CN107305348B - Dynamic system delay calculation method based on dependency measurement - Google Patents
Dynamic system delay calculation method based on dependency measurement Download PDFInfo
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- CN107305348B CN107305348B CN201710317964.2A CN201710317964A CN107305348B CN 107305348 B CN107305348 B CN 107305348B CN 201710317964 A CN201710317964 A CN 201710317964A CN 107305348 B CN107305348 B CN 107305348B
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Abstract
The invention relates to a dynamic system delay calculation method based on dependency measurement, and belongs to the technical field of system identification. The technical scheme of the invention is as follows: (1) uniformly sampling input and output signals of a dynamic system and normalizing sampling values; (2) calculating the edge distribution of the input and the output of the system; (3) calculating a connection function between input and output of the system; (4) calculating a dependency measure of the delay; (5) the delay estimate for a dynamic system is obtained by maximizing the dependency metric of the delay. The delay calculation method can be used in the fields of industrial system modeling, industrial system process control, process simulation and the like.
Description
Technical Field
The present invention relates to a system identification technology, and more particularly, to a method for calculating dynamic system latency based on dependency measurement.
Background
In the field of industrial control, establishing a dynamic mathematical model of main devices or processes of a system by using field data has become a research hotspot of system identification at present. The field data inevitably has delay due to various reasons such as industrial production flow, measurement means and the like. If the delay in the data can not be accurately calculated and eliminated, the identification precision of the system can not be guaranteed. In order to solve the control problem of an object having a time lag, the magnitude of the time lag must first be estimated. Therefore, the time delay estimation is receiving more and more attention and becomes one of the most important issues in the field of system identification, and the research of such issues has important theoretical and practical significance.
In recent years, many experts and scholars propose a plurality of time delay estimation methods according to the characteristics of time delay objects, such as a method based on conventional correlation, a method based on a least square method, a method based on interpolation, a method based on a neural network, a method based on a linear matrix inequality, a method based on a non-commutative ring theory and the like. These lag estimation methods can be classified into two more macroscopic categories, namely model-based methods and input-output data-based methods.
The model-based method takes the structure of the system as prior knowledge in the time delay estimation process, and the system is considered as a gray box or a white box, so that the delay of the system can be identified as a parameter of a known system model. When the delay estimation is performed on a linear system, the system delay can be used as a parameter in a transfer function, and the delay parameter of the system can be estimated through a regression method such as least square according to the input and output signals of the system. For a nonlinear system, with the known system result, a learner (such as a neural network) or a swarm intelligence algorithm (such as a particle swarm optimization) can be used to learn the delay parameter of the system. The model-based method is simple and easy to implement, but the method requires that the information of the system structure is known in advance, so that the application range of the method is limited. Real-world industrial systems tend to be complex, and therefore obtaining system architecture becomes a difficult task, and model-based methods are not suitable for estimating the time delay of such systems.
The delay estimation method based on input and output data considers the system as a black box and estimates the delay of the system only by means of the input and output signals of the system. Because the method does not need a system structure as prior knowledge, the difficulty of estimating the delay of the system is higher, but the application range is wider, and the applied object system is more complex. Representative of such methods is a wavelet transform-based method that performs time delay estimation by correlation between wavelet coefficients based on input and output wavelet coefficients of a discrete wavelet transform computing system.
Disclosure of Invention
In view of the above situation, in order to solve the problem that the above-mentioned delay estimation method technique is too dependent on the system structure and cannot be applied to a complex system, and also solve the problem that the accuracy of the delay estimation result is not high, the present invention provides a dynamic system delay calculation method based on dependency metric, which includes the following steps.
Uniformly sampling input and output signals of a dynamic system, and normalizing sampling values;
calculating the edge distribution of the input and the output of the system;
calculating a connection function between the input and the output of the system according to the calculated edge distribution of the input and the output;
calculating a dependency measure of the delay using the calculated connection function;
the estimate of the delay of the dynamic system is finally obtained by maximizing the aforementioned dependency metric.
In the method for calculating the dynamic system delay based on the dependency metric according to the present invention, preferably, when the edge distribution of the input and output of the system is calculated, the input and output of the system are used as random variables, and the sampling values of the input and output are used as the observed values of the random variables.
In the method for calculating dynamic system delay based on dependency metric according to the present invention, preferably, the dependency metric is defined as:
wherein
In the form of a random vector, the vector is,
in order to normalize the factors, the method comprises the steps of,
， 
as a function of the connections between the random vectors,
。
in the method for calculating the delay of the dynamic system based on the dependency metric according to the present invention, preferably, the delay in the dependency metric for calculating the delay is a relative delay, and a first random variable is taken
Delay of
。
In the method for calculating the dynamic system delay based on the dependency metric according to the present invention, preferably, the formula for calculating the delay in the dependency metric for calculating the delay is as follows:
wherein
As a random variable
The delay of (a) is delayed,
for a given random variable
The initial value of the delay of (a) is,
to represent
Is delayed by the vector of the observed valueskA corresponding random variable after each sampling time.
According to the dynamic system delay calculation method based on the dependency measurement, the functional relationship exists between the input and the output of any dynamic system, the input and the output of the dynamic system are considered as random variables, the dependency measurement among the random variables is defined through a connection function, the dependency structure of the system is quantized by utilizing the dependency measurement among the input and the output of the system, and the delay of the system is obtained by maximizing the dependency measurement among the input and the output of the system.
After the technology provided by the invention is adopted, according to the dynamic system delay calculation method based on the dependency measurement, aiming at the defect that the model-based delay estimation method takes a system model as prior knowledge and has poor generalization capability, an abstract delay model suitable for any system is established, and the defect that the existing method cannot be suitable for a complex system is overcome; aiming at the defects that the input and output based delay estimation method is high in calculation complexity and the estimation result is sensitive to data noise, the dependency measurement between the input and the output of the system is defined based on the connection function, the delay of the system is determined by maximizing the dependency measurement, the complexity of delay calculation is reduced, and the robustness of the delay calculation result to the data noise is improved.
Drawings
FIG. 1 is a flow chart of a method for calculating dynamic system latency based on dependency metrics according to the present invention
FIG. 2 illustrates a single-in single-out nonlinear delay system according to the present invention
FIG. 3 shows the estimation result of the delay of the dependence metric between the input and the output of the system under different delays according to the present invention
Detailed Description
Various preferred embodiments of the present invention will be described below with reference to the accompanying drawings. The following description with reference to the accompanying drawings is provided to assist in understanding the exemplary embodiments of the invention as defined by the claims and their equivalents. It includes various specific details to assist understanding, but they are to be construed as merely illustrative. Accordingly, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present invention. Also, in order to make the description clearer and simpler, a detailed description of functions and configurations well known in the art will be omitted.
The embodiment of the invention aims at the fuel quantity of a certain ultra-supercritical unit under 80% working condition and a main gas pressure system to perform dynamic system delay calculation based on dependency measurement.
As shown in fig. 1, the specific steps are as follows.
Step (1): and uniformly sampling input and output signals of the dynamic system, and normalizing sampling values.
Sampling input and output signals of the system at fixed time intervals simultaneously to obtain a sample sequence of the input and output signals; and the sample sequence is normalized, so that the influence of the numerical value distribution range between input and output on the calculation result is eliminated.
Step (2): an edge distribution function of the system input and output is estimated.
The input and output of the system are regarded as random variables, the sampling values of the input and output of the system are regarded as observation value sequences of the random variables, the edge distribution of the input and output is estimated by applying an empirical formula, and preparation is made for the estimation of the connection function between the input and the output.
And (3): and (3) calculating a connection function between the input and the output of the system according to the edge distribution function of the input and the output calculated in the step (2).
The correlation between the system input and output is described by the connection function, and the connection function between the system input and output is estimated by an empirical formula or other methods.
And (4): and (4) calculating the dependency measure of the system delay by using the connection function calculated in the step (3).
Defining a random vector
The measure of the dependency between them is
Wherein
In order to normalize the factors, the method comprises the steps of,
， 
is a random vector
The function of the connection between the two,
. The physical meaning of the dependency measure is the degree of existing dependency of the random variableThe integral of the difference between the degrees of dependence in the completely independent case over the spatial hypercube characterizes the structure of dependence between random variables.
Step (5) maximizes the dependency metric in step (4) to obtain the final delay result of the system.
When the observed values of single or partial components in the random vector are delayed, the edge distribution of the random variable is unchanged, but the connection function values between the random vectors are correspondingly changed. Since there must be some functional relationship between the input and output of the dynamic system, the dependency metric between the random variables can be maximized if there is a functional relationship between them. The latency of the system can thus be determined by maximizing the dependency metric between the system inputs and outputs:
wherein
As a random variable
The delay of (a) is delayed,
for a given random variable
The initial value of the delay of (a) is,
to represent
Is delayed by the vector of the observed valueskA corresponding random variable after each sampling time.
As an embodiment of the method for calculating the dynamic system delay based on the dependency metric, firstly, the input and output data of the obtained system are sampled: after reading the field data from EXCEL, it is stored in MATLAB in a certain format. Because of the large amount of noise present in the field data, the input and output can be treated as random variables. The dependency measurement between the input and the output is obtained by solving the edge distribution function between the input and the output, so that the relation between the input and the output is established. The latency of this system is calculated by the dependency metric. This completes the delayed identification of the system.
Fig. 2 and fig. 3 show the process of calculating the fuel quantity and main gas pressure system delay of an ultra-supercritical unit under 80% of working conditions by applying the method of the invention. FIG. 2 is a flow chart of the delayed thermal system, in which the expression of the nonlinear element is
Wherein the content of the first and second substances,
，
，
. It can be seen from the transfer function of the system that the system has a latency of about 48 seconds.
Fig. 3 shows the delay estimation result of the system by applying the method of the present invention. The top is 1000 input samples, the middle is 1000 output samples, the sampling period is 1 second, and the bottom is the input and output dependency measurement under different delays. It can be seen that the input-output dependency metric is very small when the delay is less than 48 seconds and greater than 56 seconds; the dependency metric is large around 48-50 seconds and takes a maximum at 49 seconds.
According to the dynamic system delay calculation method based on the dependency measurement, provided by the embodiment of the invention, aiming at the defect that a model-based delay estimation method takes a system model as prior knowledge and has poor generalization capability, an abstract delay model suitable for any system is established, and the defect that the existing method cannot be suitable for a complex system is overcome; aiming at the defects that the input and output based delay estimation method is high in calculation complexity and the estimation result is sensitive to data noise, the dependency measurement between the input and the output of the system is defined based on the connection function, the delay of the system is determined by maximizing the dependency measurement, the complexity of delay calculation is reduced, and the robustness of the delay calculation result to the data noise is improved.
The present invention has been described in detail, and the principle and embodiments of the present invention are explained herein by using specific examples, which are only used to help understand the method and the core idea of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.
From the above description of the embodiments, it will be apparent to those skilled in the art that the present invention may be practiced. Of course, the above listed cases are only examples, and the present invention is not limited thereto. It should be understood by those skilled in the art that other modifications or simplifications according to the technical solution of the present invention may be appropriately applied to the present invention and should be included in the scope of the present invention.
Claims (3)
1. A dynamic system delay calculation method based on dependency measurement is characterized in that the dynamic system delay calculation based on the dependency measurement is carried out on a fuel quantity and a main gas pressure system of an ultra-supercritical unit under 80% of working conditions, and comprises the following steps:
uniformly sampling input and output signals of a dynamic system, and normalizing sampling values;
calculating the edge distribution of the input and the output of the system;
calculating a connection function between the input and the output of the system according to the calculated edge distribution of the input and the output;
calculating a dependency measure of the delay using the calculated connection function;
finally obtaining the delay estimation value of the dynamic system by maximizing the dependency metric;
the dependency metric is defined as:
wherein X1,K,XnIs a random vector, alpha is a normalization factor, v ═ v1,K,vn]∈[0,1]nC (v) is a connection function between random vectors, Π (v) ═ v1×K×vn。
2. The method according to claim 1, wherein the edge distribution of the input and output of the system is calculated by using the input and output of the system as random variables and using the sampled values of the input and output as the observed values of the random variables.
3. The method according to claim 1, wherein the delay in the dependency metric for calculating delay is a relative delay, and a first random variable X is taken1Delay of k1＝0。
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| CN103592850A (en) * | 2013-11-21 | 2014-02-19 | 冶金自动化研究设计院 | Nonlinear multi-time-scale delay system modeling and control method |
| CN104657791A (en) * | 2015-02-28 | 2015-05-27 | 武汉大学 | Wind power plant group wind speed distribution prediction method based on correlation analysis |
| CN104834793A (en) * | 2015-05-26 | 2015-08-12 | 河海大学 | Simulation generation method for wind speed data of multiple wind power farms |
| CN106878205A (en) * | 2015-12-10 | 2017-06-20 | 电信科学技术研究院 | A kind of timing offset method of estimation, device and terminal |
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| CN101902370A (en) * | 2010-07-21 | 2010-12-01 | 中兴通讯股份有限公司 | Device, system and method for measuring frame delay |
| CN103592850A (en) * | 2013-11-21 | 2014-02-19 | 冶金自动化研究设计院 | Nonlinear multi-time-scale delay system modeling and control method |
| CN104657791A (en) * | 2015-02-28 | 2015-05-27 | 武汉大学 | Wind power plant group wind speed distribution prediction method based on correlation analysis |
| CN104834793A (en) * | 2015-05-26 | 2015-08-12 | 河海大学 | Simulation generation method for wind speed data of multiple wind power farms |
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