CN111274656B - Steady equilibrium design method for dynamic characteristics of fixed structure of stator end of generator - Google Patents

Steady equilibrium design method for dynamic characteristics of fixed structure of stator end of generator Download PDF

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CN111274656B
CN111274656B CN202010063081.5A CN202010063081A CN111274656B CN 111274656 B CN111274656 B CN 111274656B CN 202010063081 A CN202010063081 A CN 202010063081A CN 111274656 B CN111274656 B CN 111274656B
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程锦
王荣
钱炀明
胡伟飞
刘振宇
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Zhejiang University ZJU
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Abstract

The invention discloses a steady equilibrium design method for dynamic characteristics of a fixed structure of a stator end of a generator, which comprises the following steps: establishing a steady balanced design model of the dynamic characteristics of a stator end fixing structure of the generator; sampling design variables and uncertain parameters by adopting a Latin hypercube sampling method, obtaining sample points by a collaborative simulation technology, and establishing a Kriging model for predicting dynamic characteristic index values of a stator end fixing structure in a target and a constraint function; and carrying out iterative optimization by using a double-layer nested genetic algorithm based on the interval angle contact ratio coefficient and the overall performance steady balance index to obtain an optimal design scheme of the dynamic characteristic of the stator end fixing structure. The invention introduces the interval angle contact ratio coefficient, and can flexibly and conveniently obtain the design scheme of the stator end fixing structure of the generator, which can make each dynamic characteristic index steady and balanced, according to the robustness requirement to be met by the stator end fixing structure under different working conditions.

Description

Steady equilibrium design method for dynamic characteristics of fixed structure of stator end of generator
Technical Field
The invention belongs to the field of mechanical structure design, and particularly relates to a steady balanced design method for dynamic characteristics of a stator end fixing structure of a generator.
Background
In the working process of the turbonator, when the natural frequency of the stator end fixing structure of the generator is close to the excitation frequency of electromagnetic force or multiple of the excitation frequency, the stator end fixing structure can be caused to generate resonance or high-frequency resonance. Various short circuits, reclosings and other fault operation conditions inevitably occur in the operation process of the turbonator. Under the fault working condition, the maximum current of the stator winding of the generator can reach several times or even more than 10 times of that in normal operation, and the amplitude of the stator end winding and the stator end fixing structure under the action of electromagnetic force is in direct proportion to the square of the current, so that the electromagnetic force borne by the stator end fixing structure and the vibration caused by the electromagnetic force are obviously increased under the fault working condition, and serious harm is generated. Therefore, the dynamic characteristic index of the generator stator end fixing structure needs to be fully considered in the design, so that the low-order natural frequency of the generator stator end fixing structure avoids the excitation frequency of the electromagnetic force or the multiple of the excitation frequency, resonance and high-frequency resonance are prevented, and the safe and reliable operation of the generator is ensured. Because the number of the excitation frequencies to be avoided in the working process of the turbonator is more than one, and when a certain order of natural frequency is far away from the excitation frequency, the natural frequency of the adjacent order of the turbonator is often close to the excitation frequency, the dynamic characteristic optimization design of the stator end fixing structure needs to comprehensively consider the overall distribution condition of the natural frequency of each order of the turbonator, so that the degree of deviation of the natural frequency of each order from the excitation frequency is balanced, and the stability balance design of the natural frequency of each order is realized.
On the other hand, due to errors of heat treatment and machining, uncertainty exists in material properties of a stator end fixing structure of the steam turbine generator, and the uncertainty can cause certain fluctuation of dynamic characteristic indexes of the steam turbine generator. Therefore, these objectively present uncertainties must be fully accounted for in the design of the dynamic characteristics of the stator end fixing structures of the generators. Because of the sparse sampling of these uncertainty factors, the number of intervals is used to describe the uncertainty. Under the influence of interval uncertainty, the natural frequency of each stage of the steam turbine generator is also the number of intervals. Therefore, the invention provides a method for designing the steady equilibrium of the dynamic characteristics of the stator end fixing structure of the turbonator based on the interval, which utilizes a double-layer nested genetic algorithm based on the interval angle contact ratio coefficient and the integral performance steady equilibrium index to carry out iterative optimization, and obtains a design scheme of the stator end fixing structure of the turbonator with good vibration resistance under the influence of material uncertainty.
Disclosure of Invention
In order to solve the anti-vibration design problem of the stator end fixing structure of the turbonator in the practical engineering, the invention provides a steady balance design method of the dynamic characteristic of the stator end fixing structure of the turbonator, which adopts interval variables to describe the uncertain factors influencing the dynamic characteristic of the stator end fixing structure of the turbonator and establishes a steady balance design model of the dynamic characteristic of the stator end fixing structure of the turbonator; sampling design variables and uncertain parameters by adopting a Latin hypercube sampling method, obtaining sample points by a collaborative simulation technology, and establishing a Kriging model for predicting dynamic characteristic index values of a stator end fixing structure in a target and a constraint function; and carrying out iterative optimization by using a double-layer nested genetic algorithm based on the interval angle contact ratio coefficient and the overall performance steady balance index to obtain an optimal design scheme of the dynamic characteristic of the stator end fixing structure.
The invention is realized by the following technical scheme: a robust equilibrium design method for dynamic characteristics of a fixed structure of a stator end of a generator comprises the following steps:
1) establishing a steady balanced design model of the dynamic characteristics of a stator end fixing structure of a generator: taking the key size of the section of the stator end fixing structure as a design variable, considering the uncertainty of the elastic modulus and the density of the stator end fixing structure material, and describing the uncertainty as an interval variable; analyzing the specific order of the natural frequency closest to the excitation frequency in the natural frequencies of all orders of the initial design scheme, and simultaneously considering the middle point and the width of the change interval of the natural frequencies under the influence of uncertainty so as to enable the natural frequencies to be far away from the excitation frequency as far as possible and to have small fluctuation under the influence of uncertainty as a target, and establishing an expression of a target function; establishing an expression of a constraint function according to other requirements of the dynamic characteristic design of the stator end fixing structure, and further establishing a steady balanced design model of the dynamic characteristic of the stator end fixing structure of the generator:
Figure GDA0003274921360000021
wherein the content of the first and second substances,
Figure GDA0003274921360000022
fi C(x)＝(fi L(x)+fi R(x))/2；
fi W(x)＝fi R(x)-fi L(x)；
Figure GDA0003274921360000023
Figure GDA0003274921360000024
s.t.
Figure GDA0003274921360000025
wherein the content of the first and second substances,
Figure GDA0003274921360000026
x＝(x1,x2,…,xn)；
U＝(U1,U2,…,Um).
wherein x is an n-dimensional design vector, U is an m-dimensional interval uncertain parameter vector, and Ft(x) Denotes the t-th target Performance index, NOThe number of the objective functions; x is the number of0For the initial design vector, ftFor the tth excitation frequency to be avoided, imin (t) is the closest excitation frequency f in each order of natural frequency of the initial design schemetNatural frequency order of fi(x0) To the ith order natural frequency of the initial design without considering uncertainty,
Figure GDA0003274921360000027
for the closest f in each order natural frequency of the stator end fixing structure of the generatortThe natural frequency of that order varies at the midpoint of the interval under the influence of the uncertainty parameter vector U,
Figure GDA0003274921360000028
for the closest f in each order natural frequency of the stator end fixing structure of the generatortThe width of the variation interval of the order of natural frequency under the influence of the uncertainty parameter vector U; f. ofi(x, U) denotes the ith order natural frequency of the stator end fixing structure; f. ofi L(x)、fi R(x)、fi C(x) And fi W(x) The lower boundary, the upper boundary, the middle point and the width of the ith order natural frequency change interval; gj(x) Is the dynamic characteristic index value of the stator end fixing structure in the jth constraint function, NGIn order to restrict the number of functions,
Figure GDA0003274921360000031
and
Figure GDA0003274921360000032
respectively the lower and upper bounds of its variation range, BjIs a given interval constant in the jth constraint function and has an interval width of
Figure GDA0003274921360000033
And
Figure GDA0003274921360000034
is BjLower and upper bounds of (g)j(x, U) is a variation interval of a design vector x under the influence of an uncertain parameter vector U in a jth constraint function;
2) sampling design variables and uncertain parameters of a stator end fixing structure of the generator by adopting a Latin hypercube sampling method (LHS), obtaining response values of all sample points through a collaborative simulation technology, and establishing a Kriging model for predicting all dynamic characteristic index values of the stator end fixing structure in a target function and a constraint function;
3) solving a steady balanced design model of the dynamic characteristics of the stator end fixing structure of the generator by using a double-layer nested genetic algorithm to obtain a design vector which enables the overall robustness of the dynamic characteristics of the stator end fixing structure to be most balanced; the method specifically comprises the following substeps:
3.1) initializing and setting a double-layer nested genetic algorithm to generate an initial population;
3.2) calculating to obtain the upper and lower bounds f of each dynamic characteristic index change interval in the target and constraint function of the current population individuals by using the Kriging model established in the step 2) in the inner layer of the genetic algorithmi R(x)、fi L(x)、
Figure GDA0003274921360000035
And calculating a constraint performance index Gj(x) Upper and lower limits of interval angle alphaj R(x)、αj L(x) Interval angular width alphaj W(x) And given constant BjUpper and lower bounds of interval angle of
Figure GDA0003274921360000036
And width
Figure GDA0003274921360000037
Figure GDA0003274921360000038
Figure GDA0003274921360000039
αj W(x)＝αj R(x)-αj L(x)
βj R＝π/2
Figure GDA00032749213600000310
βj W＝βj R-βj L
Wherein h isjAssigning values according to the robustness requirements to be met by the stator end fixing structures under different working conditions for representing sensitivity factors of the strict degree of the constraint robustness requirements;
3.3) in the outer layer of the genetic algorithm, based on the calculation result of the interval angle contact ratio coefficient of each constraint performance index, dividing the design vector of the current population individual into a feasible design vector and an infeasible design vector, and specifically comprising the following steps:
3.3.1) calculating the current population individual alphaj R(x) And
Figure GDA0003274921360000041
coefficient of contact angle of between the sections ocbaj RL(x)，αj L(x) And
Figure GDA0003274921360000042
coefficient of contact angle of between the sections ocbaj LL(x)，αj R(x) And betaj RCoefficient of contact angle of between the sections ocbaj RR(x)，αj L(x) And betaj RCoefficient of contact angle of between the sections ocbaj LR(x)：
Figure GDA0003274921360000043
Figure GDA0003274921360000044
Figure GDA0003274921360000045
Figure GDA0003274921360000046
3.3.2) according to the contact ratio coefficient ocba of the interval anglej RL(x)(j＝1,2,…,NG) Classifying the design vectors corresponding to the current population individuals by the values of (a): if all constraint functions of a certain individual satisfy 0 ≦ ocbaj RL(x)＜1(j＝1,2,…,NG) If so, the design vector x corresponding to the individual is a feasible solution; if for a certain body, there is a certain interval constrained interval angle contact ratio coefficient ocbaj RL(x)＝1(j∈{1,2,…,NGH), the design vector x corresponding to the individual is an infeasible solution, and the total violation degree v (x) of the interval constraint can be calculated by the interval angle overlap ratio coefficient:
Figure GDA0003274921360000047
3.4) sequencing all individuals of the contemporary population according to the overall performance robust balance index and the interval constraint total violation degree, and specifically comprising the following steps:
3.4.1) sorting the feasible solutions in the current population from large to small according to the overall performance robust balance index, wherein the overall performance robust balance index Ffinal(x) The calculation formula of (a) is as follows:
Figure GDA0003274921360000048
wherein, Rft(x) The robustness factor, σ (F), for the target performance indext(x) Is the equilibrium standard deviation, σ (G), of all target performance indicatorsj(x) Equal standard deviation of all constraint performance indexes, eqf (x) is a steady equilibrium discrimination coefficient of a target performance index, and eqg (x) is a steady equilibrium discrimination coefficient of the constraint performance index, and the calculation formulas are respectively as follows:
Figure GDA0003274921360000051
Figure GDA0003274921360000052
Figure GDA0003274921360000053
Eqf(x)＝ceil[σ(Ft(x))-Δσ]
Eqg(x)＝ceil[σ(Gj(x))-Δσ]
wherein the content of the first and second substances,
Figure GDA0003274921360000054
the mean value of all target performance robustness coefficients, Rg, corresponding to the same individualj(x) In order to constrain the performance robustness factor,
Figure GDA0003274921360000055
the mean, Δ, of all constraint performance robustness coefficients corresponding to the same individualσAn equalization threshold value set for human; wherein the constraint performance robustness factor Rgj(x) Calculated from the following formula:
Figure GDA0003274921360000056
3.4.2) sorting the infeasible solutions in the current population from small to large in total violation of the interval constraint after all the feasible solutions.
3.5) if the outer layer optimization meets the convergence condition or the evolution algebra reaches a given maximum value, terminating the outer layer genetic algorithm evolution process, outputting feasible individuals with the most balanced overall robustness as an optimal solution, and obtaining a design scheme of the generator stator end fixing structure which meets the stable and balanced overall performance, otherwise, performing cross and variation operation on the individuals in the current population to generate a new population of the outer layer genetic algorithm, adding 1 to the evolution algebra, and returning to the step 3.2).
The invention has the beneficial effects that:
1) considering the influence of material uncertainty on the deviation degree and fluctuation range of the multi-order natural frequency and excitation frequency of the generator stator end fixing structure, a steady equilibrium design model of the dynamic characteristics of the generator stator end fixing structure is established, and a double-layer nested genetic algorithm based on the integral performance steady equilibrium index is used for direct solution, so that a design scheme for enabling the integral vibration resistance performance of the generator stator end fixing structure to be steady and optimal is intelligently and efficiently obtained.
2) The concept of interval angles is introduced, the relative position relation between the constraint performance index change interval of the stator end fixing structure of the generator and the corresponding given interval is accurately described through the 4 interval angle contact ratio coefficients, and then the feasibility and the robustness of the constraint performance index of each interval of the stator end fixing structure can be more accurately judged.
3) And introducing a sensitivity factor representing the strictness degree of the constraint robustness requirement, thereby realizing the self-adaptive adjustment of the constraint robustness judgment rule under different working conditions, meeting the requirement of the robustness design of the same structure under different service working conditions, and improving the engineering applicability of the robust equilibrium design method.
Drawings
FIG. 1 is a flow chart of a design of a generator stator end fixing structure for robust equalization of dynamic characteristics;
FIG. 2 is a three-dimensional model of a stator end fixing structure of a certain type of turbonator;
FIG. 3 is a sectional view of a stator end fixing structure of a certain type of steam turbine generator.
Detailed Description
The invention is described in further detail below with reference to the figures and specific examples.
The invention provides a robust balanced design method for dynamic characteristics of a stator end fixing structure of a generator, which is used for carrying out anti-vibration design on the stator end fixing structure of a nuclear power quadrupole steam turbine generator of a certain model, and comprises the following specific steps as shown in figure 1:
1) establishing a steady balanced design model of the dynamic characteristics of a stator end fixing structure of a generator: to be provided withThe stator end conical ring fixing structure of the generator shown in fig. 2 is a design object, and h in the section of the stator end conical ring fixing structure is used1、h2L as a design variable, the uncertainty of the elastic modulus E and the density ρ of the stator end fixing structure material is considered and described as an interval variable. According to the initial design scheme x0＝(h1,h2L) as a result of the first twelve-order modal analysis of (450,35,560), the second-order and tenth-order modal modes are both four-lobe deformation, and the second-order modal frequency is 98.62Hz, which is very close to the electromagnetic force excitation frequency of 100Hz, and resonance is generated; the tenth-order modal frequency is 598.46Hz, which is close to 6 times of the excitation frequency of the electromagnetic force, and high-frequency resonance is generated. Therefore, the second order and the tenth order natural frequencies of the cone ring fixed structure deviate from 100Hz and 600Hz to serve as optimization targets, the maximum first-order modal deformation and the maximum second-order modal deformation of the cone ring fixed structure serve as constraint conditions, and a steady equilibrium design model of the dynamic characteristics of the cone ring fixed structure is established:
Figure GDA0003274921360000061
s.t.
Figure GDA0003274921360000062
Figure GDA0003274921360000063
δ1(x,U)＝[δ1 L(x),δ1 R(x)]≤[0.7,0.8]；
δ2(x,U)＝[δ2 L(x),δ2 R(x)]≤[1.0,1.1]；
x＝(h1,l,h2)；
380≤h1≤480,520≤l≤580,15≤h2≤45；
U＝(U1,U2)＝(ρ,E)；
ρ＝[1950,2050]kg/mm3,E＝[24500,25500]MPa.
wherein x is (h)1,h2L) is a cone ring design vector, and U ═ is (rho, E) an interval vector; delta1(x, U) is the maximum deformation of the first-order mode of the conical ring, delta1 L(x),δ1 R(x) The lower boundary and the upper boundary of the change interval are respectively; delta2(x, U) is the maximum deformation of the second order mode of the cone ring, delta2 L(x),δ2 R(x) The lower and upper bounds of the variation range are respectively.
2) Sampling design variables and uncertain parameters of a generator stator end conical ring fixed structure by adopting a Latin hypercube sampling method (LHS), obtaining response values of all sample points through a collaborative simulation technology, and establishing a Kriging model for predicting dynamic characteristic index values of the conical ring fixed structure in a target function and a constraint function;
3) solving a steady balanced design model of the dynamic characteristics of the conical ring fixed structure at the stator end of the generator by using a double-layer nested genetic algorithm to obtain a design vector which enables the overall robustness of the dynamic characteristics of the conical ring fixed structure to be most balanced; the method specifically comprises the following substeps:
3.1) double-layer nested genetic algorithm parameter settings are as follows: the maximum evolution generations of the inner and outer layer genetic algorithms are 150 and 100 respectively, the population sizes of the inner and outer layer genetic algorithms are 150, the cross probabilities of the inner and outer layer genetic algorithms are 0.99, the variation probabilities of the inner and outer layer genetic algorithms are 0.05, and the convergence threshold is 1E-4 mm.
3.2) calculating and obtaining the upper and lower boundaries of each dynamic characteristic index change interval in all targets and constraint functions of the current population individuals by using the Kriging model established in the step 2) in the inner layer of the genetic algorithm
Figure GDA0003274921360000071
δ1 R(x)、δ1 L(x)、δ2 R(x)、δ2 L(x) Setting a sensitivity factor h1＝h2When the value is 0.2, the constraint performance index δ is calculatedj(x, U) (j 1,2) section upper and lower boundary angles αj R(x)、αj L(x) And a width alphaj W(x) Calculating a given interval [0.7,0.8 ]]And [1.0,1.1]The interval angle of (1) upper bound angle, lower bound angle and width.
3.3) calculating the overlap ratio coefficient ocba of the interval angle corresponding to each constraint in the outer layer of the genetic algorithmj RL(x)、ocbaj LL(x)、ocbaj RR(x)、ocbaj LR(x) (j ═ 1,2), and according to ocbaj RL(x) The values of (a) distinguish the design vectors of the population individuals into feasible design vectors and infeasible design vectors.
3.4) for feasible design vectors, introduce an equalization threshold ΔσCalculate the overall performance robust equalization index F ═ 0.05final(x) And are sorted from big to small according to the above; for the infeasible design vectors, the overall interval constraint violation degree V (x) is calculated and sorted from small to large according to the degree after the feasible design vectors.
3.5) after each iteration is finished, judging whether the maximum iteration number or the convergence condition is reached: if so, outputting an optimal solution; otherwise, carrying out cross and variation operation on the individuals in the current population to generate a new population of the outer layer genetic algorithm, adding 1 to the evolution algebra, and returning to the step 3.2).
After 35 iterations, the performance index of the conical ring fixed structure reaches convergence, and the obtained optimal design vector is h1＝421.5mm,h235.7mm, and 569.1mm, and the natural frequencies of the corresponding second-order mode and tenth-order mode are respectively<85.88，3.66>And<539.00，23.02>the robustness factor of each performance index is shown in table 1. It can be seen that the natural frequencies of the second-order and tenth-order modes of the optimized scheme are far away from the excitation frequency and integral multiples thereof, and the maximum deformation amounts of the first-order mode and the second-order mode in the constraint function are respectively [0.56, 0.58 ]]And [0.83, 0.85 ]]Given constraints are satisfied. In conclusion, the vibration resistance of the optimized conical ring fixing structure is improved. It can also be seen from the data in table 1 that the robustness coefficients of each target performance index and the constraint performance index of the optimized conical ring are relatively close, which indicates that the robustness of the overall performance of the optimized conical ring is relatively balanced.
In step 3.2), ifThe decision rule of the constraint robustness is relaxed, the value of the sensitivity factor is increased, and the sensitivity factor h is set1＝h2The resulting robust equalization design results are shown in table 1, 0.4. Comparing the results obtained when the values of different sensitivity factors are taken, it can be found that although the constraint performance index obtained when the sensitivity factor is taken as 0.2 is better (smaller), the requirement on the constraint robustness is higher when the coincidence sensitivity coefficient is smaller, so the calculated constraint robustness coefficient is slightly lower than that when the sensitivity factor is taken as 0.4. Therefore, different robustness requirements on the constraint performance indexes of the generator conical ring fixed structure under different working conditions can be met by modifying the values of the coincidence sensitivity factors, and the smaller the coincidence sensitivity factor is, the more rigorous the constraint performance indexes are judged to be in the robust condition.
TABLE 1 comparison of design results of steady equilibrium of dynamic characteristics of stator end taper ring fixed structure of turbonator under different values of sensitivity factors
Figure GDA0003274921360000081
The foregoing is only a preferred embodiment of the present invention, and although the present invention has been disclosed in the preferred embodiments, it is not intended to limit the present invention. Those skilled in the art can make numerous possible variations and modifications to the present teachings, or modify equivalent embodiments to equivalent variations, without departing from the scope of the present teachings, using the methods and techniques disclosed above. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention are still within the scope of the protection of the technical solution of the present invention, unless the contents of the technical solution of the present invention are departed.

Claims (3)

1. A robust equilibrium design method for dynamic characteristics of a generator stator end fixing structure is characterized by comprising the following steps:
1) establishing a steady balanced design model of the dynamic characteristics of a stator end fixing structure of a generator: taking the key size of the section of the stator end fixing structure as a design variable, considering the uncertainty of the elastic modulus and the density of the stator end fixing structure material, and describing the uncertainty as an interval variable; analyzing the specific order of the natural frequency closest to the excitation frequency in the natural frequencies of all orders of the initial design scheme, and simultaneously considering the middle point and the width of the change interval of the natural frequencies under the influence of uncertainty so as to enable the natural frequencies to be far away from the excitation frequency as far as possible and to have small fluctuation under the influence of uncertainty as a target, and establishing an expression of a target function; establishing an expression of a constraint function according to other requirements of the dynamic characteristic design of the stator end fixing structure, and further establishing a steady balanced design model of the dynamic characteristic of the stator end fixing structure of the generator:
Figure FDA0003263031950000011
wherein the content of the first and second substances,
Figure FDA0003263031950000012
fi C(x)＝(fi L(x)+fi R(x))/2；
fi W(x)＝fi R(x)-fi L(x)；
Figure FDA0003263031950000017
Figure FDA0003263031950000018
s.t.
Figure DEST_PATH_IMAGE001
；
wherein the content of the first and second substances,
Figure FDA0003263031950000014
x＝(x1,x2,…,xn)；
U＝(U1,U2,…,Um)；
wherein x is an n-dimensional design vector, U is an m-dimensional interval uncertain parameter vector, and Ft(x) Denotes the t-th target Performance index, NOThe number of the objective functions; x is the number of0For the initial design vector, ftFor the tth excitation frequency to be avoided, imin (t) is the closest excitation frequency f in each order of natural frequency of the initial design schemetNatural frequency order of fi(x0) To the ith order natural frequency of the initial design without considering uncertainty,
Figure FDA0003263031950000015
for the closest f in each order natural frequency of the stator end fixing structure of the generatortThe natural frequency of that order varies at the midpoint of the interval under the influence of the uncertainty parameter vector U,
Figure FDA0003263031950000016
for the closest f in each order natural frequency of the stator end fixing structure of the generatortThe width of the variation interval of the order of natural frequency under the influence of the uncertainty parameter vector U; f. ofi(x, U) denotes the ith order natural frequency of the stator end fixing structure; f. ofi L(x)、fi R(x)、fi C(x) And fi W(x) The lower boundary, the upper boundary, the middle point and the width of the ith order natural frequency change interval; gj(x) Is the dynamic characteristic index value of the stator end fixing structure in the jth constraint function, NGIn order to restrict the number of functions,
Figure FDA0003263031950000021
and
Figure FDA0003263031950000022
are respectively asLower and upper limits of the variation range, BjIs a given interval constant in the jth constraint function and has an interval width of
Figure FDA0003263031950000023
And
Figure FDA0003263031950000024
is BjLower and upper bounds of (g)j(x, U) is a variation interval of a design vector x under the influence of an uncertain parameter vector U in a jth constraint function;
2) sampling design variables and uncertain parameters of a stator end fixing structure of the generator by adopting a Latin hypercube sampling method, obtaining response values of all sample points through a collaborative simulation technology, and establishing a Kriging model for predicting all dynamic characteristic index values of the stator end fixing structure in a target function and a constraint function;
3) solving a steady balanced design model of the dynamic characteristics of the stator end fixing structure of the generator by using a double-layer nested genetic algorithm to obtain a design vector which enables the overall robustness of the dynamic characteristics of the stator end fixing structure to be most balanced; the method specifically comprises the following substeps:
3.1) initializing and setting a double-layer nested genetic algorithm to generate an initial population;
3.2) calculating to obtain the upper and lower bounds f of each dynamic characteristic index change interval in the target and constraint function of the current population individuals by using the Kriging model established in the step 2) in the inner layer of the genetic algorithmi R(x)、fi L(x)、
Figure FDA00032630319500000212
And calculating a constraint performance index Gj(x) Upper and lower limits of interval angle alphaj R(x)、αj L(x) Interval angular width alphaj W(x) And given constant BjUpper and lower bounds of interval angle of
Figure FDA0003263031950000025
And width
Figure FDA0003263031950000026
Figure FDA0003263031950000027
Figure FDA0003263031950000028
αj W(x)＝αj R(x)-αj L(x)
βj R＝π/2
Figure FDA0003263031950000029
βj W＝βj R-βj L
Wherein h isjAssigning values according to the robustness requirements to be met by the stator end fixing structures under different working conditions for representing sensitivity factors of the strict degree of the constraint robustness requirements;
3.3) in the outer layer of the genetic algorithm, based on the calculation result of the interval angle contact ratio coefficient of each constraint performance index, dividing the design vector of the current population individual into a feasible design vector and an infeasible design vector, and specifically comprising the following steps:
3.3.1) calculating the current population individual alphaj R(x) And
Figure FDA00032630319500000210
coefficient of contact angle of between the sections ocbaj RL(x)，αj L(x) And
Figure FDA00032630319500000211
coefficient of contact angle of between the sections ocbaj LL(x)，αj R(x) And betaj RCoefficient of contact angle of between the sections ocbaj RR(x)，αj L(x) And betaj RCoefficient of contact angle of between the sections ocbaj LR(x)：
Figure FDA0003263031950000031
Figure FDA0003263031950000032
Figure FDA0003263031950000033
Figure FDA0003263031950000034
3.3.2) according to the contact ratio coefficient ocba of the interval anglej RL(x)(j＝1,2,…,NG) Classifying the design vectors corresponding to the current population individuals by the values of (a): if all constraint functions of a certain individual satisfy 0 ≦ ocbaj RL(x)＜1(j＝1,2,…,NG) If so, the design vector x corresponding to the individual is a feasible solution; if for a certain body, there is a certain interval constrained interval angle contact ratio coefficient ocbaj RL(x)＝1(j∈{1,2,…,NG}), the design vector x corresponding to the individual is an infeasible solution, and the total violation degree V (x) of the interval constraint is calculated by the interval angle coincidence degree coefficient:
Figure FDA0003263031950000035
3.4) sequencing all individuals of the contemporary population according to the overall performance robust balance index and the interval constraint total violation degree, and specifically comprising the following steps:
3.4.1) sorting the feasible solutions in the current population from large to small according to the overall performance robust balance index, wherein the overall performance robust balance index Ffinal(x) The calculation formula of (a) is as follows:
Figure FDA0003263031950000036
wherein, Rft(x) The robustness factor, σ (F), for the target performance indext(x) Is the equilibrium standard deviation, σ (G), of all target performance indicatorsj(x) Equal standard deviation of all constraint performance indexes, eqf (x) is a steady equilibrium discrimination coefficient of a target performance index, and eqg (x) is a steady equilibrium discrimination coefficient of the constraint performance index, and the calculation formulas are respectively as follows:
Figure FDA0003263031950000041
Figure FDA0003263031950000042
Figure FDA0003263031950000043
Eqf(x)＝ceil[σ(Ft(x))-Δσ]
Eqg(x)＝ceil[σ(Gj(x))-Δσ]
wherein the content of the first and second substances,
Figure FDA0003263031950000044
the mean value of all target performance robustness coefficients, Rg, corresponding to the same individualj(x) In order to constrain the performance robustness factor,
Figure FDA0003263031950000045
is the same individual pairMean, Δ, of all constraint performance robustness coefficientsσAn equalization threshold value set for human; wherein the constraint performance robustness factor Rgj(x) Calculated from the following formula:
Figure FDA0003263031950000046
3.4.2) sorting the infeasible solutions in the current population from small to large according to the total violation degree of the interval constraint after all the feasible solutions;
3.5) if the outer layer optimization meets the convergence condition or the evolution algebra reaches a given maximum value, terminating the outer layer genetic algorithm evolution process, outputting feasible individuals with the most balanced overall robustness as an optimal solution, and obtaining a design scheme of the generator stator end fixing structure which meets the stable and balanced overall performance, otherwise, performing cross and variation operation on the individuals in the current population to generate a new population of the outer layer genetic algorithm, adding 1 to the evolution algebra, and returning to the step 3.2).
2. The robust design method for balancing dynamic characteristics of the stator end fixing structure of the generator according to claim 1, is characterized in that: in the step 3), 4 interval angle contact ratio coefficients are adopted to accurately describe the relative position relation between the constraint performance index change interval of the stator end fixing structure of the generator and the corresponding given interval, so that the feasibility and the robustness of the stator end fixing structure design scheme can be more accurately judged; specifically, for each population of individuals, the corresponding interval constraint [ g [j L(x),gj R(x)]≤[bj L,bj R]The strength of the feasible robustness depends on the overlap ratio coefficient ocba of the interval anglej RL(x) The value of (c): when ocbaj RL(x) When 0, interval constraint performance index Gj(x) Is strong, feasible and stable; when 0 < ocbaj RL(x) Interval constraint performance index G when less than 1j(x) Is weak, feasible and stable; when ocbaj RL(x) When 1, interval constraint performance index Gj(x) The constraint is not satisfied.
3. The robust design method for balancing dynamic characteristics of the stator end fixing structure of the generator according to claim 2, is characterized in that: in the step 3), when calculating the interval angle corresponding to the interval constraint performance index of the stator end fixing structure of the generator and the given interval constant thereof, introducing a sensitivity factor h representing the severity degree of constraint robustness requirementj：hjThe smaller, the constraint performance index Gj(x) The harsher the conditions are determined to be strong and robust; h isjThe larger the constraint performance index G isj(x) The more loose the conditions are judged to be strong, feasible and stable; therefore, a proper sensitivity factor value is selected according to the robustness severity required by the stator end fixing structure under different working conditions, and the robust balanced design of the dynamic characteristics of the stator end fixing structure under different working conditions is realized.
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