CN113219949B - Device system health degree online monitoring method based on v-gap metric - Google Patents

Device system health degree online monitoring method based on v-gap metric Download PDF

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CN113219949B
CN113219949B CN202110490698.XA CN202110490698A CN113219949B CN 113219949 B CN113219949 B CN 113219949B CN 202110490698 A CN202110490698 A CN 202110490698A CN 113219949 B CN113219949 B CN 113219949B
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宋春跃
王娇娆
徐祖华
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Zhejiang University ZJU
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Abstract

The invention discloses a v-gap metric-based device system health degree online monitoring method, which comprises the following steps of: the method comprises the following steps that a sensor collects input and output data on line, a system model is updated by adopting instant learning identification, and the data are mapped to an operator space; measuring the distance between an online updating model and a system reference model in an operator space, wherein a v-gap metric is selected as a measurement mode; and finally, judging whether the system has faults or not according to whether the distance between the models exceeds a set threshold value or not, wherein the threshold value is calculated according to a confidence interval of a reference model obtained by off-line identification. The method calculates the difference between the updated model and the reference model on line, is different from other data measurement methods, innovatively provides the measurement of the change of the dynamic characteristics of the system from the model level, and effectively monitors the health degree of the system in all operation stages including a transient transition stage and a steady-state operation stage. The invention provides a brand new idea for the dynamic monitoring of the health degree of the device system and provides powerful guarantee for the safe operation of the device system.

Description

Device system health degree online monitoring method based on v-gap metric
Technical Field
The invention belongs to the field of process monitoring, and particularly relates to a v-gap metric-based device system health degree online monitoring method.
Background
In recent years, with the development of modern chemical industry, metallurgy, machinery, logistics and other industries in China and the progress of related technologies, the investment and the scale of a device system are gradually increased, the complexity is higher and higher, and the systems are also coupled. For such a complex process, safety and reliability play a crucial role, and therefore health monitoring and fault early warning technologies are developed at the same time. Due to the convenience of process data acquisition, data-based methods are applied more and can be mainly classified into machine learning and multivariate statistical analysis methods. The two methods are successfully applied to monitoring the system state of the device respectively aiming at the extracted data characteristics and parameter characteristics.
In the aspect of online health monitoring research based on a multivariate statistical analysis method, Chinese patent (application number 201811282478.2) provides a blast furnace process monitoring and fault diagnosis method integrating PCA-ICA, aiming at the condition that the robustness and accuracy of the monitoring result of single PCA or single ICA are limited, the monitoring results of the PCA and the ICA are fused to improve the fault detection precision, and the extracted components are beneficial to the tracing of the fault at the later stage; chinese patent (application No. 202011031988.X) proposes a multi-condition multi-stage batch process monitoring method based on density peak value clustering and instant learning, divides collected data by using the density peak value clustering, collects quality variable tracks by instant learning for each condition corresponding to different conditions, and finally determines final fault probability by a Bayesian fusion method; in the paper "Real-Time Assessment and Diagnosis of Process Operating Performance", Biao Huang models the stable operation mode of a multi-Operating-condition system, and obtains a better monitoring effect; furthermore, Chunhui Zhao in the article "Stationary test and Bayesian monitoring for fault detection in nonlinear multi-mode processes" analyzes information of different conditions using an improved nonlinear multi-modal process monitoring strategy for discriminating local preserving projection and Stationarity detection. The method lays a foundation for the subsequent more complete online device system monitoring method.
However, the above example only performs health monitoring on the steady-state phase of the plant system, and in the actual production process, due to the change of the working condition or the set point, a dynamic transition phase often occurs, that is, the operation of the system is composed of a transient state and a steady-state process, and the complete monitoring on the whole cycle of the system should be performed. In addition, the dynamic information of the system cannot be completely obtained by performing feature extraction on the data and parameter level, so the method has a poor monitoring effect on the transient stage.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides the device system health degree online monitoring method based on the v-gap metric.
The technical scheme adopted by the invention is as follows:
a v-gap metric-based device system health degree online monitoring method comprises the following steps:
s1: updating a system model on line according to input and output data of a device system acquired by a sensor in real time, and mapping the data to an operator space;
s2: calculating v-gap metric between the online model updated online and the reference model identified offline in the operator space, and representing the difference of the dynamic characteristics of the two models;
s3: and calculating a v-gap metric threshold according to the confidence interval of the system reference model, judging whether the device system has faults according to whether the model distance obtained in the step S2 exceeds the threshold, if so, indicating that the device system has faults, and if not, indicating that the device system does not have faults.
Preferably, in S1, the online model is updated online by using the process data of the device system acquired by the sensor in real time online as the input and output data of the online model, and the updating method includes:
s11: calculating the distance d between each online acquired input and output data and all data in the historical normal database, wherein the distance d comprises a standard Euclidean distance d between the two data12Standard Euclidean distance between scheduling variables corresponding to two data
Figure BDA0003051896880000021
Two parts; adding the distances of the two parts
Figure BDA0003051896880000022
As the measurement of the distance d, selecting the first p data with the minimum distance d from the historical normal database and the online process data, and forming a local data set by the p data and the online acquired input and output data;
s12: performing online model identification according to the local data set by using a weighted least square method, wherein the weight of each data is
Figure BDA0003051896880000023
Indicating that the farther away from the online data, the lower the referential of the data; the model identification is equivalent to feature extraction, online data is mapped to an operator space, and features corresponding to the data are the online model.
Further, in S11, two data x1And x2Standard euclidean distance d between them12The calculation formula of (a) is as follows:
Figure BDA0003051896880000031
wherein the content of the first and second substances,
Figure BDA0003051896880000032
are all n-dimensional vectors, k represents a dimension; x is the number of1k、x2kAre respectively x1、x2The kth dimension of (1); s denotes the variance of the data, skRepresents the variance of the kth dimension of the data;
scheduling variable delta corresponding to two data1,δ2Standard euclidean distance between them
Figure BDA0003051896880000033
The calculation formula of (a) is as follows:
Figure BDA0003051896880000034
wherein the content of the first and second substances,
Figure BDA0003051896880000035
is an m-dimensional vector, which reflects the data x1,x2An effective working area of the mapped model; k represents a dimension; delta1k、δ2kAre respectively delta1、δ2The kth dimension of (1); ssvThe variance of the scheduling variable is represented as,
Figure BDA0003051896880000036
indicating the scheduling variable kVariance of individual dimensions.
Further, in S2, the system reference model is identified offline according to the normal operation history of the device system, and is used to represent the dynamic characteristics of the device system during normal operation.
Further, in S2, the v-gap metric between the online model and the reference model is calculated as follows:
Figure BDA0003051896880000037
Figure BDA0003051896880000038
wherein, P1Representing a reference model, P2Representing an online model; p1(jω),P2(j ω) is each P1，P2ω represents frequency, sup represents supremum function; two models psi (P) over the entire frequency domain1(jω),P2(j ω)) is the v-gap metric of the two models, using δν(P1,P2) And (4) showing.
Further, the v-gap metric calculation formula is calculated in a complex plane and can be equivalently expressed as P1(j ω) and P2(j ω) mapping the nyquist plot of (j ω) to the maximum chord distance of points on the riemann sphere; by s1,s2Representing two points on the complex plane, which are mapped respectively to a point q on the Riemann sphere1And q is2The coordinates are respectively (x)1,y1,z1) And (x)2,y2,z2)，s1,s2Distance d(s) of1,s2) Then the expression is as follows:
Figure BDA0003051896880000039
the above formula shows the relationship between complex plane calculation and Riemann sphere upper chord distance calculation, thereby obtaining the similarity of dynamic characteristics of two linear system models, which is expressed by v-gap metric and ranges from 0 to 1.
Further, in S3, a v-gap metric threshold is calculated according to a confidence interval of the system reference model identified offline; if the Nyquist curve of the online model is in the confidence interval of the Nyquist curve of the reference model, the system of the device is in a normal working condition; and if the Nyquist curve of the online model exceeds the confidence interval of the Nyquist curve of the reference model, giving fault early warning.
Preferably, the plant system is any industrial plant system that requires health monitoring.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention carries out on-line monitoring on the whole operation cycle of the device system including the transient transition process and the steady state operation process, and can early warn faults in advance.
2. The method extracts model characteristics corresponding to data, calculates the difference of the models on line by adopting v-Gap metric measurement, and captures the change of the dynamic characteristics of the system.
3. The invention improves the characteristic extraction from a data and parameter level to a model level, and provides a new idea for process monitoring.
Drawings
FIG. 1 is a schematic overall flow diagram of the process of the present invention.
FIG. 2 is a schematic diagram of data to operator space mapping.
Fig. 3 is a schematic diagram of the mapping of points on the complex plane to the riemann sphere.
FIG. 4 is a schematic diagram of confidence intervals of a Nyquist plot of a reference model.
FIG. 5 is a diagram illustrating a comparison of Nyquist plots of an online update model and a reference model.
Detailed Description
The advantages and details of the practice of the invention will become more apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings. It should be noted that the following is only a preferred embodiment of the present invention, but the present invention is not limited thereto, and the method is applicable to various industrial device systems requiring health monitoring, such as voltage and current monitoring in a traction driving control system; the influence of the temperature and the flow of reactants on the concentration of dissolved oxygen in the penicillin pharmacy process and the like.
The present invention will be described in further detail below with reference to the accompanying drawing as a simulation example of a continuous stirred reactor system (CSTR). The CSTR is a tank reactor with stirring paddles that stir the material to a uniform state, which is beneficial to the uniformity of the reaction and heat transfer, so that temperature monitoring is very important for the apparatus.
As shown in fig. 1, which is a schematic view of the overall process of the present invention, the online health monitoring method for a v-gap metric-based device system includes the following steps:
s1: and updating a system model on line according to input and output data of the CSTR system acquired by the sensor in real time, and mapping the data to an operator space.
It should be noted that the input and output data are relative to the modeling, and the sensors collect process data during the operation of the system. The input data and output data collected by the sensors in this example are the coolant temperature and the in-tank temperature of the CSTR, respectively.
For convenience of description, the online updated system model will be referred to as an online model hereinafter. In this step, the process data of the device system which is acquired by the sensor in real time on line is used as the input and output data of the on-line model, and the on-line model is updated on line by adopting an instant learning method, namely after a group of input and output data of a new CSTR system is acquired, the group of data is immediately used for updating the on-line model, and the updating method comprises the following steps:
s11: calculating the distance d between each online acquired input and output data and all data in the historical normal database, wherein the distance d comprises the standard Euclidean distance d between the two data12Standard Euclidean distance between scheduling variables corresponding to two data
Figure BDA0003051896880000051
The distance between the two parts is calculated in the following modes:
first part, two data x1And x2Standard euclidean distance d between them12The calculation formula of (a) is as follows:
Figure BDA0003051896880000052
wherein the content of the first and second substances,
Figure BDA0003051896880000053
are all n-dimensional vectors, k represents a dimension; x is the number of1k、x2kAre respectively x1、x2The kth dimension of (1); s denotes the variance of the data, skRepresents the variance of the kth dimension of the data;
second part, scheduling variable δ corresponding to two data1,δ2Standard euclidean distance between them
Figure BDA0003051896880000054
The calculation formula of (a) is as follows:
Figure BDA0003051896880000055
wherein the content of the first and second substances,
Figure BDA0003051896880000056
is an m-dimensional vector, which reflects the data x1,x2An effective working area of the mapped model; k represents a dimension; delta1k、δ2kAre respectively delta1、δ2The kth dimension of (1); ssvThe variance of the scheduling variable is represented as,
Figure BDA0003051896880000057
representing the variance of the k-th dimension of the scheduling variable.
Then, the sum of the distances of the two parts is added
Figure BDA0003051896880000058
As a measure of the distance d, i.e.
Figure BDA0003051896880000059
Therefore, for each group of online acquired input and output data, the previous p data with the minimum distance d from the online process data can be selected from the historical normal database, the p data and the online acquired group of input and output data form a local data set together, and the value of p can be determined according to experience.
In this embodiment, since the input and the output are both temperature, are slowly changing variables, and can reflect the dynamic change of the system, both are also used as scheduling variables during modeling. Sum of two distances
Figure BDA0003051896880000061
The difference between different data and their corresponding valid operating ranges can be measured. And selecting the first p which is 12 data closest to the online data and the online data to form a local data set together for subsequently identifying the model corresponding to the data to finish the feature extraction.
S12: performing online model identification according to the local data set by using a weighted least square method, wherein the weight of each data is
Figure BDA0003051896880000062
Indicating that the farther away from the online data, the lower the referential of the data. The model identification is equivalent to feature extraction, and online data is mapped to an operator space, and features corresponding to the data are the online model, as shown in fig. 2.
In this embodiment, the online models at two different times (transient transition stage and steady state stage, respectively) in the simulation are selected as follows:
Figure BDA0003051896880000063
s2: and calculating v-gap metric between the online model updated online and the reference model identified offline in the operator space, and representing the difference of the dynamic characteristics of the two models.
In this step, the reference model used for comparison is identified offline according to historical normal data, and the identification method is not unique, so that the accurate system model can be obtained and can represent the dynamic characteristics of the device system in normal operation.
In order to monitor the change of the dynamic characteristics of the system in real time, the core of the step is to calculate the difference between an online model and a reference model, and the difference between the two models is reflected in the calculated value delta of a v-gap metricν(P1,P2) The calculation method is as follows:
Figure BDA0003051896880000064
Figure BDA0003051896880000065
wherein, P1Representing a reference model, P2Representing an online model; ω represents the frequency, sup denotes the supremum function. P1(jω),P2(j ω) is each P1，P2The frequency domain transfer function of the two linear systems is obtained by identification, and the similarity of the dynamic characteristics of the two linear systems is equivalent to the calculation of the infimum limit of the distance between two corresponding points in all frequency ranges of the Nyquist curves of the two linear models. Two models psi (P) over the entire frequency domain1(jω),P2(j ω)) is the v-gap metric of the two models, using δν(P1,P2) And (4) showing.
The v-gap metric calculation formula is calculated in a complex plane and can be more visually represented as that two model Nyquist curves are mapped on a Riemann sphere to obtain the chord distance of the farthest two points, namely the calculation formula can be represented as P1(j ω) and P2The Nyquist plot of (j ω) maps the maximum chord distance of points on the Riemannian sphere.
The process of mapping points on the complex plane to Riemann spheres is shown in FIG. 3, s1And s2The distance of two points may be equivalent to the chordal distance of the points to which both map to the Riemannian sphere. Suppose using s1,s2Representing two points on the complex plane, which are mapped to a point q on the Riemann sphere, respectively1And q is2The coordinates are respectively (x)1,y1,z1) And (x)2,y2,z2)，s1,s2Distance d(s) of1,s2) Then the expression is as follows:
Figure BDA0003051896880000071
the similarity of the dynamic characteristics of the two linear system models is calculated and expressed by v-gap metric, and the range is 0-1.
In this embodiment, the CSTR has three set points, i.e. three modes, the experiment takes monitoring mode one as an example, the two online models both belong to an identification model of mode one, and the reference model is identified by a weighted least square method:
Figure BDA0003051896880000072
the v-gap metric of the two online models and the reference model can be calculated as
δν(G(jω),G1(jω))＝0.0224,δν(G(jω),G2(jω))＝0.3268。
S3: and calculating a v-gap metric threshold according to the confidence interval of the system reference model, judging whether the device system has faults according to whether the model distance obtained in the step S2 exceeds the threshold, if so, indicating that the device system has faults, and if not, indicating that the device system does not have faults.
Specifically, since the data-driven recognition model has recognition errors, the calculated value of v-Gap metric varies within a certain range even if the system is in a healthy state. The v-Gap metric threshold can thus be calculated from the confidence interval of the reference model. The confidence interval of the nyquist diagram of the reference model is shown in fig. 4, and then the confidence interval of v-Gap metric between the models can also be calculated according to the diagram, the confidence interval of the embodiment is 0-0.029, if the difference of the dynamic characteristics of the models, namely v-Gap metric value exceeds the confidence interval, the fault early warning is given. The nyquist plot of the two online identification models is shown in fig. 5, the dotted line is the range of the confidence interval, it can be obtained that the difference between the model 2 and the reference model is large, and the model exceeds the confidence interval, so that the system is in a fault state, and because the relation between the cooling liquid temperature and the temperature in the kettle is monitored, the fault related to the reaction temperature can be searched for in the follow-up fault tracing process. However, from the data point of view, the relative error between the parameters of the two online identification models and the parameters of the reference model is calculated to be 0.0420 and 0.4552, which cannot reflect the dynamic change of the system and detect the system fault. And the change of the dynamic characteristic of the system can be measured by monitoring from the angle of the model, so that the monitoring precision is improved.
The invention provides a v-gap metric based device system health online monitoring method, and a method and a way for realizing the technical scheme are many, the above description is only a preferred embodiment of the invention, and it should be noted that, for a person skilled in the art, a plurality of improvements and decorations can be made without departing from the principle of the invention, and these improvements and decorations should also be regarded as the protection scope of the invention. All the components not specified in the present embodiment can be realized by the prior art.

Claims (3)

1. A v-gap metric-based device system health degree online monitoring method is characterized by comprising the following steps:
s1: updating a system model on line according to input and output data of a device system acquired by a sensor in real time, and mapping the data to an operator space;
s2: calculating v-gapmetric between an online model updated online and a reference model identified offline in an operator space, and representing the difference of the dynamic characteristics of the two models;
s3: calculating a v-gap metric threshold according to the confidence interval of the system reference model, judging whether the device system has faults according to whether the model distance obtained in S2 exceeds the threshold, if so, indicating that the device system has faults, and if not, indicating that the device system does not have faults;
in S1, the process data of the device system acquired by the sensor on line in real time is used as the input and output data of the online model, and the online model is updated on line by using an instant learning method, where the updating method is:
s11: calculating the distance d between each online acquired input and output data and all data in the historical normal database, wherein the distance d comprises a standard Euclidean distance d between the two data12Standard Euclidean distance between scheduling variables corresponding to two data
Figure FDA0003506839230000011
Two parts; adding the distances of the two parts
Figure FDA0003506839230000012
As the measurement of the distance d, selecting the first p data with the minimum distance d from the historical normal database and the online process data, and forming a local data set by the p data and the online acquired input and output data;
s12: performing online model identification according to the local data set by using a weighted least square method, wherein the weight of each data is
Figure FDA0003506839230000013
Indicating that the farther away from the online data, the lower the referential of the data; the model identification is equivalent to feature extraction, online data are mapped to an operator space, and the features corresponding to the data are the online model;
in the S11, two data x1And x2Standard euclidean distance d between them12The calculation formula of (a) is as follows:
Figure FDA0003506839230000014
wherein the content of the first and second substances,
Figure FDA0003506839230000015
are all n-dimensional vectors, k represents a dimension; x is the number of1k、x2kAre respectively x1、x2The kth dimension of (1); s denotes the variance of the data, skRepresents the variance of the kth dimension of the data;
scheduling variable delta corresponding to two data1,δ2Standard euclidean distance between them
Figure FDA0003506839230000016
The calculation formula of (a) is as follows:
Figure FDA0003506839230000021
wherein the content of the first and second substances,
Figure FDA0003506839230000022
is an m-dimensional vector, which reflects the data x1,x2An effective working area of the mapped model; k represents a dimension; delta1k、δ2kAre respectively delta1、δ2The kth dimension of (1); ssvThe variance of the scheduling variable is represented as,
Figure FDA0003506839230000023
a variance representing the k-th dimension of the scheduling variable;
in S2, the v-gap metric calculation formula between the online model and the reference model is as follows:
Figure FDA0003506839230000024
Figure FDA0003506839230000025
wherein, P1Representing a reference model, P2Indicating presence of presenceA model; p1(jω),P2(j ω) is each P1，P2ω represents frequency, sup represents supremum function; two models psi (P) over the entire frequency domain1(jω),P2(j ω)) is the v-gap metric of the two models, using δν(P1,P2) Represents;
the v-gap metric calculation formula is calculated in a complex plane and can be equivalently expressed as P1(j ω) and P2(j ω) mapping the nyquist plot of (j ω) to the maximum chord distance of points on the riemann sphere; by s1,s2Representing two points on the complex plane, which are mapped respectively to a point q on the Riemann sphere1And q is2The coordinates are respectively (x)1,y1,z1) And (x)2,y2,z2)，s1,s2Distance d(s) of1,s2) Then the expression is as follows:
Figure FDA0003506839230000026
the above formula shows the relationship between complex plane calculation and Riemann sphere upper chord distance calculation, so as to obtain the similarity of dynamic characteristics of two linear system models, which is expressed by v-gap metric and ranges from 0 to 1;
in the step S3, a v-gap metric threshold value is calculated according to a confidence interval of a system reference model identified offline; if the Nyquist curve of the online model is in the confidence interval of the Nyquist curve of the reference model, the system of the device is in a normal working condition; and if the Nyquist curve of the online model exceeds the confidence interval of the Nyquist curve of the reference model, giving fault early warning.
2. The method according to claim 1, wherein in S2, the system reference model is identified offline according to normal data of normal operation history of the device system, and is used to represent the dynamic characteristics of the device system during normal operation.
3. The method of claim 1, wherein the plant system is any industrial plant system requiring health monitoring.
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