CN112229212A - Roller kiln energy consumption abnormity detection method based on dynamic principal component analysis - Google Patents
Roller kiln energy consumption abnormity detection method based on dynamic principal component analysis Download PDFInfo
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Abstract
The invention relates to the technical field of detection methods, in particular to a roller kiln energy consumption abnormity detection method based on dynamic principal component analysis, which comprises the following specific steps: (1) firstly, selecting sample data and constructing a dynamic principal component analysis DPCA model; (2) then, calculating an autocorrelation function value of all variables of the sample data; (3) judging the autocorrelation degree according to the result of the autocorrelation function value, setting a threshold value at the same time, and introducing no augmentation matrix to the variable meeting the threshold value range; otherwise, determining the value of the lag length h according to the degree of autocorrelation, and constructing an augmentation matrix X (h); (4) and (4) analyzing the augmentation matrix X (h) by using a traditional Principal Component Analysis (PCA) algorithm, extracting the time sequence correlation among variables and carrying out anomaly detection. The invention can effectively improve the detection rate, reduce the false alarm rate and improve the calculation efficiency; and the dynamic principal component analysis algorithm is improved, the calculation speed is improved, and the calculation resources are saved.
Description
Technical Field
The invention relates to the technical field of detection methods, in particular to a roller kiln energy consumption abnormity detection method based on dynamic principal component analysis.
Background
The roller kiln is an important ceramic kiln which is mainly used for producing building ceramics, and products are various ceramic tiles and are main energy consumption equipment in ceramic production. At present, the domestic roller kilns gradually realize the aims of automation, coal gasification, light weight and the like, and the production process is monitored by an intelligent instrument and an industrial control technology. In the ceramic production process, if the roller kiln is abnormal due to the factors such as materials, parameter control and personnel, the problems of product flaw, energy waste and the like can be caused, great economic loss is caused, and even safety accidents occur when the conditions are serious. Enterprises in the current stage usually adopt modes of manual inspection, fixed threshold value alarming and the like to check and find abnormal conditions, and have the defects of labor consumption, low accuracy, delayed abnormal finding and the like.
With the development of science and technology, at present, roller kiln equipment is generally provided with a digital instrument and an industrial computer for real-time monitoring and acquisition, transmission and storage of production data, and rich materials are provided for the application of a data-driven abnormity diagnosis technology. But the roller kiln has the characteristics of obvious dynamic property, time-varying property, strong coupling property and the like in the production process, so that the difficulty is brought to the energy consumption abnormity diagnosis of the roller kiln. Some abnormity detection methods, for example, chinese patent CN108955247A discloses a method and system for modeling firing temperature and controlling time lag of roller kiln, which mainly aims to realize intellectualization and light weight of roller kiln, improve product quality, reduce energy consumption, and reduce labor intensity of field workers.
Some other detection methods, such as the conventional Principal Component Analysis (PCA) algorithm, perform anomaly detection by mapping the state vector to principal component subspace and residual subspace through a PCA model and passing through T2And SPE statistics, where there is a key premise assumption that each isThe samples at a time should be statistically independent, i.e., the observations of the current sample are independent of the observations of the samples at the past time. For classical industrial processes this assumption is valid only for long sampling intervals, e.g. 2-12 hours, whereas in practical industrial processes shorter sampling intervals, e.g. 3-10 minutes, tend to be used in order to find anomalies and to handle them in time. For data with short sampling intervals, such as a roller kiln, due to time lag characteristics, closed-loop control and interference of a system, time sequence correlation exists between sample data at different moments, namely, sample variables have certain autocorrelation, and the characteristic is called as the dynamic characteristic of the system. For such sample data, although the conventional PCA algorithm can be used to detect and separate the anomalies, since the autocorrelation existing in the data cannot be extracted by the PCA model, the obtained principal elements cannot truly reflect the characteristics of the sample data, and the anomalies caused by small random noise or interference may cause false reports or false reports.
In order to overcome the problem that the PCA algorithm of the principal component analysis method is used for processing dynamic samples, Ku proposes a DPCA algorithm of the dynamic principal component analysis. The DPCA algorithm expands an original static sample data matrix into a time-related matrix by combining with a dynamic sequence thought, and then performs analysis by using a PCA algorithm, thereby extracting the time dynamics among variables. In recent years, DPCA has been used for anomaly detection in the fields of chemical processes, refinery distillation processes, natural gas transmission processes, and the like.
However, Ku proposes a DPCA algorithm based on a time-lag matrix, which greatly increases the computational complexity and increases the computational time due to the expansion of the data matrix. In order to improve the intelligent degree of the roller kiln and the energy efficiency of enterprises, the research of a rapid, accurate and intelligent abnormality detection method is an urgent need of the enterprises.
Disclosure of Invention
The invention provides a roller kiln energy consumption abnormity detection method based on dynamic principal component analysis, aiming at overcoming the problem of low detection efficiency of the roller kiln in abnormal conditions.
In the technical scheme, a roller kiln energy consumption abnormity detection method based on dynamic principal component analysis is provided, and the method comprises the following specific steps:
(1) firstly, selecting sample data and constructing a dynamic principal component analysis DPCA model;
(2) then, calculating an autocorrelation function value of all variables of the sample data;
(3) judging the autocorrelation degree according to the result of the autocorrelation function value, setting a threshold value at the same time, and introducing no augmentation matrix to the variable meeting the threshold value range; otherwise, determining the value of the lag length h according to the degree of autocorrelation, and constructing an augmentation matrix X (h);
(4) and (4) analyzing the augmentation matrix X (h) by using a traditional Principal Component Analysis (PCA) algorithm, extracting the time sequence correlation among variables and carrying out anomaly detection.
Preferably, in step (2), the autocorrelation function value is a correlation of sequence states between any two different time instants in signal processing and time series analysis; wherein, the autocorrelation function of the random process x (t) is defined as:
Rx(τ)＝E[x(t)x(t-τ)] (1)
the autocorrelation function of the discrete random sequence x (k) is defined as:
where n is the number of samples and τ is the lag length;
the formula for judging whether the variable has autocorrelation according to the autocorrelation function is as follows:
namely, the autocorrelation function value conforms to the formula (3), and the variable is judged to have no autocorrelation and not be classified as a time-lag variable when the lag length is tau, otherwise, the autocorrelation exists and is classified as a time-lag variable.
Preferably, in step (2), the value of the lag length τ may be 1 or 2, and in the case of one cycle of the non-periodic random process or the long-period random process, the autocorrelation function may be attenuated as τ increases, and in the case of screening the state variables, the lag length τ may be h, the corresponding value of the autocorrelation function may be obtained, and whether the state variables should be listed as the time-lag variables is determined by formula (3).
Preferably, in step (3), it is assumed that there is a sample data matrix X under normal operating conditions at time ttN samples, each sample containing m state variables, then XtCan be expressed as:
in the formula, xi∈Rm(i ═ 1, 2.., n) is the m-dimensional state vector. Concept pair X according to DPCAtFor the expansion, the amplification matrix x (h) at time t is:
namely, the method comprises the following steps:
X(h)＝[Xt Xt-1 ... Xt-h] (6)
wherein xtIs the m-dimensional state vector at time t, and the expanded augmentation matrix X (h) epsilon RN×MThe dimension is M ═ mx (h +1), and the number of samples is N-h.
Preferably, in step (1), the sample data has time sequence correlation, also called dynamic characteristic, and under the condition of a certain sampling interval, discrete sample data formed along with the time lapse can be regarded as a time sequence and described by using a difference equation; in the differential equation, if the output at the current time is related to the output at the past time only, such a differential equation is called an autoregressive model, and if the input is also included, it is called an ARX model, and the ARX model is described by the following h-order differential equation:
yt＝β0ut+α1yt-1+α2yt-2+...+αhyt-h+εt (7)
in the formula, ytAnd utOutput and input, respectively, at time ttThe random error at the moment t, h is called lag length and represents the maximum sampling times which can influence the output at the current moment to the maximum extent; therefore, in a dynamic system, a linear relationship exists between the output at the current time and the output in a past period of time, which is called Dynamic Principal Component Analysis (DPCA), or time-lapse Principal Component Analysis (PCA), namely, a dynamic relationship between state variables is acquired in a process of establishing a PCA model by using past sample data to expand a data matrix.
Preferably, in step (3), the dynamic principal component analysis DPCA calculates the lag length h by using a parallel analysis method, determines the number of linear relationships in the state variables by the variable dimension and the number of principal components, and determines whether the relationship between the correspondingly extracted variables is sufficient by the linear relationship coefficient.
Preferably, the parallel analysis method defines a static relation coefficient r (h) and a dynamic relation coefficient rnew(h) The formula is as follows:
r(h)＝M(h)-k(h) (8)
wherein M (h) and k (h) represent the number of variables and the number of principal elements of X (h) respectively, when the hysteresis length is h; the specific algorithm is as follows:
1. making h equal to 0, and solving a static correlation coefficient r (0);
2. let h equal to 1, calculate the new dynamic relation coefficient rnew(1)＝r(1)-r(0)；
3. Let h increase automatically, update the dynamic relation coefficient until rnew(h) And (5) less than or equal to 0, namely no new dynamic relation exists, and h is output.
Preferably, in step (4), a conventional Principal Component Analysis (PCA) model is established to find the initial control limit
And
the formula is as follows:
wherein, Fα(k, n-k) is the F distribution threshold with k and n-k degrees of freedom and a confidence level, cαIs a threshold value of a standard normal distribution at a confidence level alpha.
Preferably, in step (4), the initial control limit is found according to a conventional Principal Component Analysis (PCA) algorithm
And
then, amplifying and standardizing the samples according to the lag length h, taking new samples, and calculating the T of the new samples2And SPE statistics based on the statistics T2And SPE and initial control limits
And
and (4) comparing, namely judging whether the sample is abnormal or not, outputting abnormal information if the sample is abnormal, and otherwise, judging the sample is a normal sample.
Preferably, T2And the formula for the SPE statistics is as follows:
SPE＝||(I-PPT)x||2 (13)
wherein, Λk＝diag(λ1，...，λk) The first k covariance matrix eigenvalues, x the samples, P the load matrix, and I the residual subspace matrix.
Compared with the prior art, the beneficial effects are:
compared with the PCA (principal component analysis) method, the improved algorithm provided by the invention can effectively improve the detection rate and reduce the false alarm rate, and improves the calculation efficiency compared with the general dynamic principal component DPCA;
and the dynamic principal component analysis algorithm is improved, the calculation complexity is reduced by reducing the scale of the amplification matrix of the Dynamic Principal Component Analysis (DPCA), the calculation speed is improved, and the calculation resources are saved.
Drawings
FIG. 1 is a flow chart of the improved dynamic principal component analysis DPCA of the present invention;
FIG. 2 is a diagram of SPE and T of conventional principal component analysis PCA2A statistics monitor graph;
FIG. 3 is the SPE and T of the dynamic principal component analysis DPCA before improvement2A statistics monitor graph;
FIG. 4 shows the SPE and T of the DPCA after the improved dynamic principal component analysis of the present invention2A statistics monitor graph;
FIG. 5 is CPV results of a conventional principal component analysis PCA algorithm;
FIG. 6 is an ACF diagram of two state variables;
FIG. 7 is CPV results of the dynamic principal component analysis DPCA algorithm;
FIG. 8 shows SPE and T of conventional principal component analysis PCA for roller kiln production2A statistics monitor graph;
FIG. 9 shows the SPE and T of DPCA before the improved dynamic principal component analysis in the production process of roller kiln of the embodiment2A statistics monitor graph;
FIG. 10 shows the SPE and T of DPCA after improved dynamic principal component analysis in the production process of roller kiln of the embodiment2A statistics monitor graph;
FIG. 11 is a graph of the SPE contribution of conventional Principal Component Analysis (PCA) for the example roller kiln production process;
FIG. 12 is a graph of the SPE contribution of dynamic principal component analysis DPCA before modification of the example roller kiln production process;
FIG. 13 is a graph of the SPE contribution of DPCA after the improvement of the roller kiln production process of the example.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent; for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted. The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the present patent.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "long", "short", etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the drawings, it is only for convenience of description and simplicity of description, but does not indicate or imply that the device or element referred to must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationships in the drawings are only used for illustrative purposes and are not to be construed as limitations of the present patent, and specific meanings of the terms may be understood by those skilled in the art according to specific situations.
The technical scheme of the invention is further described in detail by the following specific embodiments in combination with the attached drawings:
examples
Fig. 1 to 13 show an embodiment of a method for detecting an energy consumption anomaly of a roller kiln based on dynamic principal component analysis, which includes the following steps:
(1) firstly, selecting sample data and constructing a dynamic principal component analysis DPCA model;
(2) then, calculating an autocorrelation function value of all variables of the sample data;
(3) judging the autocorrelation degree according to the result of the autocorrelation function value, setting a threshold value at the same time, and introducing no augmentation matrix to the variable meeting the threshold value range; otherwise, determining the value of the lag length h according to the degree of autocorrelation, and constructing an augmentation matrix X (h);
(4) and (4) analyzing the augmentation matrix X (h) by using a traditional Principal Component Analysis (PCA) algorithm, extracting the time sequence correlation among variables and carrying out anomaly detection.
In the step (2), the autocorrelation function value is the correlation of sequence states between any two different moments in signal processing and time series analysis; wherein, the autocorrelation function of the random process x (t) is defined as:
Rx(τ)＝E[x(t)x(t-τ)] (1)
the autocorrelation function of the discrete random sequence x (k) is defined as:
where n is the number of samples and τ is the lag length;
the formula for judging whether the variable has autocorrelation according to the autocorrelation function is as follows:
namely, the autocorrelation function value conforms to the formula (3), and the variable is judged to have no autocorrelation and not be classified as a time-lag variable when the lag length is tau, otherwise, the autocorrelation exists and is classified as a time-lag variable.
In addition, in step (2), the value of the lag length τ may be 1 or 2, and in the case of one cycle of the non-periodic random process or the long-period random process, the autocorrelation function may be attenuated as τ increases, and in the case of screening the state variables, the lag length τ may be taken as h, the corresponding value of the autocorrelation function may be obtained, and whether the state variables should be listed as the lag variable may be determined by formula (3).
Wherein, in step (3), it is assumed that there is a sample data matrix X under normal working condition at time ttN samples, each sample containing m state variables, then XtCan be expressed as:
in the formula, xi∈Rm(i ═ 1, 2.., n) is the m-dimensional state vector. Concept pair X according to DPCAtFor the expansion, the amplification matrix x (h) at time t is:
namely, the method comprises the following steps:
X(h)＝[Xt Xt-1 ... Xt-h] (6)
wherein xtIs the m-dimensional state vector at time t, and the expanded augmentation matrix X (h) epsilon RN×MThe dimension is M ═ mx (h +1), and the number of samples is N-h.
In addition, in the step (1), the sample data has time sequence correlation, also called dynamic characteristic, and under the condition of a certain sampling interval, discrete sample data formed along with the time lapse can be regarded as a time sequence and described by using a differential equation; in the differential equation, if the output at the current time is related to the output at the past time only, such a differential equation is called an autoregressive model, and if the input is also included, it is called an ARX model, and the ARX model is described by the following h-order differential equation:
yt＝β0ut+α1yt-1+α2yt-2+...+αhyt-h+εt (7)
in the formula, ytAnd utOutput and input, respectively, at time ttThe random error at the moment t, h is called lag length and represents the maximum sampling times which can influence the output at the current moment to the maximum extent; therefore, in a dynamic system, a linear relationship exists between the output at the current time and the output in a past period of time, which is called Dynamic Principal Component Analysis (DPCA), or time-lapse Principal Component Analysis (PCA), namely, a dynamic relationship between state variables is acquired in a process of establishing a PCA model by using past sample data to expand a data matrix.
In the step (3), the hysteresis length h in the dynamic principal component analysis DPCA adopts a parallel analysis method to calculate the hysteresis length h, the number of linear relations in the state variables is judged according to the variable dimension and the number of principal components, and whether the relation between the correspondingly extracted variables is sufficient or not is judged through the linear relation coefficient.
In addition, the parallel analysis method defines the static relation coefficient r (h) and the dynamic relation coefficient rnew(h) The formula is as follows:
r(h)＝M(h)-k(h) (8)
wherein M (h) and k (h) represent the number of variables and the number of principal elements of X (h) respectively, when the hysteresis length is h; the specific algorithm is as follows:
1. making h equal to 0, and solving a static correlation coefficient r (0);
2. let h equal to 1, calculate the new dynamic relation coefficient rnew(1)＝r(1)-r(0)；
3. Let h increase automatically, update the dynamic relation coefficient until rnew(h) And (5) less than or equal to 0, namely no new dynamic relation exists, and h is output.
In the step (4), a PCA (principal component analysis) model of the traditional principal component analysis is established, and the initial control limit is solved
And
the formula is as follows:
wherein, Fα(k, n-k) is the F distribution threshold with k and n-k degrees of freedom and a confidence level, cαIs a threshold value of a standard normal distribution at a confidence level alpha.
In addition, in step (4), an initial control limit is found according to the conventional Principal Component Analysis (PCA) algorithm
And
then, amplifying and standardizing the samples according to the lag length h, taking new samples, and calculating the T of the new samples2And SPE statistics based on the statistics T2And SPE and initial control limits
And
and (4) comparing, namely judging whether the sample is abnormal or not, outputting abnormal information if the sample is abnormal, and otherwise, judging the sample is a normal sample.
Wherein, T2And the formula for the SPE statistics is as follows:
SPE＝||(I-PPT)x||2 (13)
wherein, Λk＝diag(λ1，...，λk) The first k covariance matrix eigenvalues, x the samples, P the load matrix, and I the residual subspace matrix.
The specific case is as follows:
firstly, verifying the DPCA algorithm by using a mathematical model and improving the effectiveness of the DPCA algorithm in anomaly detection, and constructing a dynamic process, wherein the specific design is as follows:
x(t)＝[y(t)T，u(t)T]T (14)
z(t+1)＝A1z(t)+A2z(t-1)+Bu(t) (15)
y(t)＝z(t)+v (16)
u(t)＝Cu(t-1)+Dw(t) (17)
wherein x ∈ R8×1For the data samples used for modeling, y ∈ R5To output the vector, z ∈ R5、u∈R3For the input vector, v is subject to a Gaussian distribution N (0, 0.1)2) W is a random signal, each element has a value range of (-1, 1), and a coefficient matrix is defined as follows:
generating a total of 600 data samples according to a well-defined dynamic process, wherein the first 400 samples are normal samples, and introducing the following changes from the 401 th sample as abnormal samples:
(1) the second element of w increases by a factor of 1.5;
(2) the element of the 5 th row and 2 nd column of the coefficient matrix B is changed from-3 to 4.
As can be seen from the mathematical model definition, the model describes a dynamic process of second-order autocorrelation, so that the hysteresis length h is set to 2 when the DPCA algorithm is used for anomaly detection. With the modified DPCA algorithm, it can be observed that z and y are both second-order autocorrelation and u has only first-order autocorrelation, so that 5 attribute lag lengths of y should be taken as 2 and 3 attribute lag lengths of u should be taken as 1 in the data x used for modeling.
The corresponding modeling data for the three algorithms are shown in table 1.
TABLE 1 Algorithm modeling data comparison
The experimental operating environment of the invention is as follows: win 10 system, Python 3.6, CPU 2.5GHz, memory 8 GB.
When the abnormality detection is performed, the number of training samples is set to 200, and the number of test samples is 400, wherein the 201 st test sample is an abnormal sample. Selecting the number of main elements by using a CPV method, setting a threshold value to be 80%, and using SPE statistics and T2And performing judgment standard of abnormal conditions by the statistic. The results of the abnormality detection are shown in table 2 and fig. 2 to 4.
TABLE 2 comparison of anomaly detection results
The experimental result shows that the DPCA algorithm and the improved DPCA algorithm are obviously superior to the traditional PCA algorithm in the precision of anomaly detection. The traditional PCA algorithm has the fastest calculation speed due to the small scale of the modeled data matrix, but the false alarm rate and the detection rate are obviously poorer than those of the other two algorithms due to the fact that the modeling does not contain the autocorrelation information of the attributes. The abnormal detection effect of the improved DPCA algorithm is slightly better than that of the DPCA algorithm, the calculation time is saved by 15.87%, and the scale of the amplification matrix is reduced by introducing the ACF mainly due to the improved DPCA algorithm.
In the dynamic process anomaly detection experiment constructed by the mathematical model, the number of variables is small, and the dynamic relation among the variables is clear. The experimental results verify the feasibility and effectiveness of the DPCA algorithm in abnormal detection in the dynamic process containing the autocorrelation relationship, and the obvious effect of improving the calculation efficiency compared with the DPCA algorithm.
In addition, in order to further compare the application effects of three algorithms of PCA and DPCA and the improvement of DPCA, the invention uses the roller kiln production process data to carry out case analysis. The training set was chosen to be 300 samples, and there were 931 samples in the test set. Selecting the number of the pivot elements by using a CPV method, setting a threshold value to be 80%, and obtaining the number of the pivot elements to be 18, wherein the process is shown in FIG. 5.
The DPCA is used for detecting the energy consumption abnormity, the lag length h needs to be calculated firstly, and the calculation process is shown in the table 3. It can be seen that if h is 2, the corresponding modeled augmentation matrix is X (2) ∈ R298×294。
TABLE 3 DPCA hysteresis Length h calculation Process
When using modified DPCA, the corresponding hysteresis length is then determined by calculating the ACF for each variable. For example, FIG. 6 shows ACF images with two variables of t44 and t48, and R of t44 is shownt44(1) Exceeds a threshold value, and Rt44(2) Within the threshold range, the hysteresis length h is selected to be 1, and t48 has Rt48(2) Also outside the threshold range, a hysteresis length h of 2 should be chosen. The same calculation is carried out on all the state variables, and a modeled augmentation matrix X belongs to R298×264. The CPV method was used to select the number of primitives to be 20, as shown in FIG. 7.
The modeling data is collated as shown in table 4, and it can be seen that the scale of the dynamic data matrix can be effectively reduced by improving the DPCA, and further, the calculation resources and the calculation time can be saved.
TABLE 4 Algorithmic modeling data comparison
The energy consumption abnormality detection was performed on 931 samples of the test set, and the results are shown in table 5 and fig. 8 to 13. Experiments show that the false alarm rate and the detection rate of the DPCA and the improved DPCA are improved compared with the PCA algorithm. The PCA algorithm starts to detect the abnormity at the 966 test sample, and the DPCA and the improved DPCA algorithm respectively start to detect the abnormity at the 955 sample and the 954 sample, so that the DPCA and the improved DPCA algorithm can effectively improve the efficiency of the roller kiln energy consumption abnormity detection. Compared with the traditional DPCA, the calculation time of the improved DPCA for reducing the variable quantity of the augmented matrix by introducing the ACF is about 23.3 percent, which shows that the improved DPCA has obvious effects on improving the calculation efficiency and the algorithm performance.
TABLE 5 comparison of anomaly detection results
And (3) carrying out anomaly positioning by using the DPCA and the improved DPCA algorithm, wherein similar to the PCA algorithm, the SPE statistic contribution diagram is mainly concerned, namely the maximum variable in the SPE contribution diagram is the position with the maximum anomaly occurrence probability.
Fig. 4 and 5 are the first two samples identified as abnormal by DPCA and the modified DPCA algorithm, respectively, consistent with the abnormal diagnosis result of the PCA algorithm, and the variable with the largest contribution rate is t29, consistent with the case of simulation-induced abnormality.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (10)
1. A roller kiln energy consumption abnormity detection method based on dynamic principal component analysis is characterized by comprising the following specific steps:
(1) firstly, selecting sample data and constructing a dynamic principal component analysis DPCA model;
(2) then, calculating an autocorrelation function value of all variables of the sample data;
(3) judging the autocorrelation degree according to the result of the autocorrelation function value, setting a threshold value at the same time, and introducing no augmentation matrix to the variable meeting the threshold value range; otherwise, determining the value of the lag length h according to the degree of autocorrelation, and constructing an augmentation matrix X (h);
(4) and (4) analyzing the augmentation matrix X (h) by using a traditional Principal Component Analysis (PCA) algorithm, extracting the time sequence correlation among variables and carrying out anomaly detection.
2. The method for detecting the energy consumption abnormality of the roller kiln based on the dynamic principal component analysis as claimed in claim 1, wherein in the step (2), the autocorrelation function value is a correlation of sequence states between any two different moments in signal processing and time sequence analysis; wherein, the autocorrelation function of the random process x (t) is defined as:
Rx(τ)＝E[x(t)x(t-τ)] (1)
the autocorrelation function of the discrete random sequence x (k) is defined as:
where n is the number of samples and τ is the lag length;
the formula for judging whether the variable has autocorrelation according to the autocorrelation function is as follows:
namely, the autocorrelation function value conforms to the formula (3), and the variable is judged to have no autocorrelation and not be classified as a time-lag variable when the lag length is tau, otherwise, the autocorrelation exists and is classified as a time-lag variable.
3. The method for detecting roller kiln energy consumption abnormality based on dynamic principal component analysis according to claim 2, wherein in the step (2), the value of the lag length τ can be 1 or 2, in the case of a non-periodic random process or a long-periodic random process, the autocorrelation function will decay with the increase of τ, and when the state variable is screened, the lag length τ can be taken as h, the corresponding value of the autocorrelation function is obtained, and the formula (3) is used to determine whether the lag length τ should be listed as the time-lag variable.
4. The dynamic master based on claim 1The meta-analysis roller kiln energy consumption abnormity detection method is characterized in that in the step (3), a sample data matrix X under a normal working condition at the time t is assumedtN samples, each sample containing m state variables, then XtCan be expressed as:
in the formula, xi∈Rm(i ═ 1, 2.., n) is the m-dimensional state vector. Concept pair X according to DPCAtFor the expansion, the amplification matrix x (h) at time t is:
namely, the method comprises the following steps:
X(h)＝[Xt Xt-1...Xt-h] (6)
wherein xtIs the m-dimensional state vector at time t, and the expanded augmentation matrix X (h) epsilon RN×MThe dimension is M ═ mx (h +1), and the number of samples is N-h.
5. The method for detecting the abnormal energy consumption of the roller kiln based on the dynamic principal component analysis according to claim 1, wherein in the step (1), the sample data has time sequence correlation, also called dynamic characteristic, and under the condition of a certain sampling interval, the formed discrete sample data is a time sequence and is expressed by using a differential equation; in the differential equation, if the output at the current time is related to the output at the past time only, such a differential equation is called an autoregressive model, and if the differential equation further includes an input, it is called an ARX model, and the ARX model is represented by the following h-order differential equation:
yt＝β0ut+α1yt-1+α2yt-2+...+αhyt-h+εt (7)
in the formula, ytAnd utOutput and input, respectively, at time ttThe random error at the moment t, h is called lag length and represents the maximum sampling times which can influence the output at the current moment to the maximum extent; therefore, in a dynamic system, a linear relationship exists between the output at the current time and the output in a past period of time, which is called Dynamic Principal Component Analysis (DPCA), or time-lapse Principal Component Analysis (PCA), namely, a dynamic relationship between state variables is acquired in a process of establishing a PCA model by using past sample data to expand a data matrix.
6. The method for detecting roller kiln energy consumption abnormality based on dynamic principal component analysis according to any one of claims 1 to 5, characterized in that in step (3), the hysteresis length h in the dynamic principal component analysis DPCA is calculated by using a parallel analysis method, the number of linear relations in the state variables is judged by the variable dimension and the number of principal components, and whether the relation between the correspondingly extracted variables is sufficient is judged by the linear relation coefficient.
7. The method for detecting the abnormal energy consumption of the roller kiln based on the dynamic principal component analysis as claimed in claim 6, wherein a static relation coefficient r (h) and a dynamic relation coefficient r are defined by a parallel analysis methodnew(h) The formula is as follows:
r(h)＝M(h)-k(h) (8)
wherein M (h) and k (h) represent the number of variables and the number of principal elements of X (h) respectively, when the hysteresis length is h; the specific algorithm is as follows:
1. making h equal to 0, and solving a static correlation coefficient r (0);
2. let h equal to 1, calculate the new dynamic relation coefficient rnew(1)＝r(1)-r(0)；
3. Let h increase automatically, update the dynamic relation coefficient until rnew(h) And (5) less than or equal to 0, namely no new dynamic relation exists, and h is output.
8. The exercise base of claim 6The method for detecting the abnormal energy consumption of the roller kiln based on the state principal component analysis is characterized in that in the step (4), a traditional Principal Component Analysis (PCA) model is established to solve the initial control limit
And
the formula is as follows:
wherein, Fα(k, n-k) is the F distribution threshold with k and n-k degrees of freedom and a confidence level, cαIs a threshold value of a standard normal distribution at a confidence level alpha.
9. The method for detecting the abnormal energy consumption of the roller kiln based on the dynamic principal component analysis as claimed in claim 8, wherein in the step (4), the initial control limit is obtained according to the PCA algorithm of the traditional principal component analysis
And
then, amplifying and standardizing the samples according to the lag length h, taking new samples, and calculating the T of the new samples2And SPE statistics based on the statistics T2And SPE and initial control limits
And
and (4) comparing, namely judging whether the sample is abnormal or not, outputting abnormal information if the sample is abnormal, and otherwise, judging the sample is a normal sample.
10. The roller kiln energy consumption anomaly detection method based on dynamic principal component analysis according to claim 9, wherein T is2And the formula for the SPE statistics is as follows:
SPE＝||(I-PPT)x||2 (13)
wherein, Λk＝diag(λ1,...,λk) The first k covariance matrix eigenvalues, x the samples, P the load matrix, and I the residual subspace matrix.
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|---|---|---|---|---|
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Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2005249404A (en) * | 2004-03-01 | 2005-09-15 | Toshiba Corp | Moving target detection radar device and moving target detection processing method |
| CN103488091A (en) * | 2013-09-27 | 2014-01-01 | 上海交通大学 | Data-driving control process monitoring method based on dynamic component analysis |
| CN106444666A (en) * | 2016-09-22 | 2017-02-22 | 宁波大学 | Dynamic process monitoring method based on weighted dynamic distributed PCA model |
| CN108062565A (en) * | 2017-12-12 | 2018-05-22 | 重庆科技学院 | Double pivots-dynamic kernel principal component analysis method for diagnosing faults based on chemical industry TE processes |
| CN109542070A (en) * | 2018-12-13 | 2019-03-29 | 宁波大学 | A kind of dynamic process monitoring method based on biobjective scheduling algorithm |
| CN109634240A (en) * | 2018-12-13 | 2019-04-16 | 宁波大学 | A kind of dynamic process monitoring method based on novel dynamic principal component analysis |
| CN110705129A (en) * | 2019-10-31 | 2020-01-17 | 重庆科技学院 | Fault diagnosis method based on fully-correlated dynamic KPLS |
-
2020
- 2020-08-18 CN CN202010833831.2A patent/CN112229212A/en active Pending
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2005249404A (en) * | 2004-03-01 | 2005-09-15 | Toshiba Corp | Moving target detection radar device and moving target detection processing method |
| CN103488091A (en) * | 2013-09-27 | 2014-01-01 | 上海交通大学 | Data-driving control process monitoring method based on dynamic component analysis |
| CN106444666A (en) * | 2016-09-22 | 2017-02-22 | 宁波大学 | Dynamic process monitoring method based on weighted dynamic distributed PCA model |
| CN108062565A (en) * | 2017-12-12 | 2018-05-22 | 重庆科技学院 | Double pivots-dynamic kernel principal component analysis method for diagnosing faults based on chemical industry TE processes |
| CN109542070A (en) * | 2018-12-13 | 2019-03-29 | 宁波大学 | A kind of dynamic process monitoring method based on biobjective scheduling algorithm |
| CN109634240A (en) * | 2018-12-13 | 2019-04-16 | 宁波大学 | A kind of dynamic process monitoring method based on novel dynamic principal component analysis |
| CN110705129A (en) * | 2019-10-31 | 2020-01-17 | 重庆科技学院 | Fault diagnosis method based on fully-correlated dynamic KPLS |
Non-Patent Citations (1)
| Title |
|---|
| 龚婷婷: "基于主元分析方法的炼油厂蒸馏过程故障诊断研究", 《中国优秀硕士学位论文全文数据库》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112966222A (en) * | 2021-03-10 | 2021-06-15 | 中国民航信息网络股份有限公司 | Time series abnormal data detection method and related equipment |
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