CN103969699A - Fire source location method based on sensor array and dynamic optimization - Google Patents

Abstract

The invention relates to a fire source location method based on a sensor array and dynamic optimization. The method includes the first step of converting temperature signals collected in the sensor array into azimuth angle estimation, the second step of calculating a fusion angle estimation value and the variance of the fusion angle estimation value of the sensor array through a mathematical statistic method, the third step of obtaining coordinates of a vertex of the boundary of a fire source location area according to analytical geometry knowledge, the fourth step of establishing a dynamic optimization objective function according to coordinate information of the vertex of the boundary, and the fifth step of calculating the position of a fire source through a convex optimization tool CVX. Through the method based on dynamic optimization, the coordinates of the fire source and the location error radius of the fire source can be calculated simultaneously. Thus, compared with a traditional location method, the fire source location method based on the sensor array and dynamic optimization has the advantages of being capable of ensuring estimation accuracy, more reasonable and more effective.

Description

A kind of burning things which may cause a fire disaster localization method based on sensor array and dynamic optimization

Technical field

The invention belongs to fire locating technical field, be specifically related to a kind of burning things which may cause a fire disaster localization method based on sensor array and dynamic optimization.

Background technology

Along with the develop rapidly of China's economic construction, Process of Urbanization Construction make rapid progress, the trend of social city is more and more obvious.A large amount of gatherings of population, building, property are relative concentrated with industry, give the day by day serious hidden danger of having brought of fire, and have increased the weight of the harm causing when fire occurs.Detecting fire accurately, reliably and take appropriate measures at fire early period of origination, is a kind of effective way that reduces the loss that causes of fire.Therefore, fire source point location technology becomes the important step in the middle of auto fire-detection and auto-putting-out, also for evacuating personnel provides feasible path.

Existing fire locating method or system are taking image-type fire locating detection system as main, but this type systematic is not suitable in private place or the occasion of not wishing to be subject to watching attentively in the external world under use, thereby fire locating method research based on array of temperature sensor becomes main flow gradually.This fire locating system is mainly used in the fire locating in restricted clearance; price is very cheap compared with image shape fire locating system; constructability is installed, and can well protect the personnel of protected field and the personal secrets of property, meets the needs of human oriented design.

The fire detecting method that Thomas Kaiser delivered based on array of temperature sensor in 2000, after this method just becomes one of main method of the early stage location of fire source point.The people such as Ge Quanbo propose the burning things which may cause a fire disaster localization method (patent No.: ZL201110175035.5) based on sensor array statistical nature, and the method, based on statistical modeling thought spread estimation, has been improved former methodical location estimation precision.Not enough, first this method must estimate fire location, then could be taking fire location as the center of circle, and approximate solution calculates evaluated error radius.In fact, the rationality of this design philosophy can not be guaranteed in theory, also needs to be verified in practice.

Summary of the invention

The object of the invention is to for the existing deficiency based on sensor array location technology, a kind of burning things which may cause a fire disaster localization method based on sensor array and dynamic optimization is provided.

First the inventive method is converted into the temperature signal gathering in sensor array position angle and estimates; Then utilize mathematical statistics method calculating sensor array to merge angle estimated value and variance thereof; Then try to achieve the border vertices coordinate of burning things which may cause a fire disaster locating area according to cartesian geometry knowledge; Finally set up dynamic optimization objective function according to border vertices coordinate information, utilize protruding optimization tool CVX to calculate the position of burning things which may cause a fire disaster.Specifically comprise the following steps:

Step 1: build sensor array group

Arrange two array of temperature sensor A and B, each array is made up of 4 negative temperature coefficient temperature sensors respectively; Two sensor array A and B are arranged in to the position that ceiling any side in room is kept to the side, and distance is L.

Step 2: temperature signal collection and pre-service

Adopt far field positioning principle, array A and array B are converted into angle estimation by the temperature signal collecting respectively with variance is respectively with wherein k is discrete time mark.

Step 3: determine burning things which may cause a fire disaster locating area border vertices coordinate

Utilize the angle estimation result of array A and array B, burning things which may cause a fire disaster can be positioned in a quadrilateral area.Adopt analytic geometry method to solve the coordinate (x on each summit _i, y _i), wherein i=1,2,3,4.

Step 4: set up dynamic optimization objective function

If the source point coordinate that fire occurs is (x _s, y _s), effectively evaluated error radius is R.According to the border vertices coordinate (x obtaining in step 3 _i, y _i), can set up dynamic optimization objective function is minR ², constraint condition is: (x _s-x _i) ²+ (y _s-y _i) ²≤ R ², (i=1,2,3,4), wherein min represents minimization function.

Step 5: utilize the optimization problem of setting up in CVX kit solution procedure 4, and export net result.

Beneficial effect of the present invention: traditional localization method need first be estimated burning things which may cause a fire disaster coordinate, then utilizes angular bisector method further to solve error range.The method based on dynamic optimization that the present invention proposes can be calculated burning things which may cause a fire disaster source point coordinate and positioning error radius simultaneously.Therefore,, compared to traditional localization method, new method more rationally effectively.

Brief description of the drawings

Fig. 1 is dual sensor array burning things which may cause a fire disaster positioning principle figure

Fig. 2 is the inventive method process flow diagram

Embodiment

Below in conjunction with drawings and Examples, the present invention will be further described.

Burning things which may cause a fire disaster positioning principle based on dual sensor array as shown in Figure 1.Array A and array B form by 4 negative temperature coefficient sensors.Suppose that in array, the distance between each sensor is less than the distance L between array, also much smaller than the distance between array and burning things which may cause a fire disaster.Generally speaking, sensor array is arranged in to the position of quiet wind restricted clearance ceiling one end near corner.

Burning things which may cause a fire disaster dynamic positioning method flow process based on sensor array and dynamic optimization as shown in Figure 2.In the time that fire occurs, in sensor array, the temperature signal of collection is sent to host computer processing by each temperature sensor, obtains corresponding angle estimation signal; Then utilize mathematical statistics method calculating sensor array to merge angle estimated value and variance thereof; Moreover try to achieve the border vertices coordinate of burning things which may cause a fire disaster locating area according to cartesian geometry knowledge; Then set up dynamic optimization objective function according to border vertices coordinate information; Finally utilize protruding optimization tool CVX to calculate the position of burning things which may cause a fire disaster.Below in conjunction with burning things which may cause a fire disaster positioning principle figure and this flow process, introduce in detail each implementation step.

Step 1: initial parameter is set

Coordinate figure (the x of array A is set as shown in Figure 1, _a, y _a), the coordinate figure (x of array B _b, y _b) can be expressed as (x _a+ L, y _a), select reference frame, make the coordinate figure of array A and B all be positioned at first quartile.

Step 2: temperature signal collection and pre-service

For sensor array A, adopt far field positioning principle, can convert 3 position angles estimations to by collecting temperature signal in k moment array wherein j=1,2,3.According to mathematical statistics knowledge, estimation is merged at the position angle of array A and variance for

$\left\{\begin{array}{c}{\widehat{\mathrm{\α}}}_A\left(k\right)=\frac{1}{3}\underset{j=1}{\overset{3}{\mathrm{\Σ}}}{\widehat{\mathrm{\α}}}_{A,j}\left(k\right)\\ {\mathrm{\σ}}_A^2\left(k\right)=\frac{1}{2}\underset{j=1}{\overset{3}{\mathrm{\Σ}}}{[{\widehat{\mathrm{\α}}}_{A,j}\left(k\right)-{\widehat{\mathrm{\α}}}_A\left(k\right)]}^2\end{array}\right.---\left(1\right)$

Similarly, for sensor and array B, can convert 3 position angles estimations to by collecting temperature signal in k moment array wherein j=1,2,3.So, estimation is merged at the position angle of array B and variance for

$\left\{\begin{array}{c}{\widehat{\mathrm{\α}}}_B\left(k\right)=\frac{1}{3}\underset{j=1}{\overset{3}{\mathrm{\Σ}}}{\widehat{\mathrm{\α}}}_{B,j}\left(k\right)\\ {\mathrm{\σ}}_B^2\left(k\right)=\frac{1}{2}\underset{j=1}{\overset{3}{\mathrm{\Σ}}}{[{\widehat{\mathrm{\α}}}_{B,j}\left(k\right)-{\widehat{\mathrm{\α}}}_B\left(k\right)]}^2\end{array}\right.---\left(2\right)$

Step 3: determine burning things which may cause a fire disaster locating area border vertices coordinate

As shown in Figure 1, order ${\widehat{\mathrm{\α}}}_A^U\left(k\right)={\widehat{\mathrm{\α}}}_A\left(k\right)+{\mathrm{\σ}}_A\left(k\right),$ ${\widehat{\mathrm{\α}}}_A^L\left(k\right)={\widehat{\mathrm{\α}}}_A\left(k\right)+{\mathrm{\σ}}_A\left(k\right);$ ${\widehat{\mathrm{\α}}}_B^U\left(k\right)={\widehat{\mathrm{\α}}}_B\left(k\right)+{\mathrm{\σ}}_B\left(k\right),$ ${\widehat{\mathrm{\α}}}_B^U\left(k\right)={\widehat{\mathrm{\α}}}_B\left(k\right)+{\mathrm{\σ}}_B\left(k\right);$ Fire source point necessarily drops on quadrilateral C ₁c ₂c ₃c ₄in region.Obviously, the coordinate (x on each summit _i, y _i) (i=1,2,3,4) can solve according to analytic geometry method, detailed process is as follows:

First, make straight line l _islope be k _i, (i=1,2,3,4), have

$\left\{\begin{array}{c}{k}_1=\tan \left[{\widehat{\mathrm{\α}}}_A^L\left(k\right)\right]\\ k_2=\tan \left[{\widehat{\mathrm{\α}}}_A^U\left(k\right)\right]\\ k_3=\tan \left[{\widehat{\mathrm{\α}}}_B^L\left(k\right)\right]\\ k_4=\tan \left[{\widehat{\mathrm{\α}}}_B^U\left(k\right)\right]\end{array}\right.---\left(3\right)$

In above formula, tan represents tan.

Summit C ₁for straight line l ₁and l ₄intersection point, therefore (x ₁, y ₁) meet

$\left\{\begin{array}{c}(y_1-y_A)=k_1(x_1-x_A)\\ (y_1-y_B)=k_4(k_1-x_B)\end{array}---\left(4\right)\right.$

Solve above-mentioned linear equation in two unknowns group, can obtain

$\left\{\begin{array}{c}{x}_1=\frac{k_1{x}_A-k_4-x_B-(y_A-y_B)}{k_1-k_4}\\ y_1=\frac{\frac{y_A}{k_1}-\frac{y_B}{k_4}-(x_A-x_B)}{\frac{1}{k_1}-\frac{1}{k_4}}\end{array}\right.---\left(5\right)$

Summit C ₂for straight line l ₂and l ₄intersection point, therefore (x ₂, y ₂) meet

$\left\{\begin{array}{c}(y_2-y_A)=k_2(x_2-x_A)\\ (y_2-y_B)=k_4(x_2-x_B)\end{array}\right.---\left(6\right)$

Solve above-mentioned linear equation in two unknowns group, can obtain

$\left\{\begin{array}{c}{x}_2=\frac{k_2{x}_A-k_4-x_B-(y_A-y_B)}{k_2-k_4}\\ y_2=\frac{\frac{y_A}{k_2}-\frac{y_B}{k_4}-(x_A-x_B)}{\frac{1}{k_2}-\frac{1}{k_4}}\end{array}\right.---\left(7\right)$

Summit C ₃for straight line l ₂and l ₃intersection point, therefore (x ₃, y ₃) meet

$\left\{\begin{array}{c}(y_3-y_A)=k_2(x_3-x_A)\\ (y_3-y_B)=k_3(x_3-x_B)\end{array}\right.---\left(8\right)$

Solve above-mentioned linear equation in two unknowns group, can obtain

$\left\{\begin{array}{c}{x}_3=\frac{k_2{x}_A-k_3-x_B-(y_A-y_B)}{k_2-k_3}\\ y_3=\frac{\frac{y_A}{k_2}-\frac{y_B}{k_3}-(x_A-x_B)}{\frac{1}{k_2}-\frac{1}{k_3}}\end{array}\right.---\left(9\right)$

Summit C ₄for straight line l ₁and l ₃intersection point, therefore (x ₄, y ₄) meet

$\left\{\begin{array}{c}(y_4-y_A)=k_1(x_4-x_A)\\ (y_4-y_B)=k_3(x_4-x_B)\end{array}\right.---\left(10\right)$

Solve above-mentioned linear equation in two unknowns group, can obtain

$\left\{\begin{array}{c}{x}_4=\frac{k_1{x}_A-k_3{x}_B-(y_A-y_B)}{k_1-k_3}\\ y_4=\frac{\frac{y_A}{k_1}-\frac{y_B}{k_3}-(x_A-x_B)}{\frac{1}{k_1}-\frac{1}{k_3}}\end{array}\right.---\left(11\right)$

Step 4: set up dynamic optimization objective function

If the source point coordinate that fire occurs is (x _s, y _s), effectively evaluated error radius is R.According to the border vertices coordinate (x obtaining in step 3 _i, y _i), the process that solves burning things which may cause a fire disaster coordinate and error radius can be described as following optimization problems:

minR ²

(12)

s.t.(x _s-x _i) ²+(y _s-y _i) ²≤R ²(i＝1,2,3,4)

Wherein, min represents minimization function, and s.t. represents constraint condition.Obviously, the difficult non-protruding optimization problem to solve of formula (12) can be translated into 4 following protruding optimization problems of equivalence, for this reason

min(x _s-x ₁) ²+(y _s-y ₁) ²

(13)

s.t.(x _s-x _p) ²+(y _s-y _p) ²≤(x _s-x ₁) ²+(y _s-y ₁) ²(p＝2,3,4)

min(x _s-x ₂) ²+(y _s-y ₂) ²

(14)

s.t.(x _s-x _p) ²+(y _s-y _p) ²≤(x _s-x ₂) ²+(y _s-y ₂) ²(p＝1,3,4)

min(x _s-x ₃) ²+(y _s-y ₃) ²

(15)

s.t.(x _s-x _p) ²+(y _s-y _p) ²≤(x _s-x ₃) ²+(y _s-y ₃) ²(p＝1,2,4)

min(x _s-x ₄) ²+(y _s-y ₄) ²

(16)

s.t.(x _s-x _p) ²+(y _s-y _p) ²≤(x _s-x ₄) ²+(y _s-y ₄) ²(p＝1,2,3)

For the ease of utilizing CVX optimization tool direct solution, the described protruding optimization problem in formula (14)～(16) further equivalence is rewritten as:

min(x _s-x _i) ²+(y _s-y _i) ²

$s.t.\left\{\begin{array}{c}{2x}_s(x_i-x_p)+{2y}_s(y_i-y_p)\≤x_i^2-x_p^2+y_i^2-y_p^2\\ (i.p=\mathrm{1,2,3,4};i\≠p)\\ x_s\≥0\\ y_s\≥0\end{array}\right.---\left(17\right)$

Step 5: solving-optimizing problem, and Output rusults.

Utilize the described optimization problem of CVX kit solution procedure 4 Chinese styles (17), the optimum solution of i optimization problem of note is (i=1,2,3,4), error radius is

$R_i^2\left(k\right)={({\hat{x}}_{s,i}\left(k\right)-x_p)}^2+{({\hat{y}}_{s,i}\left(k\right)-y_p)}^2---\left(18\right)$

Therefore, the error radius of global optimum is

$R^2\left(k\right)=R_q^2\left(k\right)=\min \{R_1^2\left(k\right),R_2^2\left(k\right),R_3^2\left(k\right),R_4^2\left(k\right)\}---\left(19\right)$

Wherein, q=1,2,3,4, thereby corresponding burning things which may cause a fire disaster coordinate is estimated as

$\left\{\begin{array}{c}{\hat{x}}_s\left(k\right)={\hat{x}}_{s,p}\left(k\right)\\ {\hat{y}}_s\left(k\right)={\hat{y}}_{s,p}\left(k\right)\end{array}\right.---\left(20\right)$ 。

Claims (1)

1. the burning things which may cause a fire disaster localization method based on sensor array and dynamic optimization, is characterized in that the method comprises the following steps:

Step 1: build sensor array group

Arrange two array of temperature sensor A and B, each array is made up of four negative temperature coefficient temperature sensors respectively; Two array of temperature sensor A and B are arranged in to the position that ceiling any side in room is kept to the side, and distance is L;

Step 2: temperature signal collection and pre-service

Adopt far field positioning principle, array A and array B are converted into angle estimation by the temperature signal collecting respectively with variance is respectively with wherein k is discrete time mark;

Step 3: determine burning things which may cause a fire disaster locating area border vertices coordinate

Utilize the angle estimation result of array A and array B, burning things which may cause a fire disaster is positioned in a quadrilateral area, adopt analytic geometry method to solve the coordinate (x on each summit _i, y _i), wherein i=1,2,3,4;

Step 4: set up dynamic optimization objective function

If the source point coordinate that fire occurs is (x _s, y _s), effectively evaluated error radius is R; According to the border vertices coordinate (x obtaining in step 3 _i, y _i), setting up dynamic optimization objective function is minR ², constraint condition is: (x _s-x _i) ²+ (y _s-y _i) ²≤ R ², wherein min represents minimization function;

Step 5: utilize the optimization problem of setting up in CVX kit solution procedure 4, and export net result.