CN104318020A - Multi-objective sensor distributed point optimizing method on basis of self-adaptive differential evolution - Google Patents

Abstract

The invention discloses a multi-objective sensor distributed point optimizing method on the basis of self-adaptive differential evolution. The multi-objective sensor distributed point optimizing method includes steps of (1) setting up a finite element model of a structure to be measured, and utilizing the numerical solution method to obtain the dynamic characteristic data of the structure; extracting a vibration mode matrix of all alternative measuring points and utilizing all measuring points contained in various step vibration modes as the alternative resource of the optimization; (2) selecting more than two of the modal assurance criterion and various optimization criterions based on the modal strain energy and the measuring vibration displacement maximization as an objective function of the multi-objective constraint sensor optimization of the distributed points, wherein the objective function is used for evaluating advantages and disadvantages of clusters and is the basis for self-adaptive differential evolution algorithm operation, and the selecting process of the objective function is a process determining the optimization criterion; (3) solving the problem of the sensor optimization of the distributed points under the multi-objective constraint by means of the self-adaptive differential evolution algorithm.

Description

A kind of multiple goal Optimal Sensor Placement method of evolving based on adaptive differential

Technical field

The present invention relates to monitoring structural health conditions sensors optimum placement field, specifically a kind of multiple goal Optimal Sensor Placement method of evolving based on adaptive differential.

Background technology

Because large-scale steel structure architectural image is unique, span is large, scantling is large, and have a large amount of spatial warping component, entirety belongs to high order hyperstatic structure, stressed very complicated, employ new technology in the design, new material, new technology, design and construction height is coupled, the time variation of self structure characteristic and stress performance, the features such as the impact of the effect of operation use procedure environmental load, fatigue effect, corrosion effect and the human factor such as material aging and other improper use, structural healthy monitoring system arises at the historic moment.

The Optimizing of sensor is the prerequisite of structural healthy monitoring system, the type of sensor, position and quantity play key effect, how arranging that the sensor of limited quantity realizes the optimum collection to structural condition information, is one of key issue of monitoring structural health conditions.

In theory, the sensor installed in structure is more, and the status information of the structure collected is more detailed, and the precision of kinetic parameter identification is better.But in reality, the quantity of sensor is often subject to the restriction of the aspect such as economic factors and structure operation state, can not in the degree of freedom that structure is all placement sensor, therefore just had the preferred arrangement problem of sensor.The optimum that the single object optimization of distributing criterion rationally based on single-sensor obtains is layouted also the optimum solution of just certain condition, and cannot carry out under each criterion optimum layout mutually compare, a sensor distributing is optimum under a certain standard, may but be very poor under another standard.

Multiple goal Optimal Sensor Placement is a multi-objective optimization question, each sub-goal is likely conflicting, the improvement of a sub-goal may cause the reduction of another sub-goal performance, that is, it is impossible that multiple sub-goal will be made to reach optimum all together simultaneously, and just carry out coordinating and compromise in the middle of them, make each sub-goal reach optimum all as much as possible.

Solve multi-objective optimization question and have multiple method, as meta-heuristic algorithm can be used to solve, differential evolution algorithm is exactly the one of meta-heuristic algorithm.

Differential evolution algorithm is based on Darwinian evolutionism thought, by simulation biological evolution process and the self-organization of the Solve problems of mechanism, adaptive intelligent algorithm, operates solving of problem of implementation mainly through selection, crossover and mutation these three kinds.

There is following problem in existing method: 1, traditional numerical optimisation algorithms poor robustness, is usually only local convergence and speed of convergence is slow.2, there is randomness in optimizing; 3, sensor layout optimize be all based on single criterion.4, optimum solution has inaccessibility, and satisfactory solution solves overlong time.5, non-self-adapting differential evolution algorithm easily occurs that Premature Convergence, local search ability are not enough and speed of convergence is slow.

Therefore, in conjunction with above limitation and problem, the present invention proposes a kind of multiple goal Optimal Sensor Placement method based on adaptive differential evolution algorithm, be specially the multiple goal Optimal Sensor Placement problem utilizing adaptive differential evolution algorithm to solve structure.

Summary of the invention

The object of this invention is to provide a kind of multiple goal Optimal Sensor Placement method of evolving based on adaptive differential, to realize after multi-objective restriction is determined, utilize adaptive differential evolution algorithm to arrange to optimize sensor, reach the object of the satisfactory solution of the Optimizing sought under multiple goal criterion.

In order to achieve the above object, the technical solution adopted in the present invention is:

Based on the multiple goal Optimal Sensor Placement method that adaptive differential is evolved, it is characterized in that: comprise the following steps:

(1), set up the finite element model treating geodesic structure, utilize method of value solving to obtain the kinematic behavior data of structure, extract the vibration shape matrix of all candidate's measuring points, all point positions contained by each first order mode are as the candidate resource of preferred arrangement;

(2), objective function produces: select target function is exactly the process determining to distribute rationally criterion, objective function is used for evaluating the quality of population, it is the foundation of adaptive differential evolution algorithm operation, the layout of sensor can according to the numerous evaluation method of construction applications, determine the objective function of multi-objective restriction sensor optimization, its mathematical form is as follows:

$\left\{\begin{array}{cc}V-\min :& F\left(x\right)={[F_1\left(x\right),F_2\left(x\right),...,F_n\left(x\right)]}^T\\ s.t.& x\∈X\\ & X\⊆R^m\end{array}\right.---\left(1\right),$

g _m(x)≤0，m＝1，2，Λ，n _g (2)，

h _m(x)＝0，m＝n _g+1，Λ，n _g+n _h (3)，

Wherein in formula (1), V-min represents vectorial minimization, i.e. F (x)=[F ₁(x), F ₂(x) ..., F _n(x)] ^tin each sub-goal Function Minimization, T represents vector transpose, and n is the dimension of objective function number and object space, x=(x ₁, x ₂... .x _n) be Optimal Decision-making variable, X is continuous search volume, R ^mrepresent that m ties up real number space, it separates as Pareto forward position disaggregation; In formula (2), (3), g _mx () represents inequality constrain equation, h _mx () represents equality constraint equation, wherein n _gand n _hthe number of inequality and equation respectively;

(3), utilize adaptive differential evolution algorithm to solve above-mentioned multi-objective restriction lower sensor Optimizing problem, comprise the following steps:

(3.1), initialization: the initial value of setting algebraically counter t is 0, initialization controling parameters β and CR; Initialization population scale, comprises the population C (0) of NP individuality, adopts stochastic generation method or nonrandom generation method; Coded system designs according to demand, general real coding, binary coding, dual-structure coding, gray also can be adopted to encode and IRR coding;

(3.2), make a variation: for each individual x _it () ∈ C (t), application mutation operator produces test vector u _i(t); Wherein mutation operator and difference vector number design according to real needs, and its general mathematical form is as shown in formula (4):

$u_i\left(t\right)=x_{i_1}\left(t\right)+{\mathrm{\β}}_1(x_{i_2}\left(t\right)-x_{i_3}\left(t\right))+{\mathrm{\β}}_2(x_{i_4}\left(t\right)-x_{i_5}\left(t\right))+....{\mathrm{\β}}_n(x_{i_{j-i}}\left(t\right)-x_{i_j}\left(t\right))---\left(4\right)$

Wherein, the Different Individual of Stochastic choice from population, β _n∈ (0, ∞) is a scalar, controls the amplification degree of difference variable;

(3.3), intersect: application crossover operator produces filial generation x ' _it (), by test vector u _i(t) and parent vector x _it the discrete recombination of () is to produce offspring individual x ' _i(t), interleaved mode is that binomial intersects or index intersects,

In formula (5), x _ijt () represents vector x _ia jth element of (t), J is the set of intersection position;

(3.4), select: the objective function of its fitness function optional step (1) or its constraint violation function etc., depending on problem concrete condition; If the fitness of offspring individual is better than its parent, then its parent is replaced in filial generation; Otherwise the survival of parent individuality is to of future generation; Be specially assessment fitness f (x _i(t)); X ' _it () is better than f (x _i(t)), then by x ' _it () adds C (t+1); Otherwise by x _it () adds C (t+1);

(3.5), adaptive strategy: this strategy comprises two aspects: a, self-adaptative adjustment controlling elements, as the mutagenic factor β according to mutation operator dynamic conditioning G generation; 2, self-adaptation chooses differential strategy, certain intersection position etc. whether is fixed according in difference vector number in mutation operation and made a variation individual difference and interlace operation, differential evolution algorithm has developed multiple Mutation Strategy, available DE/x/y/z unified representation, wherein x represents when mutation operation, and it is individual or select when optimum individual in former generation is individual as father as father to be that random selecting to work as in former generation a certain individuality; Y represents when mutation operation, the number of institute's usage variance vector; Z represents interleaved scheme;

(3.6), stop condition: when running to maximum algebraically G _maxor target function value reaches given requirements and then proceeds to step (3.7), repeated execution of steps (3.2)-(3.7);

(3.7), return solution: the individuality of optimal adaptation degree returns, be required Optimal Sensor Placement scheme, separate as Pareto forward position disaggregation herein.

A kind of described multiple goal Optimal Sensor Placement method of evolving based on adaptive differential, it is characterized in that: adaptive differential evolution algorithm is used for solve multiple goal Optimal Sensor Placement problem, the objective function that the multiple sensors Optimizing evaluation method proposed using monitoring structural health conditions field is evolved as adaptive differential, solves above-mentioned multiple goal Optimal Sensor Placement problem by adaptive differential evolution algorithm.

Advantage of the present invention is: 1, provide a kind of multiple goal Optimal Sensor Placement problem solving method; 2, relatively original single goal Optimal Sensor Placement is more applicable to real structure health monitoring systems; 3, problems such as adaptive differential is evolved being applied to multiple goal Optimal Sensor Placement, solve the Premature Convergence in solution procedure, local search ability is not enough and speed of convergence is slow.

Accompanying drawing explanation

10 kinds of differential strategy charts that Fig. 1 proposes for Rainer Storn of the present invention and Kenneth Price.

Fig. 2 is the process flow diagram of process of the present invention.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

Problem to be solved: for ad hoc structure, total n degree of freedom, how an existing m sensor (n < m), arrange this m sensor, to make to arrange that result reaches optimum by certain standard.For the preferred arrangement of the vibration transducer of certain steel building.Carry out calculating according to the step of the inventive method illustrated and described by Fig. 2.

(1) structure multiple goal Optimal Sensor Placement pre-service:

(1.1) set up the finite element model treating geodesic structure, utilize method of value solving, obtain the kinematic behavior data of structure, extract the vibration shape matrix of all candidate's measuring points.The all point positions contained by each first order mode are as the candidate resource of preferred arrangement.Need the Mode Shape data of this structure when following calculating, its kinematic behavior need be drawn according to finite element analysis software, such as, its front 50 first order modes can be calculated.

(1.2) objective function produces: this example confirms criterion according to construction applications mode and measure vibration displacement to maximize the objective function determining multiple-objection optimization.

1. the objective function of criterion is confirmed based on mode

MAC matrix is the good method evaluating the Mode Shape vector space angle of cut, and its canonical form is:

${\mathrm{MAC}}_{\mathrm{ij}}=\frac{{\left({\mathrm{\&phi;}}_i^t{\mathrm{\&phi;}}_j\right)}^2}{\left({\mathrm{\&phi;}}_i^t{\mathrm{\&phi;}}_i\right)\left({\mathrm{\&phi;}}_j^t{\mathrm{\&phi;}}_j\right)}$

Wherein φ _iand φ _jbe respectively the i-th rank and jth rank Mode Shape vector.

The layout of measuring point (sensor) should make the off diagonal element of MAC matrix minimize, and when measuring point sum is certain, the Layout Problem of measuring point is converted into:

$F_1=\left\{\begin{array}{cc}\min :& \mathrm{Max}\left({\mathrm{MAC}}_{\mathrm{ij}}\right)\\ s.t.& i\&NotEqual;j\end{array}\right.$

2. based on measuring the maximized objective function of vibration displacement

If choose S rank Mode Shape, its vibration shape matrix is: Φ=[φ ₁, φ ₂, φ ₃..., φ _s], number of degrees of freedom, is n,

M measuring point need be arranged, φ _irrepresent the r component of the i-th first order mode; R ∈ m represents that r is limited to whole non-measuring point.What its was selected is the maximum point of a group vibration displacement, and Signal-to-Noise is the highest, is conducive to improving measuring accuracy.

$\min :F_2=\underset{i-1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j-1}{\overset{n}{\mathrm{\&Sigma;}}}\left|\underset{r\&Element;m}{\mathrm{\&Sigma;}}{\mathrm{\&phi;}}_{\mathrm{ir}}{\mathrm{\&phi;}}_{\mathrm{jr}}\right|$

By 1., 2. and then draw the objective function of multiple goal Optimal Sensor Placement, its mathematical form is as follows:

$\left\{\begin{array}{cc}V-\min :& F\left(x\right)={[F_1\left(x\right),F_2\left(x\right)]}^T\\ & F_1\left(x\right)=\mathrm{Max}\left({\mathrm{MAC}}_{\mathrm{ij}}\right)(i\&NotEqual;j)\\ & F_2\left(x\right)=\underset{i-1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j-1}{\overset{n}{\mathrm{\&Sigma;}}}\left|\underset{r\&Element;m}{\mathrm{\&Sigma;}}{\mathrm{\&phi;}}_{\mathrm{ir}}{\mathrm{\&phi;}}_{\mathrm{jr}}\right|\end{array}\right.$

Wherein V-min represents vectorial minimization, each sub-goal Function Minimization namely in F (x), and its solution space is Pareto forward position disaggregation.

(2) initialization: the initial value of setting algebraically counter t is 0, initialization controling parameters β and CR; Initialization population scale, comprise 60 individual population C (0), algebraically is G _max=500.Stochastic generation method is adopted to generate individual.The codes selection dual-structure coding mode of this example, its form is as follows:

For Optimal Sensor Placement problem, extra-code is exactly the node number that candidate places measuring point, and this n node number is upset order at random in the mode of shuffling and listed in up.Descending variable code is made up of m individual 1 and n-m individual 0, also upsets order to shuffle at random and lists in descending.The body one by one with regard to stochastic generation like this.

(3) make a variation: for each individual x _it () ∈ C (t), application mutation operator produces test vector u _i(t); Wherein mutation operator and difference vector number can design according to real needs.This example selects 1 difference vector, and its mutation operator is as follows:

$u_i\left(t\right)=x_{i_1}\left(t\right)+\mathrm{\&beta;}(x_{i_2}\left(t\right)-x_{i_3}\left(t\right))$

Wherein, with be three Different Individual of Stochastic choice from population, β ∈ (0, ∞) is a scalar, controls the amplification degree of difference variable.

(4) intersect: application crossover operator produces filial generation x ' _i(t); By test vector u _i(t) and parent vector x _it the discrete recombination of () is to produce offspring individual x ' _i(t).Interleaved mode can be intersected for binomial or index intersects.

Wherein, x _ijt () represents vector x _it a jth element of (), J is the set of intersection position.

(5) select: if the fitness of offspring individual is better than its parent, then its parent is replaced in filial generation; Otherwise the survival of parent individuality is to of future generation.Be specially assessment fitness f (x _i(t)); X ' _it () is better than f (x _i(t)), then by x ' _it () adds C (t+1); Otherwise by x _it () adds C (t+1).

(6) adaptive strategy: this strategy comprises two aspects, can select as required, and this example is the adjustment adaptive control factor only.

(6.1) self-adaptative adjustment controlling elements (population scale NP, mutagenic factor β, crossover probability CR etc.), make F and CR with evolutionary process slowly the successively decreasing of dullness.Get higher value at initial stage F and CR of iteration and meet the enough disturbances of generation, strengthen search capability.To diminish gradually at later stage F and CR, object avoids destroying defect individual, convergence speedup speed.Adjustment formula is:

$F=F_0\&CenterDot;e^{-a_1\&CenterDot;\left(\frac{G}{G_{\max }}\right)}$

$\mathrm{CR}={\mathrm{CR}}_0\&CenterDot;e^{-a_2\&CenterDot;\left(\frac{G}{G_{\max }}\right)}$

Wherein, F ₀for the initial value of mutagenic factor β, CR ₀for crossover probability initial value, G is current evolutionary generation, G _maxfor maximum evolutionary generation, a ₁a ₂for normal number.

(6.2) self-adaptation chooses differential strategy, does not need this step in this example.

(7) convergence judges: when running to maximum algebraically G _maxor target function value reaches given requirements then to (8), repeat (3)-(7).

(8) return solution: the individuality of optimal adaptation degree returns, be required Optimal Sensor Placement scheme, separate as Pareto optimum solution herein.

Claims (2)

1., based on the multiple goal Optimal Sensor Placement method that adaptive differential is evolved, it is characterized in that: comprise the following steps:

(1), set up the finite element model treating geodesic structure, utilize method of value solving to obtain the kinematic behavior data of structure, extract the vibration shape matrix of all candidate's measuring points, all point positions contained by each first order mode are as the candidate resource of preferred arrangement;

(2), objective function produces: select target function is exactly the process determining to distribute rationally criterion, objective function is used for evaluating the quality of population, it is the foundation of adaptive differential evolution algorithm operation, the layout of sensor can according to the numerous evaluation method of construction applications, determine the objective function of multi-objective restriction sensor optimization, its mathematical form is as follows:

$\left\{\begin{array}{cc}V-\min :F\left(x\right)=[F_1\left(x\right),F_2\left(x\right),...,F_n\left(x\right){]}^T& \\ s.t.& x\&Element;X\\ & X\&SubsetEqual;R^m\end{array}\right.---\left(1\right),$

g _m(x)≤0，m＝1,2,Λ,n _g (2)，

h _m(x)＝0，m＝n _g+1,Λ,n _g+n _h (3)，

Wherein in formula (1), V-min represents vectorial minimization, i.e. D (x)=[F ₁(x), F ₂(x) ..., F _n(x)] ^tin each sub-goal Function Minimization, T represents vector transpose, and n is the dimension of objective function number and object space, x=(x ₁, x ₂... .x _n) be Optimal Decision-making variable, X is continuous search volume, R ^mrepresent that m ties up real number space, it separates as Pareto forward position disaggregation; In formula (2), (3), g _mx () represents inequality constrain equation, h _mx () represents equality constraint equation, wherein n _gand n _hthe number of inequality and equation respectively;

(3), utilize adaptive differential evolution algorithm to solve above-mentioned multi-objective restriction lower sensor Optimizing problem, comprise the following steps:

(3.1), initialization: the initial value of setting algebraically counter t is 0, initialization controling parameters β and CR; Initialization population scale, comprises the population C (0) of NP individuality, adopts stochastic generation method or nonrandom generation method; Coded system designs according to demand, general real coding, binary coding, dual-structure coding, gray also can be adopted to encode and IRR coding;

(3.2), make a variation: for each individual x _it () ∈ C (t), application mutation operator produces test vector u _i(t); Wherein mutation operator and difference vector number design according to real needs, and its general mathematical form is as shown in formula (4):

$u_i\left(t\right)=x_{i_1}\left(t\right)+{\mathrm{\&beta;}}_1(x_{i_2}\left(t\right)-x_{i_3}\left(t\right))+{\mathrm{\&beta;}}_2(x_{i_4}\left(t\right)-x_{i_5}\left(t\right))+...{\mathrm{\&beta;}}_n(x_{i_{j-1}}\left(t\right)-x_{i_j}\left(t\right))---\left(4\right)$

Wherein, the Different Individual of Stochastic choice from population, β _n∈ (0, ∞) is a scalar, controls the amplification degree of difference variable;

(3.3), intersect: application crossover operator produces filial generation x ' _it (), by test vector u _i(t) and parent vector x _it the discrete recombination of () is to produce offspring individual x ' _i(t), interleaved mode is that binomial intersects or index intersects,

In formula (5), x _ijt () represents vector x _ia jth element of (t), J is the set of intersection position;

(3.4), select: the objective function of its fitness function optional step (1) or its constraint violation function etc., depending on problem concrete condition; If the fitness of offspring individual is better than its parent, then its parent is replaced in filial generation; Otherwise the survival of parent individuality is to of future generation; Be specially assessment fitness f (x _i(t)); X ' _it () is better than f (x _i(t)), then by x ' _it () adds C (t+1); Otherwise by x _it () adds C (t+1);

(3.5), adaptive strategy: this strategy comprises two aspects: a, self-adaptative adjustment controlling elements, as the mutagenic factor β according to mutation operator dynamic conditioning G generation; 2, self-adaptation chooses differential strategy, certain intersection position etc. whether is fixed according in difference vector number in mutation operation and made a variation individual difference and interlace operation, differential evolution algorithm has developed multiple Mutation Strategy, available D E/x/y/z unified representation, wherein x represents when mutation operation, and it is individual or select when optimum individual in former generation is individual as father as father to be that random selecting to work as in former generation a certain individuality; Y represents when mutation operation, the number of institute's usage variance vector; Z represents interleaved scheme;

(3.6), stop condition: when running to maximum algebraically G _maxor target function value reaches given requirements and then proceeds to step (3.7), repeated execution of steps (3.2)-(3.7);

(3.7), return solution: the individuality of optimal adaptation degree returns, be required Optimal Sensor Placement scheme, separate as Pareto forward position disaggregation herein.

2. a kind of multiple goal Optimal Sensor Placement method of evolving based on adaptive differential according to claim 1, it is characterized in that: adaptive differential evolution algorithm is used for solve multiple goal Optimal Sensor Placement problem, the objective function that the multiple sensors Optimizing evaluation method proposed using monitoring structural health conditions field is evolved as adaptive differential, solves above-mentioned multiple goal Optimal Sensor Placement problem by adaptive differential evolution algorithm.