CN100552668C - Leakage detecting and locating method based on pressure and sound wave information fusion - Google Patents

Abstract

Based on the leakage detecting and locating method of pressure and sound wave information fusion, belong to oil transportation (gas) pipeline fault diagnostic techniques field, it is characterized in that: all based on the Leak Detection and the leakage positioning of information fusion.The former comprises: gather the measurement data of pipeline upstream and downstream end pressure and sonic sensor respectively, send into computing machine, through the final testing result of processing acquisition of data filtering, the fusion of feature level and three levels of decision level fusion.If testing result shows leakage, then start leakage positioning process based on information fusion.This process utilizes the signal of two class different sensors to carry out leakage positioning with multiple different leakage positioning algorithm at first respectively, process is based on the fusion of the positioning result of same type of sensor and different localization methods, and, finally obtain positioning result based on the processing of two levels of fusion of the positioning result of two class different sensors.This method can effectively reduce rate of false alarm and rate of failing to report, improves bearing accuracy.

Description

Leakage detecting and locating method based on pressure and sound wave information fusion

Technical field

Leakage detecting and locating method based on pressure and sound wave information fusion belongs to oil transportation (gas) pipeline fault diagnostic techniques field.

Background technology

Pipeline transportation is the important way of modern industry fluid transport, compares with other mode of movements, and it has economy, convenience, efficient, safety and is convenient to multiple advantages such as management, so has a wide range of applications at oil, natural gas transport etc.Pipeline can leak in operational process for various reasons, not only cause huge resource loss, economic loss, also may cause the serious environmental pollution problem, bring enormous economic loss to country, therefore in time find pipe leakage and carry out leakage positioning, ensure that the pipe safety operation is very necessary.

Existing Leak Detection and localization method roughly can be divided into following 3 classes:

One class is by detection method in the pipe of detector tube wall integrity realization Leak Detection and location, the main technology such as magnetic flux, eddy current, shooting that rely on, this class methods investment is huge, and real-time is poor, and only be applicable to and the horizontal pipe of larger caliber accidents such as line clogging take place very easily.

Second class is to have the outer detection method of the pipe of realizing Leak Detection and location by direct detection leak materials, mainly comprises distribution type fiber-optic, special cables, radar, and infrared, laser imaging etc., there are the big or not strong characteristics of real-time of investment in these class methods.

The 3rd class realizes Leak Detection and location by the variation of flow state in the pipe after the monitoring pipe leakage, and using many is mass/volume balancing method, pressure gradient method, negative pressure wave method and sonic method.

In above-mentioned three class methods, the first kind and the second class methods cost are high and except the method based on profile fiber, all the other methods do not possess the ability of real-time monitoring.The 3rd class methods are owing to can realize online in real time and detect, and cost is lower, is to study and use maximum class methods at present.And the method that is based on suction wave that is most widely used in the 3rd class methods, low based on the method cost of suction wave, as can to monitor pipeline in real time leakage has obtained good effect in practice.But also there are some significant disadvantages in negative pressure wave method, comprises poor to little leakage and the sensitivity of slowly leaking and bearing accuracy, as to overcome the active station disturbance ability, rate of false alarm height, is difficult to effectively detect the leakage recurred etc.Method based on the acoustic signals analysis also belongs to the 3rd class methods, it has highly sensitive characteristics, can improve little leakage significantly, slowly leak and detectability that long-distance pipe leaks, and has the ability that better overcomes disturbance owing to the acoustic characteristic that can distinguish disturbance and leakage, but because acoustic signals does not comprise DC component, signal and actual condition lack corresponding relation intuitively, in case report by mistake, be difficult to check alarming result and further judge by the artificial nucleus.

Analysis by the front can be seen, adopts single sensor, because the limitation of sensor itself causes leak detection system to have problems in engineering is used.At the problems referred to above, the present invention adopts the thought of information fusion, proposes Leak Detection and localization method based on pressure and sound wave information fusion, has reduced the rate of false alarm and the rate of failing to report of system effectively, has improved bearing accuracy.

Summary of the invention

The objective of the invention is to, a kind of pipeline leakage testing localization method based on pressure and sound wave information fusion is proposed, its hardware connection layout as shown in Figure 1, gather the data of pressure and sonic sensor by data collecting card, the data of gathering are sent into computing machine by network, in computing machine, realize pipeline leakage testing location, adopt this method can effectively reduce rate of false alarm and rate of failing to report, improve bearing accuracy based on pressure and information fusion.

This method is characterised in that and contains following steps successively:

Step (1) is imported to computing machine

Statistical learning software package biolearing among the Matlab is used to carry out support vector machine SVM computing;

Signal processing software bag signal among the Matlab is used to carry out the medium filtering computing;

Comprise that the check of pressure average, wavelet analysis method and chaos time sequence correlation dimension analyze based on the Leak Detection of pressure sensor signal R as a result ₁, R ₂And R ₃

Comprise wavelet analysis method and Chaotic time series forecasting method based on the Leak Detection of sonic sensor signal R as a result ₄And R ₅

7 kinds of locator data d that carry out leakage positioning based on the output information of pressure transducer that comprise relevant function method, generalized correlation analytic approach, wavelet analysis method, affined transformation method, negative edge starting point method, bathmometry, Chaotic time series forecasting _i ⁽¹⁾, i=1 ...., 7, wherein, i represents the positioning result that obtains based on i kind localization method, subscript (1) expression positioning result is obtained by the pressure signal analysis;

4 kinds of locator data d that carry out leakage positioning based on the output information of sonic sensor that comprise relevant function method, generalized correlation analytic approach, wavelet analysis method, Chaotic time series forecasting etc. _j ⁽²⁾, j=1 ..., 4, wherein, j represents the positioning result that obtains based on j kind localization method, subscript (2) expression positioning result is by pressing the acoustic signals analysis to obtain;

Step (2) is carried out the Leak Detection based on information fusion according to the following steps:

Step (2.1) is used P in the time series that the pipeline upstream u that treats Leak Detection location and downstream d use the raw data of the pressure of determination of pressure sensor in the seclected time section respectively _{0, u}And P _{0, d}Expression, wherein subscript 0 expression is a raw data, the data sequence that to obtain a length be L, and respectively with P _{0, u}And P _{0, d}The input signal processing software package obtains the P as a result behind the medium filtering _uAnd P _d

Step (2.2) obtains acoustic signals raw data in section preset time with sonic sensor respectively at the pipeline upstream u that treats Leak Detection location and downstream d, uses A respectively _{0, u}And A _{0, d}, and carry out bandpass filtering according to the following steps, obtain acoustic signals reconstruction signal A _uAnd A _d:

It is L that step (2.2.1) is set acoustic signals raw data length, and the frequency band range that leaks the back acoustic signals is [f ₁, f ₂];

Step (2.2.2) is to described acoustic signals raw data A _{0, u}And A _{0, d}Carry out fast fourier transform, obtain its fourier transform coefficient FA _{0, u}And FA _{0, d}:

FA _0，u＝FFT(A _o，u)

FA _0，d＝FFT(A _o，d)

Wherein, FFT () expression is to carrying out fast fourier transform;

Step (2.2.3) reserve frequency is at [f ₁, f ₂] interior fourier transform coefficient, the coefficient zero setting in other frequency ranges obtains new fourier transform coefficient FA ' _{O, u}And FA ' _{0, d}

Step (2.2.4) is to FA ' _{O, u}And FA ' _{0, d}Carry out inverse fourier transform, obtain reconstruction signal A _uAnd A _d:

A _u＝IFFT(FA′ _o，u)

A _d＝IFFT(FA′ _0，d)

Wherein, IFFT () expression is to carrying out invert fast fourier transformation;

Step (2.3) is selected proper vector:

Step (2.3.1) is set:

The upstream and downstream pressure signal sequence that step (2.1) obtains is respectively P _uAnd P _d

Step (2.2.4) obtains upstream and downstream acoustic signals sequence and is respectively A _uAnd A _d:

Step (2.3.2) is to P _u, P _d, A _u, A _dObtain following each value, constitutive characteristic vector X:

The average value P of signal _Au, P _Ad, A _AuAnd A _Ad, wherein subscript a represents mean value;

The minimum value P of signal _Mu, P _Md, A _MuAnd A _Md, wherein subscript m is represented minimum value;

The standard deviation P of signal _{σ u}, P _{σ d}, A _{σ u}And A _{σ d}, wherein subscript σ represents standard deviation;

The frequency A of acoustic signals power spectrum maximal value correspondence _FuAnd A _Fd, wherein subscript f represents frequency, obtains:

x＝[P _au P _mu P _σu A _au A _mu A _σu A _fu P _ad P _md P _σd A _ad A _md A _σd A _fd]

Step (2.4) uses described biolearning software package to carry out Leak Detection according to the following steps:

The training of step (2.4.1) support vector machine, the training of support vector machine realizes by following optimization problem:

$\left\{\begin{array}{c}Q\left({\mathrm{\α}}^{\left[k\right]}\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i^{\left[k\right]}-\frac{1}{2}\underset{i,j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i^{\left[k\right]}{\mathrm{\α}}_j^{\left[k\right]}{y}_i{y}_{j}K(X_i^{\left[k\right]},X_j^{\left[k\right]})\\ 0\≤{\mathrm{\α}}_i^{\left[k\right]}\≤C,i=1\mathrm{K\; N}\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{\mathrm{\α}}_i^{\left[k\right]}=0\end{array}\right.$

Wherein, N represents sample number, α ^[k], α _i ^[k], α _j ^[k]The expression weights, y _i, y _j∈ 1, and 1} presentation class number, C is the relaxation factor coefficient, Q is the optimization aim function identification, K (X _i ^[k], X _j ^[k]Be kernel function, X _i ^[k], X _j ^[k]Be the proper vector of sample, [k]=[1], [2], and [3] are the kernel function numbering, i, and j is sequence number;

Obtain weights α by training _i ^[k], with non-zero α _i ^[k]Subscript identical proper vector be support vector, the intermediate value of different classes of a pair of support vector is classification thresholds b ^[k]

Above-mentioned training process is realized by biolearning, imports following data to described biolearning software package:

Training data: the feature vector, X of the leak data of choosing according to step (2.3.2) ₁Feature vector, X with the non-leak data of choosing according to step (2.3.2) _-1Wherein subscript 1 expression is leaked, wherein the non-leakage of subscript-1 expression;

Classified information 1 and classified information-1;

Kernel function title and parameter: polynomial kernel function name " polynomial ", corresponding kernel function form is:

$K^{\left[1\right]}(x,x_i^{\left[1\right]})={\left[(x\·x_i^{\left[1\right]}+1)\right]}^q,$ Its polynomial expression exponent number q selects the default value 3 of software package;

Radial basis function names " RBF ", corresponding kernel function form is:

$K^{\left[2\right]}(x,x_i^{\left[2\right]})=\exp \{-\frac{{\left|\right|x-x_i^{\left[2\right]}\left|\right|}^2}{{\mathrm{\σ}}^2}\},$ Its scale factor σ selects the default value of software package

Sigmoid function title " MLP " and parameter v=0.001, c=-0.1, corresponding kernel function form is:

$K^{\left[3\right]}(x,x_i^{\left[3\right]})=\tanh (\mathrm{\υ}(x,x_i^{\left[3\right]})+c)$

Subscript [1] wherein, [2], [3] are respectively the numbering of kernel function;

The relaxation factor coefficient is selected the default value of software package;

Obtain comprising under three kinds of kernel function conditions three classified information structure Struct of weights, support vector and classification thresholds respectively ₁, Struct ₂, Struct ₃

Step (2.4.2) is based on the Leak Detection of support vector machine: the feature vector, X of input data to be tested _tAnd the classified information structure Struct that obtains of step (2.4.1) ₁, obtain testing result R ₆Wherein subscript t represents data to be tested;

The feature vector, X of input data to be tested _tAnd the classified information structure Struct that obtains of step (2.4.1) ₂, obtain testing result R ₇

The feature vector, X of input data to be tested _tAnd the classified information structure Struct that obtains of step (2.4.1) ₃, obtain testing result R ₈

Step (2.5) adopts Dempster-Schaefer D-S evidence theory to carry out decision level fusion according to the following steps:

Step (2.5.1) is set, and representing with l of leakage arranged, and does not have to leak and represents with l, constitutes identification framework Θ={ l, the l} of D-S evidence theory;

Step (2.5.2) is expressed as R for 8 testing results of step (1) and step (2.4.2) with it _n, n=1 ..., 8;

Step (2.5.3) is according to the R of step (2.5.2) gained _n, n=1 ..., 8 calculate R _n, n=1 ..., 8 and threshold value as the distance between-0.5, and this distance divided by 2 so that be converted into numerical value p in [0,1] _{L, n}, n=1 ..., 8, p _{L, n}, n=1 ..., 8 expressions are judged as the probability of leakage, then 1-p when testifying with this testing result _{L, n}, n=1 ..., it is the probability that is judged as non-leakage that 8 expressions are done evidence with this testing result;

Step (2.5.4) is according to the p of step (2.5.3) gained _{L, n}Calculate under the evidence theory framework with R according to following formula _n, n=1 ..., 8 differentiate the probabilistic elementary probability of result when testifying distributes m _n(Θ):

m _n(Θ)＝-k _n[p _l，nlog ₂p _l，n+(1-p _l，n)log ₂(1-p _l，n)]，n＝1，...，8

K in the formula _n∈ (0,1), n=1 .., 8 is regulatory factor;

Calculating under the evidence theory framework with R _n, n=1 ..., 8 elementary probabilities of differentiating when testifying for leaking distribute m _n(l):

m _n(l)＝p _l，n(1-m _n(Θ))，n＝1，...，8

Calculating under the evidence theory framework with R _n, n=1 ..., 8 elementary probabilities of differentiating when testifying for non-leakage distribute m _n(l):

m _n(l)＝(1-p _l，n)(1-m _n(Θ))，n＝1，...，8

Among step (2.5.5) the definition evidence theory identification framework Θ burnt element S _Nk(n=1,2 ..., 8, k=1,2,3): focus element is that the elementary probability of set Θ distributes m _j(S _JnThe subclass of)＞0, that is: $S_{\mathrm{nk}}\⋐\{l,\stackrel{\‾}{l},\mathrm{\Θ}\},$ And m _n(S _Nk)＞0;

Step (2.5.6) is calculated as follows the inconsistent factor:

Wherein, symbol ⌒ represents to seek common ground, and ∏ represents to do continuously multiplication, The expression empty set;

Probability assignments when step (2.5.7) is calculated as follows corresponding the leakage:

$m\left(l\right)=\frac{\underset{I{S}_{\mathrm{nk}}=l}{\mathrm{\Σ}}\underset{n=1}{\overset{8}{\mathrm{\Π}}}{m}_n\left(S_{\mathrm{nk}}\right)}{1-K_1}$

Probability assignments when step (2.5.8) is calculated as follows corresponding non-the leakage:

$m\left(\stackrel{\‾}{l}\right)=\frac{\underset{I{S}_{\mathrm{nk}}=\stackrel{\‾}{l}}{\mathrm{\Σ}}\underset{n=1}{\overset{8}{\mathrm{\Π}}}{m}_n\left(S_{\mathrm{nk}}\right)}{1-K_1}$

Step (2.5.9)

If then there is leakage in m (l)＞m (l);

If then there is not leakage in m (l)＜m (l);

Step (3) is then carried out the leakage positioning process based on information fusion according to the following steps if step (2) is judged to have to leak to be taken place:

Step (3.1) is determined each positioning result d based on pressure sensor data in the following manner _(j) ⁽¹⁾, i=1 ...., 7 weight w _i ⁽¹⁾, i=1 ..., 7:

Step (3.1.1) is with all positioning result d _i ⁽¹⁾, i=1 ...., 7 are and expand to d _i ⁽¹⁾, i=1 ...., 7 centers, 1% of pipe range is the symmetric interval [d of radius r _i ⁽¹⁾-r, d _i ⁽¹⁾+ r], i=1 ...., 7;

Step (3.1.2) is according to a certain positioning result d _i ⁽¹⁾Symmetric interval [d _i ⁽¹⁾-r, d _i ⁽¹⁾+ r] with the number of the common factor in all 7 intervals described in the step (3.1.1) as the weight w of this positioning result _i ⁽¹⁾

Step (3.2) is calculated according to the described positioning result d of step (1) as follows to pressure transducer _i ⁽¹⁾, i=1 ...., 7 and the weight w that obtained of step (3.1) _i ⁽¹⁾, i=1 ..., 7, the location fusion results that obtains:

$d^{\left(1\right)}=\frac{\underset{i=1}{\overset{7}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^{\left(1\right)}\×d_i^{\left(1\right)}}{\underset{i=1}{\overset{7}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^{\left(1\right)}}$

Step (3.3) is determined each positioning result d based on the sonic sensor data in the following manner _j ⁽²⁾,=1 ...., 4 weight w _j ⁽²⁾, j=1 ..., 4:

Step (3.3.1) is with all positioning result d _j ⁽²⁾, j=1 ...., 4 are and expand to d _j ⁽²⁾, j=1 ...., 4 centers, 1% of pipe range is the symmetric interval [d of radius r _j ⁽²⁾-r, d _j ⁽²⁾+ r], j=1 ...., 4;

Step (3.3.2) is according to a certain positioning result d _j ⁽²⁾Symmetric interval [d _j ⁽²⁾-r, d _j ⁽²⁾+ r] with the number of the common factor in all 4 intervals described in the step (3.3.1) as the weight w of this positioning result _j ⁽²⁾

Step (3.4) is calculated according to the described positioning result d of step (1) as follows to pressure transducer _j ⁽²⁾, j=1 ...., 4 and the weight w that obtained of step (3.1) _j ⁽²⁾, j=1 ..., 4, the location fusion results that obtains:

$d^{\left(2\right)}=\frac{\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\ω}}_j^{\left(2\right)}\×d_j^{\left(2\right)}}{\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\ω}}_j^{\left(2\right)}}$

Step (3.5) merges by the positioning result of following formula to pressure and sound wave two class sensors, obtains final leakage positioning result:

$d=\frac{\underset{p=1}{\overset{2}{\mathrm{\Σ}}}{w}^{\left(p\right)}\×d^{\left(p\right)}}{\underset{p=1}{\overset{2}{\mathrm{\Σ}}}{w}^{\left(p\right)}}$

Weight w wherein ⁽¹⁾=3, w ⁽²⁾=7;

If positioning result exceeds duct length or the result is a negative value, then think not leak and take place, return step (2).

Effect of the present invention: in practice, (wherein leak data is 104 groups at 162 groups of experimental datas, 58 groups of noisy datas), original leak detection system only can detect 78 groups of leakages, have and fail to report for 26 times, 20 wrong reports are arranged simultaneously, when using institute of the present invention extracting method and carrying out Leak Detection, fail to report number of times and reduce to 16 times, and the wrong report number of times reduces to 8.The precision aspect of leakage positioning, adopt traditional single localization method: correlation analysis method, the ratio more than 1% that positioning error surpasses pipe range accounts for 28.5% of total positioning result, adopt wavelet analysis method, positioning error surpass pipe range 1% the total positioning result ratio in ratio station 41%, and the ratio that adopts the method for the invention positioning error to surpass pipe range 1% only is 14%.This shows that institute of the present invention extracting method has effectively reduced rate of false alarm and rate of failing to report, has improved the precision of leakage positioning significantly.

Description of drawings

Fig. 1 is the hardware connection layout of system.

Fig. 2 is based on information fusion Leak Detection block scheme.

Fig. 3 is the algorithm block diagram based on the leakage detecting and locating method of pressure and sound wave information fusion.

Embodiment

Native system is respectively installed a pressure transducer and a sonic sensor respectively at pipeline upstream extremity and downstream end.Two pressure data sequences to being gathered by data acquisition system (DAS) and two sonic data sequences are real-time sends into computing machine, stores in the database.Detection system is reading of data and system information from database, and at first to the measurement data of two class sensors, process data filtering, feature level merge and the processing of three levels of decision level fusion obtains final testing result.

If testing result shows leakage, then start leakage positioning process based on information fusion.Utilize the signal of two class different sensors to carry out leakage positioning at first respectively with multiple different leakage positioning algorithm, pass through fusion then based on the positioning result of the different localization methods of same type of sensor, and, finally obtain positioning result based on the processing of two levels of fusion of the positioning result of two class different sensors.This method can effectively reduce rate of false alarm and rate of failing to report, improves bearing accuracy.Introduce based on the Leak Detection of information fusion and the ultimate principle of leakage positioning below.

1 Leak Detection based on information fusion:

Leak Detection based on information fusion is to handle in real time by pressure and sonic data that the data acquisition system is obtained, to determine whether pipeline leakage has taken place, and it is characterized in that comprising following process:

(1) data filtering

The purpose of carrying out data filtering is in order to guarantee the validity of metrical information, to make subscript u represent the upstream, and subscript d represents the downstream, and subscript 0 expression raw data is the pressure time sequence data P of L to data length _{0, u}And P _{0, d}Adopt median filtering technology, to reject wild value; To data length is the sound wave time series data A of L _{0, u}And A _{0, d}Adopt band-pass filtering, to improve signal to noise ratio (S/N ratio).Wherein to pressure time sequence data P _{0, u}And P _{0, d}Median filtering algorithm realize input pressure time series data P respectively by Matlab signal processing software bag (signal software package) _{0, u}And P _{0, d}, the P as a result behind the output medium filtering _uAnd P _dTo acoustic signals time series data A _{0, u}And A _{0, d}The bandpass filtering algorithm as follows:

[1.1] establishing acoustic data signal length is L, and the frequency band range that leaks the back acoustic signals is [f ₁, f ₂], f in the present invention ₁=0.2Hz, f ₂=20Hz;

[1.2] to upstream and downstream acoustic signals A _{0, u}And A _{0, d}Carry out fast fourier transform and obtain fourier transform coefficient FA _{0, u}And FA _{0, d}

FA _0，u＝FFT(A _0，u)

FA _0，d＝FFT(A _0，d)

Wherein FFT () expression is to carrying out fast fourier transform.

[1.3] reserve frequency is at [f ₁, f ₂] fourier transform coefficient, the equal zero setting of the fourier transform coefficient of other frequencies obtains new fourier transform coefficient FA ' _{0, u}And FA ' _{0, d}

[1.4] to new fourier transform coefficient FA ' _{0, u}And FA ' _{0, u}Carry out inverse fourier transform and obtain reconstruction signal A _uAnd A _d

A _u＝IFFT(FA′ _0，u)

A _d＝IFFT(FA′ _0，d)

Wherein IFFT () expression is to carrying out invert fast fourier transformation.

(2) the feature level merges

The feature level merges the local diagnosis of finishing leakage, and this process realizes in two steps: the selected characteristic vector sum is realized the Leak Detection based on support vector machine (SVM).If upstream and downstream pressure signal time series data is respectively P _u, P _d, the acoustic signals time series data is respectively and is A _u, A _d, to P _u, P _d, A _u, A _dChoose following variable respectively: signal averaging P _Au, P _Ad, A _AuAnd A _Ad, signal minimum P _Mu, P _Md, A _MuAnd A _Md, signal standards difference P _{σ u}, P _{σ d}, A _{σ u}And A _{σ d}, acoustic signals spectrum peak frequency A _FuAnd A _FdComposition characteristic vector X, that is:

X＝[P _au P _mu P _σu A _au A _mu A _σu A _fu P _ad P _md P _σd A _ad A _md A _σd A _fd]

Leak Detection realizes by support vector machine (SVM), also realizes the i.e. training of support vector machine and based on the Leak Detection of support vector machine in two steps.Support vector machine is a kind of new machine learning method that people such as Vapnik proposes according to Statistical Learning Theory.It is theoretical foundation with the structural risk minimization, make the practical risk of learning machine reach minimum by the discriminant function in suitable choice function subclass and this subclass thereof, guaranteed that the little error classification device that obtains by limited training sample is still little to the test error of independent test collection, obtained a learning machine that has the optimal classification ability and promote generalization ability.Its ultimate principle is as follows:

For two classification problems, given training sample set: (X _i, y _i), i=1 ..., N, X _i∈ R ^d, y _i{ 1,1} is a category label to ∈, and N represents number of samples, R ^dExpression d dimension real number space; Under these conditions, the target of SVM is optimum classifier of design, guarantees two classes faultless separately.When the sample set linear separability, former problem is to seek the problem of a Generalized optimal classifying face on linear separable space.And in actual applications,, need to introduce kernel function K (X this moment because the non-linear and inseparable situation of the input space of the input space can appear in the complicacy of sample _i, X _j) input space is transformed to a high-dimensional feature space, structure optimal classification face is realized classification in high-dimensional feature space, and allow to divide between the sample in optimum face and mistake compromise, to realize empiric risk and to promote between the performance and try to achieve certain equilibrium.At Leak Detection, following three kinds of kernel function K have been adopted ^[k](X _i, X _j ^[k]) (k=1,2,3, the numbering of expression kernel function, the target purpose is in order to distinguish the support vector under the different IPs function condition in the increase) be respectively:

Adopt the inner product of polynomial form

$K^{\left[1\right]}(X_i,X_j^{\left[1\right]})={\left[(X_i\·X_j^{\left[1\right]}+1)\right]}^q$

The support vector machine that obtain this moment is a q rank polynomial expression sorter, and the default value of q software package is 3;

Adopt radial basis function type inner product

$K^{\left[2\right]}(X_i,X_j^{\left[2\right]})=\exp \{-\frac{{\left|\right|X_i-X_j^{\left[2\right]}\left|\right|}^2}{{\mathrm{\σ}}^2}\}$

The support vector machine that obtains is a kind of radial basis function classifiers, and wherein σ represents the scale factor of radial basis function, and here we get the default value of software package $\mathrm{\σ}=\sqrt{2};.$

Adopt sigmoid function type inner product

$K^{\left[3\right]}(X_i,X_j^{\left[3\right]})=\tanh (\mathrm{\υ}(X_i,X_j^{\left[3\right]})+c)$

Parameter v＞0, c＜0, the default value in the software package is respectively 1 and-1;

To each concrete kernel function K ^[k](X _i, X _j ^[k]) (k=1,2,3), also need to determine corresponding support vector X _s ^[k]And corresponding weights α _s ^[k](subscript s expresses support for vector), can realize by finding the solution following optimization dual problem:

$\left\{\begin{array}{c}Q\left({\mathrm{\α}}^{\left[k\right]}\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i^{\left[k\right]}-\frac{1}{2}\underset{i,j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i^{\left[k\right]}{\mathrm{\α}}_j^{\left[k\right]}{y}_i{y}_{j}K(X_i^{\left[k\right]},X_j^{\left[k\right]})\\ 0\≤{\mathrm{\α}}_i^{\left[k\right]}\≤C,i=1\mathrm{K\; N}\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{\mathrm{\α}}_i^{\left[k\right]}=0\end{array}\right.$

In the formula, k=1,2,3, C is the relaxation factor coefficient, the introducing of relaxation factor is in order to allow the existence of wrong sample.

Following formula is the problem of quadratic function optimizing under the inequality constrain, has unique solution.Some (normally small part) α in separating _j ^[k]Non-vanishing, be defined as α _s ^[k], corresponding sample is support vector X _s ^[k]

After finishing above-mentioned training process, realize Leak Detection by following formula: with α _s ^[k], X _s ^[k], by the feature vector, X of extracting data to be detected _t(wherein subscript t represents data to be tested) and kernel function K ^[k](X _i, X _j ^[k]) (k=1,2,3) send into following formula:

$f^{\left[k\right]}\left(X_t\right)=\mathrm{sgn}(\underset{s=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_s^{\left[k\right]}{y}_s{K}^{\left[k\right]}(X_s^{\left[k\right]},X_t)+b^{\left[k\right]})$

If go out f ^[k](x) be to represent in 1 o'clock to exist to leak, otherwise work as f ^[k](x) represented not leak for-1 o'clock, summation is only to support vector X in the following formula _s ^[k]Carry out b ^[k]Be classification thresholds, can get in two classes any a pair of support vector and get intermediate value.

In this process, the SVM algorithm all adopts statistical learning software package biolearning realization among the Matlab, in training process, imports following data to described biolearning software package:

Training data: the feature vector, X of 9 groups of leak data choosing according to mode noted earlier ₁Feature vector, X with 6 groups of non-leak data _-1, wherein subscript 1 expression is leaked, wherein the non-leakage of subscript-1 expression;

Classified information 1 and classified information-1;

Kernel function title (a kernel function title is only imported in each training): polynomial kernel function name " polynomial ";

Radial basis function names " RBF ";

Sigmoid function title " MLP " and parameter v=0.001, c=-0.1;

The exponent number of other parameters such as polynomial kernel function, the scale factor of radial basis function and relaxation factor coefficient are all selected the default value of software package;

Each all export one with the corresponding classified information structure of importing of kernel function, totally three on this classified information structure is respectively: Struct ₁, Struct ₂, Struct ₃, at classified information structure Struct ₁, Struct ₂, Struct ₃In, have seven unit, first unit is that SupportVectors preserves support vector, second unit Alpha preserves the weights of each support vector, the 3rd unit B ias preserves classification thresholds, and the 4th unit KernelFunction preserves the kernel function title, and the 5th unit KernelFunctionArgs preserves the parameter information of kernel function, the 6th unit GroupNames preserves classified information, and the 7th unit F igureHandles preserves the drawing flag information.

As example, when adopting the kernel function of polynomial form, the Struct of output ₁In have four support vectors:

4.2182	4.2	0.0126	9.9123	8.3279	0.4907	0.3906	2.0047	1.9554	0.0283	10.105	9.2616	0.3088	3.125
														3.3394	3.3222	0.0051	9.9511	8.1092	0.4889	0.3906	1.2422	1.1299	0.0386	10.212	9.7459	0.1911	0.7812
3.392188	3.42147	0.090403	10.07036	8.308008	0.5392	0.481	1.305138	1.142112	0.180867	10.32118	9.818864	0.2506	5.5351
														3.7557	3.7521	0.002	10.068	9.9764	0.040	0.781	1.3672	1.3603	0.0026	10.247	9.3201	0.3314	2.7344

Its weights are respectively:

0.26646

0.19402

0.11259

0.57307

Classification thresholds is-8.485;

When adopting the kernel function of radial basis function form, the Struct of output ₂In have 9 support vectors:

3.7663	3.7448	0.0179	9.6384	8.0584	0.56615	0.78125	1.4093	1.4785	0.008	10.233	9.6756	0.22112	0.78125
														4.2182	4.2	0.0126	9.9125	8.3279	0.49074	0.39063	2.0047	1.9554	0.0283	10.105	9.2616	0.3088	3.125
3.3656	3.3077	0.0497	9.8775	7.7537	0.5077	0.39063	1.4382	1.3315	0.0732	10.274	9.4061	0.27063	2.9297
														3.3419	3.3267	0.0076	9.9786	8.2967	0.45802	0.39063	1.2895	1.1299	0.1046	10.249	9.7537	0.17524	5.4698
3.3394	3.3222	0.0051	9.9511	8.1092	0.48896	0.39063	1.2422	1.1299	0.0386	10.212	9.7459	0.1911	0.78125
														3.380643	3.541062	0.10428	0.939182	8.036706	0.648007	0.425607	1.471612	1.427692	0.052653	10.34716	9.461925	0.34678	0.409137
3.415691	3.337876	0.045975	10.06484	8.382408	0.539956	0.4152	1.379259	1.1900112	0.118573	10.26513	9.842015	0.273099	5.528932
														3.4524	3.448	0.003	10.085	9.9998	0.030947	0.78125	1.1371	1.1262	0.0044	10.179	9.4647	0.31717	2.3138
3.800632	3.794423	0.10172	10.15341	10.10641	0.122011	1.253398	1.435964	1.391165	0.05842	10.24268	9.553308	0.353483	3.527083

Its weights are respectively:

0.22071

0.54117

0.43808

0.21458

0.28486

0.17037

0.34956

1.1143

1.105

Classification thresholds is-0.442;

When adopting the kernel function of S type function form, the Struct of output ₃In have 5 support vectors:

4.2182	4.2	0.0126	9.9123	8.3279	0.49074	0.39063	2.0047	1.9554	0.0283	10.105	9.2616	0.3088	3.125
														3.356573	3.367212	0.021805	10.01302	8.351693	0.462263	0.413826	1.329379	1.141969	0.148863	10.25415	9.853365	0.244678	5.530302
3.401115	3.405174	0.103029	9.994843	8.193821	0.528668	0.432667	1.331399	1.164466	0.119441	10.31143	9.824006	0.276281	0.847311
														3.7557	3.7521	0.002	10.068	9.9764	0.040947	0.78125	1.3672	1.3603	0.0026	10.247	9.3201	0.33145	2.7344
3.848998	3.813567	0.075831	10.13165	9.993413	0.068181	0.862495	1.407526	1.426308	0.031206	10.34314	9.377756	0.428113	2.785792

Its weights are respectively:

297.77

138.48

245.88

520.59

154.85

Classification thresholds is-8.90;

Said process has been finished the training of support vector machine, finishes after the above-mentioned training process, realizes Leak Detection based on support vector machine by the biolearning software package: the feature vector, X of importing data to be tested respectively _tWith classified information structure Struct ₁, obtain testing result R ₆

The feature vector, X of input data to be tested _iWith classified information structure Struct ₂, obtain testing result R ₇

The feature vector, X of input data to be tested _tWith classified information structure Struct ₃, obtain testing result R ₈

(3) decision level fusion

In data filtering, adopt the check of pressure average, wavelet analysis method and the analysis of chaos time sequence correlation dimension to obtain Leak Detection R as a result to pressure sensor signal ₁, R ₂And R ₃Adopt wavelet analysis method and Chaotic time series forecasting method to obtain Leak Detection R as a result to the sonic sensor signal ₄And R ₅, have testing result R when leaking _n, n=1 ..., 5 is 1, does not have testing result R when leaking _n, n=1 ..., 5 is-1, the Leak Detection that the feature level in this testing result and the process (2) merges is R as a result _n, n=6 ..., 8 are used for realizing decision level fusion as evidence together.Decision level fusion adopts Dempster-Schaefer (D-S) evidence theory, will leak l and the non-leakage l identification framework Θ as the D-S evidence theory, i.e. Θ={ l, l}.

In the decision level fusion process, at first calculate R _n, n=1 ..., 8 and preset threshold (as-0.5) between distance, and should distance divided by 2 so that be converted into interval numerical value p of [0,1] _{L, n}, n=1 ..., 8, p _{L, n}, n=1 ..., 8 expressions are adopted these testing results to testify and are judged as the probability of leakage, and the probability that then adopts this this testing result to testify to be judged as non-leakage is 1-p _{L, n}, n=1 ..., 8.Determine the elementary probability distribution m that this testing result of employing is testified and is judged as leakage under the evidence theory framework then _n(l), n=1 ..., 8, the elementary probability that adopts this testing result to testify to be judged as non-leakage distributes m _n(l), n=1 ..., 8 and adopt this testing result to testify to differentiate the probabilistic elementary probability of result and distribute m _n(Θ), n=1 ..., 8.Wherein probabilistic elementary probability distribution formula adopts:

m _n(Θ)＝-k _n[p _l，nlog ₂p _l，n+(1-p _l，n)log ₂(1-p _l，n)]，n＝1，...，8

K in the formula _n∈ (0,1), n=1 ..., 8 is regulatory factor.m _n(l) and m _n(l) computing formula is:

m _n(l)＝p _l，n(1-m _n(Θ))，n＝1，...，8

m _n(l)＝(1-p _l，n)(1-m _n(Θ))，n＝1，...，8

Obtain after the above-mentioned elementary probability distribution, the probability assignments that obtains leaking under a plurality of evidences according to the D-S fusion criterion is:

$m\left(l\right)=\frac{\underset{I{S}_{\mathrm{nk}}=l}{\mathrm{\Σ}}\underset{n=1}{\overset{8}{\mathrm{\Π}}}{m}_n\left(S_{\mathrm{nk}}\right)}{1-K_1}$

The probability assignments of non-leakage is:

$m\left(\stackrel{\‾}{l}\right)=\frac{\underset{I{S}_{\mathrm{nk}}=\stackrel{\‾}{l}}{\mathrm{\Σ}}\underset{n=1}{\overset{8}{\mathrm{\Π}}}{m}_n\left(S_{\mathrm{nk}}\right)}{1-K_1}$

Uncertain probability assignments is:

$m\left(\mathrm{\Θ}\right)=\frac{\underset{n=1}{\overset{8}{\mathrm{\Π}}}{m}_n\left(\mathrm{\Θ}\right)}{1-K_1}$

Wherein:

Be the inconsistent factor.S _Nk(n=1,2 ..., 8, k=1,2,3) represent that focus element among the Θ, focus element are defined as elementary probability m among the set Θ _n(S _NkThe subclass of)＞0, that is: $S_{\mathrm{nk}}\⋐\{l,\stackrel{\‾}{l},\mathrm{\Θ}\},$ And m _n(S _Nk)＞0.

After obtaining m (l) and m (l), judge: if m (l)＞m (l) then be judged as exist to leak, if m (l)＜m (l) then be judged as and do not have leakage by following criterion.

For certain leak-testing data, Leak Detection is R as a result _n, n=1 ..., 8 numerical value is as follows: R ₁=0, R ₅=0, R ₈=0, R ₂=1, R ₃=1, R ₄=1, R ₆=1, R ₇=1, after merging by the D-S evidence theory, obtain existing the probability of leakage to be: 0.7032, do not exist the probability of leakage to be: 0.2967, can obtain conclusion according to described judgment criterion: leakage has taken place in pipeline.

2 leakage positioning based on information fusion

When 1 judgement has the generation of leakage, start leakage positioning process based on information fusion, carry out leakage positioning.We have adopted pressure sensor signal and have comprised correlation analysis, the generalized correlation analysis, and wavelet analysis, affined transformation, negative edge starting point method, bathmometry, Chaotic time series forecasting method in interior 7 is carried out leakage positioning, has obtained 7 positioning result d _i ⁽¹⁾, i=1 ...., 7, wherein, and the positioning result that i represents and obtains based on localization method among the i, subscript (1) expression positioning result is obtained by the pressure signal analysis; The sonic sensor signal adopted comprise correlation analysis, the generalized correlation analysis, wavelet analysis, Chaotic time series forecasting method in interior 4 is carried out leakage positioning, has obtained 4 positioning result d _j ⁽²⁾, j=1 ..., 4, wherein, and the positioning result that j represents and obtains based on localization method among the j, subscript (2) expression positioning result is by pressing the acoustic signals analysis to obtain.Obtaining the signal based on two class sensors, the positioning result d of the multiple distinct methods of employing _i ⁽¹⁾And d _i ⁽²⁾After, the thought of employing information fusion merges above-mentioned a plurality of positioning results.It is characterized in that comprising following process:

1. the positioning result based on same type of sensor signal and multiple distinct methods is merged.

In fusion process, at first the positioning result based on same type of sensor, algorithms of different is merged.To each positioning result d based on pressure sensor data _i ⁽¹⁾, i=1 ...., 7, the weight w of at first definite each positioning result _i ⁽¹⁾, i=1 ..., 7: with all positioning result d based on pressure sensor signal _i ⁽¹⁾, i=1 ...., 7 are and expand to d _i ⁽¹⁾, i=1 ...., 7 centers, 1% of pipe range is the symmetric interval [d of radius r _i ⁽¹⁾-r, d _i ⁽¹⁾+ r], i=1 ...., 7; Then according to a certain positioning result d _i ⁽¹⁾Symmetric interval [d _i ⁽¹⁾-r, d _i ⁽¹⁾+ r] with the number of the common factor in described all 7 intervals weight w as this positioning result _i ⁽¹⁾

After determining the weights of each positioning result, the pressure transducer positioning result is merged as follows the location fusion results that obtains:

$d^{\left(1\right)}=\frac{\underset{i=1}{\overset{7}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^{\left(1\right)}\×d_i^{\left(1\right)}}{\underset{i=1}{\overset{7}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^{\left(1\right)}}$

To each positioning result d based on the sonic sensor data _j ⁽²⁾, j=1 ...., 4, the weight w of at first definite each positioning result _j ⁽²⁾, j=1 ..., 4: with all positioning result d based on the sonic sensor signal _j ⁽²⁾, j=1 ...., 4 are and expand to d _j ⁽²⁾, j=1 ...., 4 centers, 1% of pipe range is the symmetric interval [d of radius r _j ⁽²⁾-r, d _j ⁽²⁾+ r], j=1 ...., 4; According to a certain positioning result d _j ⁽²⁾Symmetric interval [d _j ⁽²⁾-r, d _j ⁽²⁾+ r] with the number of the common factor in described all 4 intervals weight w as this positioning result _j ⁽²⁾

After determining the weights of each positioning result, the pressure transducer positioning result is merged as follows the location fusion results that obtains:

$d^{\left(2\right)}=\frac{\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\ω}}_j^{\left(2\right)}\×d_j^{\left(2\right)}}{\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\ω}}_j^{\left(2\right)}}$

2. to the fusion of two class sensor positioning results

On the basis of finishing 1., carry out two class sensor positioning result d ⁽¹⁾And d ⁽²⁾Fusion, this process adopts weighted-average method, that is:

$d=\frac{\underset{k}{\mathrm{\Σ}}{w}^{\left(k\right)}\×d^{\left(k\right)}}{\underset{k}{\mathrm{\Σ}}{w}^{\left(k\right)}}$

Obtain final leakage positioning result, wherein weight w ⁽¹⁾=3, w ⁽²⁾=7.If positioning result exceeds duct length or the result is a negative value, then think not leak and take place, then return Leak Detection part based on information fusion.

Claims (1)

1, based on the leakage detecting and locating method of pressure and sound wave information fusion, it is characterized in that, contain following steps successively:

Step (1) is imported to computing machine

Statistical learning software package biolearing among the Matlab is used to carry out support vector machine SVM computing;

Signal processing software bag signal among the Matlab is used to carry out the medium filtering computing;

Comprise that the check of pressure average, wavelet analysis method and chaos time sequence correlation dimension analyze based on the Leak Detection of pressure sensor signal R as a result ₁, R ₂And R ₃

Comprise wavelet analysis method and Chaotic time series forecasting method based on the Leak Detection of sonic sensor signal R as a result ₄And R ₅

7 kinds of locator data d that carry out leakage positioning based on the output information of pressure transducer that comprise relevant function method, generalized correlation analytic approach, wavelet analysis method, affined transformation method, negative edge starting point method, bathmometry, Chaotic time series forecasting _i ⁽¹⁾, i=1 ...., 7, wherein, i represents the positioning result that obtains based on i kind localization method, subscript (1) expression positioning result is obtained by the pressure signal analysis;

4 kinds of locator data d that carry out leakage positioning based on the output information of sonic sensor that comprise relevant function method, generalized correlation analytic approach, wavelet analysis method, Chaotic time series forecasting etc. _j ⁽²⁾, j=1 ..., 4, wherein, j represents the positioning result that obtains based on j kind localization method, subscript (2) expression positioning result is by pressing the acoustic signals analysis to obtain;

Step (2) is carried out the Leak Detection based on information fusion according to the following steps:

Step (2.1) is used P in the time series that the pipeline upstream u that treats Leak Detection location and downstream d use the raw data of the pressure of determination of pressure sensor in the seclected time section respectively _{0, u}And P _{0, d}Expression, wherein subscript 0 expression is a raw data, the data sequence that to obtain a length be L, and respectively with P _{0, u}And P _{0, d}The input signal processing software package obtains the P as a result behind the medium filtering _uAnd P _d

Step (2.2) obtains acoustic signals raw data in section preset time with sonic sensor respectively at the pipeline upstream u that treats Leak Detection location and downstream d, uses A respectively _{0, u}And A _{0, d}, and carry out bandpass filtering according to the following steps, obtain acoustic signals reconstruction signal A _uAnd A _d:

It is L that step (2.2.1) is set acoustic signals raw data length, and the frequency band range that leaks the back acoustic signals is [f ₁, f ₂];

Step (2.2.2) is to described acoustic signals raw data A _{0, u}And A _{0, d}Carry out fast fourier transform, obtain its fourier transform coefficient FA _{0, u}And FA _{0, d}:

FA _0，u＝FFT(A _0，u)

FA _0，d＝FFT(A _0，d)

Wherein, FFT () expression is to carrying out fast fourier transform;

Step (2.2.3) reserve frequency is at [f ₁, f ₂] interior fourier transform coefficient, the coefficient zero setting in other frequency ranges obtains new fourier transform coefficient FA ' _{0, u}And FA ' _{0, d}

Step (2.2.4) is to FA ' _{0, u}And FA ' _{0, d}Carry out inverse fourier transform, obtain reconstruction signal A _uAnd A _d:

A _u＝IFFT(FA′ _0，u)

A _d＝IFFT(FA′ _0，d)

Wherein, IFFT () expression is to carrying out invert fast fourier transformation;

Step (2.3) is selected proper vector:

Step (2.3.1) is set:

The upstream and downstream pressure signal sequence that step (2.1) obtains is respectively P _uAnd P _d

Step (2.2.4) obtains upstream and downstream acoustic signals sequence and is respectively A _uAnd A _d:

Step (2.3.2) is to P _u, P _d, A _u, A _dObtain following each value, constitutive characteristic vector X:

The average value P of signal _Au, P _Ad, A _AuAnd A _Ad, wherein subscript a represents mean value;

The minimum value P of signal _Mu, P _Md, A _MuAnd A _Md, wherein subscript m is represented minimum value;

The standard deviation P of signal _{σ u}, P _{σ d}, A _{σ u}And A _{σ d}, wherein subscript σ represents standard deviation;

The frequency A of acoustic signals power spectrum maximal value correspondence _FuAnd A _Fd, wherein subscript f represents frequency, obtains:

x＝[P _au P _mu P _σu A _au A _mu A _σu A _fu P _ad P _md P _σd A _ad A _md A _σd A _fd]

Step (2.4) uses described biolearning software package to carry out Leak Detection according to the following steps:

The training of step (2.4.1) support vector machine, the training of support vector machine realizes by following optimization problem:

$\left\{\begin{array}{c}Q\left({\mathrm{\α}}^{\left[k\right]}\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i^{\left[k\right]}-\frac{1}{2}\underset{i,j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i^{\left[k\right]}{\mathrm{\α}}_j^{\left[k\right]}{y}_i{y}_{j}K(X_i^{\left[k\right]},X_j^{\left[k\right]})\\ 0\≤{\mathrm{\α}}_i^{\left[k\right]}\≤C,i=1\mathrm{KN}\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_i{\mathrm{\α}}_i^{\left[k\right]}=0\end{array}\right.$

Wherein, N represents sample number, α ^[k], α _i ^[k], α _j ^[k]The expression weights, y _i, y _j∈ 1, and 1} presentation class number, C is the relaxation factor coefficient, Q is the optimization aim function identification, K (X _i ^[k], X _j ^[k]Be kernel function, X _i ^[k], X _j ^[k]Be the proper vector of sample, [k]=[1], [2], and [3] are the kernel function numbering, i, and j is sequence number;

Obtain weights α by training _i ^[k], with non-zero α _i ^[k]Subscript identical proper vector be support vector, the intermediate value of different classes of a pair of support vector is classification thresholds b ^[k]

Above-mentioned training process is realized by biolearning, imports following data to described biolearning software package:

Training data: the feature vector, X of the leak data of choosing according to step (2.3.2) ₁Feature vector, X with the non-leak data of choosing according to step (2.3.2) _-1Wherein subscript 1 expression is leaked, wherein the non-leakage of subscript-1 expression;

Classified information 1 and classified information-1;

Kernel function title and parameter: polynomial kernel function name " polynomial ", corresponding kernel function form is:

$K^{\left[1\right]}(x,x_i^{\left[1\right]})={[(x\·x_i^{\left[1\right]})+1]}^q,$ Its polynomial expression exponent number q selects the default value 3 of software package;

Radial basis function names " RBF ", corresponding kernel function form is:

$K^{\left[2\right]}(x,x_i^{\left[2\right]})=\exp \{-\frac{{\left|\right|x-x_i^{\left[2\right]}\left|\right|}^2}{{\mathrm{\σ}}^2}\},$ Its scale factor σ selects the default value of software package

Sigmoid function title " MLP " and parameter υ=0.001, c=-0.1, corresponding kernel function form is:

$K^{\left[3\right]}(x,x_i^{\left[3\right]})=\tanh (\mathrm{\υ}(x,x_i^{\left[3\right]})+c)$

Subscript [1] wherein, [2], [3] are respectively the numbering of kernel function;

The relaxation factor coefficient is selected the default value of software package;

Obtain comprising under three kinds of kernel function conditions three classified information structure Struct of weights, support vector and classification thresholds respectively ₁, Struct ₂, Struct ₃

Step (2.4.2) is based on the Leak Detection of support vector machine: the feature vector, X of input data to be tested _tAnd the classified information structure Struct that obtains of step (2.4.1) ₁, obtain testing result R ₆Wherein subscript t represents data to be tested;

The feature vector, X of input data to be tested _tAnd the classified information structure Struct that obtains of step (2.4.1) ₂, obtain testing result R ₇

The feature vector, X of input data to be tested _tAnd the classified information structure Struct that obtains of step (2.4.1) ₃, obtain testing result R ₈

Step (2.5) adopts Dempster-Schaefer D-S evidence theory to carry out decision level fusion according to the following steps:

Step (2.5.1) is set, and representing with l of leakage arranged, and does not have to leak and represents with l, constitutes identification framework Θ={ l, the l} of D-S evidence theory;

Step (2.5.2) is expressed as R for 8 testing results of step (1) and step (2.4.2) with it _n, n=1 ..., 8;

Step (2.5.3) is according to the R of step (2.5.2) gained _n, n=1 ..., 8 calculate R _n, n=1 ..., 8 and threshold value as the distance between-0.5, and this distance divided by 2 so that be converted into numerical value p in [0,1] _{L, n}, n=1 ..., 8, p _{L, n}, n=1 ..., 8 expressions are judged as the probability of leakage, then 1-p when testifying with this testing result _{L, n}, n=1 ..., it is the probability that is judged as non-leakage that 8 expressions are done evidence with this testing result;

Step (2.5.4) is according to the p of step (2.5.3) gained _{L, n}Calculate under the evidence theory framework with R according to following formula _n, n=1 ..., 8 differentiate the probabilistic elementary probability of result when testifying distributes m _n(Θ):

m _n(Θ)＝-k _n[p _l，nlog ₂p _l，n+(1-p _l，n)log ₂(1-p _l，n)]，n＝1，...，8

K in the formula _n∈ (0,1), n=1., 8 is regulatory factor;

Calculating under the evidence theory framework with R _n, n=1 ..., 8 elementary probabilities of differentiating when testifying for leaking distribute m _n(l):

m _n(l)＝p _l，n(1-m _n(Θ))，n＝1，...，8

Calculating under the evidence theory framework with R _n, n=1 ..., 8 elementary probabilities of differentiating when testifying for non-leakage distribute m _n(l):

m _n(l)＝(1-p _l，n)(1-m _n(Θ))，n＝1，...，8

Among step (2.5.5) the definition evidence theory identification framework Θ burnt element S _Nk(n=1,2 ..., 8, k=1,2,3): focus element is that the elementary probability of set Θ distributes m _j(S _JnThe subclass of)＞0, that is: $S_{\mathrm{nk}}\⋐\{l,\stackrel{\‾}{l},\mathrm{\Θ}\},$ And m _n(S _Nk)＞0;

Step (2.5.6) is calculated as follows the inconsistent factor:

Wherein, symbol ∩ represents to seek common ground, and ∏ represents to do continuously multiplication,

The expression empty set;

Probability assignments when step (2.5.7) is calculated as follows corresponding the leakage:

$m\left(l\right)=\frac{I\underset{S_{\mathrm{nk}}=l}{\mathrm{\Σ}}\underset{n=1}{\overset{8}{\mathrm{\Π}}}{m}_n\left(S_{\mathrm{nk}}\right)}{1-K_1}$

Probability assignments when step (2.5.8) is calculated as follows corresponding non-the leakage:

$m\left(\stackrel{\‾}{l}\right)=\frac{I\underset{S_{\mathrm{nk}}=\stackrel{\‾}{l}}{\mathrm{\Σ}}\underset{n=1}{\overset{8}{\mathrm{\Π}}}{m}_n\left(S_{\mathrm{nk}}\right)}{1-K_1}$

Step (2.5.9)

If then there is leakage in m (l)＞m (l);

If then there is not leakage in m (l)＜m (l);

Step (3) is then carried out the leakage positioning process based on information fusion according to the following steps if step (2) is judged to have to leak to be taken place:

Step (3.1) is determined each positioning result d based on pressure sensor data in the following manner _i ⁽¹⁾, i=1 ...., 7 weight w _i ⁽¹⁾, i=1 ..., 7:

Step (3.1.1) is with all positioning result d _i ⁽¹⁾, i=1 ...., 7 are and expand to d _i ⁽¹⁾, i=1 ...., 7 centers, 1% of pipe range is the symmetric interval [d of radius r _i ⁽¹⁾-r, d _i ⁽¹⁾+ r], i=1 ...., 7;

Step (3.1.2) is according to a certain positioning result d _i ⁽¹⁾Symmetric interval [d _i ⁽¹⁾-r, d _i ⁽¹⁾+ r] with the number of the common factor in all 7 intervals described in the step (3.1.1) as the weight w of this positioning result _i ⁽¹⁾

Step (3.2) is calculated according to the described positioning result d of step (1) as follows to pressure transducer _i ⁽¹⁾, i=1 ...., 7 and the weight w that obtained of step (3.1) _i ⁽¹⁾, i=1 ..., 7, the location fusion results that obtains:

$d^{\left(1\right)}=\frac{\underset{i=1}{\overset{7}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^{\left(1\right)}\×d_i^{\left(1\right)}}{\underset{i=1}{\overset{7}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^{\left(1\right)}}$

Step (3.3) is determined each positioning result d based on the sonic sensor data in the following manner _j ⁽²⁾, j=1 ...., 4 weight w _j ⁽²⁾, j=1 ..., 4:

Step (3.3.1) is with all positioning result d _j ⁽²⁾, j=1 ...., 4 are and expand to d _j ⁽²⁾, j=1 ...., 4 centers, 1% of pipe range is the symmetric interval [d of radius r _j ⁽²⁾-r, d _j ⁽²⁾+ r], j=1 ...., 4;

Step (3.3.2) is according to a certain positioning result d _j ⁽²⁾Symmetric interval [d _j ⁽²⁾-r, d _j ⁽²⁾+ r] with the number of the common factor in all 4 intervals described in the step (3.3.1) as the weight w of this positioning result _j ⁽²⁾

Step (3.4) is calculated according to the described positioning result d of step (1) as follows to pressure transducer _j ⁽²⁾, j=1 ...., 4 and the weight w that obtained of step (3.1) _j ⁽²⁾, j=1 ..., 4, the location fusion results that obtains:

$d^{\left(2\right)}=\frac{\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\ω}}_j^{\left(2\right)}\×d_j^{\left(2\right)}}{\underset{j=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\ω}}_j^{\left(2\right)}}$

Step (3.5) merges by the positioning result of following formula to pressure and sound wave two class sensors, obtains final leakage positioning result:

$d=\frac{\underset{p=1}{\overset{2}{\mathrm{\Σ}}}{w}^{\left(p\right)}\×d^{\left(p\right)}}{\underset{p=1}{\overset{2}{\mathrm{\Σ}}}{w}^{\left(p\right)}}$

Weight w wherein ⁽¹⁾=3, w ⁽²⁾=7;

If positioning result exceeds duct length or the result is a negative value, then think not leak and take place, return step (2).

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