A spatial plume feature clustering method based on dirichlet process mixture model

Abstract

The application relates to a spatial plume feature clustering method based on a Dirichlet process mixture model, which comprises the following steps: acquiring plume features in a plume diffusion space by using a robot provided with a gas sensor and a positioning device, and constructing a plume feature set; clustering plume features with similar characteristics by using a Dirichlet process mixture model method to obtain a plume spatial distribution type; and designing a Collapsed Gibbs sampling inference parameter to output final spatial plume feature clustering data. The application can consider the complex conditions of plume distribution in a non-structural environment, and can realize rapid, accurate and comprehensive clustering of plume types in the space.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of spatial plume feature clustering, and particularly relates to a spatial plume feature clustering method based on a Dirichlet process mixture model. BACKGROUND

[0002] With the rapid development of industrial manufacturing, flammable and explosive, toxic chemical products such as petroleum, coal gas, and natural gas bring convenience to our daily life, but at the same time, humans are increasingly facing the leakage, discharge, and poisoning of flammable and explosive, toxic media, which poses a great threat to people's health and safety.

[0003] In a non-structured environment (such as an unstructured underground corridor), once a dangerous source leaks, the traditional manual source-finding scheme is extremely dangerous, and it is of great practical significance to replace manual searching with a robot.

[0004] Due to the influence of surrounding atmospheric parameters (such as air pressure, temperature, Reynolds number, etc.) and terrain and obstacle distribution, the movement of plumes in the atmosphere has obvious instability, and the existing plume feature (plume concentration information and plume spatial position information) clustering method needs to specify the number of plume feature types in the plume diffusion area in advance, ignores the complex distribution of plumes in space, and leads to inaccurate division of plume feature types in a non-structured environment.

[0005] If the captured plume dynamic information can be divided into states, it is expected to obtain more unknown rules and knowledge of the movement of plumes in the transport medium in a non-structured environment, and to mine potential plume distribution rules, so as to timely adjust the movement strategy of the robot and speed up the determination process of the plume source.

[0006] The Dirichlet process is a non-parametric Bayesian method, and the Dirichlet process mixture model (DPMM) is a typical clustering model of the Dirichlet process. The model has the outstanding advantage of not needing to specify the clustering categories or the number in advance, and through the DPMM, the plume features with different characteristics in space are identified and labeled, the plume type probability distribution is obtained, the plume area is divided, and the complex distribution of plumes in space is more in line with the situation. SUMMARY

[0007] The present application is proposed to overcome the deficiencies in the existing plume clustering process, and provides a spatial plume feature clustering method based on a Dirichlet process mixture model.

[0008] To achieve the above-mentioned application purposes, the present application adopts the following technical solutions.

[0009] The spatial plume feature clustering method based on the Dirichlet process mixture model of the application is carried out in the following steps:

[0010] S1: using a robot carrying a gas sensor and a positioning device to obtain plume features in a plume space, the plume features including concentration information obtained by the robot and spatial position information of the robot;

[0011] S1-1: calculating the total number N of plume features obtained by the robot;

[0012] S1-2: constructing a plume feature set M obtained by the robot, M ∈ {x1, x2,..., xi,..., xN}, wherein xi represents the i-th plume feature obtained by the robot; i}, wherein x i represents the i-th plume feature obtained by the robot;

[0013] S2: based on the plume feature set M obtained by the robot, constructing a non-parametric Bayesian model Dirichlet process mixture model DPMM;

[0014] S2-1: for the i-th plume feature obtained by the robot, generating the plume type to which the i-th plume feature belongs according to formula (1);

[0015] z i ~ Multinomial (π), π ~ Dirichlet (α) (1)

[0016] In formula (1), ~ represents subject to, z i represents the plume type to which the i-th plume feature belongs, Multinomial (·) represents a multinomial distribution, Dirichlet (·) represents a Dirichlet distribution, π represents a hyperparameter of the multinomial distribution, and α represents a hyperparameter of the Dirichlet distribution;

[0017] S2-2: for the i-th plume feature obtained by the robot, generating the probability of the k-th plume type in the original plume type to which the i-th plume feature belongs according to formula (2);

[0018]

[0019] In formula (2), K represents the total number of plume types, z -i represents all plume type sets except z i , n -i,k represents the number of plume features in the k-th plume type, and N is the total number of plume features obtained by the robot;

[0020] S2-3: for the i-th plume feature obtained by the robot, generating the probability of the K+1-th new plume category to which the i-th plume information belongs according to formula (3);

[0021]

[0022] S2-4: For the i-th plume feature acquired by the robot, generate the original plume type prediction posterior distribution according to formula (4);

[0023] x i |z i =k~Guassian(μ k ,∑ k ),{μ k ,∑ k}~NIW(Φ k ) (4)

[0024] In formula (4), Guassian(·) represents a Gaussian distribution, NIW(·) represents an inverse Wishart distribution, μ k , Σ k represent the mean and variance of the Gaussian distribution corresponding to the k-th plume type, and Φ k represents the hyperparameter of the inverse Wishart distribution corresponding to the k-th plume type;

[0025] S2-5: For the i-th plume feature acquired by the robot, generate the new plume type prediction posterior distribution according to formula (5);

[0026] x i |z i =K+1~Guassian(μ,∑),{μ,∑}~NIW(Φ) (5)

[0027] In formula (5), μ, Σ represent the mean and variance of the Gaussian distribution corresponding to the K+1-th plume type, and Φ represents the hyperparameter of the inverse Wishart distribution corresponding to the K+1-th plume type;

[0028] S2-6: For the i-th plume feature acquired by the robot, generate the posterior probability of the original plume class z i to which the i-th plume feature belongs according to formula (6);

[0029] p(z i =k|x i ,z -i ,α,Φ k )∝p(z i =k|z -i ,α)p(x i |z i =k) (6)

[0030] In formula (6), ∝ represents proportional to;

[0031] S2-7: For the i-th plume feature acquired by the robot, generate the new plume type zi The posterior probability;

[0032] p(z i =K+1|x i , z -i ,α,Φ)∝p(z i =K+1|z -i ,α)p(x i |z i =K+1) (7)

[0033] S3: Based on the plume feature set M obtained by the robot, CollapsedGibbs sampling is designed to infer the plume type to which each plume feature belongs;

[0034] S3-1: Randomly generate an integer K no greater than N, and assign the plume feature x i Randomly assigned to K plume types;

[0035] S3-2: Set m = 1;

[0036] S3-3: x i Remove the existing plume type, update the mean, variance and hyperparameters of the Gaussian distribution corresponding to the plume type. If the number of plume features in this plume type is zero, then delete this plume type and K-1.

[0037] S3-4: Generate plume characteristics x according to equation (6) i The posterior probability in the original plume type;

[0038] S3-5: Generate plume characteristics x according to equation (7) i Posterior probability in the new feather flow type;

[0039] S3-6: From p(z) i =k|x i , z -i , α, Φ k ) or p(z i =K+1|x i , z -i z in , α, Φ) i Sampling new plume types;

[0040] S3-7: If a new plume type is generated, then K = K + 1;

[0041] S3-8: Generate new plume features x from the plume feature set M. i Assign m+1 to m, and return to S3-3 to execute until m = N;

[0042] S3-9: repeating S3-2 to S3-8, in the process of the Collapsed Gibbs sampling, constantly updating the plume type to which each plume feature belongs, and constantly updating the distribution of the plume type in which the i-th plume feature is located, when the plume type to which all plume features belong no longer changes, outputting the final distribution of each plume type;

[0043] S4: clustering all plume features obtained by the robot according to the final distribution of each plume type;

[0044] S5: dividing the plume features in the space according to the concentration information and the concentration gradient information obtained by the robot in each plume type area, and obtaining the distribution state of the plume features in the space.

[0045] The present application considers the complex situation of plume distribution in a non-structured environment, utilizes the good performance of DPMM in clustering, clusters and divides the plume distribution in the space, identifies multiple plume distribution types from the plume distribution space, solves the current problem of incomplete plume type clustering, provides strategy and method support for robot plume source seeking and source positioning, and has important practical significance for promoting regional safety and ensuring people's health.

[0046] The present application uses the inverse Wishart distribution of Gauss as the prior of the Dirichlet process, solves the distribution of each plume type, and uses the Collapsed Gibbs sampling to solve the hidden variable z i , so as to automatically determine the number of plume types in the space, and realize fast, accurate and comprehensive clustering of the plume types in the space. BRIEF DESCRIPTION OF DRAWINGS

[0047] The present application will be further described in detail below in combination with the drawings and embodiments:

[0048] Figure 1 is a flow chart of a space plume feature clustering method based on a Dirichlet process mixture model according to the present application;

[0049] Figure 2 is a plume diffusion simulation at a fixed height under a Gauss plume diffusion model;

[0050] Figure 3 is the number of each plume type after clustering based on the Dirichlet process mixture model;

[0051] Figure 4 is the plume feature clustering result of the Gauss plume diffusion model based on the Dirichlet process mixture model. DETAILED DESCRIPTION

[0052] The present application will be further described in detail below in combination with the drawings and embodiments:

[0053] In the examples of the present application, a spatial plume feature clustering method based on Dirichlet process mixture model is provided, first, an atmospheric diffusion model is selected as a Gaussian plume diffusion model, which can be expressed as formula (1), the model parameters are set under the Gaussian plume diffusion model, the plume diffusion simulation of the Gaussian plume diffusion model is carried out in the simulation software, and the simulation diagram is as shown in Figure 2 .

[0054]

[0055] In formula (1), x represents the distance of a spatial point on the wind direction axis to the plume source, y represents the distance of a spatial point in the vertical direction of the wind direction axis to the plume source, z represents the height of the spatial point, H is the height of the plume source, C represents the plume concentration information of the spatial point, u represents the wind speed, σ y represents the plume parameter in the y direction, and the diffusion σ z represents the plume diffusion parameter in the vertical direction.

[0056] S1: A robot carrying a gas sensor and a positioning device acquires a plume feature in a plume space, the plume feature including concentration information acquired by the robot and spatial position information of the robot;

[0057] S1-1: The total number N of the plume features acquired by the robot is calculated;

[0058] S1-2: A plume feature set M acquired by the robot is constructed, M ∈ {x1, x2,..., xi,..., xN}, where xi represents the i-th plume feature acquired by the robot; i i .

[0059] In the present embodiment, the robot acquires a total of 2500 plume features, and the statistical information of the plume features acquired by the robot in the present embodiment is shown in Table 1:

[0060] Table 1 Statistical information of the plume features acquired by the robot

[0061] Number of plume features 2500 Range of lengths of plume feature distributions acquired by the robot 0～50m Range of widths of plume feature distributions acquired by the robot 0～50m Height of plume feature distributions acquired by the robot 0.3m Number of plume concentration information 897 Number of no plume concentration information 1603

[0062] S2: Based on the plume feature set M acquired by the robot, a non-parametric Bayesian model Dirichlet process mixture model DPMM is constructed;

[0063] S2-1: For the i-th plume feature acquired by the robot, the plume type to which the i-th plume feature belongs is generated according to formula (2);

[0064] z i ~ Multinomial (π), π ~ Dirichlet (α) (2)

[0065] In formula (2), ~ represents subjecting to, z​i represents the i-th plume feature belongs to the plume type, Multinomial(·) represents a multinomial distribution, Dirichlet(·) represents a Dirichlet distribution, π represents a hyperparameter of the multinomial distribution, and α represents a hyperparameter of the Dirichlet distribution;

[0066] S2-2: For the i-th plume feature obtained by the robot, a probability that the i-th plume feature belongs to the k-th plume type in the original plume type to which the i-th plume feature belongs is generated according to formula (3);

[0067]

[0068] In formula (3), K represents the total number of plume types, z -i represents a set of all plume types other than z i , n -i,k represents the number of plume features in the k-th plume type, and N represents the total number of plume features obtained by the robot;

[0069] S2-3: For the i-th plume feature obtained by the robot, a probability that the i-th plume information belongs to the K+1-th plume category in the new plume category is generated according to formula (4);

[0070]

[0071] S2-4: For the i-th plume feature obtained by the robot, an original plume type prediction posterior distribution is generated according to formula (5);

[0072] x i |z i =k~Guassian(μ k ,∑ k ),{μ k ,∑ k}~NIW(Φ k ) (5)

[0073] In formula (5), Guassian(·) represents a Gaussian distribution, NIW(·) represents an inverse Wishart distribution, μ k ,Σ k represent the mean and variance of the Gaussian distribution corresponding to the k-th plume type, and Φ k represents a hyperparameter of the inverse Wishart distribution corresponding to the k-th plume type;

[0074] S2-5: For the i-th plume feature obtained by the robot, a new plume type prediction posterior distribution is generated according to formula (6);

[0075] x i |z i= K + 1 ~ Guassian (μ,∑), {μ,∑} ~ NIW (Φ) (6)

[0076] In formula (6), μ,∑ represent the mean and variance of the Gaussian distribution corresponding to the K+1th plume type, and Φ represents the hyperparameter of the inverse Wishart distribution corresponding to the K+1th plume type;

[0077] S2-6: For the i th plume feature obtained by the robot, the posterior probability of the original plume class z i to which the i th plume feature belongs is generated according to formula (7);

[0078] p(z i = k | x i , z -i , α, Φ k ) ∝ p(z i = k | z -i , α) p(x i | z i = k) (7)

[0079] In formula (7), ∝ represents proportional to;

[0080] S2-7: For the i th plume feature obtained by the robot, the posterior probability of the new plume type z i to which the i th plume feature belongs is generated according to formula (8);

[0081] p(z i = K + 1 | x i , z -i , α, Φ) ∝ p(z i = K + 1 | z -i , α) p(x i | z i = K + 1) (8)

[0082] S3: Based on the plume feature set M obtained by the robot, a CollapsedGibbs sampling is designed to infer the plume type to which each plume feature belongs;

[0083] S3-1: Randomly generate an integer K not greater than N, and randomly allocate the plume feature x i to K plume types;

[0084] S3-2: Set m = 1;

[0085] S3-3: Remove x i from the original plume type, update the mean, variance of the Gaussian distribution and the hyperparameter of the inverse Wishart distribution corresponding to the plume type, and if the number of plume features in this plume type is zero, delete this plume type and K-1;

[0086] S3-4: Generate plume characteristics x according to equation (7) i The posterior probability in the original plume type;

[0087] S3-5: Generate plume characteristics x according to equation (8) i Posterior probability in the new feather flow type;

[0088] S3-6: From p(z) i =k|x i ,z -i ,α,Φ k ) or p(z i =K+1|x i ,z -i In (α, Φ), z is... i Sampling new plume types;

[0089] S3-7: If a new plume type is generated, then K = K + 1;

[0090] S3-8: Generate new plume features x from the plume feature set M. i Assign m+1 to m, and return to S3-3 to execute until m = N;

[0091] S3-9: Repeat S3-2 to S3-8. During the CollapsedGibbs sampling process, continuously update the plume type to which each plume feature belongs, and continuously update the distribution of the plume type to which the i-th plume feature belongs. When the plume types to which all plume features belong no longer change, output the final distribution of each plume type.

[0092] S4: Based on the final distribution of each plume type, cluster all plume features acquired by the robot;

[0093] In this embodiment, the CollapsedGibbs sampling was set to a maximum of 100 iterations, and a total of 4 plume types were found. Based on the concentration information and concentration gradient information obtained by the robot, the plume feature distribution in space can be roughly divided into a low-concentration plume region, a low-concentration gradient plume region, a stable concentration gradient plume region, and a high-concentration gradient plume region.

[0094] The number of each type of plume is as follows Figure 3 As shown:

[0095] The percentage of each type of plume is shown in Table 2 below:

[0096] Table 2. Proportion of Feather Stream Types

[0097]

[0098] In the embodiment, the plume feature distribution divided in the space can clearly show the approximate outline of the plume distribution, the characteristics of the plume distribution features and the type quantity of the plume distribution features, thereby the information perception ability of the robot in the plume diffusion area can be improved, the decision of the robot motion planning is provided, and the theoretical and technical support for accelerating the source-seeking speed of the robot is provided.

[0099] The plume feature clustering result of the Gaussian plume diffusion model based on the Dirichlet process mixture model is as shown in Figure 4

[0100] The above merely illustrates the preferred embodiments of the present application and is not intended to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application shall be included in the protection scope of the present application.​

Claims

1. A spatial plume feature clustering method based on a Dirichlet process hybrid model, characterized by: Follow these steps: S1: Use a robot equipped with gas sensors and a positioning device to acquire plume characteristics in the plume space. The plume characteristics include the concentration information and the robot's spatial position information acquired by the robot. S1-1: Calculate the total number N of plume features acquired by the robot; S1-2: Construct the plume feature set M∈{x1,x2,...,x} acquired by the robot. i }, where x i This represents the i-th plume feature acquired by the robot; S2: Based on the plume feature set M obtained by the robot, construct a nonparametric Bayesian model Dirichlet process hybrid model DPMM; S2-1: For the i-th plume feature acquired by the robot, generate the plume type to which the i-th plume feature belongs according to equation (1); With i ~Multinomial(π),π~Dirichlet(a) (1) In equation (1), ~ indicates obedience, z i The i-th plume feature represents the plume type, Multinomial(·) represents the multinomial distribution, Dirichlet(·) represents the Dirichlet distribution, π represents the hyperparameter of the multinomial distribution, and α represents the hyperparameter of the Dirichlet distribution. S2-2: For the i-th plume feature acquired by the robot, generate the probability of the k-th plume type among the original plume types to which the i-th plume feature belongs according to equation (2); In equation (2), K represents the total number of plume types, z -i Indicates the difference between z and z i The set of all other feather types, n -i,k This represents the number of plume features in the k-th plume type, and N is the total number of plume features acquired by the robot. S2-3: For the i-th plume feature acquired by the robot, generate the probability of the (K+1)-th plume category to which the i-th plume information belongs according to equation (3); S2-4: For the i-th plume feature acquired by the robot, generate the original plume type prediction posterior distribution according to equation (4); x i |z i =k~Guassian(μ k ,∑ k ),{μ k ,∑ k )~NIW(Φ k ) (4) In equation (4), Guassian(·) represents the Gaussian distribution, NIW(·) represents the inverse Wishart distribution, and μ k , Σ k Let Φ represent the mean and variance of the Gaussian distribution corresponding to the k-th plume type. k The hyperparameters of the inverse Wishart distribution corresponding to the k-th plume type are represented. S2-5: For the i-th plume feature acquired by the robot, generate the posterior distribution of the new plume type prediction according to equation (5); x i |z i =K+1~Guassian(μ,∑),{μ,∑}~NIW(Φ) (5) In equation (5), μ and Σ represent the mean and variance of the Gaussian distribution corresponding to the (K+1)th plume type, and Φ represents the hyperparameter of the inverse Wishart distribution corresponding to the (K+1)th plume type. S2-6: For the i-th plume feature acquired by the robot, generate the original plume category z to which the i-th plume feature belongs according to equation (6). i The posterior probability; p(z i =k|x i ,With -i ,α,Φ k )∝p(z i =k|z -i ,α)p(x i |from i =k) (6) In equation (6), ∝ represents proportional to; S2-7: For the i-th plume feature acquired by the robot, generate the new plume type z to which the i-th plume feature belongs according to equation (7). i The posterior probability; p(z i =K+1|x i ,With -i ,α,Φ)∝p(z i =K+1|z -i ,α)p(x i |from i =K+1) (7) S3: Based on the plume feature set M obtained by the robot, Collapsed Gibbs sampling is designed to infer the plume type to which each plume feature belongs; S3-1: Randomly generate an integer K no greater than N, and assign the plume feature x i Randomly assign to K plume types; S3-2: Set m = 1; S3-3: x i Remove the existing plume type, update the mean, variance and hyperparameters of the Gaussian distribution corresponding to the plume type. If the number of plume features in this plume type is zero, then delete this plume type and K-1. S3-4: Generate plume characteristics x according to equation (6) i The posterior probability in the original plume type; S3-5: Generate plume characteristics x according to equation (7) i Posterior probability in the new feather flow type; S3-6: From p(z) i =k|x i , z -i , α, Φ k ) or p(z i =K+1|x i , z -i z in , α, Φ) i Sampling new plume types; S3-7: If a new plume type is generated, then K = K + 1; S3-8: Generate new plume features x from the plume feature set M. i Assign m+1 to m, and return to S3-3 to execute until m = N; S3-9: Repeat S3-2 to S3-8. During the CollapsedGibbs sampling process, continuously update the plume type to which each plume feature belongs, and continuously update the distribution of the plume type to which the i-th plume feature belongs. When the plume types to which all plume features belong no longer change, output the final distribution of each plume type. S4: Based on the final distribution of each plume type, cluster all plume features acquired by the robot; S5: Based on the concentration information and concentration gradient information obtained by the robot, the spatial plume feature distribution is divided in each plume type region to obtain the spatial plume feature distribution state.

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