Power generation equipment performance evaluation method based on Markov process dimension reduction algorithm

Abstract

The invention provides a power generation equipment performance evaluation method based on a Markov process dimension reduction algorithm. The power generation equipment performance evaluation method comprises the following steps: establishing a k-in-n system; establishing a state probability differential equation set of the system according to the Markov process; obtaining a steady-state probability equation set based on the state probability differential equation set; forward and reverse recursion is carried out on an analytic relational expression between the steady state of each state and the steady probability of the initial stage from the edge state of the system failure shutdown; representing different state indexes of the system based on the obtained analytic relational expression; and evaluating the system according to the obtained state index. According to the method, the edge state of system fault shutdown is solved forwards, so that the complex relation between system multivariate equation sets is converted into a one-dimensional linear relation, and the probability of all steady states can be obtained by establishing a recursive expression.

Description

Technical Field

[0001] The invention relates to the technical field of engineering calculation, and in particular to a method for evaluating the performance of power generation equipment based on a Markov process dimensionality reduction algorithm. Background Art

[0002] In the field of engineering technology, there are a large number of multi-stage and multi-state tasks, such as repairmen repairing mechanical equipment, production lines processing products, and performance evaluation of large-scale power generation grid systems. For multi-state or multi-stage tasks, in order to obtain the specific conditions of different stages (especially their performance level, work efficiency, etc.), certain calculations are required. Markov process is an important tool for such state characterization and analytical calculation.

[0003] Markov process is an important method for analyzing and describing the state of a system. For a multi-state system, it can give its various indicators well. When evaluating the performance level of a certain type of power generation equipment, it is known that it has several different states (intact state, incomplete state, usable state, unusable state, etc.), corresponding to different power generation. Through observation or historical data collection, the failure rate and repair rate of this type of power generation equipment can be obtained. By establishing the state transition model of the generator, the probability of it being in different states (intact state, incomplete state, usable state, unusable state, etc.) can be obtained, and the performance level expectation of the generator can be obtained from this probability. This situation belongs to a relatively simple situation. In the actual industrial production process, due to the increasing degree of refinement, the division of stage states is also becoming more and more detailed. A system often has more states, corresponding to more performance levels (such as aerospace, nuclear industry and other high-tech industries, complex systems have hundreds of states), which will generate a large amount of state space when establishing the Markov model, resulting in an explosion in the number of state spaces when performing calculations.

[0004] Considering the complexity of existing industrial production and multi-stage tasks, when using Markov processes for modeling and calculation, the state exponential explosion may often occur, that is, the number of states in the entire operation space is too large, resulting in low computer calculation efficiency and directly affecting the output results. In response to this situation, in addition to continuously strengthening the computing function of the computer itself, Ushakov, Lisnianski and Levitin proposed the use of a universal generating function (UGF) to merge the same or similar state spaces, and omit the state spaces with less impact as appropriate, which can simplify the calculation of multi-state systems to a certain extent. However, this method will have certain deviations, and its applicability is reduced in certain situations with high precision requirements.

[0005] It can be seen that, at present, in the face of the exponential explosion that may occur in the Markov process, the existing technology either relies on higher computer computing power to directly solve it, or obtains similar results through approximate and simplified methods (such as universal generating functions). These methods have high requirements for software and hardware, and may also sacrifice some accuracy. In most engineering cases, although it can have a certain effect and will not affect the actual situation, with the continuous deepening of scientific research and the development of more and more high-tech fields, facing complex multi-state systems, the number of state spaces has increased dramatically, and it is very likely that the computer computing power will be insufficient. At the same time, as the complexity of the system increases and the task stage lengthens, if the approximate calculation method is adopted, after several links of changes, it may also lead to the accumulation and amplification of errors, resulting in the final result being far from the actual result. Summary of the invention

[0006] In view of the shortcomings of the above-mentioned prior art, the present invention proposes a power generation equipment performance evaluation method based on a Markov process dimensionality reduction algorithm, which is used to obtain various performance indicators of a certain type of power generation network in different states, and evaluate the current system according to the obtained indicators, so as to guide subsequent system maintenance and guarantee work.

[0007] The technical idea of ​​the present invention is as follows: based on the analysis of the analytical relationship between each state space, a reverse layer-by-layer recursive method is adopted to establish corresponding analytical expressions for the steady-state probabilities of each state space in the Markov process of the multi-state system and the steady-state probabilities in the initial stage, thereby directly reducing the complex multi-dimensional operations to linear operations.

[0008] The technical solution adopted by the present invention comprises the following steps:

[0009] Step 1: A power generation network is formed by n power generation equipment. When at least k power generation equipment in the power generation network generates electricity, the system can meet the requirements, thereby establishing a k-out-of-n system;

[0010] Step 2: Establish the system's state probability differential equations according to the Markov process;

[0011] Step 3: Considering the actual background of long-term operation of the system, the steady-state probability equations are obtained based on the state probability differential equations;

[0012] Step 4: From the edge state of the power generation network failure shutdown, the analytical relationship between the steady state of each state and the steady state probability of the power generation network in the initial stage of zero failure and zero repairman is deduced backward, and the probability of the power generation network in each state is obtained based on the state probability of the system in the state of zero failure and zero repairman The analytical relationship of , according to the probability of each state, the different state indicators of the system are obtained;

[0013] Step 5: Evaluate the system based on the different status indicators obtained.

[0014] Furthermore, the steady-state probability equations established in step 3 are:

[0015]

[0016] in, It represents the probability that the constructed system is in the state of zero failure and zero repairman, that is, the state probability in the initial state; It indicates the state probability that there is a fault in one power generation equipment in the system and one repairman is working on it; It indicates the probability of a state in which there are nk generating equipment failures and zero repair operations in the system; It represents the probability of a state in which there are i power generation equipment failures and zero repair operations in the system; represents the state probability that there are n-k+1 faulty power generation equipments with zero repair work in the system; c represents the number of repair workers; It indicates the readiness rate of a single repairman before starting work; Indicates the failover rate of the system when there are no devices in the system that are faulty; Indicates the repair transfer rate when there is 1 repair job in the system.

[0017] Furthermore, the specific steps of step 4 include:

[0018] Step 4.1: Order and

[0019] Step 4.2: Combine equations (1) and (2) to calculate the probability of i-1 generator failures and 1 repair operation in the system It is expressed as:

[0020]

[0021] According to formula (3)-(4), Depend on It is expressed as:

[0022]

[0023] Among them, Q i and W i is a constant;

[0024] Step 4.3: Can be organized as:

[0025]

[0026] Step 4.4: Simplify equation (5)-equation (6) to:

[0027]

[0028] Among them, Q' i-1 , W' i-1 are constants respectively;

[0029] Step 4.5: According to equation (7)-equation (8), we can get:

[0030]

[0031] in,

[0032]

[0033] Step 4.6: Based on the above formula, perform transformation operation and get:

[0034]

[0035] in, It indicates the state probability of one repair operation when there are n-k+1 power generation equipment failures in the system;

[0036] Step 4.7: Repeat formula (3)-formula (10) to obtain the steady-state probabilities of all rows 1 to c-1 about The expression is:

[0037]

[0038] in, It indicates the state probability of c-1 repair operations in the system when i generating equipment fails; It indicates the state probability of n-k+1 generating equipment failures and c-1 repair operations in the system;

[0039] Step 4.8: Based on the above formula, we can get the steady-state probability of the cth row about The expression is:

[0040]

[0041] Re-order

[0042]

[0043] Rewrite equation (12) as:

[0044] A i -A i-1 =B i+1 -B i +C i c≤i≤nk (13)

[0045] By recursion from formula (13), we can get:

[0046]

[0047] in, represents the state probability of i power generation equipment failure and c repair work in the system; let

[0048]

[0049] Then we can get:

[0050]

[0051] in, represents the state probability of c repair work operations when there are i+1 faulty power generation equipment in the system, and

[0052] Step 4.9: Based on the above derivation process, we can get The general expression of is:

[0053]

[0054] Step 4.10: According to Solve According to The probabilities of all system states can be calculated, and the corresponding performance indicators can be obtained by combining the performance levels of the power generation network in different states.

[0055] Therefore, the present invention adopts the above-mentioned power generation equipment performance evaluation method based on Markov process dimensionality reduction algorithm, which has the following beneficial effects:

[0056] First, the present invention aims at the Markov process of the k-out-of-n system constructed based on the power generation network. On the basis of analyzing the analytical relationship of each state space, a reverse layer-by-layer recursive method is adopted to establish a corresponding analytical expression for the steady-state probability of each state space in the Markov process of the multi-state system and the steady-state probability in the initial stage, thereby directly reducing the complex multi-dimensional operations to linear operations.

[0057] Second, the present invention simplifies multi-dimensional operations into one-dimensional operations, greatly reducing the time and resources required for computer operations, and making it easier for operators to operate. It can also directly characterize the state space by various parameters, and establish an analytical relationship between the steady-state probability of the state space and the initial parameters (such as production efficiency, personnel efficiency, mechanical performance level, etc.). On this basis, the initial parameters can be directly input using calculation expressions to quickly obtain results, making it easier for operators to operate.

[0058] Third, the present invention adopts a reverse layer-by-layer recursive method, which can analyze and calculate more complex multi-state systems compared to traditional direct calculation methods or direct analysis methods, facilitate large-scale system analysis research, and is conducive to further developing precise analysis of systems in all stages and processes.

[0059] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a Markov state transition process of a k-out-of-n system, which is the reverse recursive process of the steady-state probability from the right boundary forward. DETAILED DESCRIPTION

[0061] In the description of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art make various changes or modifications to the present invention, and these equivalent forms also fall within the scope limited by the claims attached to the application.

[0062] The present invention provides a dimensionality reduction method for the corresponding state space quantity calculation for the Markov model of the k-out-of-n system, and can also play a good role in the calculation dimensionality reduction for similar more complex Markov models, liberating the computing power and eliminating the exponential explosion. It is used for the performance evaluation of power generation equipment in the power grid system and can also be applied to the engineering calculation of large multi-state systems.

[0063] Generally, the direct solution method can be used to solve the steady-state equations of the system. However, as the number of state spaces increases, the difficulty of solution and the amount of calculation will increase exponentially. In this regard, according to the characteristics of system state transfer, the reverse solution idea of ​​solving from the edge state of system failure shutdown is adopted to realize the process of computational dimension reduction, transform the complex relationship between the multivariate equations of the system into a one-dimensional linear relationship, and obtain all steady-state probabilities by establishing a recursive expression.

[0064] The calculation method proposed by the present invention comprises the following steps:

[0065] Step 1: A power generation network is formed by n power generation equipment. When at least k power generation equipment in the power generation network generates electricity, the system can meet the requirements, thereby establishing a k-out-of-n system;

[0066] Step 2: Establish the system's state probability differential equations according to the Markov process;

[0067] Step 3: Considering the actual background of long-term operation of the system, the steady-state probability equations are obtained based on the state probability differential equations;

[0068] Step 4: From the edge state of the power generation network failure shutdown, the analytical relationship between the steady state of each state and the steady state probability of the power generation network in the initial stage of zero failure and zero repairman is deduced backward, and the probability of the power generation network in each state is obtained based on the state probability of the system in the state of zero failure and zero repairman The analytical relationship of , according to the probability of each state, the different state indicators of the system are obtained;

[0069] Step 5: Different state indicators reflect the performance level of the system. The probability of the system being at each performance level can be known based on the obtained probabilities of each state of the system. Based on user requirements (such as reaching a certain performance level), indicators such as the system's availability can be obtained and the system can be evaluated.

[0070] by Figure 1 As shown in the figure, a power generation network composed of n power generation equipment, at least k of which are working, is in working state. When n-k+1 devices in the power generation network fail, the network is shut down for maintenance, and the network is equipped with c repairmen, thereby constructing a k-out-of-n system.

[0071] First, the state probability differential equations are established according to the Markov process, and on this basis, the steady-state probability equations are obtained:

[0072]

[0073] in, It indicates the probability that the constructed system is in a state of zero failure and zero repairman; Indicates the state probability that there is a fault in one power generation equipment in the system and one repairman is working; It indicates the probability of a state in which there are nk generating equipment failures and zero repair operations in the system; It represents the probability of a state in which there are i power generation equipment failures and zero repair operations in the system; represents the state probability that there are n-k+1 faulty power generation equipments with zero repair work in the system; c represents the number of repair workers; It represents the fuzzy preparation rate of a single repairman before starting work; It indicates the fuzzy failover rate of the system when there are 0 devices in the system that are in failure; It represents the fuzzy repair transfer rate when there is one repair operation in the system;

[0074] On this basis, we can further Can be and In order to facilitate the solution, we can let:

[0075] and

[0076] Then we can get:

[0077]

[0078] Through formula (3)-formula (4), we can get:

[0079]

[0080] Among them, Q i and W i is a constant.

[0081] Furthermore, we can get:

[0082]

[0083] X i , Y i , Z i By replacing the representation and simplifying equations (5) and (6) in analytical form, we can obtain:

[0084]

[0085] Among them, Q' i-1 , W' i-1 are constants respectively.

[0086] From formula (7)-formula (8), we can get:

[0087]

[0088] in,

[0089]

[0090] Notice

[0091]

[0092] The recursive formula is:

[0093]

[0094] So we can find:

[0095]

[0096] Substituting the above formula into formula (9)-formula (10), we can get:

[0097]

[0098] So far, all Can be Expression, and Qi and W i The coefficients can be obtained from the previous process. By repeatedly using equations (3) - (10), the expressions of all steady-state probabilities from the first row to the (c - 1)-th row with respect to can be obtained:

[0099]

[0100] For the c-th row, we can get

[0101]

[0102] Let

[0103]

[0104] Substituting the above equation into equation (12), equation (12) can be rearranged as:

[0105] A i -A i-1 = B i+1 -B i + C i c ≤ i ≤ n - k (13)

[0106] By gradually recursive derivation from this process, we can get

[0107]

[0108] Obviously, can also be represented by Let

[0109]

[0110] Then we can get

[0111]

[0112] In the formula, From this, according to step-by-step reasoning, we can get The general term expression of is:

[0113]

[0114] So far, the expressions of all steady-state probabilities with respect to have been obtained. And from we can obtain Furthermore, all can be obtained, where 1 < i < c and 0 < j < c. After obtaining all state probabilities and combining the performance levels of the power generation network in different states, the corresponding performance indicators such as availability and power generation expected value can be obtained.

[0115] As can be seen from the above, the present invention can transform multi-dimensional operations into one-dimensional linear operations, which can greatly improve the operation efficiency and at the same time enhance the reliability of the calculation results. Therefore, by establishing the corresponding steady-state probability relationship from a certain critical moment of the system (mainly states such as fault shutdown and task stage suspension), and using the method of layer-by-layer reverse recursion, the analytical relationship between the steady-state probabilities of each layer can be obtained layer by layer. For models with many layers, the multi-dimensional and multi-level models can be quickly solved by programming methods, and all are one-dimensional linear operations, with high efficiency. For models with fewer layers, the relationship can also be established layer by layer and directly calculated manually.

[0116] Embodiment

[0117] Consider a mechanical system composed of 5 devices. The system operates normally when at least 2 devices are in good condition, and the system shuts down if the number of good devices is less than 2. Considering that after the system has been running for a long time, the failure rates of each device are often not definite values and there is a certain degree of ambiguity, and when repairing the devices, due to the influence of repair conditions and repair workers, the repair rates of the devices are also not definite values and there is also ambiguity. Therefore, it can be assumed that the fuzzy failure transition rate of the device during independent failure is The repair rate of a single repair worker is The repair preparation rate is The incomplete coverage rate of the fault is The external load borne by the system is W = 1000t, and the fault-related threshold of the device is δ = 300t (when the load borne by the device exceeds δ = 300t, fault-related phenomena will occur, that is, a certain device fails, causing the remaining devices to bear more load, and when the load borne by the remaining devices reaches a certain threshold, it will accelerate their failure rate). At the same time, the Power Law rule is introduced into the model calculation, and the load distribution coefficient is taken as β 0 = 1.2. After calculation, it can be obtained that:

[0118] 1) When c < n - k + 1, considering the case where the number of repair workers is 2, that is, c = 2. Using the above calculation method for reducing the dimension and simplifying the number of states of the specific Markov process, it can be known after calculation that the steady-state availability of the system is between 0.872 and 0.992, the steady-state probability of the repair worker being busy is between 0.28 and 0.67, the number of repair workers in the blind period in the system is between 0.335 and 0.965, the average number of faulty parts in the system is between 0.62 and 1.75, and the average number of devices that need to be repaired by replacing parts in the system is between 0.026 and 0.265.

[0119] 2) When c≥n-k+1, since a single repairman can only repair one faulty part at a time, we only need to consider the case of c=n-k+1, that is, c=4. Using the above-mentioned calculation method of reducing the number of states of a specific Markov process, it can be calculated that the steady-state availability of the system is between 0.922 and 0.996, the steady-state probability of a busy repairman is between 0.275 and 0.635, the number of repairmen in the blind period in the system is between 0.42 and 1.35, the average number of faulty parts in the system is between 0.6 and 1.55, and the average number of equipment that needs to be replaced and repaired in the system is 0.0265 to 0.235.

[0120] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for evaluating the performance of power generation equipment based on a Markov process dimensionality reduction algorithm, characterized in that: The following steps are involved: Step 1: A power generation network is formed by n power generation equipment. When at least k power generation equipment in the power generation network generates electricity, the system can meet the requirements, thereby establishing a k-out-of-n system; Step 2: Establish the system's state probability differential equations according to the Markov process; Step 3: Considering the actual background of long-term operation of the system, the steady-state probability equations are obtained based on the state probability differential equations; Step 4: From the edge state of the power generation network failure shutdown, the analytical relationship between the steady state of each state and the steady state probability of the power generation network in the initial stage of zero failure and zero repairman is deduced backward, and the probability of the power generation network in each state is obtained based on the state probability of the system in the state of zero failure and zero repairman The analytical relationship of , according to the probability of each state, the different state indicators of the system are obtained; Step 5: Evaluate the system based on the different status indicators obtained.

2. The method for evaluating the performance of power generation equipment based on the Markov process dimensionality reduction algorithm according to claim 1, characterized in that: The steady-state probability equations established in step 3 are: in, It represents the probability that the constructed system is in the state of zero failure and zero repairman, that is, the state probability in the initial state; Indicates the state probability that there is a fault in one power generation equipment in the system and one repairman is working; It indicates the probability of a state in which there are nk generating equipment failures and zero repair operations in the system; It represents the probability of a state in which there are i power generation equipment failures and zero repair operations in the system; represents the state probability that there are n-k+1 faulty power generation equipments with zero repair work in the system; c represents the number of repair workers; It indicates the readiness rate of a single repairman before starting work; Indicates the failover rate of the system when there are no devices in the system that are faulty; Indicates the repair transfer rate when there is 1 repair job in the system.

3. The method for evaluating the performance of power generation equipment based on the Markov process dimensionality reduction algorithm according to claim 2, characterized in that: The specific steps of step 4 include: Step 4.1: Order and Step 4.2: Combine equations (1) and (2) to calculate the probability of i-1 generator failures and 1 repair operation in the system It is expressed as: According to formula (3)-(4), Depend on It is expressed as: Among them, Q i and W i is a constant; Step 4.3: Can be organized as: Step 4.4: Simplify equation (5)-equation (6) to: Among them, Q i ' -1 , W i ' -1 are constants respectively; Step 4.5: According to equation (7)-equation (8), we can get: in, Step 4.6: Based on the above formula, perform transformation operation and get: in, It indicates the state probability of one repair operation when there are n-k+1 power generation equipment failures in the system; Step 4.7: Repeat formula (3)-formula (10) to obtain the steady-state probabilities of all rows 1 to c-1 about The expression is: …… in, It indicates the state probability of c-1 repair operations in the system when i generating equipment fails; It indicates the state probability of n-k+1 generating equipment failures and c-1 repair operations in the system; Step 4.8: Based on the above formula, we can get the steady-state probability of the cth row about The expression is: Re-order Rewrite equation (12) as: A i -A i-1 =B i+1 -B i +C i c≤i≤n-k (13) By recursion from formula (13), we can get: in, It indicates the state probability of c repair operations in the system when i power generation equipment fails; Re-order Then we can get: in, represents the state probability of c repair work operations when there are i+1 faulty power generation equipment in the system, and Step 4.9: Based on the above derivation process, we can get The general expression of is: Step 4.10: According to Solve According to The probabilities of all system states can be calculated, and the corresponding performance indicators can be obtained by combining the performance levels of the power generation network in different states.

Images