Fault Detection Method for Petroleum Catalytic Cracking Process Based on Hidden Markov Model

Abstract

The present invention discloses a fault detection method for a petroleum catalytic cracking process based on a hidden Markov model, comprising the following steps: the first step: establishing a mathematical model of the petroleum catalytic cracking process; the second step: designing a fault detection filter as a residual generator to generate a residual signal; the third step: selecting an evaluation function, determining a threshold, and thus establishing a fault detection strategy. The beneficial effects of the present invention are: being able to simultaneously consider the system state that is constantly changing under the internal and external environments, the proposed fault detection scheme is able to detect the petroleum catalytic cracking process under constantly changing internal and external environments; designing an asynchronous fault detection filter under the mechanism of a hidden Markov model, solving the asynchronous phenomenon that occurs between the filter and the controlled system, and realizing asynchronous fault detection of the petroleum catalytic cracking process; considering the time-varying time lag that is dependent on the mode and using a fault weighting system and multi-cycle initial faults to prove the effectiveness of the designed fault detection strategy.

Description

Technical Field

[0001] The invention relates to the field of fault detection filters, and in particular to a fault detection method for a petroleum catalytic cracking process based on a hidden Markov model. Background Art

[0002] With the development of modern society, petroleum catalytic cracking is the most important secondary processing process in the current petroleum refining industry, and it is also the core process for lightening heavy oil. Catalytic cracking is the core technology used by modern refineries to upgrade heavy gas oil and residual oil, and it is an important means for refineries to obtain economic benefits. Therefore, it is very important to model the petroleum catalytic cracking process as a singular Markov jump system for fault detection. Singular systems are also called implicit systems, description systems, algebraic-differential systems, etc. In the past few decades, singular systems have attracted widespread attention from many scholars and experts due to their wide application in modeling a large number of practical systems such as power and circuit systems, economic and social systems, and biological systems. Compared with normal state space systems, singular systems need to ensure not only their stability, but also their regularity, pulse-free (continuous case) and causality (discrete case). Therefore, the analysis and control of singular systems will be more complex and difficult than that of regular systems. On the other hand, it is noted that Markov jump systems can be used to simulate a large number of complex real dynamic systems, such as robots, chemical and circuit factories, etc., where their structures and parameters often undergo sudden changes due to changes in the internal or external environment, mode switching, component failures, etc.

[0003] Fault detection can detect system faults in time, thereby ensuring the reliability of the system and maintaining the special performance of the system. Therefore, the use of robust fault detection filter design methods based on state estimation to solve the fault detection problem has gradually attracted the attention of many scholars. Fault detection requires that the residual signal is robust to external interference and inevitable modeling errors that may seriously affect the performance of the system. At the same time, in order to quickly and efficiently detect system faults, the residual signal must be sensitive to various errors and faults. It is worth pointing out that most of the existing inventions only focus on synchronous control without solving the asynchronous problem. However, due to the inevitable time delay, packet loss and other facts, in practical applications, the filter or controller often cannot access the mode of the controlled device, resulting in the mode of the filter or controller being asynchronous with the plant mode. Recently, the hidden Markov model mechanism has been proposed. The hidden Markov model is described by two Markov processes that depend on a conditional probability matrix. In recent years, the hidden Markov model has been widely used as an effective tool to represent and deal with asynchronous control problems and filtering problems. Summary of the invention

[0004] In order to solve the above problems, the present invention discloses a fault detection method for a petroleum catalytic cracking process based on a hidden Markov model.

[0005] The specific plan is as follows:

[0006] The fault detection method of petroleum catalytic cracking process based on hidden Markov model includes the following steps: mathematical modeling of petroleum catalytic cracking process; designing fault detection filter as residual generator to generate residual signal, selecting evaluation function, determining threshold, so as to establish fault detection strategy; constructing modal-related and time-delay-related LK functionals, and using linear matrix inequality to propose the conditions of asynchronous fault detection filter. In view of the admissibility problem of singular jump system, the modal-related time-varying delay is considered, and the asynchronous H is designed under the hidden Markov model mechanism and fault weighting strategy. ∞ Filter to realize H of singular jump system ∞ Finally, the proposed asynchronous filtering and H ∞ Effectiveness of fault detection techniques.

[0007] As a further improvement of the present invention, the present invention specifically comprises the following steps:

[0008] (a) Establishment of a petroleum catalytic cracking process with multiple cycle incipient failures:

[0009]

[0010] Where x1(t) is the state vector such as regeneration temperature, valve position or blower capacity that should be adjusted, and x2(t) is the state vector reflecting management, policy, commercial interests, etc. ω(t) represents the additional disturbance, and u(t) is the adjustment value.

[0011] Taking into account the inevitable environmental impact, the complex petroleum catalytic cracking process can be rewritten as the following singular Markov jump system with time-varying delay:

[0012]

[0013] in, is a singular matrix and rank(H)=r<n; is the system status; is the measurement output; is the control input, It is external interference. is a fault, u(t), ω(t), f(t) belongs to

[0014] {σ t} means in The Markov jump process with values ​​in , and its trajectory is a continuous step function. For i,j∈S1, Λ=[λ ij] represents the transfer rate matrix that satisfies general conditions.

[0015] represents time-varying lag and has the following characteristics

[0016] 0≤d i (t)≤d<∞, For each σ t =i∈S1, (3)

[0017] Among them, d, is a known constant.

[0018] (b) The following asynchronous fault detection filter is designed as the residual generator

[0019]

[0020] in, And rank(H f )=r f ≤n f ; is the asynchronous fault detection filter state, is the residual signal, A f (r t ,σ t ), B f (r t ,σ t ), C f (r t ,σ t ), D f (r t ,σ t ) are the parameters of the asynchronous fault detection filter that need to be designed.

[0021] {r t} is a finite set The value is determined by {σ t} Markov process, Π=[π iθ ] is the conditional probability matrix, where

[0022] P{r t =θ|σ t =i}=π iθ , (5)

[0023] For any i∈S1,π iθ ≥0, Use (σ t ,r t ,Λ,Π) represents a hidden Markov model.

[0024] (c) In order to constrain the fault frequency and improve the performance of the fault detection system, we introduce a given weight function w(s) so that f w (s) = w(s)f(s), where f w (s), f(s) represent f w The Laplace transform of f(t) and f(t). The minimum state space realization of the fault-weighted system can be described as

[0025]

[0026] in is the fault weight system state, A w , B w , C w , D w is the given parameter.

[0027] (d) Combining (2), (4), and (6), we obtain the time-delay singular jump error system as follows:

[0028]

[0029] Where e(t) = z(t) - z w (t),

[0030]

[0031]

[0032]

[0033] C c (r t ,σ t )=[D f (r t ,σ t )E(σ t ) C f (r t ,σ t ) -C w ],

[0034] C dc (r t ,σ t )=[D f (r t ,σ t )E d (σ t ) 0 0],

[0035] D c (r t ,σt )=[D f (r t ,σ t )F(σ t ) D f (r t ,σ t )G(σ t ) D f (r t ,σ t )I(σ t )-D w ].

[0036] (e) For any σ t =i∈S1,r t =θ∈S2, the augmented time-delay singular error system is expressed as

[0037]

[0038] in,

[0039] C ciθ =[D fiθ E i C fiθ -C w ], C dciθ =[D fiθ E di 0 0],

[0040] D ciθ =[D fiθ F i D fiθ G i D fiθ I i -D w ].

[0041] (f) Definitions:

[0042] (A) For each σ t =i∈S1,r t =θ∈S2, for (H c ,A ciθ ) is regular and pulse-free, and the time-delay singular jump error system (7) is regular and pulse-free;

[0043] (B) If there is a scalar If the following formula holds, the time-delay singular jump error system (7) is considered to be stochastically stable;

[0044]

[0045] (C) If the time-delay singular jump error system (7) is regular, pulse-free and stochastically stable, then the time-delay singular jump error system (7) is called stochastically admissible;

[0046] (D) For non-zero And the initial condition is zero. If the following conditions are met, the time-delay singular jump error system (7) satisfies H ∞ Performance level κ (κ>0):

[0047]

[0048] (g) Fault detection strategy:

[0049] ①Choose appropriate evaluation function and threshold.

[0050] Select and As residual evaluation function and threshold respectively:

[0051]

[0052]

[0053] ②Decision-making based on logical relationships:

[0054] It means no trouble;

[0055] Means there is a fault and generates a warning; (13)

[0056] (h) For all σ t =i∈S1,r t =θ∈S2, define P i , R>0 and scalar Design the Lyapunov functional to study the stability conditions of the time-delay singular jump error system (7):

[0057]

[0058] in,

[0059]

[0060]

[0061]

[0062] Define the random process {η t ,σ t}Action Weakly infinitesimal operators on

[0063]

[0064] have:

[0065]

[0066]

[0067]

[0068] Combining (15)-(17), when v(t) = 0, we have

[0069]

[0070] in,

[0071]

[0072] For non-zero and zero initial condition, we get

[0073]

[0074] in,

[0075]

[0076] (i) According to Schur's complement lemma and Lyapunov's theorem, when the following conditions are met,

[0077]

[0078]

[0079]

[0080] in,

[0081] Then the system can satisfy random admissibility and have H ∞ Performance indicators.

[0082] (j) Design asynchronous filters for fault detection.

[0083] make

[0084] (k) According to Schur's complement lemma, when the following linear matrix inequality is satisfied

[0085]

[0086]

[0087]

[0088] in,

[0089]

[0090]

[0091]

[0092]

[0093] Γ iθ5 =diag{( i -1)R1,( i -1)R2,( i -1)R3},

[0094] Γ iθ7 =-diag{γI,γI,γI},

[0095]

[0096] Then the fault detection filter parameters (4) can be expressed as:

[0097]

[0098] Then the system satisfies random admissibility and satisfies H ∞ Performance indicators.

[0099] This method combines some practical problems and designs an asynchronous fault detection filter for a petroleum catalytic cracking process with multi-cycle initial faults. Compared with the prior art, the technical solution provided by the present invention has the following beneficial effects:

[0100] 1. The modeled singular Markov system can simultaneously consider the influence of the constantly changing internal and external environments in the process of catalytic cracking of petroleum, and model the systems in different internal and external environments as subsystems of the Markov system, and the jumps between the subsystems obey the Markov chain; compared with the existing modeling of the catalytic cracking process of petroleum as a general singular linear system to study the fault detection filter, the present invention can simultaneously consider the system state affected by the constantly changing internal and external environments, so the fault detection scheme proposed by the present invention can detect the catalytic cracking process of petroleum in which the internal and external environments are constantly changing;

[0101] 2. Due to inevitable delays, networking mechanisms, measurement errors, etc., the modal information of the petroleum catalytic cracking process is not fully accessible, which may lead to asynchronous phenomena between the filter and the controlled system. The present invention solves this problem by designing an asynchronous fault detection filter under the hidden Markov model mechanism and realizes asynchronous fault detection in the petroleum catalytic cracking process;

[0102] 3. Since time delay is inevitable in the process of petroleum catalytic cracking, especially time-varying time delay, they often lead to poor performance or even instability of the controlled system. In different Markov subsystems, time delay is often different. To address this thorny problem, the present invention considers the time-varying time delay that is dependent on the mode. On the other hand, the present invention uses the fault weighting system and multi-cycle incipient faults to prove the effectiveness of the designed fault detection strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 The present invention provides a fault detection flow chart based on a hidden Markov model.

[0104] Figure 2 It is a fault detection algorithm diagram based on the hidden Markov model provided by the present invention.

[0105] Figure 3 is a multi-cycle incipient fault given by the present invention, where the initial condition x t0 =[-1.5 -0.3] T , fault signal f(t), let ω(t) be a uniform noise bounded by (-0.06, 0.06).

[0106] Figure 4 The present invention provides the petroleum catalytic cracking process state and Markov jump mode when d=2.5.

[0107] Figure 5 It is the residual signal z(t) based on the hidden Markov model strategy when d=2.5 given by the present invention.

[0108] Figure 6 It is the residual evaluation function value and threshold value given by the present invention. DETAILED DESCRIPTION

[0109] The specific implementation of the present invention is described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0110] As shown in the figure, the present invention provides a fault detection method for a petroleum catalytic cracking process based on a hidden Markov model, which specifically includes the following steps:

[0111] (a) Establishment of a petroleum catalytic cracking process with multiple cycle incipient failures:

[0112]

[0113] Where x1(t) is the state vector such as regeneration temperature, valve position or blower capacity that should be adjusted, and x2(t) is the state vector reflecting management, policy, commercial interests, etc. ω(t) represents the additional disturbance, and u(t) is the adjustment value.

[0114] Taking into account the inevitable environmental impact, the complex petroleum catalytic cracking process can be rewritten as the following singular Markov jump system with time-varying delay:

[0115]

[0116] in, is a singular matrix and rank(H)=r<n; is the system status; is the measurement output; is the control input, It is external interference. is a fault, u(t), ω(t), f(t) belongs to

[0117] {σ t} means in The Markov jump process with values ​​in , and its trajectory is a continuous step function. For i,j∈S1, Λ=[λ ij ] represents the transfer rate matrix that satisfies general conditions.

[0118] represents time-varying lag and has the following characteristics

[0119] 0≤d i (t)≤d<∞, For each σ t =i∈S1,

[0120] Among them, d, is a known constant.

[0121] (b) The following asynchronous fault detection filter is designed as the residual generator

[0122]

[0123] in, And rank(H f )=r f ≤n f ; is the asynchronous fault detection filter state, is the residual signal, A f (r t ,σ t ), B f (r t ,σ t ), C f (r t ,σ t ), D f (r t ,σ t ) are the parameters of the asynchronous fault detection filter that need to be designed.

[0124] {r t} is a finite set The value is determined by {σ t} Markov process, Π=[π iθ ] is the conditional probability matrix, where

[0125] P{r t =θ|σ t =i}=π iθ ,

[0126] For any i∈S1,π iθ ≥0, Use (σ t ,r t ,Λ,Π) represents a hidden Markov model.

[0127] (c) In order to constrain the fault frequency and improve the performance of the fault detection system, we introduce a given weight function w(s) so that f w (s) = w(s)f(s), where f w (s), f(s) represent f w The Laplace transform of f(t) and f(t). The minimum state space realization of the fault-weighted system can be described as

[0128]

[0129] in is the fault weight system state, A w , B w , C w , D w is the given parameter.

[0130] (d) Combining (2), (4), and (6), we get the time-delay singular jump error system as follows:

[0131]

[0132] Where e(t) = z(t) - z w (t),

[0133]

[0134]

[0135]

[0136] C c (r t ,σ t )=[D f (r t ,σ t )E(σ t ) C f (r t ,σ t ) -C w ],

[0137] C dc (r t ,σ t )=[D f (r t ,σ t )E d (σ t ) 0 0],

[0138] D c (r t ,σ t )=[D f (r t ,σ t )F(σ t ) D f (r t ,σ t )G(σ t ) D f (r t ,σ t )I(σ t )-D w ].

[0139] (e) For any σ t =i∈S1,r t =θ∈S2, the augmented time-delay singular error system is expressed as

[0140]

[0141] in,

[0142] C ciθ =[D fiθ E i C fiθ -C w ], C dciθ =[D fiθ E di 0 0],

[0143] D ciθ =[D fiθ F i D fiθ G i D fiθ I i -D w ].

[0144] (f) Definitions:

[0145] (A) For each σ t =i∈S1,r t =θ∈S2, for (H c ,A ciθ ) is regular and pulse-free, and the time-delay singular jump error system (7) is regular and pulse-free;

[0146] (B) If there is a scalar If the following formula holds, the time-delay singular jump error system (7) is considered to be stochastically stable;

[0147]

[0148] (C) If the time-delay singular jump error system (7) is regular, pulse-free and stochastically stable, then the time-delay singular jump error system (7) is called stochastically admissible;

[0149] (D) For non-zero And the initial condition is zero. If the following conditions are met, the time-delay singular jump error system (7) satisfies H ∞ Performance level κ (κ>0):

[0150]

[0151] (g) Fault detection strategy:

[0152] ①Choose appropriate evaluation function and threshold.

[0153] Select and As residual evaluation function and threshold respectively:

[0154]

[0155]

[0156] ②Decision-making based on logical relationships:

[0157] It means no trouble;

[0158] It means there is a fault and a warning is generated;

[0159] In this embodiment, the parameters shown in Table 1 are selected:

[0160] Table 1: System parameters and design parameters

[0161]

[0162]

[0163] The technical means disclosed in the scheme of the present invention are not limited to the technical means disclosed in the above-mentioned implementation mode, but also include technical schemes composed of any combination of the above-mentioned technical features. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications are also regarded as the protection scope of the present invention.

Claims

1. A fault detection method for a petroleum catalytic cracking process based on a hidden Markov model, characterized in that: The following steps are included Step 1: Establish a mathematical model of the petroleum catalytic cracking process; Step 2: Design a fault detection filter as a residual generator to generate a residual signal; Step 3: Select the evaluation function and determine the threshold to establish the fault detection strategy; The specific steps include: (a) Establishment of a petroleum catalytic cracking process with multiple cycle incipient failures Where x1(t) is the state vector of the regeneration temperature, valve position or blower capacity to be adjusted, x2(t) is the state vector reflecting management, policy and commercial interests; ω(t) is the additional disturbance, and u(t) is the adjustment value; Taking into account the inevitable environmental impact, the complex petroleum catalytic cracking process is rewritten as the following singular Markov jump system with time-varying delay: in, is a singular matrix and rank(H)=r<n; is the system status; is the measurement output; is the control input, It is external interference. is the fault, u(t), ω(t); {σ t } means in The Markov jump process with values ​​in is a continuous step function; for i,j∈S1, Λ=[λ ij ] is the transfer rate matrix that satisfies the general conditions; is a time-varying lag with the following characteristics Among them, d, is a known constant; (b) The following asynchronous fault detection filter is designed as the residual generator in, And rank(H f )=r f ≤n f ; is the asynchronous fault detection filter state, is the residual signal, A f (r t ,σ t ), B f (r t ,σ t ), C f (r t ,σ t ), D f (r t ,σ t ) are the parameters of the asynchronous fault detection filter that needs to be designed; {r t } is a finite set The value is determined by {σ t } Markov process, Π=[π iθ ] is the conditional probability matrix, where P{r t =θσ t =i}=π iθ , (5) For any i∈S1,π iθ ≥0, Use (σ t ,r t ,Λ,Π) represents a hidden Markov model; (c) In order to constrain the fault frequency and improve the performance of the fault detection system, a given weight function w(s) is introduced so that f w (s) = w(s)f(s), where f w (s), f(s) represent f w The Laplace transform of f(t) and f(t); the minimum state space realization of the fault-weighted system is described as: in is the fault weight system state, A w , B w , C w , D w is a given parameter; (d) Combining (2), (4), and (6), we obtain the time-delay singular jump error system as follows: where e(t) = z(t) - z w (t), C c (r t ,s t )=[D f (r t ,s t )E(s t )C f (r t ,s t )-C w ], C dc (r t ,s t )=[D f (r t ,s t )E d (s t )00], D c (r t ,s t )=[D f (r t ,s t )F(s t )D f (r t ,s t )G(s t )D f (r t ,s t )I(s t )-D w ]; (e) For any σ t =i∈S1,r t =θ∈S2, the augmented time-delay singular error system is expressed as in, C dciθ =[D fiθ E di 00],D ciθ =[D fiθ F i D fiθ G i D fiθ I i -D w ]; (f) Definitions: (A) For each σ t =i∈S1,r t =θ∈S2, for (H c ,A ciθ ) is regular and pulse-free, and the time-delay singular jump error system (7) is regular and pulse-free; (B) If there is a scalar If the following formula holds, the time-delay singular jump error system (7) is considered to be stochastically stable; (C) If the time-delay singular jump error system (7) is regular, pulse-free and stochastically stable, then the time-delay singular jump error system (7) is called stochastically admissible; (D) For non-zero And the initial condition is zero. If the following conditions are met, the time-delay singular jump error system (7) satisfies H ∞ Performance level κ, κ>0: (g) Fault detection strategy: ①Select appropriate evaluation function and threshold; Select and As residual evaluation function and threshold respectively: ②Decision-making based on logical relationships: (h) For all σ t =i∈S1,r t =θ∈S2, define P i , R>0 and scalar Design the Lyapunov functional to study the stability conditions of the time-delay singular jump error system (7): in, Define the random process {η t ,σ t }Action Weakly infinitesimal operators on have: Combining (15)-(17), when v(t) = 0, we have in, For non-zero and zero initial condition, we get: in, (i) According to Schur's complement lemma and Lyapunov's theorem, when the following conditions are met, in, Then the system can satisfy random admissibility and have H ∞ Performance indicators; (j) Design asynchronous filters for fault detection: make (k) According to Schur's complement lemma, when the following linear matrix inequality is satisfied: in, Then the fault detection filter parameters (4) are expressed as: Then the system satisfies random admissibility and satisfies H ∞ Performance indicators.

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