Safety control method of multi-rate heavy medium coal mine separation system under covert attack

Abstract

The present invention discloses a safety control method for a multi-rate heavy medium coal mine sorting system under covert attacks, comprising the following steps: establishing a model of a multi-rate heavy medium coal mine sorting system subjected to covert attacks on water supply valves and density sensors; obtaining an outer ellipsoid approximation set of new information of a Kalman filter by solving an optimization problem; and solving a convex optimization problem to obtain a desired controller gain. The present invention is directed to a multi-rate heavy medium coal mine sorting system, and considering the situation in which the system is subjected to covert attacks on water supply valves and density sensors, an output feedback controller is designed to minimize the impact of the attack on the performance of the multi-rate heavy medium coal mine sorting system, so that the density of the heavy medium suspension can always be maintained within a safe numerical range, thereby obtaining the best sorting effect, which is of great significance for improving the economic benefits of coal preparation plants.

Description

Technical Field

[0001] The invention relates to the field of multi-rate heavy medium coal mine sorting systems, and in particular to a safety control method for a multi-rate heavy medium coal mine sorting system under covert attack. Background Art

[0002] In recent years, with the development of automatic control technology and communication technology, network control systems have been widely used. In the process of networking, the performance of coal mine sorting systems in many aspects has been improved, but the open and interconnected operating environment also makes it more vulnerable to various malicious attacks, seriously affecting the safe operation of the system. As one of the most efficient coal preparation methods currently, the multi-rate heavy medium sorting method has the characteristics of high sorting accuracy and wide adjustment range of sorting density, and is widely used in the construction of coal preparation plants. In order to obtain better sorting effects and improve the economic benefits of coal preparation plants, it is necessary to design a controller so that when the system is subjected to covert attacks, the density of the heavy medium suspension can still be maintained within a certain safety range. Summary of the invention

[0003] In order to ensure that the density of the heavy medium suspension can still be maintained within a certain safe range when the system is subjected to a covert attack, the present invention provides a safety control method for a multi-rate heavy medium coal mine sorting system under a covert attack. Considering that the multi-rate heavy medium coal mine sorting system is subjected to a covert attack on a water supply valve and a density sensor, an output feedback controller is designed so that the system can still ensure that the density of the heavy medium suspension is always maintained within a safe numerical range under the above circumstances, thereby obtaining the best sorting effect.

[0004] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

[0005] A safety control method for a multi-rate heavy medium coal mine sorting system under covert attack comprises the following steps:

[0006] S1: Model a multi-rate dense medium coal separation system subject to covert attacks on feedwater valves and density sensors;

[0007] S2: Obtain the outer ellipsoid approximation set of the Kalman filter’s innovations by solving the optimization problem;

[0008] S3: Solve a convex optimization problem and obtain the desired controller gains.

[0009] Compared with the prior art, the present invention has the following beneficial effects:

[0010] The present invention is aimed at a multi-rate heavy medium coal mine sorting system. Considering the situation where the system is subjected to covert attacks on the water supply valve and the density sensor, an output feedback controller is designed to minimize the impact of the attack on the performance of the multi-rate heavy medium coal mine sorting system, so that the density of the heavy medium suspension can always be maintained within a safe numerical range, thereby obtaining the best sorting effect, which is of great significance for improving the economic benefits of the coal preparation plant. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0012] Figure 1 It is a flow chart of the method of the present invention.

[0013] Figure 2 It is a reachable set of states of a multi-rate heavy medium coal mine separation system that is subject to covert attack under the method of the present invention. DETAILED DESCRIPTION

[0014] The specific implementation of the present invention will be further described below in conjunction with the accompanying drawings.

[0015] like Figure 1 As shown, a safety control method for a multi-rate heavy medium coal mine separation system under covert attack comprises the following steps:

[0016] S1: Build a model of a multi-rate heavy medium coal sorting system subject to covert attacks on the water supply valve and density sensor; the model of the multi-rate heavy medium coal sorting system is as follows:

[0017]

[0018] Among them, k and k+1 represent the number of steps in the frame cycle, and the n-dimensional vector x k 、x k+1 are the states of the kth and k+1th steps of the heavy medium coal separation system, u k is the opening of the water supply valve, the m-dimensional vector y k is the error between the density of the heavy medium suspension and the set value, u k a It is a covert attack on the water supply valve. k a is a covert attack on density sensors, w k and v kThey are the process noise and measurement noise in the actual sorting production, and both are independent and identically distributed zero-mean Gaussian noises, and the covariance matrices are Σ w and Σ v , A, B, C, and D are the parameters of the multi-rate heavy medium coal separation system.

[0019] S2: Obtain the outer ellipsoid approximation set of the Kalman filter's innovations by solving the optimization problem; the specific steps are as follows:

[0020] The multi-rate heavy medium coal separation system uses a Kalman filter of the following form to estimate the state x k :

[0021]

[0022] in, is the state x k The estimated value of is the state x k+1 The estimated value of filter gain K = APC T (CPC T +Σ v ) -1 , P = APA T +Σ w -APC T (CPC T +Σ v ) -1 CPA T ;

[0023] The Kalman filter innovation is defined as Its mean is η k , the inverse of the covariance matrix is ​​Σ k Gaussian distribution, the new information when not attacked is recorded as It obeys an independent and identically distributed zero-mean Gaussian distribution with a covariance of Q = CPC T +Σ v ;

[0024] KL divergence is used to describe the stealth of the attack. In order to ensure stealth, the KL divergence between the new information of the Kalman filter when it is not attacked and when it is attacked is It needs to be no greater than a positive threshold δ. The specific formula is as follows:

[0025]

[0026] in, and f(r k ξ) are the probability density functions of the Kalman filter new information when not attacked and attacked respectively;

[0027] Define the reachable set R(x k ), which is used to describe the set to which the system state belongs with a certain probability, as shown below:

[0028]

[0029] The parameters a, b, and c are predetermined based on the probabilities F(a, m), F(b, n), and F(c, m) that the Kalman filter innovations, process noise, and measurement noise that the defender wishes to examine belong to the corresponding ellipsoid sets, where F is the cumulative distribution function of the chi-square distribution;

[0030] Perform eigenvalue decomposition on the covariance Q:

[0031]

[0032] Among them, diag(μ 1 ,μ 2 ,...,μ m ) is expressed in μ 1 ,μ 2 ,...,μ m is a diagonal matrix with diagonal elements, μ 1 ,μ 2 ,...,μ m is the eigenvalue of the matrix Q, is the matrix composed of the eigenvectors of Q;

[0033] Solve the following convex optimization problem with a scalar ι as a variable:

[0034]

[0035] The value of the scalar ι can be obtained;

[0036] The solution is as follows: r Convex optimization problem with variables:

[0037]

[0038] in, I m is the m-order unit matrix, Tr(Σ r ) represents the matrix Σ r traces;

[0039] The matrix Σ can be obtained r The value of , then the outer ellipsoid approximation set of the Kalman filter's innovation is

[0040] S3: Solve a convex optimization problem to obtain the desired controller gain. The specific steps are as follows:

[0041] The safe area of ​​the multi-rate heavy medium coal separation system is an ellipsoid Where Φ is a positive definite matrix describing the safe area. In order to ensure that the state of the multi-rate heavy medium coal mine separation system can be kept in the safe area, the following output feedback controller is adopted:

[0042]

[0043] in, are the states of the controller at step k and step k+1 respectively, L 1 and L 2 is the controller gain;

[0044] remember Given α∈(0,1);

[0045] The solution is as follows: and the scalar α i , i=1,2,3 are convex optimization problems with variables:

[0046]

[0047] in,

[0048]

[0049]

[0050]

[0051] represent The Moore-Penrose generalized inverse,

[0052] The matrix can be obtained The value of

[0053] Solve the following system of equations:

[0054]

[0055] The controller gain L can be obtained 1 and L 2 The value of .

[0056] Example:

[0057] The safety control method of the multi-rate heavy medium coal mine sorting system under covert attack of the present invention is adopted. Considering the covert attack of the water supply valve and density sensor in the system, the controller gain is designed to ensure that the density of the heavy medium suspension is always stable within a certain safe range. The specific implementation method is as follows:

[0058]

[0059] The parameter matrix is ​​as follows:

[0060] A=[1.6090], B=[-2.8595 -2.4403 -2.0825],

[0061]

[0062] w k and v k The covariance matrix of w =0.005 and Σ v =0.005I 2 , the initial state x of the multi-rate heavy medium coal separation system 0 and the initial state of the controller are all 0, the threshold value of KL divergence δ is 0.1, and α = 0.35 is given. In addition, consider the case where the probability of process noise, measurement noise and Kalman filter innovation in the actual sorting production in the corresponding ellipsoid set is 99%, that is, a = c = 9.21 and b = 6.63. Assume that the error between the density of the heavy medium suspension and the set value cannot exceed 4kg / m 3 , so the set of safe areas of the multi-rate heavy medium coal mine separation system state is in like Figure 2 As shown, the controller parameters obtained by the safety control method of the present invention are L 2 =[0 -0.0867] makes the error between the density of the heavy medium suspension and the set value smaller, which can ensure that the reachable set of the state of the multi-rate heavy medium coal mine separation system under covert attack is within a safe range.

[0063] From the simulation results, the safety control method of the present invention ensures that the density of the heavy medium suspension in the multi-rate heavy medium coal mine sorting system can always be stabilized within a certain safe range under covert attacks.

[0064] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A safety control method for a multi-rate heavy medium coal mine sorting system under covert attack, characterized in that: The steps include: S1: Build a model of a multi-rate heavy medium coal sorting system subject to covert attacks on the water supply valve and density sensor; the model of the multi-rate heavy medium coal sorting system is as follows: in, , represents the number of steps in the frame cycle, Dimensional vector , They are respectively the heavy medium coal separation system step, The state of the step, is the opening of the water supply valve, Dimensional vector is the error between the density of the heavy medium suspension and the set value, It is a covert attack on the water supply valve. It is a covert attack against density sensors. and They are the process noise and measurement noise in actual sorting production, and both are independent and identically distributed zero-mean Gaussian noises. The covariance matrices are and , , , , Parameters for multi-rate heavy medium coal separation system; S2: Obtain the outer ellipsoid approximation set of the Kalman filter innovations by solving the optimization problem; S3: Solve a convex optimization problem and obtain the desired controller gains.

2. The safety control method for a multi-rate heavy medium coal mine sorting system under covert attack according to claim 1 is characterized in that: The specific steps of obtaining the outer ellipsoid approximation set of the Kalman filter's innovation by solving the optimization problem are as follows: The multi-rate heavy medium coal separation system uses a Kalman filter of the following form to estimate the state : in, It is the status The estimated value of It is the status The estimated value of the filter gain , ; The Kalman filter innovation is defined as , which obeys the mean , the inverse of the covariance matrix is Gaussian distribution, the new information when not attacked is recorded as , which obeys an independent and identically distributed zero-mean Gaussian distribution, and the covariance is ; KL divergence is used to describe the stealth of the attack. In order to ensure stealth, the KL divergence between the new information of the Kalman filter when it is not attacked and when it is attacked is Need to be no greater than a positive threshold , the specific formula is as follows: in, and are the probability density functions of the Kalman filter innovations when not attacked and attacked respectively; Defining the reachable set of states of a multi-rate dense medium coal separation system , which is used to describe the set to which the system state belongs with a certain probability, as shown below: parameter , and The probability that the Kalman filter's innovation, process noise, and measurement noise belong to the corresponding ellipsoid set according to the defender's expectation , and to predetermine, where is the cumulative distribution function of the chi-square distribution; Pair Covariance Perform eigenvalue decomposition: in, Indicates is a diagonal matrix with diagonal elements, For the matrix The characteristic value of for The matrix composed of the eigenvectors of ; The solution is as follows: Convex optimization problem with variables: You can get the scalar The value of The solution is as follows: Convex optimization problem with variables: in, , for The unit matrix, Representation Matrix traces; The matrix can be obtained The value of , then the outer ellipsoid approximation set of the Kalman filter's innovation is .

3. The safety control method for a multi-rate heavy medium coal mine sorting system under covert attack according to claim 2 is characterized in that: The specific steps to obtain the desired controller gain are as follows: The safe area of ​​the multi-rate heavy medium coal separation system is an ellipsoid ,in Is a positive definite matrix describing the safe area. In order to ensure that the state of the multi-rate heavy medium coal mine separation system can be kept in the safe area, the following output feedback controller is adopted: in, , They are step, The state of the step controller, and is the controller gain; remember , , given ; The solution is as follows: , , , , and scalar Convex optimization problem with variables: in, ， ， ， ， ， represent The Moore-Penrose generalized inverse, The matrix can be obtained , , , and The value of Solve the following system of equations: The controller gain can be obtained and The value of .

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