CN100440090C - Method for designing sensor measuring network - Google Patents

Method for designing sensor measuring network Download PDF

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CN100440090C
CN100440090C CNB2007100671951A CN200710067195A CN100440090C CN 100440090 C CN100440090 C CN 100440090C CN B2007100671951 A CNB2007100671951 A CN B2007100671951A CN 200710067195 A CN200710067195 A CN 200710067195A CN 100440090 C CN100440090 C CN 100440090C
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pipeline
instrument
cut
unobservable
flow diagram
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CN101013320A (en
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荣冈
王旭
李笕列
冯毅萍
金星
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Zhejiang University ZJU
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Abstract

The invention discloses a sensor measuring network design method. The method uses graph theory to present the practical industrial processes as the directional map description mode, and aims at the highest reliability for measuring network and the minimum investment costs, to obtain the optimal sensor measuring network. The invention has following advantages: 1) it can ensure that after adding the sensor or instrument, making the largest number of not measured variables to obtain the calculated value, and making the highest reliability of the system measuring data; 2) this invention applies to measuring network design under limited investment circumstances, and meanwhile, it can guide the transformation design of the measuring network; 3) this invention tallies with the actual industrial process, and since the requirements of control, optimization, and process monitoring, it must measure the a number of key variables, and since the technical or technological constraints, a number of process variables can not be measured directly, it can provide the measuring network design method; 4) the invention has simple principle, convenient implementation, ease for achieve and data integration of other application systems.

Description

A kind of sensor measuring network design method
Technical field
The present invention relates to a kind of sensor measuring network design method.
Background technology
Production data is the basis of modern enterprise running, and the completeness of data and accuracy directly have influence on monitoring, optimization, scheduling and the decision-making of production run, thereby have influence on the benefit of enterprise.Yet, owing to economical and technical reason, can not measure all variablees, can only measure wherein a part of variable, other variable can only be estimated by the data coordination technique.Like this, select which variable to measure, i.e. sensors configured how, thus guarantee that the data source of the corporate operation that obtains after data are coordinated can satisfy the requirement of completeness and accuracy, it is extremely important just to seem.
In the petrochemical production process, for guaranteeing the implementation result of advanced technologies such as advanced control, on-line optimization, must proofread and correct balance and the relatively poor data of consistance,, simultaneously important not measurand be estimated to improve its precision and consistance from process units.Original Measurement Network is to design for the requirement that adapts to work such as control and plan, row's product in the petrochemical iy produced device, and reckons without the requirement of the adjustment of data.Design, transformation Measurement Network are Measurement Network design and one of main contents of transforming research with the requirement of satisfying the adjustment of data.
The primary prerequisite of sensor configuration is to guarantee the completeness of data, promptly guarantees all may observe of all variablees, and this and redundancy are analyzed closely related.Sensor configuration expense and coordination precision are no doubt important, but from long-term goal, sensors configured is in order to measure logistics, for production control, optimization and scheduling etc. provide authentic data.In case deviation occurs, can influence production undoubtedly, finally cause economic loss.For expensive logistics, measured deviation is big, and the loss that causes is serious more.This just requires us will be with the completeness of data and fiduciary level as important reference index in design and when improving sensor network.
Summary of the invention
The objective of the invention is for production control, optimization and scheduling etc. provide authentic data, and propose a kind of sensor measuring network design method.
Sensor measuring network design method of the present invention, step is as follows:
1) represent the industrial process measuring system with graph theory, make set of graphs G=(V, E), node set V={v wherein 1, v 2... } and be used for reaction unit, the storage tank in the expression process, the confluence and the burble point of pipeline; The set E={e of pipeline 1, e 2... } and be used for representing to connect the pipeline of each process unit, each bar pipeline e iBy two summit (v i, v j) unique definite;
2) determine the pipeline position that some must be measured, the set that these pipelines are formed is expressed as E m, determine that simultaneously the set that these pipelines are formed is expressed as E owing to the immeasurable pipeline position of technical reason c, by the operational instrument number of investment decision NS;
3) establish pipeline or the set E of the may observe pipeline that can calculate by measured value with instrument measurement value o=E m, the number of degrees that obtain each node are simultaneously gathered D (V)={ d (v 1), d (v 2) ..., d (v k), d (v k) represent the number of degrees of k node, promptly flow to and flow out the number of lines of k device;
4) find the solution the set A llcutsets={A of all cut sets of Measurement Network process flow diagram 1, A 2..., A i... }, A iRepresent i cut set, all pipe flow will values that each cut set comprises satisfy the material balance equation of constraint;
5) the whole pipeline set E with the Measurement Network process flow diagram are divided into E oAnd E UoTwo pipeline set, i.e. E Uo=E-E o, pair set is judged, E UoExpression does not have the unobservable pipeline set of instrument measurement value and estimated value, if E UoBe null set or NS=0, the algorithm computing finishes and output E as a result so o, determine the installation site of instrument in Measurement Network, otherwise algorithm forwards step 6) to;
6) the set A llcutsets of all cut sets of traversal Measurement Network process flow diagram, the cut set that finds all only to contain a unobservable pipeline constitutes set B by the unobservable pipeline that satisfies above condition, if B is null set, forward step 7) to, otherwise upgrade set E o=E o+ B forwards step 5) to;
7) set E will be belonged to simultaneously cWith set E oPipeline eliminate the set E c
8) the set A llcutsets of all cut sets of traversal Measurement Network process flow diagram finds out the cut set A that all only contain two unobservable pipelines j, and the cut set that will satisfy above condition is formed new set C={A J1, A J2, A J3... }, A J3Represent j3 cut set, if cut set A JiWith cut set A JkAll comprise two identical unobservable pipelines, from set C, delete A so Jk, repeat the cut set delet method in this step, in set C, there is not the cut set of repetition, if set C is null set, the algorithm execution in step 9 so), otherwise algorithm forwards step 10) to;
9) by calculating set D (E Uo)={ d (e 1), d (e 2) ..., d (e i) ..., d (e wherein i) expression pipeline e iThe number of degrees, by determining pipeline e in the process flow diagram iTwo node (v i, v j) number of degrees summations obtain i.e. d (e i)=d (v i)+d (v j), if pipeline e iBelong to set E c, so with d (e i) eliminate and gather D (E Uo), find set D (E Uo) in the pipeline of number of degrees minimum, in this pipeline sensor installation or instrument, and this pipeline added set E oIn, calculating NS=NS-1, algorithm forwards step 5) to simultaneously;
10) definition pipeline set U all unobservable pipelines of representing to gather among the C and being comprised, order set N (U)={ N (e 1), N (e 2) ..., N (e Ij) ..., N (e Ij) the unobservable pipeline e of expression IjThe number that in set C, occurs, i.e. pipeline e IjCan be obtained the pipeline number of calculated value after the installation instrument, be found maximum N (e Ij), and defining variable MAX=N (e Ij), if having a plurality of elements to equal MAX among the set N (U), find these corresponding pipelines so and they are formed set E s={ e S1, e S2..., e Si... }, if E sBe null set, forward step 11) so to, otherwise forward step 12) to;
11) find the pipeline of corresponding MAX in the Measurement Network process flow diagram, instrument is installed on this pipeline and this pipeline is added set E oIn, calculating NS=NS-1, algorithm forwards step 5) to simultaneously;
12) set up Measurement Network process flow diagram relevant tube dimension manifold and close D (E s)={ d (e S1), d (e S2) ..., d (e Si) ..., d (e wherein Si) expression pipeline e SiThe number of degrees, find minimum d (e Si) corresponding pipeline, instrument is installed on this pipeline and this pipeline is added set E oIn, calculating NS=NS-1, algorithm forwards step 5) to simultaneously.
Beneficial effect of the present invention is:
1) after sensor measuring network design method of the present invention can be guaranteed to add sensor or instrument, makes the not measurand of maximum quantity obtain calculated value, and make that the fiduciary level of systematic survey data is the highest;
2) the inventive method is applicable to and carries out the Measurement Network design under the situation of limited investment, can instruct the improvement and design of Measurement Network simultaneously so that maximum pipeline flows is calculated;
3) in the realistic industrial process of the inventive method because the demand of control, optimization and process monitoring, can instruct the engineering staff must be measured and owing to technology and technologic the restriction under the situation that some process variable can not directly be measured provide the Measurement Network design proposal at some key variables;
4) the inventive method principle is simple, and it is convenient to implement, and is convenient to realize the data integration with other application system.
Description of drawings
Fig. 1 is the preparation process process flow diagram of ammonia;
Fig. 2 is single device synoptic diagram;
Fig. 3 is the inventive method FB(flow block), and φ wherein represents null set;
Fig. 4 is the vapour survey network chart of simplifying.
Embodiment
Preparation process with ammonia shown in Figure 1 is an example, and cut set and the fiduciary level that the present invention relates to is described:
At first actual industrial process is described with the graph theory form.The industrial process measuring system be expressed as G=(V, E), node set V={v wherein 1, v 2... } and be used for reaction unit, the storage tank in the expression process, the confluence and the burble point of measurement line; The set E={e of pipeline 1, e 2... } and be used for representing to connect the pipeline of each process unit, each bar pipeline e iBy two summit (v i, v j) unique definite.In the describing method of this industrial process, we have defined a virtual vertex that is called as the environment node, and all raw materials of regulation industrial process and other inputs flow into this summit from this summit and all product and other output objects.Because the existence of environment node, whole industrial process measuring system forms an airtight connected graph.
Concerning a connected graph, a closing face (shown in Fig. 1 frame of broken lines) is the figure separated into two parts, some of them summit (v 1And v 5) be positioned at the inside of this closing face, and other summits (v 2, v 3, v 4, v 6) then be positioned at the outside of this closing face.If the pipeline e that passes this closing face 1, e 4, e 6, e 7All remove (but the node at branch road two ends still keeps), then former connected graph promptly is split into separated portions just.Pipeline e 1, e 4, e 6, e 7The set of forming is called a cut set (cutset) of this connected graph.One group of pairing flow variable of pipeline that each cut set comprised satisfies the material balance constraint:
f e 4 + f e 6 - f e 1 - f e 7 = 0 - - - ( 1 )
Wherein
Figure C20071006719500072
Expression pipeline e iPairing flow.
By formula (1) as can be known, and if only if except pipeline e in a cut set iPairing flow
Figure C20071006719500073
Other flow variable in addition all has under the situation of measured value, flow Be observable (estimated value can be calculated by other measuring amount).In the methods of the invention, if our definition can be judged a certain flow variable
Figure C20071006719500075
Be observable, so when judging the state of other flow variables, flow variable
Figure C20071006719500076
Be considered to be and measure flow.Illustrate, in Fig. 1, if
Figure C20071006719500077
The instrument measurement value is arranged, so
Figure C20071006719500078
Can calculate by formula (1).When judging the state of other flow variables, flow variable
Figure C20071006719500079
Be considered to be and measure flow.We can calculate to use the cut set pipeline flow meters that satisfies the material balance constraint to calculate formula
Figure C200710067195000710
Figure C200710067195000711
Among Fig. 1, when initial situation has only e 6When the instrument measurement value is arranged, select different positions that instrument is installed on this basis, measurement effect can be very different.If this moment is at pipeline e 7Instrument is installed obtains measured value, have only so
Figure C200710067195000712
Can be calculated.If at pipeline e 2Place instrument and obtain measured value, so
Figure C200710067195000714
Article three, measured value can calculate on the pipeline.Owing to place instrument, the effect of Measurement Network is made a world of difference, so we at first defined an index N (e before the design Measurement Network in different positions Ij) weigh this difference.At pipeline e iAfter the placement instrument obtained measured value, the measured value of some other pipelines can be calculated, N (e Ij) be used for representing the number of the pipeline that can be calculated.In the inventive method, we when select placing the position of sensor or instrument, N (e among the selection course figure always Ij) pipeline of index maximum.
We need also to consider that one is optimized index, i.e. fiduciary level when the design Measurement Network.In the present invention, the flow measurement instrument of each pipeline all adopts uniform instrument, so their fiduciary level can be thought equally.Be exactly to consider how to make the pipeline of the fiduciary level minimum in each variable to reach maximum fiduciary level when we design Measurement Network, this is the minimum greatest problem in the optimization problem in fact.By graph theory as can be known, the minimal reliability in the Measurement Network is to appear at not measurand certainly, because their value calculates by other measured values, therefore the possibility that breaks down is very big.Not measurand in the Measurement Network that we design can calculate by the instrument measurement value of some other pipelines, and therefore the fiduciary level of measurand is not by these instrument measurement value failure rate decisions, and formula is:
R ( i ) = Π j ∈ K i f j ≠ i ( 1 - p j ) - - - ( 2 )
Wherein, R (i) expression
Figure C200710067195000716
Fiduciary level, K i fBe by e iWith provide e iOne group of fundamental cutset that pipeline is formed of calculated value, p jThe failure rate of representing j instrument, the fiduciary level of j instrument equals 1-p j
The failure rate of the instrument of using in the Measurement Network is known and uncorrelated mutually, and the fiduciary level of a certain variable is by the failure rate decision of Measurement Network structure and institute's instrumentation.With simple procedure unit shown in Figure 2 is example, and the mass rate of all pipelines is obtained by instrument measurement, and the failure rate of each instrument all is 0.1.Three flow variable F in this example 1, F 2, F 3Between restriction relation can be by following material balance formulate:
F 1＝F 2+F 3 (3)
Three instrument S as shown in Figure 2 are installed 1, S 2, S 3The time, mass rate F 1RELIABILITY INDEX R (F 1) can be expressed as:
R (F 1)=Pr{S 1Operate as normal } or Pr{S 2And S 3Operate as normal }
＝(1-p 1)+(1-p 2)×(1-p 3)-(1-p 1)×(1-p 2)×(1-p 3)
＝(1-0.1)+(1-0.1)×(1-0.1)-(1-0.1)×(1-0.1)×(1-0.1)
＝0.9+0.81-0.729
＝0.981
If mass rate F 1When not having instrument measurement, F 1RELIABILITY INDEX R (F 1) can be expressed as:
R (F 1)=Pr{S 2And S 3Operate as normal }
＝0.9×0.9
＝0.81
The vapour survey network of simplifying with Fig. 4 is an example below, sets forth sensor measuring network design method, and whole flow processs of Measurement Network method for designing as shown in Figure 3.
Embodiment 1 considers three kinds of different situations, because the investment constraint, the metered quantity that provides can not make all variablees that measured value or calculated value are all arranged.
In the practical design process, we need consider such a case, promptly are used for limited investment that instrument purchases and install and are not enough to make all may observe (promptly directly measured or calculated by other measured values) of all variablees.N=12 device and m=28 pipeline are arranged in industrial process in this example, by graph theory as can be known if make and all may observe of all pipeline flows need n-m+1=28-12+1=17 flow sensor or instrument so at least.Situation when method for designing of the present invention has been considered under-capitalization can provide in real process under the situation of sensor of limited quantity, makes maximum pipeline flows to be observed.
First kind of situation C1, step is as follows:
1) represents the industrial process measuring system with graph theory, make set of graphs G=that (V, E), system shown in Figure 4 comprises 12 node v 1, v 2..., v 12With 28 pipeline e 1, e 2..., e 28, wherein environment node (summit 12) does not provide in the drawings.The probability of malfunction of each instrument is 0.1.Node set V={v wherein 1, v 2..., v 12Be used for reaction unit in the expression process; The set E={e of pipeline 1, e 2..., e 28Be used for representing to connect the pipeline of each process unit;
2) definite pipeline position E that must measure m={ e 2, e 3, e 6, e 7, e 11, e 13, e 15, e 19, determine simultaneously because the immeasurable pipeline position set of technical reason E c={ e 1, e 12, e 16, by operational sensor of investment decision or instrument number NS=3;
3) establish pipeline or the initial sets E of the may observe pipeline that can calculate by measured value with instrument measurement value o=E m={ e 2, e 3, e 6, e 7, e 11, e 13, e 15, e 19, the number of degrees that obtain each node are simultaneously gathered D (V)={ d (v 1), d (v 2) ..., d (v 12)=4,5,3,3,7,3,6,5,4,4,4,8}, d (v 1) represent the number of degrees of the 1st node, promptly flow to and flow out the number of lines of the 1st device, E oRepresent observable pipeline set, E mExpression has the pipeline set of instrument measurement value;
4) find the solution the set A llcutsets={A of all cut sets of Measurement Network process flow diagram 1, A 2..., A 853, all pipe flow will values that each cut set comprises satisfy the material balance equation of constraint;
5) the whole pipeline set E with the Measurement Network process flow diagram are divided into E oAnd E UoTwo pipeline set, i.e. E Uo=E-E o={ e 1, e 4, e 5, e 8, e 9, e 10, e 12, e 14, e 16, e 17, e 18, e 20, e 21, e 22, e 23, e 24, e 25, e 26, e 27, e 28, pair set is judged, E UoExpression does not have the unobservable pipeline set of instrument measurement value and estimated value, because E UoBe not null set, algorithm forwards step 6) to;
6) the set A llcutsets of all cut sets of traversal Measurement Network process flow diagram, the cut set that finds all only to contain a unobservable pipeline constitutes set B by the unobservable pipeline that satisfies above condition, because B is null set, algorithm forwards step 7) to;
7) this example does not exist and belongs to set E simultaneously cAnd E oPipeline, algorithm forwards step 8) to;
8) the set A llcutsets of all cut sets of traversal Measurement Network process flow diagram finds out the cut set A that all only contain two unobservable pipelines j, obtain gathering C={A J1, A J2}={ { e 1, e 2, e 3, e 4, { e 10, e 11, e 12.Set C is not null set, so algorithm forwards step 10) to;
9) because this example set C is not null set, therefore save step 9);
10) definition pipeline set U all unobservable pipelines of representing to gather among the C and being comprised obtain gathering N (U)={ N (e 4), N (e 10)=1,1}, N (e 4) the unobservable pipeline e of expression 4The number that in set C, occurs, i.e. pipeline e 4The pipeline number that can be calculated after the instrument is installed, is found maximum N (e 4), and defining variable MAX=N (e 4)=N (e 10)=1, pipeline set E s={ e 4, e 10, because E sBe not null set, algorithm forwards step 12) to;
11) because this example set E sNot null set, therefore save step 11);
12) set up Measurement Network process flow diagram relevant tube dimension manifold and close D (E s)={ d (e 4), d (e 10)={ 12,6} is at pipeline e 10Last installation instrument also adds set E with this pipeline oIn.Calculate NS=NS-1=2, algorithm forwards step 5) to.
Repeat above step up to E UoBecome null set or NS=0, can obtain pipeline set { e 10, e 5, e 8Should be placed instrument or sensor, pipeline E in the Measurement Network o={ e 1, e 4, e 5, e 8, e 9, e 10, e 12May observe.
Second kind of situation C2, starting condition satisfies E m={ e 2, e 3, e 6, e 7, e 11, e 13, e 15, e 19, E cBe empty set
Close and during NS=3.Utilization the inventive method can get pipeline set { e 10, e 1, e 8Should be placed sensor or instrument, pipeline E in the Measurement Network o={ e 1, e 4, e 5, e 8, e 9, e 10, e 12Be observable.
The third situation C3, starting condition satisfies E m={ e 2, e 3, e 6, e 7, e 11, e 13, e 15, e 19, E cDuring for null set and NS=6.Utilization the inventive method can get pipeline set { e 10, e 1, e 8, e 26, e 23, e 20Should be placed sensor or instrument, pipeline E in the Measurement Network o={ e 1, e 4, e 5, e 8, e 9, e 10, e 12, e 20, e 23, e 26, e 27, e 28Be observable.
More than the result and analyze of three kinds of situations describe by table 1.
Table 1
Figure C20071006719500101
In embodiment 1, the order of placing instrument (is E aIn order) also be very important, it has shown in the Measurement Network because instrument should at first be placed in some position of difference of importance.
The measurement instrument quantity that embodiment 2. provides just in time satisfies to make that all variablees are measured or calculates.
Still the vapour survey network of simplifying with Fig. 4 is an example, ergodic algorithm (" An optimalalgorithm for scanning all spanning trees of undirected graphs " SIAM Journal onComputing.1997 of utilization graph theory, 26 (3), p678) the optimum Measurement Network fiduciary level among Fig. 4 is 0.53 (i.e. 0.9 6 powers) as can be known.Five kinds of situations (C1, C2, C3, C4, C5) in this example, all satisfying Ec is the starting condition of null set, concrete result of calculation describes in detail in table 2.
Table 2
Starting condition NS Should be placed the pipeline set E of instrument a Measure the net fiduciary level
C1 E m＝{e 6，e 7，e 11，e 13，e 15，e 19} NS＝11 {e 10，e 1，e 8，e 3，e 26，e 23，e 20，e 22，e 16，e 18，e 14} 0.53
C2 E m＝{e 3，e 6，e 7，e 11，e 13，e 15，e 18，e 19} NS＝9 {e 10，e 1，e 8，e 26，e 23，e 22，e 20，e 16，e 14} 0.53
C3 E m＝{e 3，e 6，e 7，e 11，e 13，e 15，e 18，e 19，e 22，e 26} NS＝7 {e 23，e 10，e 1，e 8，e 20，e 16，e 14} 0.53
C4 E m＝{e 1，e 3，e 6，e 11，e 13，e 15，e 19} NS＝10 {e 10，e 26，e 23，e 8，e 20，e 7，e 22，e 16，e 18，e 14} 0.53
C5 E m＝{e 5，e 6，e 11，e 13，e 20，e 23} NS＝11 {e 10，e 3，e 26，e 8，e 19，e 7，e 22，e 16，e 18，e 15，e 14} 0.53
Characteristics of the present invention are that principle is simple, and it is convenient to implement, and can satisfy the actual Design ﹠ reform of finishing sensor measuring network of commercial Application. Improve the Data correction precision of enterprise's measurement data, guarantee the reliability of data.

Claims (1)

1. sensor measuring network design method, its step is as follows:
1) represent the industrial process measuring system with graph theory, make set of graphs G=(V, E), node set V={v wherein 1, v 2... be used for reaction unit, the storage tank in the expression process, the confluence and the burble point of pipeline; The set E={e of pipeline 1, e 2... be used for representing to connect the pipeline of each process unit, each bar pipeline e iBy two summit (v i, v j) unique definite;
2) determine the pipeline position that some must be measured, the set that these pipelines are formed is expressed as E m, determine that simultaneously the set that these pipelines are formed is expressed as E owing to the immeasurable pipeline position of technical reason c, by the operational instrument number of investment decision NS;
3) establish pipeline or the set E of the may observe pipeline that can calculate by measured value with instrument measurement value o=E m, the number of degrees that obtain each node are simultaneously gathered D (V)={ d (v 1), d (v 2) ..., d (v k), d (v k) represent the number of degrees of k node, promptly flow to and flow out the number of lines of k device;
4) find the solution the set A llcutsets={A of all cut sets of Measurement Network process flow diagram 1, A 2..., A i..., A iRepresent i cut set, all pipe flow will values that each cut set comprises satisfy the material balance equation of constraint;
5) the whole pipeline set E with the Measurement Network process flow diagram are divided into E oAnd E UoTwo pipeline set, i.e. E Uo=E-E o, pair set is judged, E UoExpression does not have the unobservable pipeline set of instrument measurement value and estimated value, if E UoBe null set or NS=0, the algorithm computing finishes and output E as a result so o, determine the installation site of instrument in Measurement Network, otherwise algorithm forwards step 6) to;
6) the set A llcutsets of all cut sets of traversal Measurement Network process flow diagram, the cut set that finds all only to contain a unobservable pipeline constitutes set B by the unobservable pipeline that satisfies above condition, if B is null set, forward step 7) to, otherwise upgrade set E o=E o+ B forwards step 5) to;
7) set E will be belonged to simultaneously cWith set E oPipeline eliminate the set E c
8) the set A llcutsets of all cut sets of traversal Measurement Network process flow diagram finds out the cut set A that all only contain two unobservable pipelines j, and the cut set that will satisfy above condition is formed new set C={A J1, A J2, A J3..., A J3Represent j3 cut set, if cut set A JiWith cut set A JkAll comprise two identical unobservable pipelines, from set C, delete A so Jk, repeat the cut set delet method in this step, in set C, there is not the cut set of repetition, if set C is null set, the algorithm execution in step 9 so), otherwise algorithm forwards step 10) to;
9) by calculating set D (E Uo)={ d (e 1), d (e 2) ..., d (e i) ..., d (e wherein i) expression pipeline e iThe number of degrees, by determining pipeline e in the process flow diagram iTwo node (v i, v j) number of degrees summations obtain i.e. d (e i)=d (v i)+d (v j), if pipeline e iBelong to set E c, so with d (e i) eliminate and gather D (E Uo), find set D (E Uo) in the pipeline of number of degrees minimum, in this pipeline sensor installation or instrument, and this pipeline added set E oIn, calculating NS=NS-1, algorithm forwards step 5) to simultaneously;
10) definition pipeline set U all unobservable pipelines of representing to gather among the C and being comprised, order set N (U)={ N (e 1), N (e 2) ..., N (e Ij) ..., N (e Ij) the unobservable pipeline e of expression IjThe number that in set C, occurs, i.e. pipeline e IjCan be obtained the pipeline number of calculated value after the installation instrument, be found maximum N (e Ij), and defining variable MAX=N (e Ij), if having a plurality of elements to equal MAX among the set N (U), find these corresponding pipelines so and they are formed set E s={ e S1, e S2..., e Si..., if E sBe null set, forward step 11) so to, otherwise forward step 12) to;
11) find the pipeline of corresponding MAX in the Measurement Network process flow diagram, instrument is installed on this pipeline and this pipeline is added set E oIn, calculating NS=NS-1, algorithm forwards step 5) to simultaneously;
12) set up Measurement Network process flow diagram relevant tube dimension manifold and close D (E s)={ d (e S1), d (e S2) ..., d (e Si) ..., d (e wherein Si) expression pipeline e SiThe number of degrees, find minimum d (e Si) corresponding pipeline, instrument is installed on this pipeline and this pipeline is added set E oIn, calculating NS=NS-1, algorithm forwards step 5) to simultaneously.
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