CN105260546B - The method for building up and its method for solving of optimized design model based on uniform accuracy life principle - Google Patents
The method for building up and its method for solving of optimized design model based on uniform accuracy life principle Download PDFInfo
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Abstract
The invention discloses a kind of method for building up and its method for solving of the optimized design model based on uniform accuracy life principle, it is characterized in that carrying out as follows：1. dynamic measurement system and its respective Precision losing function of n error unit are obtained with source tracing method using dynamic error separation；2. according to the n+1 loss of significance limit and n+1 Precision losing function to dynamic measurement system and its n error unit setting, dynamic measurement system and its error unit respective accuracy life is obtained；3. the non-uniformity of dynamic measurement system is obtained using non-uniformity definition in the present invention；4. the mean accuracy loss speed that n error unit is obtained using total system dynamic error model is weighed；5. the service life for establishing dynamic measurement system uniform optimized design model.The present invention can realize the optimization design of measuring system uniform accuracy life so that each unit precision can fail within the roughly the same time in system, play the maximal efficiency of resource.
Description
Technical field
The present invention relates to measuring system accuracy life design field, it is specially a kind of based on uniform accuracy life principle most
The method for building up and its method for solving of mathematical optimization models.
Background technology
Precision is one of important indicator for weighing measuring instrument quality.With the continuous development of science and technology, modern test
Technology, the application that particularly dynamic measures is more and more extensive, and the research and development of dynamic measurement precision theory also proposed newly
Subject.
A large amount of experiment with practice have shown that, measuring system, especially dynamic measurement system, precision be not it is constant always,
But can be continuously decreased with the extension of time of measuring, this phenomenon is referred to as " loss of significance ".Once the essence of measuring system
Degree penalty values reach the loss of significance limit of permission, then it is assumed that measuring system precision fails, recalibrated, repair or
Update is scrapped, the corresponding out-of-service time is " accuracy life ".Meanwhile the overall accuracy of measuring system is each error list of whole system
Metasynthesis effect as a result, therefore measuring system overall accuracy loss should also be as be composition system each error unit loss of significance
The result of comprehensive function.But the differences such as principle, structure, material, performance of each error unit of system, then loss of significance mechanism
It is also not quite similar with the loss of significance limit of permission, it is early so as to the unit precision having in entire measuring system failure occur, have
The universal phenomenon in unit precision failure evening, i.e. the accuracy life of each error unit of measuring system is uneven, accuracy life short list
Member will influence the normal measurement of whole system, so as to cause the waste of social resources and the increase of every cost.
To solve the above problems, Fei Yetai professor first proposed measuring system accuracy life uniform design, i.e., it is logical
The loss of significance design that each error unit is scientific and reasonable to measuring system is crossed, realizes the precision longevity of measuring system and its component units
Basically identical target is ordered, improves the utilization rate of instrument and equipment, saves social resources.Jiang Minlan mainly measures system to how to analyze
The inhomogeneities of system is studied, it is proposed that determines each error unit loss of significance power and system using grey correlation theory
Heteropical method.But above-mentioned pertinent literature does not all provide the specific embodiment party for establishing uniform design optimal model
Method.Liu Fangfang is given based on loss of significance uniformity consistency principle and designed a model, but this achievement in research can not solve to move
Accuracy life non-uniform problem in state measuring system.
Invention content
The present invention is to overcome the shortcomings of the prior art part, is provided a kind of based on uniform accuracy life principle
Optimized design model method for building up and its method for solving, to realize the optimization design of system uniform accuracy life,
Each unit precision within the roughly the same time in system is failed, so as to play the maximal efficiency of resource.
The present invention in order to achieve the above object, adopts the following technical scheme that：
A kind of method for building up of the optimized design model based on uniform accuracy life principle of the present invention is to be applied to dynamic
The characteristics of in measuring system is to carry out as follows：
Step 1 obtains the dynamic measurement system and its n error unit is each using dynamic error separation and source tracing method
From Precision losing function model；
Step 2 sets the dynamic measurement system and its respective loss of significance limit of n error unit, is denoted as { δs,
δ1,δ2,…,δi,…,δn}；δsRepresent the loss of significance limit of the dynamic measurement system, δiRepresent i-th of error unit
The loss of significance limit, 1≤i≤n, n represent the total number of the error unit；
Step 3, according to the n+1 set loss of significance limit and the n+1 Precision losing function model, institute is obtained
Dynamic measurement system and its error unit respective accuracy life are stated, is denoted as { Ts,T1,T2..., Ti,…,Tn}；TsDescribed in expression
The accuracy life of dynamic measurement system, TiRepresent the accuracy life of i-th of error unit；
Step 4, the non-uniformity ρ that the dynamic measurement system is obtained using formula (1)：
Step 5, the mean accuracy loss speed power that n error unit is obtained using total system dynamic error model, are denoted as
{p1,p2,…,pi,…,pn}；piRepresent the mean accuracy loss speed power of i-th of error unit；
Step 6, the service life uniform optimized design model for establishing the dynamic measurement system；
Step 6.1 determines design parameter vector X：
Defining the respective mean accuracy loss speed of the n error unit is
Represent the mean accuracy loss speed of i-th of error unit；
Speed is lost with the n mean accuracy and n+1 accuracy life is formed the determining design parameter vector X, i.e.,TsThe accuracy life optimal design of ' expression dynamic measurement system
Value；T′iRepresent the accuracy life optimal design value of i-th of error unit；
Step 6.2 determines object function：
With accuracy life uniformly for design object, non-uniformity object function is obtained using formula (2)：
With accuracy life uniform accuracy life up to design object, accuracy life object function is obtained using formula (3)：
Max T'=min { T1',…,Tn',Ts'} (3)
In formula (3), T' is represented in the accuracy life optimal design value of the dynamic measurement system and its n error unit
Minimum value；
With the accuracy life uniform minimum design object of total improving cost, improving cost target letter is obtained using formula (4)
Number：
In formula (4), C represents total improving cost of the n error unit；CiRepresent changing for i-th of error unit
Into cost；And have：
Formula (5) represents the improving cost C of i-th of error unitiSpeed is lost with the mean accuracy of i-th of error unit
DegreeBetween relationship；
Step 6.3 determines constraints：
The constraints of non-uniformity ρ is obtained using formula (6)：
ρ≤ε (6)
In formula (6), ε represents the limiting value of the non-uniformity ρ；
The constraints of mean accuracy loss speed is obtained using formula (7)：
In formula (7),Represent the mean accuracy loss speed of i-th of error unitLower limit；It represents
The mean accuracy loss speed of i-th of error unitThe upper limit；
The constraints of accuracy life is obtained using formula (8)：
min{T1',T2',…,Tn',Ts' ＞ T0 (8)
In formula (8), T0Represent the desired value of the accuracy life of the dynamic measurement system；
The constraints between mean accuracy loss speed, accuracy life and the loss of significance limit is obtained using formula (9)：
The constraints of total improving cost is obtained using formula (10)：
C≤C0 (10)
In formula (10), C0Represent the upper limit of total improving cost of the dynamic measurement system.
A kind of the characteristics of method for solving of optimized design model based on uniform accuracy life principle of the present invention, lies also in
It is to carry out as follows：
Step 1 constructs the initial value that m groups meet the design parameter vector X of constraints using numerical method；
Step 2 finds locally optimal solution corresponding to the m groups initial value using Sequential Quadratic Programming method respectively；
Step 3 searches for globally optimal solution from the locally optimal solution of the m groups initial value, so as to obtain globally optimal solution
And its corresponding best design parameter vector.
Compared with the prior art, beneficial effects of the present invention are embodied in：
1st, currently invention addresses the development trend of measurement accuracy theory and the social goals of " green manufacturing ", it is proposed that a kind of
The modeling of dynamic measurement system optimized design and method for solving based on uniform accuracy life, realize measuring system component units
The theory of accuracy life uniformity consistency；The basis traced to the source is decomposed in Whole system dynamic accuracy theory and to the loss of system overall accuracy
On, it is proposed that the definition of novel non-uniformity and loss of significance power determine method, using the average loss speed of each error unit as
Design variable considers and devises the constraintss such as range of variables, non-uniformity, accuracy life, improving cost, establishes conjunction
The optimized design model of reason simultaneously solves, and realizes the optimization design of system uniform accuracy life so that each unit energy in system
Precision fails within the roughly the same time, has played the maximal efficiency of resource.
2nd, it is relatively very poor non-to define present invention employs dynamic measurement system and its each error unit accuracy life
The uniformity, this definition formula not only overcome in existing document that accuracy life non-uniformity concept is not readily understood, calculating process is complicated
The problem of, and it is simple and easy to do, provide condition for the optimized design modeling based on uniform accuracy life principle.
3rd, basic conception of the present invention according to loss of significance power employs total system dynamic error model acquisition dynamic and measures
The mean accuracy loss speed power of each error component units of system specifies the loss of significance velocity variable of each error unit
To the impact factor of system accuracy loss velocity variable, the not foundation of only optimized design model provides foundation, may be used also
To determine the main optimization design unit of dynamic measurement system, model and its solution procedure are simplified.
4th, the present invention loses speed as design parameter using each error unit mean accuracy of dynamic measurement system, both overcomes
The problem of design parameter is excessive in existing document, solving complexity, and can reduce the requirement to project planner, only it is to be understood that
With the loss of significance average speed of grasp associated materials or parts under certain operating mode, help to instruct dynamic measurement system
Improve the realization with optimized design result.
5th, the present invention can be directed to different optimization design targets, consider and devise range of variables, non-uniformity, essence
The constraintss such as service life, improving cost are spent, establish rational optimized design model.
6th, numerical method and Sequential Quadratic Programming method are combined and solve the dynamic based on uniform accuracy life principle by the present invention
Measuring system optimized design model is overcome and is caused due to initial value selection is improper when being solved using Sequential Quadratic Programming method merely
Locally optimal solution problem.
Specific embodiment
In the present embodiment, a kind of method for building up of the optimized design model based on uniform accuracy life principle is application
It is to carry out as follows in dynamic measurement system：
Step 1 obtains studied dynamic measurement system and its n error list using dynamic error separation and source tracing method
The respective Precision losing function of member, is denoted as { δs(t),δ1(t),…,δi(t),…,δn(t) }, wherein, t represents time of measuring, δs
(t) Precision losing function of the dynamic measurement system, δ are representedi(t) Precision losing function of i-th of error unit, 1≤i are represented
≤ n, n represent the total number of entire measurement system error unit.
For specific dynamic measurement system, isolate each measuring phases in the life cycle management of system first is
System overall error, and their accuracy characteristic amount is estimated, total system error model is established, appropriate error is selected to decompose with tracing to the source
Method, such as spectrum analysis, wavelet neural network, Xi Er bauds-Huang, so as to obtain measuring system and its error unit
In the loss of significance sequence of each measuring phases, then managed using suitable Mathematical Modeling Methods, such as least square fitting, grey
By, neural network, support vector machines etc., establish system and its respective Precision losing function { δ of error units(t),δ1
(t),…,δi(t),…,δn(t)}。
Step 2, setting dynamic measurement system and its respective loss of significance limit of n error unit, are denoted as { δs,δ1,
δ2,…,δi,…,δn}；δsRepresent the loss of significance limit of dynamic measurement system, δiRepresent the loss of significance of i-th of error unit
The limit.
Step 3, according to the n+1 set loss of significance limit and n+1 Precision losing function, dynamic is obtained and measures system
System and its error unit respective accuracy life, it is denoted as { Ts,T1,T2,…,Ti,…,Tn}；TsRepresent the essence of dynamic measurement system
The service life is spent, TiRepresent the accuracy life of i-th of error unit；
The accuracy life of system and each error unit should meet relationship below (1)：
Since Precision losing function is usually monotonic function, the precision longevity of measuring system and its error unit thus can be solved
Order estimated value Ts,T1,…,Tn。
Step 4, the non-uniformity ρ that dynamic measurement system is obtained using formula (2)：
Non-uniformity ρ characterizes the accuracy life dispersibility of system and its error unit, 0≤ρ≤1, and ρ is smaller, is
System is more uniform, and design is better.According to the actual conditions of system and uniform design target, it may be determined that the non-uniformity of measuring system
Index request ε as non-uniformity ρ≤ε of system, then illustrates that system accuracy has realized uniform design target.
Step 5, the mean accuracy loss speed power that n error unit is obtained using total system dynamic error model, are denoted as
{p1,p2,…,pi,…,pn}；piRepresent the mean accuracy loss speed power of i-th of error unit；
During the overall accuracy loss of measuring system in system each integral link or unit loss of significance comprehensive function as a result, and
And influence and different of the loss of significance variation of each unit to the loss variation of system overall accuracy.Realize dynamic measurement system
Accuracy life uniform design, it is necessary to research and design be carried out to the loss of significance rule of each unit, this will directly influence system
Overall accuracy loss rule and its service life, therefore the influence degree that system overall accuracy is lost in the loss of significance of clear and definite each unit,
It is the precondition for realizing service life uniform design.
Here, p is weighed using loss of significanceiLoss of significance characteristic quantity to reflect unit loses characteristic quantity to system overall accuracy
Influence degree,
I.e. for a certain dynamic measurement system being made of n unit, overall accuracy loss characteristic quantity δsT(t) it can represent
For：
In formula (3), δiT(t) the loss of significance characteristic quantity of i-th of error unit is represented.
It can be seen that the loss of significance characteristic quantity of influence of the loss of significance of each unit to system not only with itself has
It closes, is also weighed with the loss of significance of the unit closely related.Loss of significance power is bigger, and the variation of unit loss of significance is always smart to system
Degree loss variation role is bigger, is preferentially considered as when improving system overall accuracy loss rule；Loss of significance power is got over
Small, unit is smaller to the loss variation role of system overall accuracy, when sufficiently small, then can be ignored, so as to simplify
It designs a model and designing scheme.
Loss of significance characteristic quantity can be by absolute precision loss amount, relative accuracy loss amount and average loss of significance speed etc.
It represents, then corresponding power is respectively absolute precision loss power, relative accuracy loss power and average loss speed power.For convenience of excellent
Change design and engineer application, only give the determining method of mean accuracy loss speed power, the determining side of other forms power herein
Method can similarly obtain.Total system dynamic accuracy model inherently reflects the functional relation between system overall accuracy and unit precision,
Therefore, measuring system is being fully understood on the basis of grasp, total system dynamic accuracy " albefaction " model can be established, therefore
The mean accuracy loss speed power of each unit can be determined by total system dynamic error model.
1. the average loss speed power of tandem dynamic measurement system
Assuming that certain tandem measuring system has the unit of n influence measurement result precision, including input element error e1(t)
With output element error en(t), total system dynamic error model is：
In formula (4), es(t) it is output overall error of the dynamic measurement system in moment t；fi() is i-th of unit of system
Transmission function；ei(t) it is error of i-th of error unit in t moment.
If representing measurement result precision with average error, the Accuracy extimate value of t measuring systems is at any time
According to the definition of Precision losing function,
So, mean accuracy loss speed is：
In formula (7), t0It can be seen that tandem measuring system each unit corresponds to the mean accuracy loss speed of average error
Degree power piThe as equivalent transfer chain function of each unit：
If representing measurement result precision with variance, the Accuracy extimate value of t measuring systems is at any time
Then system overall accuracy loss function is：
Then mean accuracy loss speed is：
Therefore, tandem measuring system each unit corresponds to the average loss speed power of varianceAs each unit is equivalent
Square of transfer chain function：
According to other characteristic quantities, during such as the accuracy characteristic amount of standard deviation or uncertainty characterization measuring system, system is total
Functional relation between loss of significance and unit loss of significance is complex, and therefore, accurate for convenience of loss of significance power determines,
It is recommended that as possible using average error or the precision of variance characterization measuring system.
2. the absolute precision loss power of parallel dynamic measurement system
The total system dynamic error model of canonical parallel formula dynamic measurement system is：
In formula (13), es(t) it is output overall error of the dynamic measurement system in moment t；fi() is i-th of unit of system
Transmission function；e1(t) it is input element error, ei(t) it is parallel-connection structure elemental error.
Similarly, if representing measurement result precision with average error, each unit can be obtained and correspond to being averaged for average error
Lose speed power：
If representing measurement result precision with variance, the average loss speed power that each unit corresponds to variance can be obtained：
For general series parallel type measuring system, because structure and the number of unit are different, then total system error model is not then
Together, the average loss speed weight function of each unit is also different, need to make a concrete analysis of as the case may be.
Step 6, the service life uniform optimized design model for establishing dynamic measurement system；
Step 6.1 determines design parameter vector X：
A variety of materials, each part or all parts are understood and grasped under certain operating mode in view of project planner
Loss of significance average speedRelatively easily, therefore, for convenience of optimization design, the design in uniform design model is become
Amount is determined as the average speed of unit loss of significanceAfter the completion of optimized design, can according to the design value of average speed come
Sophisticated systems.
Defining the respective mean accuracy loss speed of n error unit is It represents
The mean accuracy loss speed of i-th of error unit；
Speed is lost with n mean accuracy and n+1 accuracy life is formed and determine design parameter vector X, i.e.,TsThe accuracy life optimal design value of ' expression dynamic measurement system；T′i
Represent the accuracy life optimal design value of i-th of error unit.
Step 6.2 determines object function：
In the optimal model of uniform design, can mainly have as the parameter of design object：The non-uniformity of system
ρ, the accuracy life T' of system or the total improving cost C of system etc..Purpose and requirement according to accuracy life uniform design, mesh
Scalar functions can be following several situations：
With accuracy life uniformly for design object, non-uniformity object function is obtained using formula (16)：
With accuracy life uniform accuracy life up to design object, accuracy life target letter is obtained using formula (17)
Number：
Max T'=min { T1',…,Tn',Ts'} (17)
In formula (17), in the accuracy life optimal design value of T' expression dynamic measurement systems and its n error unit most
Small value；
With the accuracy life uniform minimum design object of total improving cost, improving cost target letter is obtained using formula (18)
Number：
In formula (18), C represents total improving cost of n error unit；CiRepresent the improving cost of i-th of error unit；
And have：
Formula (19) represents the improving cost C of i-th of error unitiSpeed is lost with the mean accuracy of i-th of error unitBetween relationship；
Certainly, above-mentioned three kinds of situations, can be combined reach at this time by the possible more than one of target being concerned about sometimes
To the purpose considered.
Step 6.3 determines constraints：
According to the various demands that the principle of accuracy life uniform design and measuring instrument design, need to mainly consider following several
Point constraints：
The constraints of non-uniformity ρ is obtained using formula (20)：
ρ≤ε (20)
In formula (20), ε represents the limiting value of non-uniformity ρ；
The constraints of mean accuracy loss speed is obtained using formula (21)：
In formula (21),Represent the mean accuracy loss speed of i-th of error unitLower limit；Represent i-th
The mean accuracy loss speed of a error unitThe upper limit；It can be according to the composition structure of unit, the material used, reality
The factors such as operating mode determine.
The constraints of accuracy life is obtained using formula (22)：
min{T1',T2',…,Tn',Ts' ＞ T0 (22)
In formula (22), T0Represent the desired value of the accuracy life of dynamic measurement system；
The constraints between mean accuracy loss speed, accuracy life and the loss of significance limit is obtained using formula (23)：
The constraints of total improving cost is obtained using formula (24)：
C≤C0 (24)
In formula (24), C0Represent the upper limit of total improving cost of dynamic measurement system.
The above-mentioned object function listed and its constraints might not have in concrete model, establish accuracy life
During uniform design optimal model, according to the complexity of the concrete condition of system, the specific requirement of design and realization come
Determine object function and its constraints.
A kind of method for solving sign of optimized design model based on uniform accuracy life principle is to carry out as follows：
Step 1 constructs the initial value that m groups meet the design parameter vector X of constraints using numerical method；
Step 2 finds locally optimal solution corresponding to m group initial values using Sequential Quadratic Programming method respectively；
Step 3 searches for globally optimal solution from the locally optimal solution of m group initial values, so as to obtain globally optimal solution and its
Corresponding best design parameter vector.
Optimized design model based on uniform accuracy life principle is complex, and is non-linear, constrained, adopts
The method being combined with numerical method and Sequential Quadratic Programming method finds best design parameter, can overcome merely using sequence two
When secondary law of planning solves locally optimal solution problem is caused due to initial value selection is improper.
Service life uniform design example:
Assuming that the loss of significance of dynamic measurement system is mainly caused by two error links.Know through analysis, the two errors
The loss of significance power of link is 1, i.e. p1=p2=1, and the loss of significance limit index of known they and system is δ1=0.5,
δ2=5, δ3=6.It is respectively δ to obtain the Precision losing function of two error links and system in original system after tested1(t)、δ2
(t)、δs(t)：
δ1(t)=0.03t2+0.1t
δ2(t)=0.01t2+t
δs(t)=p1δ1(t)+p2δ2(t)=0.04t2+1.1t
According to their loss of significance limit index, can solve to obtain accuracy life and its non-uniformity of original system
Value：
T1≈2.7429；T2≈4.7723；Ts≈4.6636
ρ≈0.425
The non-uniformity of original system is larger, can not meet requirement of system design, then needs to redesign, to realize system essence
It is uniform to spend the service life, can be carried out according to following three steps：
1) design parameter vector X is determined first.
Here speed is lost with the mean accuracy of unit 1 and unit 2And accuracy life T1'、T2'、Ts' make
To be designed parameter, Construction designing parameter vector
2) optimized design model is established, including object function and constraints.
If designer's major concern be system homogeneity level, can using non-uniformity it is the smaller the better as design
Target：
For this problem, optimization design mainly has two class constraintss：One kind is the variation range of design parameters itself,
Here it is mainly the optional range of loss of significance speed of two units, so as to form one group of inequality constraints；Another kind of is design
Boundary constraint between parameter is made of limit of accuracy index and loss average speed, Life Relation, constitute one group it is non-linear
Equality constraint.Always Constrained equations are：
Wherein, the loss of significance velocity interval [0.10.5] of two units and [0.53] assume that.In practical application mistake
Cheng Zhong, can according to it is possible that loss of significance speed of the unit composition structure, material etc. replaced under the conditions of currently used and
It determines.
3) optimized parameter is solved using sequential quadratic programming SQP algorithms.
Using the optimization tool box in MATLAB softwares, with reference to above-mentioned Optimized model, use sequential quadratic programming can be with
Solution obtains the locally optimal solution of design parameter.Numerical method is combined with optimization algorithm SQP, it can be deduced that above-mentioned optimization problem
Optimal solution
ρmin=0.0833
When being designed in view of system, accuracy life, generally the longer the better, then unit 1 and the loss of significance of unit 2 are averaged
Speed is the smaller the better.Due to being limited by other constraint equations, in this example, each unit loss of significance average speed is most
Excellent solution should be：
Optimal accuracy life is accordingly：
T1'=5；T2'=5；Ts'=5.4545
After optimizing uniform design, the loss of significance average speed of each formant should relatively be declined originally,
The non-uniformity of system falls to ρ by original ρ ≈ 0.425min=0.0833, the accuracy life of system is by original 2.7429
5 are extended to, achieves preferable design effect.
Claims (2)
1. a kind of method for building up of the optimized design model based on uniform accuracy life principle is to be applied to dynamic measurement system
In, it is characterized in that carrying out as follows：
Step 1 obtains the dynamic measurement system and its n error unit is respective using dynamic error separation and source tracing method
Precision losing function model；
Step 2 sets the dynamic measurement system and its respective loss of significance limit of n error unit, is denoted as { δs,δ1,
δ2,…,δi,…,δn}；δsRepresent the loss of significance limit of the dynamic measurement system, δiRepresent the precision of i-th of error unit
The limit is lost, 1≤i≤n, n represent the total number of the error unit；
Step 3, according to the n+1 set loss of significance limit and the n+1 Precision losing function model, be obtained described dynamic
State measuring system and its error unit respective accuracy life, it is denoted as { Ts,T1,T2,…,Ti,…,Tn}；TsRepresent the dynamic
The accuracy life of measuring system, TiRepresent the accuracy life of i-th of error unit；
Step 4, the non-uniformity ρ that the dynamic measurement system is obtained using formula (1)：
Step 5, the mean accuracy loss speed power that n error unit is obtained using total system dynamic error model, are denoted as { p1,
p2,…,pi,…,pn}；piRepresent the mean accuracy loss speed power of i-th of error unit；
Step 6, the service life uniform optimized design model for establishing the dynamic measurement system；
Step 6.1 determines design parameter vector X：
Defining the respective mean accuracy loss speed of the n error unit is Represent institute
State the mean accuracy loss speed of i-th of error unit；
Speed is lost with the n mean accuracy and n+1 accuracy life is formed the determining design parameter vector X, i.e.,TsThe accuracy life optimal design value of ' expression dynamic measurement system；
TiThe accuracy life optimal design value of ' expression i-th of error unit；
Step 6.2 determines object function：
With accuracy life uniformly for design object, non-uniformity object function is obtained using formula (2)：
With accuracy life uniform accuracy life up to design object, accuracy life object function is obtained using formula (3)：
Max T'=min { T1',…,Tn',Ts'} (3)
In formula (3), T' represents the minimum in the accuracy life optimal design value of the dynamic measurement system and its n error unit
Value；
With the accuracy life uniform minimum design object of total improving cost, improving cost object function is obtained using formula (4)：
In formula (4), C represents total improving cost of the n error unit；CiRepresent being modified to for i-th of error unit
This；And have：
Formula (5) represents the improving cost C of i-th of error unitiSpeed is lost with the mean accuracy of i-th of error unit
Between relationship；
Step 6.3 determines constraints：
The constraints of non-uniformity ρ is obtained using formula (6)：
ρ≤ε (6)
In formula (6), ε represents the limiting value of the non-uniformity ρ；
The constraints of mean accuracy loss speed is obtained using formula (7)：
In formula (7),Represent the mean accuracy loss speed of i-th of error unitLower limit；Represent described
The mean accuracy loss speed of i error unitThe upper limit；
The constraints of accuracy life is obtained using formula (8)：
min{T1',T2',…,Tn',Ts'}>T0 (8)
In formula (8), T0Represent the desired value of the accuracy life of the dynamic measurement system；
The constraints between mean accuracy loss speed, accuracy life and the loss of significance limit is obtained using formula (9)：
The constraints of total improving cost is obtained using formula (10)：
C≤C0 (10)
In formula (10), C0Represent the upper limit of total improving cost of the dynamic measurement system.
2. the optimized design model based on uniform accuracy life principle that a kind of the method as described in claim 1 is established is asked
Solution method, it is characterized in that carrying out as follows：
Step 1 constructs the initial value that m groups meet the design parameter vector X of constraints using numerical method；
Step 2 finds locally optimal solution corresponding to the m groups initial value using Sequential Quadratic Programming method respectively；
Step 3 searches for globally optimal solution from the locally optimal solution of the m groups initial value, so as to obtain globally optimal solution and its
Corresponding best design parameter vector.
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