CN113778027B - Nonlinear autocorrelation data monitoring method based on generalized likelihood ratio control diagram - Google Patents
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- 238000000034 method Methods 0.000 title claims abstract description 40
- 238000012544 monitoring process Methods 0.000 title claims abstract description 34
- 238000010586 diagram Methods 0.000 title claims abstract description 17
- 230000008569 process Effects 0.000 claims abstract description 15
- 238000009826 distribution Methods 0.000 claims description 8
- 238000005315 distribution function Methods 0.000 claims description 6
- 238000009827 uniform distribution Methods 0.000 claims description 6
- 238000004364 calculation method Methods 0.000 claims description 4
- 238000007476 Maximum Likelihood Methods 0.000 claims description 3
- 230000005856 abnormality Effects 0.000 claims description 3
- 230000009191 jumping Effects 0.000 claims description 3
- 238000004088 simulation Methods 0.000 claims description 3
- 238000012360 testing method Methods 0.000 claims description 3
- 238000000342 Monte Carlo simulation Methods 0.000 claims description 2
- 238000004519 manufacturing process Methods 0.000 abstract description 9
- 241000039077 Copula Species 0.000 abstract description 5
- 238000003723 Smelting Methods 0.000 abstract description 3
- 230000009286 beneficial effect Effects 0.000 abstract description 2
- 230000036541 health Effects 0.000 abstract description 2
- 238000009776 industrial production Methods 0.000 abstract description 2
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- G—PHYSICS
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/418—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS] or computer integrated manufacturing [CIM]
- G05B19/41885—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS] or computer integrated manufacturing [CIM] characterised by modeling, simulation of the manufacturing system
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- G—PHYSICS
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
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- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
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Abstract
The invention relates to the technical field of flow-type industrial production and manufacturing, in particular to a nonlinear autocorrelation data monitoring method based on a generalized likelihood ratio control diagram, which comprises the following implementation steps: acquiring a group of autocorrelation data of a controlled state, and calculating a sample mean value, a variance and an autocorrelation coefficient; establishing a first-order autocorrelation model based on a Copula model; estimating controlled model parameters according to the correlation coefficient of the autocorrelation data; constructing a co-derived related data generation method; designing a control chart based on generalized likelihood ratios; monitoring a nonlinear autocorrelation process; the beneficial effects are as follows: the self-correlation data monitoring method provided by the invention provides a novel control chart based on nonlinear process data modeling according to a generalized likelihood ratio theory, expands the application range of the control chart, enables the self-correlation data to be monitored more effectively, has a wide application range, and is especially suitable for monitoring process data in industries such as health monitoring, smelting, petrochemical industry and the like.
Description
Technical Field
The invention relates to the technical field of flow-type industrial production and manufacturing, in particular to a nonlinear autocorrelation data monitoring method based on a generalized likelihood ratio control diagram.
Background
Statistical process control (STATISTICAL PROCESS CONTROL, SPC) is a process control method that uses statistical and mathematical knowledge to analyze, monitor, and mine process data. Among them, the control chart is the most commonly used, most intuitive and effective SPC tool, widely used in the manufacturing process. The common scheme is that firstly, historical controlled data is collected, a traditional control chart is selected, and a control line is determined; and then calculating statistics and dotting in a control chart by combining the process data acquired in real time on site. Once the statistics exceeds the control line, an alarm is given, the process is determined to be out of control, and on-site personnel need to analyze reasons and timely take corrective measures to restore the process to a controlled state. For continuous quality characteristics, a houhat (Shewhart) graph, an Exponentially Weighted Moving Average (EWMA) graph, or a cumulative sum (CUSUM) graph is typically chosen, and these conventional control graphs typically assume that the process data is independent, co-distributed, and subject to normal distribution. However, in flow-based industrial processes (e.g., smelting, chemical) and partially automated manufacturing processes, sensor sampling frequently results in observations that are often time-dependent. The direct use of the traditional control map has two serious consequences: on the one hand, the average operating chain length ARL controlled is very different from the ideal value; on the other hand, the monitoring capability of the control diagram is greatly reduced due to the influence of data autocorrelation after the process is out of control.
The most common method at present is to model the related data by adopting a time series model first and then monitor the residual error by adopting a traditional control chart. Common time series models include a first order autoregressive model (AR (1)), a first order moving average model (MA (1)), and a combination ARMA (1, 1) model thereof. However, these models can only describe linear correlations between data, and cannot fully explain the autocorrelation data of a complex manufacturing process, and cannot meet the requirement of monitoring the complex manufacturing process.
Disclosure of Invention
The invention aims to provide a nonlinear autocorrelation data monitoring method based on a generalized likelihood ratio control diagram, which mainly solves the problem that the existing control diagram cannot accurately monitor nonlinear autocorrelation data; specifically, under the condition that the error of the traditional control diagram monitoring autocorrelation data is large, the autocorrelation data monitoring performance is improved, and the production process abnormality is found as early as possible and accurately.
In order to achieve the above purpose, the present invention provides the following technical solutions:
The nonlinear autocorrelation data monitoring method based on the generalized likelihood ratio control diagram is characterized by comprising the following steps of:
Step one: acquiring a group of autocorrelation data of a controlled state, and calculating the mean value, variance and autocorrelation coefficient of the autocorrelation data; calculating the mean value of the samples from a set of stationary time sequences x t, t=1, …, N monitored in a controlled state Variance/>And kendall-type correlation coefficient τ;
step two: establishing a first-order Markov model based on a Clayton Copula function:
Wherein F (x t-1,xt) is the joint distribution function of the immediately adjacent two observations x t-1 and x t; f t-1 and F t are distribution functions of x t-1 and x t, respectively; θ is the only parameter of the Clayton Copula function, and theta is as small as (-1), ++ infinity a) is provided;
Step three: estimating controlled model parameters according to the correlation coefficient of the autocorrelation data;
Step four: constructing a same source related data generation method, generating T pieces of simulation data according to a Clayton Copula model and a parameter estimation result,
(1): Randomly generating U 1 from standard uniform distribution U (0, 1), note t=2;
(2): randomly generating a variable q t from the standard uniform distribution U (0, 1), and solving an equation q t＝h(ut|ut-1 to obtain U t;
(3): if t=t, terminate; otherwise, making i=i+1, jumping to (2) and continuing to execute;
(4): calculation of all u t Wherein/>Is normal distribution/>Is an inverse function of (c).
Step five: designing a control chart for monitoring mean shift based on a generalized likelihood ratio theory; original assumption H 0：μn＝μ0, alternative assumption H 1：μn＝μ1, and constructing test statistics according to log-likelihood ratios:
Step six: monitoring nonlinear autocorrelation process, setting initial value as S 1 =0, recursion form of control diagram for monitoring
Sn＝max{0,Sn-1+Ln},n＝1.2…
Wherein L n＝ln(h(xn|xn-1,μ1))-ln(h(xn|xn-1,μ0)).
Further, in the first step, the collected observed value x t is subjected to normal distribution, belongs to a stationary time sequence, and has first-order Markov property.
Further, in step six, the control limits of the control map are determined by first requiring a given controlled average operating chain length ARL 0 and then generating co-derived correlation data; finally, a Monte Carlo simulation method is adopted to obtain the product.
Further, if the monitoring statistic S n > CL at the time n, it is considered that obvious abnormality occurs in the process and the cause needs to be found and corrected; otherwise, the system is considered to be in a stable running state and is kept continuously.
The invention has the following beneficial effects: according to the self-correlation data monitoring method provided by the invention, on the basis of nonlinear process data modeling, a novel control chart is provided according to the generalized likelihood ratio theory, the application range of the control chart is enlarged, and the self-correlation data is monitored more effectively. The implementation steps are as follows: 1. acquiring a group of autocorrelation data of a controlled state, and calculating a sample mean value, a variance and an autocorrelation coefficient; 2. establishing a first-order autocorrelation model based on a Copula model; 3. estimating controlled model parameters according to the correlation coefficient of the autocorrelation data; 4. constructing a co-derived related data generation method; 5. designing a control chart based on generalized likelihood ratios; 6. the nonlinear autocorrelation process is monitored. The invention has wide application range, and is especially suitable for monitoring process data in industries such as health monitoring, smelting, petrochemical industry and the like.
Drawings
For a clearer understanding of the present invention, the disclosure is further rendered by reference to the appended drawings and to the illustrated embodiments, which are to be considered illustrative and not limiting of the disclosure.
FIG. 1 is a flow chart of an implementation of the monitoring method of the present invention.
Detailed Description
The present invention will be described in further detail below. The principles of algorithms and strategies, advantages and disadvantages and other features are presented below in more clear description by way of example, and these principles are not limited to the examples presented, and more in line with the problems encountered in actual production.
Examples
A nonlinear autocorrelation data monitoring method based on a generalized likelihood ratio control diagram comprises the following steps:
Step one: acquiring autocorrelation data of a set of controlled states, and calculating the average value of the samples Variance/>And kendall-type correlation coefficient τ;
The calculation method of kendall coefficients tau for representing the autocorrelation degree comprises the following steps:
(1): reconstructing the resulting stationary time sequence x t into N-1 pairs of samples, each sample S t-1 being representable as paired data (x t-1,xt), where t = 2,3, …, N;
(2): judging whether the first condition is met one by one, S i[1]>Sj [1] and S i[2]>Sj [2]; or condition two, S i[1]<Sj [1] and S i[2]<Sj [2]. If one of them is satisfied, consider S i to have consistency with S j; otherwise, consider that there is no consistency;
(3): the statistics have a consistent sample logarithm C, and an element logarithm D with non-consistency.
Step two: establishing a first-order Markov model based on a Clayton Copula model:
The joint distribution function and density function of two adjacent observed values x t-1 and x t are
Wherein F t-1 and F t are distribution functions of x t-1 and x t, respectively; f t-1 and f t are density functions of x t-1 and x t; θ is the only parameter of the Clayton Copula function, and theta is as small as (-1), ++ infinity A kind of electronic device.
Step three: estimating controlled model parameters according to the correlation coefficient of the autocorrelation data; a two-stage maximum likelihood estimation method may be employed.
(1): Estimating normal distribution parameters, wherein the result in the first step can be adopted;
(2): on the basis of the above step, copula parameters are estimated, and the maximum likelihood estimation is as follows: wherein/> Sample mean and sample variance/>, for the normal distribution obtained in step oneUnique parameters for the estimated Clayton Copula model;
Step four: constructing a same source related data generation method, generating T pieces of simulation data according to a Clayton copula model and parameter estimation results, recording u t＝Ft(xt), and t=1, … and T.
(1): Randomly generating U 1 from standard uniform distribution U (0, 1), note t=2;
(2): randomly generating a variable q t from the standard uniform distribution U (0, 1), and solving an equation q t＝h(ut|ut-1 to obtain U t;
(3): if t=t, terminate; otherwise, making i=i+1, jumping to the second step and continuing to execute;
(4): calculation of all u t Wherein/>Is normal distribution/>Is an inverse function of (2);
wherein, when Clayton copula is adopted to generate the autocorrelation data, the condition density in the third step is that
Step five: based on the generalized likelihood ratio theory, designing a control chart for monitoring mean shift, and constructing test statistics according to the generalized likelihood ratio, wherein the original assumption H 0：μn＝μ0 and the alternative assumption H 1：μn＝μ1:
due to the lack of aftereffect of first order Markov,
Step six: monitoring nonlinear autocorrelation process, setting initial value as S 1 =0, recursion form of control diagram for monitoring
Sn＝max{0,Sn-1+Ln},n＝1.2…
Wherein L n＝ln(h(xn|xn-1,μ1))-ln(h(xn|xn-1,μ0)).
The foregoing has shown and described the basic principles and main features of the present invention and the advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (4)
1. The nonlinear autocorrelation data monitoring method based on the generalized likelihood ratio control diagram is characterized by comprising the following steps of:
Step one: acquiring a group of autocorrelation data of a controlled state, and calculating the mean value, variance and kendall type correlation coefficient tau; calculating the mean value of the samples from a set of stationary time sequences x t, t=1, …, N monitored in a controlled state Variance/>And kendall-type correlation coefficient τ;
Step two: establishing a first-order Markov model based on ClaytonCopula functions:
Wherein F (x t-1,xt) is the joint distribution function of the immediately adjacent two observations x t-1 and x t; f t-1 and F t are distribution functions of x t-1 and x t, respectively; θ is the only parameter of the Clayton Copula function, and theta is as small as (-1), ++ infinity a) is provided;
step three: estimating controlled model parameters according to the correlation coefficient of the autocorrelation data, and specifically adopting a two-stage maximum likelihood estimation method and unique parameter estimation of a Clayton Copula model;
Step four: constructing a same source related data generation method, generating T pieces of simulation data according to a Clayton Copula model and a parameter estimation result,
(1): Randomly generating U 1 from standard uniform distribution U (0, 1), note t=2;
(2): randomly generating a variable q t from the standard uniform distribution U (0, 1), and solving an equation q t＝h(ut|ut-1 to obtain U t;
(3): if t=t, terminate; otherwise, making i=i+1, jumping to (2) and continuing to execute;
(4): calculation of all u t Wherein/>Is normal distribution/>Is an inverse function of (2);
step five: designing a control chart for monitoring mean shift based on a generalized likelihood ratio theory; original assumption H 0：μn＝μ0, alternative assumption H 1:μn＝μ1, and constructing test statistics according to log-likelihood ratios:
Step six: monitoring nonlinear autocorrelation process, setting initial value as S 1 =0, recursion form of control diagram for monitoring
Sn＝max{0,Sn-1+Ln},n＝1,2,…
Wherein L n＝ln(h(xn|xn-1,μ1))-ln(h(xn|xn-1,μ0)).
2. The nonlinear autocorrelation data monitoring method based on a generalized likelihood ratio control diagram of claim 1 wherein: in the first step, the collected observed value x t is subjected to normal distribution, belongs to a stable time sequence, and has first-order Markov property.
3. The nonlinear autocorrelation data monitoring method based on a generalized likelihood ratio control diagram of claim 1 wherein: in step six, the control limits of the control map are determined by first giving a controlled average operating chain length ARL 0 and then generating co-derived correlation data; finally, a Monte Carlo simulation method is adopted to obtain the product.
4. The nonlinear autocorrelation data monitoring method based on a generalized likelihood ratio control diagram of claim 1 wherein: if the monitoring statistic S n at the moment n is larger than CL, the obvious abnormality of the process is considered to be needed to find the reason and correct; otherwise, the system is considered to be in a stable running state and is kept continuously.
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| WO2012129561A1 (en) * | 2011-03-24 | 2012-09-27 | Pariyani Ankur | Dynamic risk analysis using alarm database |
| CN112114578A (en) * | 2020-09-22 | 2020-12-22 | 沈阳农业大学 | Steady method for multi-process multivariable process online monitoring and abnormal source diagnosis |
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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2012129561A1 (en) * | 2011-03-24 | 2012-09-27 | Pariyani Ankur | Dynamic risk analysis using alarm database |
| CN112114578A (en) * | 2020-09-22 | 2020-12-22 | 沈阳农业大学 | Steady method for multi-process multivariable process online monitoring and abnormal source diagnosis |
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| Title |
|---|
| Asymptotic efficiency of the two-stage estimation method for copula-based models;Harry Joe;Journal of Multivariate Analysis;401-419 * |
| Multivariate copulas on the MCUSUM control chart;Saowanit Sukparungsee 等;Cogent Mathematics;1-9 * |
| 基于copula函数的风力发电机组可靠性分析模型;韩思远 等;兰州交通大学学报(06);90-94 * |
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