x _i, y _i) (i=1,5,6,7,10) water body ion concentration of detecting constantly at t

The steady state (SS) of step 3, pollution source diffusion is judged

Of step 2, sensor node (x _i, y _i) (i=1,5,6,7,10) detect the existence of pollution source constantly at t, the water body ion concentration is C _i(t), sensor node (x _i, y _i) (i=1,5,6,7,10) when time interval Δ t=3600s, to record the water body ion concentration be C _i(t+3600), the water body ion concentration C that is detected _i(t+3600) shown in table 2.2:

Table 2.2 sensor node (x _i, y _i) (i=1,5,6,7,10) record the water body ion concentration when time interval Δ t=3600s

Suppose that be isotropic near the impervious boundary pollution source when spreading, promptly the coefficient of diffusion of pollution source on x axle and y axle is D _x=D _y=0.1m ²/ s, δ _cReach the concentration difference threshold values of steady state (SS) for the pollution source diffusion;

${\mathrm{\δ}}_c=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(C(x_i,y_i,t_a+\mathrm{\ΔT})-C(x_i,y_i,t_a))/n---\left(1\right)$

In the formula (1)

t _aFor pollution source begin to diffuse to stable time, t _aUsually got 100 days;

Δ T is that pollution source diffuse to the time interval of getting ion concentration after stable, and Δ T got 1 day usually;

$C(x_1,y_1,t_a)=\frac{{\mathrm{QC}}_0}{2\sqrt{\mathrm{\πD}}f}[\frac{1}{r_1}\mathrm{erfc}\left(\frac{r_1}{2\sqrt{{\mathrm{Dt}}_a}}\right)+\frac{1}{\stackrel{\‾}{r_1}}\mathrm{erfc}\left(\frac{\stackrel{\‾}{r_1}}{2\sqrt{{\mathrm{Dt}}_a}}\right)]=248.8502\mathrm{mg}/l---\left(2\right)$

$C(x_1,y_1,t_a+\mathrm{\ΔT})=\frac{{\mathrm{QC}}_0}{2\sqrt{\mathrm{\πD}}f}[\frac{1}{r_1}\mathrm{erfc}\left(\frac{r_1}{2\sqrt{D(t_a+\mathrm{\ΔT})}}\right)+\frac{1}{\stackrel{\‾}{r_1}}\mathrm{erfc}\left(\frac{\stackrel{\‾}{r_1}}{2\sqrt{D(t_a+\mathrm{\ΔT})}}\right)]=248.8903\mathrm{mg}/l---\left(3\right)$

δ _c1＝C(x ₁,y ₁,t _a+ΔT)-C(x ₁,y ₁,t _a)＝00401m

In formula (2) and the formula (3):

erfc(x)＝1-erf(x) （4）

$\stackrel{\‾}{r_1}=\sqrt{{(x_1-L)}^2+{y_1}^2}=10.0209m---\left(5\right)$

$r_1=\sqrt{{(x_1-L)}^2+{y_1}^2}=9.9624m---\left(6\right)$

In formula (5) and the formula (6):

In 10m≤L≤40m present embodiment:

L＝40m；

In like manner can get δ _Ci(i=1,2,3....10), δ _CiShown in table 2.3:

Table 2.3 δ _Ci(i=1,2, value 3....10)

Can get by table 2.3:

${\mathrm{\δ}}_c=\underset{i=1}{\overset{10}{\mathrm{\Σ}}}(C(x_i,y_i,t_a+\mathrm{\ΔT})-C(x_i,y_i,t_a))/10=\underset{i=1}{\overset{10}{\mathrm{\Σ}}}{\mathrm{\δ}}_{c_i}=0.0401\mathrm{mg}/l$

When time interval Δ t=3600s, sensor node (x _i, y _i) (i=1,5,6,7,10) ion concentration difference C of recording _i(t+3600)-C _i(t) shown in table 2.4:

Table 2.4 sensor node (x _i, y _i) (i=1,5,6,7,10) ion concentration of recording is poor

Can find out from table 2.4, at time interval Δ t=3600s inner sensor node (x _i, y _i) (i=1,5) ion concentration difference of recording is greater than δ _c=0.0401mg/l, then the pollution source diffusion does not reach steady state (SS); Sensor node (x _i, y _i) (i=6,7,10) ion concentration difference of recording is less than or equal to δ _c=0.0401mg/l, then the pollution source diffusion reaches steady state (SS).

Step 4, near the location of impervious boundary pollution source

In the present embodiment, get 10 sensor node (x near the impervious boundary stochastic distribution _i, y _i) (i=1,2, detect 5 node (x that pollution source exist in 3....10) _i, y _i) (i=1,5,6,7,10) position other 5 node (x _i, y _i) (i=2,3,4,8,9) because C _i(t)-0.1mg/l＜10mg/l do not detect the existence of pollution source, so do not participate in the location.

The pollution source diffusion does not reach steady state (SS), promptly works as C ₁(t+3600)-C ₁(t)＞during 0.0401mg/l, through sensor node (x ₁, y ₁) length l of the blow-off pipe of locating constantly at t is separating of formula (7):

$\left\{\begin{array}{c}188.919-25.523=\frac{1.5*5000}{2*5\sqrt{\mathrm{\π}*0.1}}(\frac{1}{2\sqrt{0.1*t}}-\frac{1}{2\sqrt{0.1*(t+3600)}})\\ 25.523=\frac{1.5*5000}{2*5\sqrt{\mathrm{\π}*0.1}}(\frac{1}{r1}-\frac{1}{2\sqrt{0.1*t}})\end{array}\right.---\left(7\right)$

In the formula (7):

$r_1=\sqrt{{(x_1-l)}^2+{y_1}^2}=9.2195\mathrm{mg}/l.$

Find the solution: l ₁=6.638m

In like manner can get: l ₅=5.9294m;

The pollution source diffusion reaches steady state (SS), promptly works as C ₃(t+3600)-C ₃(t)≤during 0.0401mg/l, through sensor node (x ₆, y ₆) length l of the blow-off pipe of locating constantly at t is that formula (8) is separated:

$\left\{\begin{array}{c}{C}_i(t+3600)-C_i\left(t\right)=\frac{1.5*5000}{2*5\sqrt{\mathrm{\π}*0.1}}(\frac{1}{\sqrt{0.1*t}}-\frac{1}{\sqrt{0.1*(t+3600)}})\\ C_i\left(t\right)=\frac{1.5*5000}{2*5\sqrt{\mathrm{\π}*0.1}}(\frac{1}{r_3}+\frac{1}{\stackrel{\‾}{r_3}}-\frac{1}{\sqrt{0.1*t}})\end{array}\right.---\left(8\right)$

In the formula (8):

$\stackrel{\‾}{r_6}=\sqrt{{(x_6+l)}^2+{y_6}^2}=11.5169\mathrm{mg}/l;$

$r_6=\sqrt{{(x_6-l)}^2+{y_6}^2}=10.0319\mathrm{mg}/l.$

Find the solution: l ₆=10.0284m;

In like manner can get: l ₇=10.0319m;

l ₁₀＝10.0232m。

The l that t is located constantly _jAverage

Length as blow-off pipe:

$\stackrel{\‾}{l}=\underset{j=1}{\overset{5}{\mathrm{\Σ}}}{l}_j/5=8.5301m.$

Then the position coordinates of pollution source is (8.5301,0).

The main flow of the software management system of present embodiment 2 is with embodiment 1.

Embodiment 3

A kind of based on the surveying and localization method of wireless senser near the impervious boundary pollution source, the steps include:

Step 1, deployment wireless sensor node

Remove sensor node (x _i, y _i) (i=1,2, be beyond 15 3....15), all the other are with embodiment 1.

Step 2, near the detection of impervious boundary pollution entering the water

Except that following technical parameter, all the other are with embodiment 1.

15 sensor node (x _i, y _i) (i=1,2,6 sensor node (x are arranged in 3....15) _i, y _i) (i=1,5,6,7,10,13) to detect the water body ion concentration be C _i(t), the water body ion concentration C that is detected _i(t) shown in table 3.1, i.e. C _i(t)-01mg/l>=10mg/l, then sensor node (x _i, y _i) (i=1,5,6,7,10,13) detect the existence near the impervious boundary pollution source.

Table 3.1 sensor node (x _i, y _i) (i=1,5,6,7,10,13) detect the water body ion concentration constantly at t

The steady state (SS) of step 3, pollution source diffusion is judged

Of step 2, sensor node (x _i, y _i) (i=1,5,6,7,10,13) detect the existence of pollution source constantly at t, the water body ion concentration is C _i(t), sensor node (x _i, y _i) (i=1,5,6,7,10,13) when time interval Δ t=3600s, to record the water body ion concentration be C _i(t+3600), the water body ion concentration C that is detected _i(t+3600) shown in table 3.2:

Table 3.2 sensor node (x _i, y _i) (i=1,5,6,7,10,13) record the water body ion concentration when time interval Δ t=3600s

Suppose that be isotropic near the impervious boundary pollution source when spreading, promptly the coefficient of diffusion of pollution source on x axle and y axle is D _x=D _y=0.1m ²/ s, δ _cReach the concentration difference threshold values of steady state (SS) for the pollution source diffusion;

${\mathrm{\δ}}_c=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(C(x_i,y_i,t_a+\mathrm{\ΔT})-C(x_i,y_i,t_a))/n---\left(1\right)$

In the formula (1)

t _aFor pollution source begin to diffuse to stable time, t _aUsually got 100 days,

Δ T is that pollution source diffuse to the time interval of getting ion concentration after stable, and Δ T got 1 day usually,

$C(x_1,y_1,t_a)=\frac{{\mathrm{QC}}_0}{2\sqrt{\mathrm{\πD}}f}[\frac{1}{r_1}\mathrm{erfc}\left(\frac{r_1}{2\sqrt{{\mathrm{Dt}}_a}}\right)+\frac{1}{\stackrel{\‾}{r_1}}\mathrm{erfc}\left(\frac{\stackrel{\‾}{r_1}}{2\sqrt{{\mathrm{Dt}}_a}}\right)]=236.1102\mathrm{mg}/l---\left(2\right)$

$C(x_1,y_1,t_a+\mathrm{\ΔT})=\frac{{\mathrm{QC}}_0}{2\sqrt{\mathrm{\πD}}f}[\frac{1}{r_1}\mathrm{erfc}\left(\frac{r_1}{2\sqrt{D(t_a+\mathrm{\ΔT})}}\right)+\frac{1}{\stackrel{\‾}{r_1}}\mathrm{erfc}\left(\frac{\stackrel{\‾}{r_1}}{2\sqrt{D(t_a+\mathrm{\ΔT})}}\right)]=236.1503\mathrm{mg}/l---\left(3\right)$

δ _c1＝C(x ₁,y ₁,t _a+ΔT)-C(x ₁,y ₁,t _a)＝0.0401m

In formula (2) and the formula (3):

erfc(x)＝1-erf(x) （4）

$\stackrel{\‾}{r_1}=\sqrt{{(x_1-L)}^2+{y_1}^2}=11.1485m---\left(5\right)$

$r_1=\sqrt{{(x_1-L)}^2+{y_1}^2}=10.7838m---\left(6\right)$

In formula (5) and the formula (6):

10m≤L≤40m

In the present embodiment:

L＝20m；

In like manner can get δ _Ci(i=1,2,3....15) shown in table 3.3:

Table 3.3 δ _Ci(i=1,2, value 3....15)

Can get by table 3.3:

${\mathrm{\δ}}_c=\underset{i=1}{\overset{15}{\mathrm{\Σ}}}(C(x_i,y_i,t_a+\mathrm{\ΔT})-C(x_i,y_i,t_a))/15=\underset{i=1}{\overset{15}{\mathrm{\Σ}}}{\mathrm{\δ}}_{c_i}=0.0401\mathrm{mg}/l$

When time interval Δ t=3600s, sensor node (x _i, y _i) (i=1,5,6,7,10,13) ion concentration difference C of recording _i(t+3600)-C _i(t) shown in table 3.4:

Table 3.4 sensor node (x _i, y _i) (i=1,5,6,7,10,13) ion concentration of recording is poor

Can find out from table 3.4, at time interval Δ t=3600s inner sensor node (x _i, y _i) (i=1,5,6,7,10,13) ion concentration difference of recording is less than or equal to δ _c=0.0401mg/l, then the pollution source diffusion reaches steady state (SS).

Step 4, near the location of impervious boundary pollution source, get 15 sensor node (x in the present embodiment near the impervious boundary stochastic distribution _i, y _i) (i=1,2, detect 6 node (x that pollution source exist in 3....15) _i, y _i) (i=1,5,6,7,10,13) position other 9 node (x _i, y _i) (i=2,3,4,8,9,11,12,14,15) because C _i(t)-0.1mg/l＜10mg/l do not detect the existence of pollution source, so do not participate in the location;

The pollution source diffusion reaches steady state (SS), promptly works as C ₁(t+3600)-C ₁(t)＜during 0.0401mg/l, through sensor node (x ₁, y ₁) length l of the blow-off pipe of locating constantly at t is separating of formula (7);

$\left\{\begin{array}{c}236.1503-236.1102=\frac{1.5*5000}{2*5\sqrt{\mathrm{\π}*0.1}}(\frac{1}{\sqrt{0.1*t}}-\frac{1}{\sqrt{0.1*(t+3600)}})\\ 236.1102=\frac{1.5*5000}{2*5\sqrt{\mathrm{\π}*0.1}}(\frac{1}{r_1}+\frac{1}{\stackrel{\‾}{r_1}}-\frac{1}{\sqrt{0.1*t}})\end{array}\right.---\left(7\right)$

In the formula (7):

$\stackrel{\‾}{r_1}=\sqrt{{(x_1+l)}^2+{y_1}^2}=11.1485\mathrm{mg}/l,$

$r_1=\sqrt{{(x_1-l)}^2+{y_1}^2}=10.7838\mathrm{mg}/l;$

Find the solution: l ₁=10.0304m.

In like manner can get: l ₅=10.025m;

l ₆＝10.0238m；

l ₇＝10.0364m；

l ₁₀＝10.026m；

l ₁₃＝10.0237m。

The l that t is located constantly _jAverage

Length as blow-off pipe:

$\stackrel{\‾}{l}=\underset{j=1}{\overset{6}{\mathrm{\Σ}}}{l}_j/6=10.0276m;$

Then the position coordinates of pollution source is (10.0276,0).

The main flow of the software management system of present embodiment 3 is with embodiment 1.

This embodiment meets the water pollution of actual lake water from the factory's discharging characteristics near bank or dykes and dams (being the impervious boundary), therefore has actual using value.In actual mechanical process, only need be with n sensor node stochastic distribution in the scope of offshore limit 1m, sensor node is connected with 1 terminal node with RF-wise, terminal node and 1 gateway wireless connections, gateway is connected with PC through Serial Port Line; In PC, set up one-dimensional random diffusion time continuously near impervious boundary pollution source diffusion model, then can confirm the pollution source position coordinates according to the diffusion phase at pollution source places, thus easy to operate, simply.

In addition, because this embodiment adopts wireless senser, node is densely distributed, has increased the monitored area that covers, and is easy to the perception monitoring objective, and is with low cost; Sensor node distributes and does not receive the restriction in geographic position; In some special applications; When detecting target and be motion state or the mankind and can't directly monitor; The node of sensor can well be accomplished the monitoring task, and it is not strong to have overcome technological in the past operability, the shortcoming that involve great expense, the cycle is long.Especially the localization method that adopts uses Newton iteration method, is optimized, so possess very high precision.

Therefore, the present invention have workable, degree of accuracy is high, with low cost and meet the characteristics of actual blowdown situation.

Claims (6)

1. one kind based on the surveying and localization method near the impervious boundary pollution source of wireless senser, it is characterized in that carrying out as follows:

Step 1, dispose wireless sensor node near the impervious boundary to be measured

Near an impervious boundary stochastic distribution n sensor node, the sensor node coordinate is (x to be measured _i, y _i) (i=1,2,3...n>=3), sensor node is connected with terminal node with the mode of radio frequency, terminal node and gateway wireless connections, and gateway is connected with PC through Serial Port Line; Software management system is housed in the PC, and software management system comprises pollution source detecting module, pollution source diffusion phase analysis module, first locating module and second locating module;

Step 2, near the detection of impervious boundary pollution entering the water

Set: water depth is f, and water body initial ion concentration is Cc, has one section to stretch into the unknown blow-off pipe of middle of a lake length l near the impervious boundary; Known: the rate of release of this blow-off pipe is Q, and the concentration of pollution source is C ₀With the impervious boundary is the Y axle, stretches into blow-off pipe that direction is the X axle in the lake, is that initial point is set up rectangular coordinate system M with the intersection point of blow-off pipe and Y axle;

Sensor node (x _i, y _i) to detect the water body ion concentration be C _i(t), if C _i(t)-Cc>=10mg/l, then sensor node (x _i, y _i) detect existence near the impervious boundary pollution source;

The steady state (SS) of step 3, pollution source diffusion is judged

Sensor node (x _i, y _i) detecting the existence of pollution source constantly at t, the water body ion concentration is C _i(t), sensor node (x _i, y _i) when time interval Δ t, to record ion concentration be C _i(t+ Δ t);

Suppose that be isotropic near the impervious boundary pollution source when spreading, promptly the coefficient of diffusion of pollution source on x axle and y axle is D _x=D _y=D, δ _cFor pollution source spread the concentration difference threshold values that reaches steady state (SS),

${\mathrm{\δ}}_c=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(C(x_i,y_i,t_a+\mathrm{\ΔT})-C(x_i,y_i,t_a))/n---\left(1\right)$

In the formula (1):

t _aFor pollution source begin to diffuse to time of steady state (SS), t _aUsually got 100 days,

Δ T is the time interval that pollution source diffuse to detect ion concentration after the steady state (SS), and Δ T got 1 day usually,

$C(x_i,y_i,t_a)=\frac{{\mathrm{QC}}_0}{2\sqrt{\mathrm{\πD}}f}[\frac{1}{r_i}\mathrm{erfc}\left(\frac{r_i}{2\sqrt{{\mathrm{Dt}}_a}}\right)+\frac{1}{\stackrel{\‾}{r_i}}\mathrm{erfc}\left(\frac{\stackrel{\‾}{r_i}}{2\sqrt{{\mathrm{Dt}}_a}}\right)]---\left(2\right)$

$C(x_i,y_i,t_a+\mathrm{\ΔT})=\frac{{\mathrm{QC}}_0}{2\sqrt{\mathrm{\πD}}f}[\frac{1}{r_i}\mathrm{erfc}\left(\frac{r_i}{2\sqrt{D(t_a+\mathrm{\ΔT})}}\right)+\frac{1}{\stackrel{\‾}{r_i}}\mathrm{erfc}\left(\frac{\stackrel{\‾}{r_i}}{2\sqrt{D(t_a+\mathrm{\ΔT})}}\right)]---\left(3\right)$

In formula (2) and the formula (3):

erfc(x)＝1-erf(x) （4）

$\stackrel{\‾}{r_i}=\sqrt{{(x_i-L)}^2+{y_i}^2}---\left(5\right)$

$r_i=\sqrt{{(x_i-L)}^2+{y_i}^2}---\left(6\right)$

In formula (5) and the formula (6):

10m≤L≤40m；

If at time interval Δ t inner sensor node (x _i, y _i) the ion concentration difference that records is greater than δ _c, then the pollution source diffusion does not reach steady state (SS); If at time interval Δ t inner sensor node (x _i, y _i) the ion concentration difference that records is less than or equal to δ _c, then the pollution source diffusion reaches steady state (SS);

Step 4, near the location of impervious boundary pollution source

(1) when spreading, pollution source do not reach steady state (SS), i.e. C _i(t+ Δ t)-C _i(t)＞δ _cThe time, through sensor node (x _i, y _i) length l of the blow-off pipe of locating constantly at t is separating of formula (7):

$\left\{\begin{array}{c}{C}_i(t+\mathrm{\Δt})-C_i\left(t\right)=\frac{{\mathrm{QC}}_0}{2f\sqrt{\mathrm{\πD}}}(\frac{1}{2\sqrt{\mathrm{Dt}}}-\frac{1}{2\sqrt{D(t+\mathrm{\Δt})}})\\ C_i\left(t\right)=\frac{{\mathrm{QC}}_0}{2f\sqrt{\mathrm{\πD}}}(\frac{1}{r_i}-\frac{1}{2\sqrt{\mathrm{Dt}}})\end{array}\right.---\left(7\right)$

In the formula (7):

$r_i=\sqrt{{(x_i-l)}^2+{y_i}^2};$

(2) when spreading, pollution source reach steady state (SS), i.e. C _i(t+ Δ t)-C _i(t)≤δ _cThe time, through sensor node (x _i, y _i) length l of the blow-off pipe of locating constantly at t is separating of formula (8):

$\left\{\begin{array}{c}{C}_i(t+\mathrm{\Δt})-C_i\left(t\right)=\frac{{\mathrm{QC}}_0}{2f\sqrt{\mathrm{\πD}}}(\frac{1}{\sqrt{\mathrm{Dt}}}-\frac{1}{\sqrt{D(t+\mathrm{\Δt})}})\\ C_i\left(t\right)=\frac{{\mathrm{QC}}_0}{2f\sqrt{\mathrm{\πD}}}(\frac{1}{r_i}+\frac{1}{\stackrel{\‾}{r_i}}-\frac{1}{\sqrt{\mathrm{Dt}}})\end{array}\right.---\left(8\right)$

In the formula (8):

$\stackrel{\‾}{r_i}=\sqrt{{(x_i+l)}^2+{y_i}^2},$

$r_i=\sqrt{{(x_i-l)}^2+{y_i}^2};$

(3) in actual measurement, use n sensor node (x near the impervious boundary stochastic distribution _i, y _i) in detect k the node (x that pollution source exist _j, y _j) (j=1,2,3...k, 3≤k≤n) position works as C _j(t+ Δ t)-C _j(t)>=δ _cThe time, find the solution l according to formula (7) _jValue; Work as C _j(t+ Δ t)-C _j(t)＜δ _cThe time, find the solution l according to formula (8) _jValue, the l that t is located constantly _jAverage

Length as blow-off pipe is

Then the position coordinates of pollution source does

2. according to claim 1 based on the surveying and localization method of wireless senser near the impervious boundary pollution source, it is characterized in that the main flow of said software management system is:

S-101, initialization;

S-102, reception data;

Do S-103, data finish receiving?

S-104, if accept completion, carry out S-105; If do not accept completion, carry out S-102;

S-105, call the pollution source detecting module;

S-106, detect the existence of pollution source?

S-107, be to carry out S-108; , do not carry out S-102;

The related data that S-108, preservation detect the node of pollution source existence arrives database;

Whether the data recording of same node is greater than 2 times in S-109, the database

S-110, be to carry out S-113; , do not carry out S-111;

Does the time interval of writing down same node in S-111, current time and the database for the first time equal Δ t?

S-112, be to carry out S-102; , do not carry out S-111;

S-113, call pollution source diffusion phase analysis module;

S-114、C _i(t+Δt)-C _i(t)＞δ _c?

S-115, be, data are saved to not steady state (SS) data set, call first locating module; Not, data are saved to the steady state (SS) data set, call second locating module;

S-116, the value in the database is averaged, this mean value is preserved as last positioning result;

S-117, demonstration pollution source position coordinateses

3. according to claim 2 based on the surveying and localization method of wireless senser near the impervious boundary pollution source, it is characterized in that described detecting module main flow is:

S-201, device initialize;

S-202, accept new data message?

S-203, be to carry out S-204; , do not carry out S-202;

The data that S-204, extraction PC are accepted;

S-205, calculating are also judged C _i(t)-Cc>=10mg/l?

S-206, be to preserve the position (x of this node _i, y _i) and C _i(t) to database; , do not carry out S-202;

S-207, end.

4. according to claim 2 based on the surveying and localization method of wireless senser near the impervious boundary pollution source, it is characterized in that described analysis module main flow is:

S-301, device initialize;

The data message of same node in S-302, the extraction database;

S-303, judgement C _i(t+ Δ t)-C _i(t)＞δ _c

S-304, be, data are saved to not steady state (SS) data set, call first locating module; Not, data are saved to the steady state (SS) data set, call second locating module;

5. according to claim 2 based on the surveying and localization method of wireless senser near the impervious boundary pollution source, it is characterized in that the described first locating module main flow is:

S-401, device initialize;

S-402, extract the data message of same node in the steady state (SS) data set not;

S-403, call the value that formula (7) is calculated l;

S-404, the value of positioning result l is saved in database;

S-405, end.

6. according to claim 2 based on the surveying and localization method of wireless senser near the impervious boundary pollution source, it is characterized in that the described second locating module main flow is:

S-501, device initialize;

The data message of same node in S-502, the extraction steady state (SS) data set;

S-503, call the value that formula (8) is calculated l;

S-504, the value of positioning result l is saved in database;

S-505, end.

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