CN113836673A - Drainage pipe network monitoring point arrangement method based on information entropy - Google Patents

Drainage pipe network monitoring point arrangement method based on information entropy Download PDF

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CN113836673A
CN113836673A CN202111038115.6A CN202111038115A CN113836673A CN 113836673 A CN113836673 A CN 113836673A CN 202111038115 A CN202111038115 A CN 202111038115A CN 113836673 A CN113836673 A CN 113836673A
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何敏
高徐军
马勃
任姿徉
刘盼盼
高焕焕
赵钦
包磊
季文静
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Xian University of Technology
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Abstract

The invention discloses a method for arranging drainage pipe network monitoring points based on information entropy, which specifically comprises the following steps: firstly, acquiring relevant parameters such as coordinates, a generalized area, a surface type, a node pollutant inflow rate and the like of a relevant pipe network, monitoring a drainage pipe network area, and determining a pollutant emission time peak section in the area; determining prior distribution information of the pollution source identification parameters of the drainage pipe network, combining the prior distribution with a likelihood function, converting the prior distribution information into posterior probability distribution to obtain a posterior probability density function of the parameters, and substituting the posterior probability density function into information entropy calculation to obtain information entropy approximate values of each node of the pipe network model of different monitoring schemes; and finally, drawing minimum information entropy change curves of different monitoring numbers, and screening the number of monitoring points with obvious information entropy reduction according to the change condition of the information entropy. The method combines various algorithms to realize breakthrough research on the arrangement of the monitoring points of the drainage pipe network and realize quick, information and intelligent arrangement of the monitoring points of the drainage pipe network.

Description

Drainage pipe network monitoring point arrangement method based on information entropy
Technical Field
The invention belongs to the technical field of water quality monitoring of drainage systems, and particularly relates to an arrangement method of drainage pipe network monitoring points based on information entropy.
Background
At present, research on optimal arrangement of monitoring points of a drainage pipe network is very limited, an optimal arrangement method mainly refers to the field of water supply pipe networks, optimization of the monitoring points of the relevant drainage pipe network is few and few, existing research for pollution events at home and abroad mainly focuses on two aspects of optimal site selection of the monitoring points and pollution source position identification, and water quality monitoring point optimal site selection taking pollution source position identification as a target is rarely considered.
The main monitoring point optimization basically takes fuzzy clustering, dynamic closeness and other methods as main methods, but the two methods only consider the correlation between related pipe wells, and rely on manual analysis and understanding of the pipe network topological structure, the identification of the correlation is only an auxiliary effect, and the final arrangement result of the monitoring points is greatly influenced by human factors. Therefore, it is necessary to perform optimal design of monitoring points by using more objective and measurable indexes, and it is a common practice to define a certain objective function and quantify the information content of the monitoring scheme. The Signal-to-noise Ratio (SNR) and the relative entropy based on the bayesian formula are often used as the measure of the information content of the monitoring well scheme. However, the signal-to-noise ratio is researched, only the interference influence of the monitoring error on the monitoring data is considered, and the influence of the parameter prior distribution on the posterior distribution is not considered in the relative entropy.
Aiming at the problem, a monitoring point optimization model based on information entropy is provided, the information entropy is the measurement of information uncertainty, and the larger the uncertainty is, the larger the information entropy is. The monitoring scheme can be well evaluated, and optimization of the drainage pipe network monitoring well with the purpose of pollution source identification is achieved.
Disclosure of Invention
The invention aims to provide a drainage pipe network monitoring point arrangement method based on information entropy, which realizes accurate identification of drainage pipe network pollutant discharge nodes, discharge time and discharge amount.
The technical scheme adopted by the invention is that the method for arranging the monitoring points of the drainage pipe network based on the information entropy is implemented according to the following steps:
step 1, acquiring relevant geographic coordinates and earth surface gradients of a pipe network area, pipe diameters, lengths and gradients of pipelines, and pollutant attenuation coefficients and roughness coefficients in the pipelines; carrying out SWMM model instance area generalization treatment; then setting the source, the components and the reduction mode of the pollution source; setting the node inflow rate;
step 2, monitoring a drainage pipe network area, and determining a pollutant discharge time peak section in the area;
step 3, determining prior distribution information of the pollution source identification parameters of the drainage pipe network, firstly randomly collecting N samples from unknown parameters x prior distribution p (x), utilizing an SWMM model to carry out water quality simulation, comparing actual observation data with SWMM5 model simulation data, combining the prior distribution and a likelihood function, converting the actual observation data into posterior probability distribution, and obtaining a posterior probability density function of the parameters;
step 4, substituting the probability densities under different monitoring conditions obtained by the calculation in the step 3 into information entropy calculation to obtain information entropy approximate values of each node of the pipe network model of different monitoring schemes;
and 5, drawing minimum information entropy change curves of different monitoring numbers according to the information entropy approximate values of all nodes of the pipe network model of different monitoring schemes obtained through calculation in the step 4, and screening the number of monitoring points with obvious information entropy reduction according to the change condition of the information entropy.
The present invention is also characterized in that,
in the step 2, the monitoring time is set to be 65-90 min; the monitoring time interval is set to 5 min; the number of monitoring was 6.
In step 3, the method specifically comprises the following steps:
step 3.1, determining prior distribution information of the pollution source identification parameters of the drainage pipe network, wherein the prior distribution information comprises node prior distribution, discharge amount prior distribution, time prior distribution, pipe diameter of the pipeline, shape of the section of the pipeline, rough coefficients and attenuation coefficients of pollutants in the pipeline; the probability density function expression is shown as the formula (1):
Figure BDA0003248035930000031
aiand biIs a uniformly distributed parameter, aiIs 1, biIs 20;
the total prior distribution p (x) is shown in equation (2):
Figure BDA0003248035930000032
step 3.2, randomly collecting N samples from unknown parameter x prior distribution p (x), and recording the N samples as xi(i ═ 1,2, …, Π); the likelihood function of the error probability distribution is defined as shown in equation (3):
Figure BDA0003248035930000033
in the formula (3), p (y | x) is a likelihood function; m is the amount of pollutants; j. the design is a squarexSetting the name of the model node; t is the pollutant discharge time; n is the number of measured data; giSetting pollutant discharge amount at a certain node of a pipe network; y isiTo discharge contaminants at the network nodes;
for each i ∈ N, from the conditional probability density function p (y | x) according to equation (3)iS) randomly computing 1 sample yiN in total are obtained, and S represents a monitoring node scheme; each group xiAnd yiSubstitution of formula (1) to give p (y)i|xiS) the conditional probability density calculation formula of the node is shown as formula (4):
Figure BDA0003248035930000041
in step 4, the method specifically comprises the following steps:
step 4.1, the information entropy definition of the posterior distribution of the true value parameter alpha of the pollution source tracking model parameter is shown as the formula (5):
H(S,y)＝-∫p(x|y,S)ln p(x|y,S)dx (5)；
the information entropy H (S, y) is desirably as shown in equation (6):
E(H(S,y))＝-∫[∫p(x|y,S)ln p(x|y,S)dx]p(y|S)dy
＝-∫∫p(x|y,S)p(y|S)ln p(x|y,S)dx dy (6)；
approximate solution is carried out by using a Monte Carlo method; firstly, rewriting the formula (6) to obtain a formula (7);
Figure BDA0003248035930000042
step 4.2, a priori distribution p (x) given by equations (1) and (2):
therefore, the prior distribution information entropy of the inversion parameter x in equation (5) is shown in equation (8):
-∫∫p(y|x,S)p(x)lnp(x)dxdy＝-lnp(x) (8)；
4.3, when the prior probability distribution p (x) is not changed, the information entropy value-ln p (x) is kept unchanged, so that the minimum value of E (S) is obtained, the second half part is extracted, as shown in the formula (9), the minimum value of U (S) is calculated, and the information entropy minimum value of the corresponding monitoring scheme is obtained;
U(S)＝-∫∫p(y|x,S)p(x)[ln p(y|x,S)-ln p(y|S)]dxdy (9)；
4.4, solving the formula (9) by using a Monte Carlo method to obtain a formula (10);
Figure BDA0003248035930000051
it is understood that p (y) in formula (10)i|S)＝∫p(x)p(yi| x, S) dx, and solving the integral by adopting a Monte Carlo method, wherein the integral is shown as a formula (11);
Figure BDA0003248035930000052
the invention has the beneficial effects that:
1) the Bayesian theory, the information entropy algorithm and the Monte Carlo sampling method are adopted to calculate the expected value of the information entropy of each node of the drainage pipe network, and the most reasonable monitoring scheme which takes pollution source identification as the main purpose is screened out through the information entropy accumulation calculation mode, so that the later-stage monitoring and management of pipe network pollutant emission are further improved;
2) the existing monitoring point arrangement basically focuses on the fields of water quality monitoring of a water supply pipe network and waterlogging monitoring point arrangement of a drainage pipe network.
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FIG. 1 is a concrete pipe network diagram of a monitoring point optimization model in the method of the present invention;
FIG. 2 is a graph of minimum information entropy change for different numbers of monitors in the method of the present invention;
FIG. 3 is a histogram of the posterior probability of emissions M in the method of the present invention;
FIG. 4 is a Jx posterior probability histogram of nodes in the method of the present invention;
FIG. 5 is a time T posterior probability histogram for the method of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a drainage pipe network monitoring point arrangement method based on information entropy, which is implemented according to the following steps:
step 1, establishing an SWMM pipe network model, specifically comprising the following steps:
step 1.1, acquiring relevant geographic coordinates and earth surface gradient of a pipe network area, pipe diameter, length and gradient of a pipeline, and attenuation coefficient and roughness coefficient of pollutants in the pipeline;
step 1.2, carrying out SWMM model instance region generalization treatment; adding or deleting catch basins according to the length of the pipe diameter; adding or deleting catch basins according to the change of pipe diameters; rainwater wells are required to be added at the crossed road sections, and the generalized results of the inspection well, the pipe sections and the sub-catchment areas of the pipe network area are finally obtained, wherein the generalized results comprise a plurality of parameters including the serial numbers, the coordinates, the inner bottom elevation and the pipe length of the pipe network, the pipe channel and the catchment area;
step 1.3, setting sources, components and a reduction mode of a pollution source;
step 1.4, setting the node inflow rate;
FIG. 1 shows an optimization model of monitoring points, the total number of model nodes is 32, the prior distribution of time is [1min, 180min ], the prior distribution of emission is [900000g, 1000000g ], and inversion parameters of the model include three parameters of time T, nodes Jx and pollutant amount M. Before calculating the model information entropy, the real emission time, the emission nodes and the emission amount need to be assumed, and the pollution source identification is carried out on the three parameters.
Step 2, monitoring a drainage pipe network area, and determining a pollutant discharge time peak section in the area; the monitoring time is set to be 65-90 min; the monitoring time interval is set to 5 min; the number of monitoring times is 6;
step 3, determining prior distribution information of the pollution source identification parameters of the drainage pipe network, firstly randomly acquiring N samples from the prior distribution p (x) of the unknown parameters x, and recording the N samples as xi(i ═ 1,2, …, Π), using SWMM model to simulate water quality, comparing actual observation data with SWMM5 model simulation data, combining prior distribution and likelihood function, converting into posterior probability distribution, and finally obtaining the final resultCalculating the posterior probability density function of the parameters, namely the node conditional probability density in the monitoring optimization; the method specifically comprises the following steps:
step 3.1, determining prior distribution information of the pollution source identification parameters of the drainage pipe network, wherein the prior distribution information comprises node prior distribution, discharge amount prior distribution, time prior distribution, pipe diameter of the pipeline, shape of the section of the pipeline, rough coefficients and attenuation coefficients of pollutants in the pipeline; the drainage time and the drainage nodes of the drainage pipe network are uniform discrete variables, the prior distribution of the drainage pipe network is set to be distributed, and all parameter intervals are independent. When the prior distribution range of each parameter is known, the probability density function expression is shown as formula (1):
Figure BDA0003248035930000071
aiand biIs a uniformly distributed parameter, aiIs 1, biIs 20;
the total prior distribution p (x) is shown in equation (2):
Figure BDA0003248035930000072
step 3.2, randomly collecting N samples from unknown parameter x prior distribution p (x), and recording the N samples as xi(i ═ 1,2, …, Π); two common observation errors of water quality monitoring are prediction deviation of a water quality diffusion model and measurement error of a sensor, are independent from a measured value, and can be modeled in any probability distribution mode according to specific conditions. These errors are independent of each other and usually follow a normal distribution with a mean of 0 and a covariance matrix of σ. Based on the above, the likelihood function of the error probability distribution is defined as shown in equation (3):
Figure BDA0003248035930000081
p (y | x) in formula (3) is a likelihood function; representing model parametersDegree of fit to the observed data; m is the amount of pollutants; j. the design is a squarexSetting (x ═ 1,2,3,. n, n is the number of nodes) for the model node name; t is the pollutant discharge time; n is the number of measured data; giSetting pollutant discharge amount at a certain node of a pipe network; y isiTo discharge contaminants at the network nodes;
for each i ∈ N, from the conditional probability density function p (y | x) according to equation (3)iRandomly calculating 1 sample yi in S) to obtain N samples, wherein S represents a monitoring node scheme; each group xiAnd yiSubstitution of formula (1) to give p (y)i|xiS) the conditional probability density calculation formula of the node is shown as formula (4):
Figure BDA0003248035930000082
and 4, constructing a drainage pipe network monitoring optimization model, substituting the probability densities under different monitoring conditions obtained by the calculation in the step 3 into information entropy calculation, and calculating optimal monitoring well schemes under different monitoring types by taking an information entropy algorithm as an evaluation index to obtain information entropy approximate values of each node of the pipe network model of different monitoring schemes.
Step 4.1, the information entropy definition of the posterior distribution of the true value parameter alpha of the pollution source tracking model parameter is shown as the formula (5):
H(S,y)＝-∫p(x|y,S)ln p(x|y,S)dx (5)；
the information entropy H (S, y) is desirably as shown in equation (6):
E(H(S,y))＝-∫[∫p(x|y,S)ln p(x|y,S)dx]p(y|S)dy
＝-∫∫p(x|y,S)p(y|S)ln p(x|y,S)dx dy (6)；
approximate solution is carried out by using a Monte Carlo method; firstly, rewriting the formula (6) to obtain a formula (7);
Figure BDA0003248035930000093
step 4.2, a priori distribution p (x) given by equations (1) and (2):
therefore, the prior distribution information entropy of the inversion parameter x in equation (5) is shown in equation (8):
-∫∫p(y|x,S)p(x)ln p(x)dxdy＝-ln p(x) (8)；
and 4.3, as can be known from the formula (8), the larger the prior range of the inversion parameter x is, the larger the information entropy calculation value of the parameter x is, and the larger the uncertainty of the inversion result of the parameter x is. When the prior probability distribution p (x) is unchanged, the information entropy value-ln p (x) is kept unchanged, so that the minimum value of E (S) is required to be obtained, the second half part is extracted, and as shown in formula (9), the information entropy minimum value of the corresponding monitoring scheme can be obtained only by calculating the minimum value of U (S).
U(S)＝-∫∫p(y|x,S)p(x)[ln p(y|x,S)-lnp(y|S)]dxdy (9)；
And 4.4, knowing that U (S) is less than or equal to 0, so that the uncertainty of the inversion parameter x is reduced by using the monitoring points in the Bayesian formula according to the information entropy concept and the formula (7).
Solving the formula (9) by using a Monte Carlo method to obtain a formula (10);
Figure BDA0003248035930000091
it is understood that p (y) in formula (10)i|S)＝∫p(x)p(yi| x, S) dx, and solving the integral by adopting a Monte Carlo method, wherein the integral is shown as a formula (11);
Figure BDA0003248035930000092
and 5, drawing minimum information entropy change curves of different monitoring numbers according to the information entropy approximate values of all nodes of the pipe network model of different monitoring schemes obtained through calculation in the step 4, screening the number of monitoring points with obvious information entropy reduction according to the change condition of the information entropy, and realizing effective utilization of resources.
Fig. 2 is a minimum information entropy change curve diagram of different monitoring numbers, a monitoring scheme with the minimum information entropy exists under different monitoring point numbers, the information entropy and posterior mean value estimation are in a positive linear correlation relationship, and therefore the monitoring scheme with the minimum information entropy needs to be screened out to serve as a final optimal monitoring arrangement scheme of the drainage pipe network. The graph summarizes the change of the minimum information entropy value under different monitoring node numbers. The graph can analyze the change situation of the information entropy value under each monitoring scheme along with the change of the monitoring nodes.
To further verify the authenticity of the monitoring point optimization based on information entropy, Markov Chain (Markov Chain) was set to 10000 using MCMC as a sampling method. The simulation calculation of the pollution source tracking is performed on the monitoring scheme, and the obtained posterior probability histogram is shown in fig. 3-5. The change of the relative error along with the change of the number of monitoring points can be analyzed and obtained by a series of graphs shown in FIGS. 3-5, which shows that the information entropy can describe the uncertainty of the model more accurately.

Claims (4)

1. A method for arranging drainage pipe network monitoring points based on information entropy is characterized by comprising the following steps:
step 1, acquiring relevant geographic coordinates and earth surface gradients of a pipe network area, pipe diameters, lengths and gradients of pipelines, and pollutant attenuation coefficients and roughness coefficients in the pipelines; carrying out SWMM model instance area generalization treatment; then setting the source, the components and the reduction mode of the pollution source; setting the node inflow rate;
step 2, monitoring a drainage pipe network area, and determining a pollutant discharge time peak section in the area;
step 3, determining prior distribution information of the pollution source identification parameters of the drainage pipe network, firstly randomly collecting N samples from unknown parameters x prior distribution p (x), utilizing an SWMM model to carry out water quality simulation, comparing actual observation data with SWMM5 model simulation data, combining the prior distribution and a likelihood function, converting the actual observation data into posterior probability distribution, and obtaining a posterior probability density function of the parameters;
step 4, substituting the probability densities under different monitoring conditions obtained by the calculation in the step 3 into information entropy calculation to obtain information entropy approximate values of each node of the pipe network model of different monitoring schemes;
and 5, drawing minimum information entropy change curves of different monitoring numbers according to the information entropy approximate values of all nodes of the pipe network model of different monitoring schemes obtained through calculation in the step 4, and screening the number of monitoring points with obvious information entropy reduction according to the change condition of the information entropy.
2. The method for arranging drainage pipe network monitoring points based on information entropy according to claim 1, wherein in the step 2, the monitoring time is set to 65-90 min; the monitoring time interval is set to 5 min; the number of monitoring was 6.
3. The method for arranging drainage pipe network monitoring points based on information entropy according to claim 1, wherein in the step 3, the method specifically comprises the following steps:
step 3.1, determining prior distribution information of the pollution source identification parameters of the drainage pipe network, wherein the prior distribution information comprises node prior distribution, discharge amount prior distribution, time prior distribution, pipe diameter of the pipeline, shape of the section of the pipeline, rough coefficients and attenuation coefficients of pollutants in the pipeline; the probability density function expression is shown as the formula (1):
Figure FDA0003248035920000021
the total prior distribution p (x) is shown in equation (2):
Figure FDA0003248035920000022
step 3.2, randomly collecting N samples from unknown parameter x prior distribution p (x), and recording the N samples as xi(i ═ 1,2, …, Π); the likelihood function of the error probability distribution is defined as shown in equation (3):
Figure FDA0003248035920000023
in the formula (3), p (y | x) is a likelihood function; m is the amount of pollutants; j. the design is a squarexSetting the name of the model node; t is the pollutant discharge time; n is the number of measured data; giSetting pollutant discharge amount at a certain node of a pipe network; y isiTo discharge contaminants at the network nodes;
for each i ∈ N, from the conditional probability density function p (y | x) according to equation (3)iS) randomly computing 1 sample yiN in total are obtained, and S represents a monitoring node scheme; each group xiAnd yiSubstitution of formula (1) to give p (y)i|xiS) the conditional probability density calculation formula of the node is shown as formula (4):
Figure FDA0003248035920000031
4. the method for arranging drainage pipe network monitoring points based on information entropy according to claim 3, wherein in the step 4, the method specifically comprises the following steps:
step 4.1, the information entropy definition of the posterior distribution of the true value parameter alpha of the pollution source tracking model parameter is shown as the formula (5):
H(S,y)＝-∫p(x|y,S)ln p(x|y,S)dx (5)；
the information entropy H (S, y) is desirably as shown in equation (6):
E(H(S,y))＝-∫[∫p(x|y,S) ln p(x|y,S)dx ]p(y|S)dy
＝-∫∫p(x|y,S)p(y|S)ln p(x|y,S)dx dy (6)；
approximate solution is carried out by using a Monte Carlo method; firstly, rewriting the formula (6) to obtain a formula (7);
Figure FDA0003248035920000032
step 4.2, a priori distribution p (x) given by equations (1) and (2):
therefore, the prior distribution information entropy of the inversion parameter x in equation (5) is shown in equation (8):
-∫∫p(y|x,S)p(x)ln p(x)dxdy＝-ln p(x) (8)；
4.3, when the prior probability distribution p (x) is not changed, the information entropy value-ln p (x) is kept unchanged, so that the minimum value of E (S) is obtained, the second half part is extracted, as shown in the formula (9), the minimum value of U (S) is calculated, and the information entropy minimum value of the corresponding monitoring scheme is obtained;
U(S)＝-∫∫p(y|x,S)p(x)[ln p(y|x,S)-ln p(y|S)]dxdy (9)；
4.4, solving the formula (9) by using a Monte Carlo method to obtain a formula (10);
Figure FDA0003248035920000033
it is understood that p (y) in formula (10)i|S)＝∫p(x)p(yi| x, S) dx, and solving the integral by adopting a Monte Carlo method, wherein the integral is shown as a formula (11);
Figure FDA0003248035920000041
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114757296A (en) * 2022-04-29 2022-07-15 广东技术师范大学 Cooperative data-based pollutant analysis method and device
CN116091035A (en) * 2022-12-21 2023-05-09 合肥中科国禹智能工程有限公司 Intelligent monitoring and point distribution system and method for urban drainage
CN116628914A (en) * 2023-07-24 2023-08-22 长江三峡集团实业发展(北京)有限公司 Inflow and infiltration analysis method for drainage pipe network, computer equipment and medium

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2007198033A (en) * 2006-01-27 2007-08-09 Toshiba Corp Portable discarded water testing device
US20110042324A1 (en) * 2007-02-02 2011-02-24 Matthew Hughes System and method for water restoration
JP2012212275A (en) * 2011-03-31 2012-11-01 Denso It Laboratory Inc Inference device, inference method and inference program
CA2940637A1 (en) * 2016-08-30 2018-02-28 Aerovirus Technologies Inc. Aptamers, nucleic acid molecules, synthetic antibodies and compositions for detecting mycoplasma hyopneumoniae and treating mycoplasma hyopneumoniae infection
CN108897964A (en) * 2018-07-09 2018-11-27 重庆大学 A kind of Bayesian statistics source tracing method of sewage network discharge beyond standards industrial wastewater
WO2019232667A1 (en) * 2018-06-04 2019-12-12 大连理工大学 Sensor arrangement method for reducing uncertainty in structural mode identification
EP3620983A1 (en) * 2018-09-05 2020-03-11 Sartorius Stedim Data Analytics AB Computer-implemented method, computer program product and system for data analysis

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2007198033A (en) * 2006-01-27 2007-08-09 Toshiba Corp Portable discarded water testing device
US20110042324A1 (en) * 2007-02-02 2011-02-24 Matthew Hughes System and method for water restoration
JP2012212275A (en) * 2011-03-31 2012-11-01 Denso It Laboratory Inc Inference device, inference method and inference program
CA2940637A1 (en) * 2016-08-30 2018-02-28 Aerovirus Technologies Inc. Aptamers, nucleic acid molecules, synthetic antibodies and compositions for detecting mycoplasma hyopneumoniae and treating mycoplasma hyopneumoniae infection
WO2019232667A1 (en) * 2018-06-04 2019-12-12 大连理工大学 Sensor arrangement method for reducing uncertainty in structural mode identification
CN108897964A (en) * 2018-07-09 2018-11-27 重庆大学 A kind of Bayesian statistics source tracing method of sewage network discharge beyond standards industrial wastewater
EP3620983A1 (en) * 2018-09-05 2020-03-11 Sartorius Stedim Data Analytics AB Computer-implemented method, computer program product and system for data analysis

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
HUAN X等: "Simulation-based optimal Bayesian experimental design for nonlinear systems", JOURNAL OF COMPUTATIONAL PHYSICS, pages 288 - 317 *
MIRA A: "Ordering and improving the performance of Monte Carlo Markov Chains", STATISTICAL SCIENCE, pages 340 - 350 *
张双圣 等: "基于贝叶斯公式的地下水污染源识别", 《中国环境科学》, pages 1568 - 1578 *
杨秋侠;刘天;: "基于关联熵与复合物元的地下管网健康度评估", 西安建筑科技大学学报(自然科学版), no. 04, pages 64 - 70 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114757296A (en) * 2022-04-29 2022-07-15 广东技术师范大学 Cooperative data-based pollutant analysis method and device
CN116091035A (en) * 2022-12-21 2023-05-09 合肥中科国禹智能工程有限公司 Intelligent monitoring and point distribution system and method for urban drainage
CN116628914A (en) * 2023-07-24 2023-08-22 长江三峡集团实业发展(北京)有限公司 Inflow and infiltration analysis method for drainage pipe network, computer equipment and medium
CN116628914B (en) * 2023-07-24 2023-11-24 长江三峡集团实业发展(北京)有限公司 Inflow and infiltration analysis method for drainage pipe network, computer equipment and medium

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