CN117094164A - Sensor layout optimization method based on mixed information entropy - Google Patents
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Abstract
The invention discloses a sensor layout optimization method based on mixed information entropy. The method comprises the steps of establishing a dynamic fault tree, setting the number and the positions of sensors, converting the dynamic fault tree into a Bayesian network to obtain the fault rate corresponding to each sensor, selecting a plurality of sensors from all sensors to form a sensor subset, taking the selection mode of the sensor subset as a sensor layout scheme, calculating the reliability parameters of the sensors in different sensor layout schemes by using the fault rate corresponding to each sensor, calculating the final evaluation parameters of the sensor layout schemes by using the reliability parameters, evaluating the advantages and disadvantages of the different sensor layout schemes by using the final evaluation parameters, and determining the optimal sensor layout scheme. The invention evaluates the importance of each sensor by quantitative parameters, so that the limited sensors are placed at the most critical parts in the mechanical instrument to be detected, the running and maintenance cost is saved, the reliability of the system is improved, and the safe running of the system is ensured.
Description
Technical Field
The invention belongs to a sensor layout optimization method in the field of sensor layout optimization, and particularly relates to a sensor layout optimization method based on mixed information entropy.
Background
With the progress of the modern science and technology level and the development of industrial production, various mechanical equipment and production systems are increasingly complicated and intelligent. Due to the relatively high cost of diagnosis and maintenance, the rapid localization and diagnosis of faults in such devices is particularly important. Among these, the longest approach is to incorporate sensors at strategic locations to monitor the system. The location, type and cost of the sensors determine the cost competitiveness, functional rows and effectiveness of the sensor network. The proper placement of the sensors has an important impact on the reliability and diagnostic performance of the system. The prior art lacks a method that can incorporate reliability theory and multi-attribute decision methods into the layout of the sensors to facilitate placement of a limited number of sensors in the most critical locations, thereby saving operational maintenance costs.
Disclosure of Invention
In order to solve the problems in the background art, the invention aims to provide a sensor layout optimization method based on mixed information entropy. The method takes the number and the positions of the sensors as design variables, establishes a dynamic fault tree analysis system by analyzing the logical relation between the sensor system and the sensors thereof, converts the dynamic fault tree analysis system into a corresponding dynamic Bayesian network, and realizes the determination and layout optimization of the potential positions of the sensors by combining the parameters of the reliability of the system.
Firstly, establishing a dynamic fault tree model for system fault identification based on dynamic characteristics among sensors; secondly, each leaf node and root node in the dynamic fault tree are corresponding to a bottom event and a top event in the Bayesian network, and a dynamic Bayesian network is established to improve the operation precision and reduce the operation complexity; and then, in order to characterize the contribution degree of each sensor to the system identification fault, establishing reliability parameters of information values (Value of Information, VOI) and cross-information entropy (Transinformation Entropy, TE), obtaining final evaluation parameters of the sensor layout scheme by utilizing the reliability parameters, and selecting the final evaluation parameter optimal layout scheme from each scheme as an optimal sensor layout scheme. The key idea of this optimization is to introduce reliability parameters to characterize the degree of necessity of the corresponding position sensor placement and algorithms for multi-attribute decision making to ensure its implementation.
The technical scheme of the invention is as follows, comprising the following steps:
step 1: establishing a dynamic fault tree of fault events to be detected, and setting a sensors X 1 ,X 2 ,X 3 ,...,X a Correspondingly placed on each component in the mechanical instrument to be detected;
step 2: converting the dynamic fault tree into a corresponding Bayesian network, and then obtaining the fault rate of each sensor corresponding component by using the Bayesian network;
step 3: from a sensors X 1 ,X 2 ,X 3 ,...,X a Is selected arbitrarily from the b sensor subsets [ X ]' b ]Said subset of sensors [ X ]' b ]For the selected set of sensors, and subset the sensors [ X ]' b ]The selected mode of the sensor is used as a sensor layout scheme;
step 4: calculating reliability parameters of the sensors in different sensor layout schemes by utilizing the failure rate of the corresponding parts of each sensor, wherein the reliability parameters comprise information value and cross-information entropy;
step 5: obtaining final evaluation parameters of the sensor layout scheme through the reliability parameters;
step 6: and 5, judging the advantages and disadvantages of different sensor layout schemes by utilizing the final evaluation parameters obtained in the step 5, and further selecting an optimal sensor layout scheme from the different sensor layout schemes.
The specific operation of the step 1 is as follows: firstly, taking a fault in a mechanical instrument to be detected as a fault event to be detected, and then determining a sub-fault event of the fault event to be detected, wherein the sub-fault event is specifically one of inducements causing the occurrence of the fault event to be detected, and constructing by taking the fault event to be detected as a top event node and taking the sub-fault event as a bottom event nodeSetting up corresponding dynamic fault tree, and then setting a sensors X 1 ,X 2 ,X 3 ,...,X a Respectively and correspondingly placed on each component which is prone to sub-fault events.
The step 2 of converting the dynamic fault tree into the corresponding bayesian network includes the following steps: the method comprises the steps of firstly, corresponding bottom event nodes in a dynamic fault tree to root nodes in a Bayesian network, corresponding top event nodes in the dynamic fault tree to leaf nodes in the Bayesian network, then, corresponding other nodes of the dynamic fault tree to other nodes in the Bayesian network one by one, and then, establishing the Bayesian network by utilizing the corresponding relation between the dynamic fault tree and the Bayesian network nodes.
In the step 2, the failure rate corresponding to each sensor is obtained by using a bayesian network specifically includes: after the sensors are correspondingly placed on all components in the mechanical instrument to be detected, the fault rate of each sensor is obtained, and then the fault rate of each sensor is substituted into a Bayesian network to perform logic operation, so that the fault rate of each sensor corresponding component is obtained.
The step 4 specifically comprises the following steps:
step 4.1: obtained as a sensor X i And sensor X j Are all sensor subsets [ X ]' b ]In the case of the element in (a), at the sensor X j Under influence of sensor X i Information value VOI i (j) Information value VOI i (j) The method is obtained by processing according to the following formula:
wherein:
i. j each represents a serial number of the sensor;
s represents sensor X i The working state of the corresponding component is a normal state or a fault state; m represents sensor X j The working state of the corresponding component is a normal state or a fault state;
s represents sensor X j S is 2, which corresponds to the number of working states of the components; m is MRepresenting sensor X j The number of working states of corresponding parts is M, and 2 is taken;
p(s) represents sensor X i Probability of the corresponding component being in an s working state; p (m) represents sensor X j Probability of the corresponding component being in m working state;
p (s|m) represents sensor X j Sensor X when corresponding component is in m working state i Probability of the corresponding component being in an s working state;
c(s) represents sensor X i The time cost required by the working state of the corresponding component can be accurately detected;
max () represents a maximum function;
step 4.2: calculating the cross-information entropy TE (X) i ,X j )
Sensor X j And sensor X i Cross information entropy TE (X) i ；X j ) The method is obtained by processing according to the following formula:
wherein p (s, m) represents sensor X i The corresponding part is in an s working state and the sensor X j The joint probability distribution of the corresponding component in the m operating state.
The step 5 specifically comprises the following steps:
using a subset of sensors [ X ]' b ]Information value VOI of each sensor in (B) i (j) And the cross-information entropy TE (X) i ；X j ) Calculating final evaluation parameters of the sensor layout scheme, wherein the final evaluation parameters comprise total information value maximum Z1, total cross-information entropy minimum Z2 and sensor number minimum Z3:
Minimize Z3＝b
wherein [ VOI ]]Representing a subset of sensors [ X ]' b ]Information value VOI of all sensors in (a) i (j) Is a collection of (3); [ TE]Representing a subset of sensors [ X ]' b ]Cross information entropy TE (X) i ；X j ) Max { } represents taking the maximum function.
The specific operation of the step 6 is as follows: judging whether the sensor layout scheme selected in the step 3 is a qualified sensor layout scheme or not:
if the total information value maximum Z1 of the sensor layout scheme is larger than a preset information value threshold value and the total cross information entropy minimum Z2 is smaller than a preset information entropy threshold value, the sensor layout scheme is a qualified sensor layout scheme;
otherwise, indicating that the sensor layout scheme is an unqualified sensor layout scheme;
and selecting the sensor layout scheme with the least number of sensors in the qualified sensor layout schemes as the optimal sensor layout scheme.
The establishment of the dynamic fault tree is based on the clear normal state and fault state of the mechanical instrument to be detected, firstly, the normal state and fault state of the mechanical instrument to be detected are clear, then, a plurality of fault events which are least expected to appear are selected as the top event nodes of the fault tree to be detected, the boundary conditions of the dynamic fault tree are determined according to the initial state of the mechanical instrument to be detected, namely, the bottom event nodes are determined, thus, the complete dynamic fault tree can be obtained, and the complete dynamic fault tree can be correspondingly simplified according to actual requirements and can be used for system analysis.
The Bayesian network adopts a directed acyclic graph and a conditional probability table to describe graph theory of probability relation, intuitively expresses joint probability distribution among variables in a graphical mode, greatly reduces calculation complexity by utilizing condition independence assumption, and provides a good solution for complex uncertainty reasoning.
Sensing in different sensor layoutsInformation value VOI of such schemes when the number of devices is the same or close i (j) With approximation, using cross-information entropy TE (X i ；X j ) To determine the merits of different schemes when the number of sensors is the same, and cross information entropy TE (X i ；X j ) The concept based on information entropy is extended to describe the degree of information redundancy of a scheme. When TE (X) i ；X j ) The larger the sensor X i And sensor X j The stronger the correlation between, i.e. sensor X i And sensor X j The greater the degree of information redundancy.
The invention is characterized in that in the layout of the sensor optimized by utilizing reliability theory and multi-attribute decision analysis, the importance of each sensor is quantitatively evaluated by utilizing the information value and cross-information entropy of the sensor, then the evaluation parameters of the sensor layout scheme are determined by utilizing the information value and cross-information entropy, and the optimal layout scheme is selected by utilizing the quantitative evaluation parameters. The limited sensors can be placed at the most critical parts of the mechanical instrument to be detected, so that the operation and maintenance cost is saved, the reliability of the system is improved, and the safe operation of the system is ensured.
The beneficial effects of the invention are as follows:
1. the Bayesian network is introduced, so that the calculation complexity is reduced and the calculation accuracy is improved;
2. the parameter based on the information value covers all decision spaces, and does not limit the sensor placement position;
3. the parameter of the base span information entropy simplifies redundant information and reduces the calculation complexity;
4. the algorithm provided by the invention has lower computational complexity and higher accuracy, and can be applied to most sensor optimization layout occasions.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
fig. 2 is a dynamic fault tree of the hydraulic segment elevator according to an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples.
As shown in fig. 1, a sensor layout optimization method based on mixed information entropy includes the following steps:
step 1: establishing a dynamic fault tree of fault events to be detected, and setting a sensors X 1 ,X 2 ,X 3 ,...,X a Correspondingly placed on each component in the mechanical instrument to be detected;
the step 1 specifically comprises the following steps: firstly, taking a fault in a mechanical instrument to be detected as a fault event to be detected, then determining a sub-fault event of the fault event to be detected, wherein the sub-fault event is specifically one of inducements for causing the fault event to be detected to occur, establishing a corresponding dynamic fault tree by taking the fault event to be detected as a top event node and taking the sub-fault event as a bottom event node, and then connecting a sensor X to a sensor X 1 ,X 2 ,X 3 ,...,X a The sensor is respectively and correspondingly arranged on each component which is easy to generate sub-fault events, wherein each component which is easy to generate sub-fault events is a place where destructive events occur in a simulation process or a daily production process, such as a stress concentration place in a bearing system or a place with larger load in a circuit system, one or more sensors can be arranged on each component, each sensor is used for judging whether the corresponding component is faulty, a represents the total number of the sensors, and in particular implementation, the total number a of the sensors is 21.
In the concrete implementation, a pipe sheet lifting hydraulic instrument of a shield pipe sheet splicing machine is taken as an example. The segment erector has six degrees of freedom, and can translate axially and radially along the tunnel and rotate axially. Wherein, the common fault of the pipe lifting loop is that the hydraulic cylinder crawls, so the hydraulic cylinder crawls to be used as a fault event to be detected, namely a top event node T, the obtained dynamic fault tree is shown as a figure 2, wherein AND represents AND gate operation in a logic gate, OR represents OR gate operation in the logic gate, AND D d The node obtained by the bottom event through logic operation is represented, the subscript d represents the ordinal number of the node, and the HSP represents the spare part gate.
Step 2: converting the dynamic fault tree into a corresponding Bayesian network, and then obtaining the fault rate of each sensor corresponding component by using the Bayesian network, wherein the sensor corresponding component is specifically a component at the position of the sensor;
the process of converting the dynamic fault tree into the corresponding bayesian network in the step 2 is as follows: the method comprises the steps of firstly, corresponding bottom event nodes in a dynamic fault tree to root nodes in a Bayesian network, corresponding top event nodes in the dynamic fault tree to leaf nodes in the Bayesian network, then, corresponding the rest nodes of the dynamic fault tree except the bottom event nodes and the top event nodes to the rest nodes in the Bayesian network except the root nodes and the leaf nodes one by one, and then, establishing the Bayesian network by utilizing the corresponding relation between the dynamic fault tree and the Bayesian network nodes.
The method for obtaining the fault rate corresponding to each sensor by using the Bayesian network comprises the following steps: after the sensors are correspondingly placed on all the components in the mechanical instrument to be detected, the fault rate of each sensor can be obtained according to simulation results and empirical formulas, and the fault rate of each sensor is substituted into a Bayesian network to carry out logic operation, so that the fault rate of the corresponding component of each sensor is obtained.
In specific implementation, the failure rates of the corresponding sensor components obtained by establishing the bayesian network are shown in table 1:
TABLE 1
| Sensor for detecting a position of a body | Sub-fault event | Failure rate of corresponding parts |
| X1,X2 | The oil tank is not enough | 0.0003 |
| X3,X4 | Bending of piston rod | 0.0062 |
| X5,X6 | Failure of seal ring | 0.0174 |
| X7,X8 | Pump shaft oil seal damage | 0.0008 |
| X9,X10 | Reversing valve internal leakage | 0.0031 |
| X11,X12 | Disqualification of coaxiality | 0.0056 |
| X13,X14 | Wearing of piston and cylinder | 0.0178 |
| X15,X16 | Balance valve internal leakage | 0.0031 |
| X17,X18 | Pump shaft oil seal damage | 0.0008 |
| X19 | Pump piston and cylinder wear | 0.0036 |
| X20 | The oil liquid contains gas | 0.0112 |
| X21 | Wear of cylinder and port plate | 0.0036 |
Step 3: from a sensors X 1 ,X 2 ,X 3 ,...,X a Is selected arbitrarily from the b sensor subsets [ X ]' b ]Said subset of sensors [ X ]' b ]For the selected set of sensors, and subset the sensors [ X ]' b ]The selected mode of the sensor is used as a sensor layout scheme;
step 4: calculating reliability parameters of the sensors in different sensor layout schemes by using the failure rate of the corresponding parts of each sensor, wherein the reliability parameters comprise information values (Value of Information, VOI) and cross-information entropy (Transinformation Entropy, TE);
the step 4 is specifically as follows:
step 4.1: obtained as a sensor X i And sensor X j Are all sensor subsets [ X ]' b ]In the case of the element in (a), at the sensor X j Under influence of sensor X i Information value VOI i (j) The specific formula is as follows:
wherein:
i. j each represents a serial number of the sensor;
s represents sensor X i The working state of the corresponding component is a normal state or a fault state; m represents sensor X j The working state of the corresponding component is a normal state or a fault state;
s represents sensor X j The number of operating states of the corresponding component,s is taken as 2; m represents a sensor X j The number of working states of the corresponding parts is M, namely 2;
p(s) represents sensor X i Probability of the corresponding component being in an s working state; p (m) represents sensor X j Probability of the corresponding component being in m working state;
p (s|m) represents sensor X j Sensor X when corresponding component is in m working state i Probability of the corresponding component being in an s working state;
c(s) represents sensor X i The time cost of the working state of the corresponding component can be accurately detected, the sensors of each component of a system have an upstream-downstream relation sometimes, and after the upstream information is detected by the sensors, the state or physical information corresponding to the upstream can be transmitted to the downstream after a certain time is required, so that the downstream perceives the upstream state to have a certain time cost;
max () represents a maximum function;
the sensors X being present in the same sensor arrangement i And sensor X j Information value VOI i (j) The larger the indication is at sensor X j Under influence of sensor X i The more information value is possessed.
Step 4.2: calculating the cross-information entropy TE (X) i ,X j )
Information entropy can be used to describe the amount of information or uncertainty of a random variable, and when the information entropy is larger, the system is more chaotic, the system state cannot be determined, and more information is needed when the system is represented. Sensor X i Information entropy H (X) i ) The formula is as follows:
sensor X j And sensor X i Cross information entropy TE (X) i ；X j ) The calculation formula of (2) is as follows:
wherein H (X) i |X j ) Representing sensor X j The corresponding part is in an s working state and the sensor X j Information entropy of corresponding component in m working state, p (s, m) represents sensor X i The corresponding part is in an s working state and the sensor X j The joint probability distribution of the corresponding component in the m working state;
in a specific implementation, the information value VOI and the cross-information entropy TE of the whole system are shown in table 2.
TABLE 2
Step 5: obtaining final evaluation parameters of the sensor layout scheme by using the reliability parameters obtained in the step 4, wherein the final evaluation parameters are specifically as follows:
using a subset of sensors [ X ]' b ]Information value VOI of each sensor in (B) i (j) And the cross-information entropy TE (X) i ；X j ) Calculating final evaluation parameters of the sensor layout scheme, wherein the final evaluation parameters comprise total information value maximum Z1, total cross-information entropy minimum Z2 and sensor number minimum Z3:
minimize Z3＝b
wherein [ VOI ]]Representing a subset of sensors [ X ]' b ]Information value VOI of all sensors in (a) i (j) Is a collection of (3); [ TE]Representing a subset of sensors [ X ]' b ]Cross-information entropy TE (X) i ；X j ) Max { } represents the maximum of the elements in the fetch setValues.
The number of sensors reflects the cost of monitoring faults by the method of the invention, and therefore, the number of sensors is also used as a final evaluation parameter. Information value VOI in total information value maximum Z1 and total cross information entropy minimum Z2 calculation formula i (j) And cross-information entropy TE (X i ；X j ) All taken from a subset of sensors [ X 'under the same sensor layout scheme' b ]Is a kind of medium.
Step 6: and 5, evaluating the advantages and disadvantages of different sensor layout schemes by utilizing the final evaluation parameters obtained in the step 5, and further selecting an optimal sensor layout scheme from the different sensor layout schemes.
The larger the total information value maximaze Z1 is, the smaller the total cross-information entropy minimum Z2 is, the fewer the number of sensors minimum Z3 is, and the more optimal the layout mode of the sensor layout scheme is.
The three final evaluation parameters are taken into account comprehensively, an optimal sensor layout scheme is determined, and in order to save cost, the optimal scheme of the sensor layout is usually determined under the condition that the number of sensors is limited.
Therefore, an information value threshold and an information entropy threshold are set first, and whether the sensor layout scheme selected in the step 3 is a qualified sensor layout scheme is judged by utilizing the information value threshold and the information entropy threshold:
if the total information value maximum Z1 of the sensor layout scheme is larger than a preset information value threshold value and the total cross information entropy minimum Z2 is smaller than a preset information entropy threshold value, the sensor layout scheme is a qualified sensor layout scheme;
otherwise, indicating that the sensor layout scheme is an unqualified sensor layout scheme;
and selecting the sensor layout scheme with the least number of sensors in the qualified sensor layout schemes as the optimal sensor layout scheme.
The above-described embodiments are intended to illustrate the present invention, not to limit it, and any modifications and variations made thereto are within the spirit of the invention and the scope of the appended claims.
Claims (7)
1. The sensor layout optimization method based on the mixed information entropy is characterized by comprising the following steps of:
step 1: establishing a dynamic fault tree of fault events to be detected, and setting a sensors X 1 ,X 2 ,X 3 ,...,X a Correspondingly placed on each component in the mechanical instrument to be detected;
step 2: converting the dynamic fault tree into a corresponding Bayesian network, and then obtaining the fault rate of each sensor corresponding component by using the Bayesian network;
step 3: from a sensors X 1 ,X 2 ,X 3 ,...,X a Is selected arbitrarily from the b sensor subsets [ X ]' b ]Said subset of sensors [ X ]' b ]For the selected set of sensors, and subset the sensors [ X ]' b ]The selected mode of the sensor is used as a sensor layout scheme;
step 4: calculating reliability parameters of the sensors in different sensor layout schemes by utilizing the failure rate of the corresponding parts of each sensor, wherein the reliability parameters comprise information value and cross-information entropy;
step 5: obtaining final evaluation parameters of the sensor layout scheme through the reliability parameters;
step 6: and 5, judging the advantages and disadvantages of different sensor layout schemes by utilizing the final evaluation parameters obtained in the step 5, and further selecting an optimal sensor layout scheme from the different sensor layout schemes.
2. The sensor layout optimization method based on the mixed information entropy according to claim 1, wherein: the step 1 specifically comprises the following steps: firstly, taking a fault in a mechanical instrument to be detected as a fault event to be detected, then determining a sub-fault event of the fault event to be detected, wherein the sub-fault event is one of inducements for causing the fault event to be detected, establishing a corresponding dynamic fault tree by taking the fault event to be detected as a top event node and taking the sub-fault event as a bottom event node, and thena number of sensors X 1 ,X 2 ,X 3 ,...,X a Respectively and correspondingly placed on each component which is prone to sub-fault events.
3. The sensor layout optimization method based on the mixed information entropy according to claim 1, wherein: the step 2 of converting the dynamic fault tree into the corresponding bayesian network includes the following steps: the method comprises the steps of firstly, corresponding bottom event nodes in a dynamic fault tree to root nodes in a Bayesian network, corresponding top event nodes in the dynamic fault tree to leaf nodes in the Bayesian network, then, corresponding other nodes of the dynamic fault tree to other nodes in the Bayesian network one by one, and then, establishing the Bayesian network by utilizing the corresponding relation between the dynamic fault tree and the Bayesian network nodes.
4. The sensor layout optimization method based on the mixed information entropy according to claim 1, wherein: in the step 2, the failure rate corresponding to each sensor is obtained by using a bayesian network specifically includes: after the sensors are correspondingly placed on all components in the mechanical instrument to be detected, the fault rate of each sensor is obtained, and then the fault rate of each sensor is substituted into a Bayesian network to perform logic operation, so that the fault rate of each sensor corresponding component is obtained.
5. The sensor layout optimization method based on the mixed information entropy according to claim 1, wherein: the step 4 specifically comprises the following steps:
step 4.1: obtained as a sensor X i And sensor X j Are all sensor subsets [ X ]' b ]In the case of the element in (a), at the sensor X j Under influence of sensor X i Information value VOI i (j) Information value VOI i (j) The method is obtained by processing according to the following formula:
wherein:
i. j each represents a serial number of the sensor;
s represents sensor X i The working state of the corresponding component is a normal state or a fault state; m represents sensor X j The working state of the corresponding component is a normal state or a fault state;
s represents sensor X j S is 2, which corresponds to the number of working states of the components; m represents a sensor X j The number of working states of corresponding parts is M, and 2 is taken;
p(s) represents sensor X i Probability of the corresponding component being in an s working state; p (m) represents sensor X j Probability of the corresponding component being in m working state;
p (s|m) represents sensor X j Sensor X when corresponding component is in m working state i Probability of the corresponding component being in an s working state;
c(s) represents sensor X i The time cost required by the working state of the corresponding component can be accurately detected;
max () represents a maximum function;
step 4.2: calculating the cross-information entropy TE (X) i ,X j )
Sensor X j And sensor X i Cross information entropy TE (X) i ；X j ) The method is obtained by processing according to the following formula:
wherein p (s, m) represents sensor X i The corresponding part is in an s working state and the sensor X j The joint probability distribution of the corresponding component in the m operating state.
6. The sensor layout optimization method based on the mixed information entropy according to claim 1, wherein: the step 5 specifically comprises the following steps:
using a subset of sensors [ X ]' b ]Each of the transmissions ofInformation value VOI of sensor i (j) And the cross-information entropy TE (X) i ；X j ) Calculating final evaluation parameters of the sensor layout scheme, wherein the final evaluation parameters comprise total information value maximum Z1, total cross-information entropy minimum Z2 and sensor number minimum Z3:
Minimize Z3＝b
wherein [ VOI ]]Representing a subset of sensors [ X ]' b ]Information value VOI of all sensors in (a) i (j) Is a collection of (3); [ TE]Representing a subset of sensors [ X ]' b ]Cross information entropy TE (X) i ；X j ) Max { } represents taking the maximum function.
7. The sensor layout optimization method based on the mixed information entropy according to claim 1, wherein: the step 6 specifically comprises the following steps: judging whether the sensor layout scheme selected in the step 3 is a qualified sensor layout scheme or not:
if the total information value maximum Z1 of the sensor layout scheme is larger than a preset information value threshold value and the total cross information entropy minimum Z2 is smaller than a preset information entropy threshold value, the sensor layout scheme is a qualified sensor layout scheme;
otherwise, indicating that the sensor layout scheme is an unqualified sensor layout scheme;
and selecting the sensor layout scheme with the least number of sensors in the qualified sensor layout schemes as the optimal sensor layout scheme.
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| CN117313499A (en) * | 2023-11-30 | 2023-12-29 | 国网山东省电力公司枣庄供电公司 | Multi-source sensor arrangement method and system for isolating switch state signals of combined electrical appliance |
| CN117313499B (en) * | 2023-11-30 | 2024-02-13 | 国网山东省电力公司枣庄供电公司 | Multi-source sensor arrangement method and system for isolating switch state signals of combined electrical appliance |
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