CN117454691A - Power station distortion model-based performance driving-separation similarity prediction method - Google Patents
Power station distortion model-based performance driving-separation similarity prediction method Download PDFInfo
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Abstract
The invention discloses a power station distortion model-based performance driving-separation similarity prediction method, which comprises the steps of obtaining a preliminary similarity law of a condensing unit according to dimension analysis and equation analysis; determining performance parameters sensitive to the distortion model according to the preliminary similarity law; decomposing the distortion model into a complete similar reduced scale model and a partial similar reduced scale model, and respectively deducing a complete similar reduced scale model similarity law and a partial similar reduced scale model similarity law; obtaining a distortion model similarity law according to the Buckingham-pi theorem; predicting the performance of the prototype by the distortion model through a distortion model similarity law; aiming at the distortion condition of the reduced scale model of the condensing unit in the similarity analysis, the performance parameters sensitive to the distortion model are determined, the distortion model is separated into a complete similarity model and a partial similarity model, a similarity law between the distortion model and the prototype is indirectly established, the influence of distortion factors on the application of a similarity theory is eliminated, and the performance prediction precision of the distortion model on the prototype can be remarkably improved.
Description
Technical Field
The invention belongs to the technical field of prediction of structural performance of a space solar power station, and particularly relates to a power station distortion model-based performance driving-separation similarity prediction method.
Background
The space solar power station (SpaceSolarPowerStation, SSPS) has great development potential and application prospect in space exploration and ground energy solutions by the characteristic of continuously collecting space solar energy in all weather. The innovative scheme of the OMEGA space solar power station (SSPS-OMEGA) proposed by the Baoyan academy of the Western Anelectron technology university has the characteristics of easy modularization, high light concentration ratio and high quality ratio, and is widely focused and researched by industry students. SSPS-OMEGA is a kilometer scale power generation system that mainly includes three major parts, solar energy collection and conversion, microwave wireless transmission and energy reception and rectification. The spherical concentrator responsible for space solar energy collection is the front end of the whole power generation system and has an important influence on the energy output of a terminal. In order to predict the mechanical properties of the spherical concentrator and to further verify the engineering feasibility of the whole system, a reduced scale model needs to be built for similarity analysis.
The spherical condenser consists of a condensing unit array, when a traditional similarity theory is applied to guide the construction of a reduced scale model, the situation that the thickness cannot be scaled in an equal scale to generate a distortion model exists, so that the mechanical property prediction accuracy of the spherical condenser is reduced, and the engineering feasibility verification of the space solar power station is affected.
Disclosure of Invention
The invention aims to provide a performance driving-separation similarity prediction method based on a power station distortion model, which solves the problem that the mechanical property prediction precision of a spherical condenser is reduced under the condition that the distortion model is generated due to the fact that the thickness cannot be scaled equally.
The technical scheme adopted by the invention is that the 'performance driving-separation similarity' prediction method based on the power station distortion model is implemented according to the following steps:
step 1, obtaining a preliminary similarity law S of a spherical condenser and a condensing unit of the omega space solar power station according to dimension analysis and equation analysis methods 0 ；
Step 2, according to the preliminary similarity law S 0 Determining a pair distortion model m 0 Sensitive performance parameters;
step 3, the distortion model m 0 Decomposition into completely similar scale models m 1 And a partially similar scale model m 2 Respectively deducing a similarity law S of a complete similarity reduced model m1 Similarity law S with partial similarity reduced scale model m2 ；
Step 4, obtaining a distortion model similarity law S according to the Buckingham-pi theorem m0 ；
Step 5, distortion model m 0 Similarity law S through distortion model m0 The performance of prototype P is predicted.
The invention is also characterized in that:
the specific process of the step 1 is as follows:
step 1.1, obtaining a global similarity law S based on dimension analysis G ；
Step 1.2, obtaining a local similarity law S based on an equation analysis method L ；
Step 1.3, according to the global similarity law S G And local similarity law S L Obtain the preliminary similarity law S of the condensing unit 0 。
The specific process of the step 1.1 is as follows:
for a spherical condenser and a condensing unit of the omega space solar power station, main physical parameters are selected: spherical condenser radius R, spherical crown central angle theta, condensing unit length l along the weft direction, length w along the warp direction, thickness h, material density rho, poisson ratio mu, elastic modulus E, bending rigidity D, external load Q, natural vibration modeNatural frequency f, deflection u, shouldForce sigma;
defining similar scales of corresponding parameters of the prototype and the model:
wherein X represents a physical parameter, the superscript (p) represents a prototype system, the superscript (m) represents a model system, lambda X Representing a similar reduced scale corresponding to the physical parameter X;
obtaining a dimensionality homogeneous equation by using a dimensionality homogeneous principle and merging the dimensionality homogeneous equation into a dimensionless number to finally obtain a global similarity law S G ：
Where λ represents a geometric scale.
The specific process of the step 1.2 is as follows:
the local similarity law is obtained by adopting an equation analysis method, the condensing unit of the spherical condenser is a rectangular thin plate, and a free vibration differential equation is established according to the elastic mechanics theory:
and has the following steps:
the expression of the free vibration solution of the thin plate is as follows:
wherein the amplitude A mn And B mn The values of m and n are integers determined by the initial conditions, and ω is obtained when m=n=1 11 Is the lowest natural frequency, namely the fundamental frequency of the thin plate;
for the reduced scale model, the reduced scale model also satisfies the formula (3) -formula (5) to obtain the local similarity law S L ：
The specific process of the step 1.3 is as follows:
according to the global similarity law S G And local similarity law S L Obtain the preliminary similarity law S of the condensing unit 0 ：
The specific process of the step 2 is as follows:
step 2.1, preliminary similarity law S obtained in step 1 0 It is known that the physical parameters related to the geometry of the condensing unit in equation (7) satisfy:
λ l ＝λ h ＝λ w ＝λ (8)
because the length direction size of the condensing unit is larger than the thickness direction size by more than two orders of magnitude, the thickness parameter h of the condensing unit is determined to be a distortion parameter, and the corresponding thickness reduction lambda is determined h Reducing the scale of the distortion model;
step 2.2, according to the preliminary similarity law S 0 In combination with the determined distortion parameter h, determining a performance parameter sensitive to the distortion parameter: the bending rigidity D, the natural frequency f and the deflection u are shown in the formula (9) according to the corresponding distortion and scale relationship:
the specific process of the step 3 is as follows:
step 3.1, according to the completely similar reduced scale lambda and the partially similar reduced scale delta h Separating distortion parameters;
the distortion parameters are separated according to a completely similar reduced scale lambda:
according to the partially similar scale delta h The distortion parameters are separated, namely:
step 3.2, according to the distortion model m 0 Thickness reduction lambda between prototype and prototype h The method comprises the steps of carrying out a first treatment on the surface of the The thickness of the condensing unit is scaled lambda according to the equal scale to build a completely similar scaled model m 1 The method comprises the steps of carrying out a first treatment on the surface of the At m 1 On the basis of the partially similar reduced scale delta h Only the thickness is reduced to obtain a partial similar model m 2 ；
And 3.3, writing the similar scales of all physical parameters in the similar criteria into a power relation:
wherein alpha is i,j Is thatIs an index of (1) representing X i For X j Is obtained by taking the logarithm of the equation of formula (12) on both sides:
obtaining an index alpha from a first order sensitivity analysis i,j The expression:
wherein X is j,i (1) And X j,i (0) Respectively correspond toAnd->Delta is the increment of the dependent variable similarity scaling, k=1, 2,..r,/-j>At each increment of the change kΔ, the index value α at that time is calculated according to equation (14) i,j (k) The method comprises the steps of carrying out a first treatment on the surface of the Respectively establishing completely similar reduced scale models m according to the formula (14) 1 And a partially similar scale model m 2 Performing simulation analysis on the finite element model to obtain performance parameter simulation data sensitive to distortion parameters;
step 3.4, adopting a power-variable coefficient method to process the simulation data to obtain a full-similarity scale model similarity lawSimilarity law of partial similarity scale model>
The specific process of the step 3.4 is as follows:
defining the exponent alpha according to the exponentiation coefficient method i,j Is thatA power function of (2):
obtaining r group alpha according to formula (14) i,j Is represented by the coefficient gamma in the formula (16) i And beta i Converting to a least squares problem:
solving by using Levenberg-Marquardt algorithm to obtain a plurality of groups of coefficients gamma in a formula (15) i And beta i The index alpha shown in formula (12) is determined i,j The method comprises the steps of carrying out a first treatment on the surface of the Combining the formula (12) to obtain a full-similarity scale model similarity lawSimilarity law of partial similarity scale model>
The specific process of the step 4 is as follows:
obtaining natural frequency f and maximum deflection u of a condensing unit of the spherical condenser of the omega space solar power station according to a formula (12) max Is the predictive equation of:
wherein,respectively represent thickness distortion models m of condensing units 0 With respect to natural frequency f, maximum deflection u between prototypes of concentrator units max Corresponding predictive indices are:
the corresponding y= [ γ ] is obtained according to step 3.4 i ,β i ](i＝1,2,…,4)；
Obtaining a distortion model similarity law by combining the formula (12)The method comprises the following steps:
wherein diag () represents a diagonal matrix.
The specific process of the step 5 is as follows:
establishing a distortion model m 0 Performing simulation analysis on the finite element model to obtain corresponding natural frequencyMaximum deflection->
Scaled law according to distortion modelPredicting natural frequency f of prototype P (pre) Maximum deflection u max (pre) As shown in formula (21):
the invention has the beneficial effects that:
according to the performance driving-separation similarity prediction method based on the power station distortion model, aiming at the condition that a reduced scale model distortion exists in a space solar power station condensation unit in similarity analysis, performance parameters sensitive to the distortion model are determined, the distortion model is separated into a complete similarity model and a partial similarity model, a similarity law between the distortion model and a prototype is indirectly established, the influence of distortion factors on similarity theoretical application is eliminated, and the accuracy of predicting the performance of the prototype by the distortion model can be remarkably improved.
Drawings
FIG. 1 is a flow chart of a "performance driven-separation similarity" prediction method based on a plant distortion model of the present invention;
FIG. 2 is a schematic diagram of spherical concentrator and concentrating unit structures of an omega space solar power station used in the present invention;
FIG. 3 is a schematic diagram showing comparison of the first-order natural frequency prediction results of a prototype by applying different methods to multiple groups of scale models in the embodiment of the present invention;
FIG. 4 is a schematic diagram showing comparison of the results of predicting prototype second-order natural frequencies by applying different methods to multiple groups of scale models in the embodiment of the present invention;
FIG. 5 is a schematic diagram showing comparison of the results of predicting the third-order natural frequency of a prototype by applying different methods to multiple groups of scale models in the embodiment of the present invention;
FIG. 6 is a schematic diagram showing comparison of the results of predicting the prototype fourth-order natural frequency by applying different methods to multiple groups of scale models in the embodiment of the present invention;
FIG. 7 is a schematic diagram showing a comparison of the first-order natural frequency prediction errors of a prototype using different methods for multiple sets of scale models according to an embodiment of the present invention;
FIG. 8 is a schematic diagram showing a comparison of the prototype second-order natural frequency prediction error by applying different methods to multiple sets of scale models according to an embodiment of the present invention;
FIG. 9 is a schematic diagram showing a comparison of the prediction errors of the prototype third-order natural frequencies by applying different methods to multiple sets of scale models according to an embodiment of the present invention;
FIG. 10 is a schematic diagram showing a comparison of the prediction errors of the prototype fourth-order natural frequencies by applying different methods to multiple sets of scale models according to an embodiment of the present invention;
FIG. 11 is a schematic diagram showing comparison of the maximum deflection prediction results of a prototype by applying different methods to multiple groups of scale models in the embodiment of the invention;
FIG. 12 is a schematic diagram showing a comparison of prototype maximum deflection prediction errors using different methods for multiple sets of scale models.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings and detailed description.
Example 1
The invention provides a performance-driven-separation similarity prediction method based on a power station distortion model, and provides a separation similarity method with dominant performance, so as to establish a distortion model similarity lawThe mechanical property prediction precision of the spherical condenser of the high omega space solar power station aims at improving the mechanical property prediction precision of the spherical condenser of the high omega space solar power station. As shown in fig. 1, the method is specifically implemented according to the following steps: obtaining a preliminary similarity law S of the spherical condenser and the condensing unit of the omega space solar power station according to the dimensional analysis and the equation analysis method 0 The method comprises the steps of carrying out a first treatment on the surface of the According to the preliminary similarity law S 0 Determining a pair distortion model m 0 Sensitive performance parameters; model m of distortion 0 Decomposition into completely similar scale models m 1 And a partially similar scale model m 2 Respectively deducing the similarity law of the completely similar reduced scale modelSimilarity law of partial similarity scale model>Obtaining a distortion model similarity law according to the Buckingham-pi theorem>Distortion model m 0 Similarity law by distortion model>The performance of prototype P is predicted. In the embodiment, aiming at the condition that a reduced scale model distortion exists in a space solar power station condensation unit in similarity analysis, performance parameters sensitive to the distortion model are determined, the distortion model is separated into a complete similarity model and a partial similarity model, a similarity law between the distortion model and a prototype is indirectly established, the influence of distortion factors on application of a similarity theory is eliminated, and the accuracy of predicting the performance of the prototype by the distortion model is remarkably improved.
Example 2
The invention relates to a 'performance driving-separation similarity' prediction method based on a power station distortion model, which is implemented as shown in figure 1, and specifically comprises the following steps:
step 1, obtaining a preliminary similarity law S of a spherical condenser and a condensing unit of the omega space solar power station according to dimension analysis and equation analysis methods 0 The method comprises the steps of carrying out a first treatment on the surface of the The specific process is as follows:
step 1.1, obtaining a global similarity law S based on dimension analysis G The method comprises the steps of carrying out a first treatment on the surface of the The specific process is as follows:
for a spherical condenser and a condensing unit of the omega space solar power station, the structure is shown in fig. 2, and main physical parameters are selected: spherical condenser radius R, spherical crown central angle theta, condensing unit length l along the weft direction, length w along the warp direction, thickness h, material density rho, poisson ratio mu, elastic modulus E, bending rigidity D, external load Q, natural vibration modeNatural frequency f, deflection u, stress sigma;
defining similar scales of corresponding parameters of the prototype and the model:
wherein X represents a physical parameter, the superscript (p) represents a prototype system, the superscript (m) represents a model system, lambda X Representing a similar reduced scale corresponding to the physical parameter X;
obtaining a dimensionality homogeneous equation by using a dimensionality homogeneous principle and merging the dimensionality homogeneous equation into a dimensionless number to finally obtain a global similarity law S G ：
Where λ represents a geometric scale.
Step 1.2, obtaining a local similarity law S based on an equation analysis method L The method comprises the steps of carrying out a first treatment on the surface of the The specific process is as follows:
based on the step 1.1, an equation analysis method is adopted to obtain a local similarity law, a condensing unit of the spherical condenser is a rectangular thin plate, and a free vibration differential equation is established according to an elastic mechanics theory:
and has the following steps:
the expression of the free vibration solution of the thin plate is as follows:
wherein the amplitude A mn And B mn The values of m and n are integers determined by the initial conditions, and ω is obtained when m=n=1 11 Is the lowest natural frequency, namely the fundamental frequency of the thin plate;
for the reduced scale model, the reduced scale model also satisfies the formula (3) -formula (5) to obtain the local similarity law S L ：
Step 1.3, according to the global similarity law S G And local similarity law S L Obtain the preliminary similarity law S of the condensing unit 0 . The specific process is as follows:
according to the global similarity law S G And local similarity law S L Obtain the preliminary similarity law S of the condensing unit 0 ：
Step 2, according to the preliminary similarity law S 0 Determining a distortion model m 0 Sensitive performance parameters; the specific process is as follows:
step 2.1, preliminary similarity law S obtained in step 1 0 It is known that the physical parameters related to the geometry of the condensing unit in equation (7) satisfy:
λ l ＝λ h ＝λ w ＝λ (8)
due to the length of the condensing unitThe dimension in the thickness direction is larger than that in the thickness direction by more than two orders of magnitude, and the reduced scale model cannot meet the requirement of equal scale reduction in the thickness direction, namely lambda h Not equal to λ, thickness distortion occurs. Namely, the thickness parameter h of the condensing unit is determined as a distortion parameter, and the corresponding thickness scale lambda is reduced h Reducing the scale of the distortion model;
step 2.2, according to the preliminary similarity law S 0 In combination with the determined distortion parameter h, determining a performance parameter sensitive to the distortion parameter: the bending rigidity D, the natural frequency f and the deflection u are shown in the formula (9) according to the corresponding distortion and scale relationship:
step 3, the distortion model m 0 Decomposition into completely similar scale models m 1 And a partially similar scale model m 2 Respectively deducing the similarity law of the completely similar reduced scale modelSimilarity law of partial similarity scale model>The specific process is as follows:
step 3.1, according to the completely similar reduced scale lambda and the partially similar reduced scale delta h Separating distortion parameters;
the distortion parameters are separated according to a completely similar reduced scale lambda:
according to the partially similar scale delta h The distortion parameters are separated, namely:
step 3.2, according to distortionModel m 0 Thickness reduction lambda between prototype and prototype h The method comprises the steps of carrying out a first treatment on the surface of the The thickness of the condensing unit is scaled lambda according to the equal scale to build a completely similar scaled model m 1 The method comprises the steps of carrying out a first treatment on the surface of the At m 1 On the basis of the partially similar reduced scale delta h Only the thickness is reduced to obtain a partial similar model m 2 ；
And 3.3, writing the similar scales of all physical parameters in the similar criteria into a power relation:
wherein alpha is i,j Is thatIs an index of (1) representing X i For X j Is obtained by taking the logarithm of the equation of formula (12) on both sides:
obtaining an index alpha from a first order sensitivity analysis i,j The expression:
wherein X is j,i (1) And X j,i (0) Respectively correspond toDelta is the increment of the dependent variable similarity scaling, k=1, 2,..r,/-j>Each time the change amount kdelta is increased, the change of the system response parameter is caused, and the index value alpha is calculated according to the formula (14) i,j (k) The method comprises the steps of carrying out a first treatment on the surface of the The value of each change should be as small as possible and cause a change in the system responseTherefore, take the initial value->The variation Δ=0.05, r=4. Respectively establishing completely similar reduced scale models m according to the formula (14) 1 And a partially similar scale model m 2 Performing simulation analysis on the finite element model to obtain performance parameter simulation data sensitive to distortion parameters;
step 3.4, adopting a power-variable coefficient method to process the simulation data to obtain a full-similarity scale model similarity lawSimilarity law of partial similarity scale model>The specific process is as follows:
defining the exponent alpha according to the exponentiation coefficient method i,j Is thatA power function of (2):
obtaining r group alpha according to formula (14) i,j Is represented by the coefficient gamma in the formula (16) i And beta i Converting to a least squares problem:
solving by using Levenberg-Marquardt algorithm to obtain a plurality of groups of coefficients gamma in a formula (15) i And beta i The index alpha shown in formula (12) is determined i,j The method comprises the steps of carrying out a first treatment on the surface of the Combination formula (12)Obtaining the similarity law of the completely similar reduced scale modelSimilarity law of partial similarity scale model>
Step 4, obtaining a distortion model similarity law according to the Buckingham-pi theoremThe specific process is as follows:
obtaining natural frequency f and maximum deflection u of a condensing unit of the spherical condenser of the omega space solar power station according to a formula (12) max Is the predictive equation of:
wherein,respectively represent thickness distortion models m of condensing units 0 With respect to natural frequency f, maximum deflection u between prototypes of concentrator units max Corresponding predictive indices are:
the corresponding y= [ γ ] is obtained according to step 3.4 i ,β i ](i＝1,2,…,4)；
Obtaining a distortion model similarity law by combining the formula (12)The method comprises the following steps:
wherein diag () represents a diagonal matrix.
Step 5, distortion model m 0 By distortion model similarity lawThe performance of prototype P is predicted. The specific process is as follows:
establishing a distortion model m 0 Performing simulation analysis on the finite element model to obtain corresponding natural frequencyMaximum deflection->
Scaled law according to distortion modelPredicting natural frequency f of prototype P (pre) Maximum deflection u max (pre) As shown in formula (21):
example 3
The effect of the invention is verified and illustrated by simulation experiments. Comparison of methods (LM-VPM) in the prior art (L.Li, Z.Luo, F.He, et al, an improved partial similitude method for dynamic characteristic of rotor systems based on Levenberg-Marquardt method [ J ]. Mech. System. Signal Process.2022,165 ]) and methods (I & CSM) in the literature (PT Liu, X Pwang, Y Q Wang, et al, research on coupling distorted similitude method of coupled cylindrical-comparative shells [ J ]. Thin-walled Structures,2022, 179:109734.).
The geometrical parameters and load parameters of the prototype of the omega spherical condenser condensing unit are shown in table 1, and the first four-order natural frequency and the maximum deflection of the prototype are shown in table 2 by establishing finite element model simulation according to table 1.
TABLE 1
TABLE 2
The separation model and the distortion model scaling are set as shown in Table 3, the natural frequency similarity law prediction indexes corresponding to each set of scaling models are obtained by using the method, the LM-VPM and the I & CSM respectively as shown in Table 4, and the maximum deflection similarity law prediction indexes corresponding to each set of scaling models are obtained by using the method, the LM-VPM and the I & CSM respectively as shown in Table 5.
TABLE 3 Table 3
TABLE 4 Table 4
TABLE 5
The comparison of the predicted value and the theoretical value of the fourth-order natural frequency before the prototype of the omega space solar power station concentrating unit by the six groups of scale models respectively using different methods is shown in fig. 3, 4, 5 and 6, and according to fig. 3, 4, 5 and 6, the predicted value and the theoretical value of the prototype obtained by the method are basically consistent, and the corresponding error comparison is shown in fig. 7, 8, 9 and 10, and according to fig. 7, 8, 9 and 10, the prediction accuracy of the method is obviously higher than that of the other two methods.
The comparison of the predicted value and the theoretical value of the maximum deflection of the prototype of the concentrating unit of the omega space solar power station by using the six groups of scale models by using different methods is shown in fig. 11, and the corresponding error comparison is shown in fig. 12. As can be seen from fig. 11 and 12, the maximum deflection predicted value obtained by the method is basically consistent with the prototype theoretical value, the overall fluctuation of the predicted result is small, and the prediction precision is obviously higher than that of the other two methods.
By means of the mode, the performance driving-separation similarity prediction method based on the power station distortion model is used for determining performance parameters sensitive to the distortion model aiming at the condition that the reduced scale model distortion exists in the similarity analysis of the space solar power station condensation unit, the distortion model is separated into a complete similarity model and a partial similarity model, a similarity law between the distortion model and a prototype is indirectly established, the influence of distortion factors on the application of a similarity theory is eliminated, and the accuracy of predicting the performance of the prototype by the distortion model can be remarkably improved.
Claims (10)
1. The 'performance driving-separation similarity' prediction method based on the power station distortion model is characterized by comprising the following steps of:
step 1, obtaining a preliminary similarity law S of a spherical condenser and a condensing unit of the omega space solar power station according to dimension analysis and equation analysis methods 0 ；
Step 2, according to the preliminary similarity law S 0 Determining a pair distortion model m 0 Sensitive performance parameters;
step 3, the distortion model m 0 Decomposition into completely similar scale models m 1 And a partially similar scale model m 2 Respectively deducing the similarity law of the completely similar reduced scale modelSimilarity law of partial similarity scale model>
Step 4, obtaining a distortion model similarity law according to the Buckingham-pi theorem
Step 5, distortion model m 0 By distortion model similarity lawThe performance of prototype P is predicted.
2. The power station distortion model-based performance driving-separation similarity prediction method according to claim 1, wherein the specific process of step 1 is as follows:
step 1.1, obtaining a global similarity law S based on dimension analysis G ；
Step 1.2, obtaining a local similarity law S based on an equation analysis method L ；
Step 1.3, according to the global similarity law S G And local similarity law S L Obtain the preliminary similarity law S of the condensing unit 0 。
3. The power station distortion model-based "performance driven-separation similarity" prediction method according to claim 2, wherein the specific process of step 1.1 is:
for a spherical condenser and a condensing unit of the omega space solar power station, main physical parameters are selected: spherical condenser radius R, spherical crown central angle theta, condensing unit length l along the weft direction, length w along the warp direction, thickness h, material density rho, poisson ratio mu, elastic modulus E, bending rigidity D, external load Q, natural vibration modeNatural frequency f, deflection u, stress sigma;
defining similar scales of corresponding parameters of the prototype and the model:
wherein the method comprises the steps ofX represents a physical parameter, the superscript (p) represents a prototype system, the superscript (m) represents a model system, lambda X Representing a similar reduced scale corresponding to the physical parameter X;
obtaining a dimensionality homogeneous equation by using a dimensionality homogeneous principle and merging the dimensionality homogeneous equation into a dimensionless number to finally obtain a global similarity law S G ：
Where λ represents a geometric scale.
4. The power station distortion model-based "performance driven-separation similarity" prediction method according to claim 3, wherein the specific process of step 1.2 is:
the local similarity law is obtained by adopting an equation analysis method, the condensing unit of the spherical condenser is a rectangular thin plate, and a free vibration differential equation is established according to the elastic mechanics theory:
and has the following steps:
the expression of the free vibration solution of the thin plate is as follows:
wherein the amplitude A mn And B mn The values of m and n are integers determined by the initial conditions, and ω is obtained when m=n=1 11 Is the lowest natural frequency, namely the fundamental frequency of the thin plate;
for the reduced scale model, the model also satisfies the formulas (3) - (5) to obtain local similarityLaw S L ：
5. The power station distortion model-based "performance driven-separation similarity" prediction method according to claim 4, wherein the specific process of step 1.3 is:
according to the global similarity law S G And local similarity law S L Obtain the preliminary similarity law S of the condensing unit 0 ：
6. The power station distortion model-based performance driving-separation similarity prediction method according to claim 5, wherein the specific process of step 2 is as follows:
step 2.1, preliminary similarity law S obtained in step 1 0 It is known that the physical parameters related to the geometry of the condensing unit in equation (7) satisfy:
λ l ＝λ h ＝λ w ＝λ (8)
because the length direction size of the condensing unit is larger than the thickness direction size by more than two orders of magnitude, the thickness parameter h of the condensing unit is determined to be a distortion parameter, and the corresponding thickness reduction lambda is determined h Reducing the scale of the distortion model;
step 2.2, according to the preliminary similarity law S 0 In combination with the determined distortion parameter h, determining a performance parameter sensitive to the distortion parameter: the bending rigidity D, the natural frequency f and the deflection u are shown in the formula (9) according to the corresponding distortion and scale relationship:
7. the power station distortion model-based "performance driven-separation similarity" prediction method according to claim 6, wherein the specific process of step 3 is:
step 3.1, according to the completely similar reduced scale lambda and the partially similar reduced scale delta h Separating distortion parameters;
the distortion parameters are separated according to a completely similar reduced scale lambda:
according to the partially similar scale delta h The distortion parameters are separated, namely:
step 3.2, according to the distortion model m 0 Thickness reduction lambda between prototype and prototype h The method comprises the steps of carrying out a first treatment on the surface of the The thickness of the condensing unit is scaled lambda according to the equal scale to build a completely similar scaled model m 1 The method comprises the steps of carrying out a first treatment on the surface of the At m 1 On the basis of the partially similar reduced scale delta h Only the thickness is reduced to obtain a partial similar model m 2 ；
And 3.3, writing the similar scales of all physical parameters in the similar criteria into a power relation:
wherein alpha is i,j Is thatIs an index of (1) representing X i For X j Is obtained by taking the logarithm of the equation of formula (12) on both sides:
obtaining an index alpha from a first order sensitivity analysis i,j The expression:
wherein X is j,i (1) And X j,i (0) Respectively correspond toAnd->Delta is the increment of the dependent variable similarity scaling, k=1, 2,..r,/-j>At each increment of the change kΔ, the index value α at that time is calculated according to equation (14) i,j (k) The method comprises the steps of carrying out a first treatment on the surface of the Respectively establishing completely similar reduced scale models m according to the formula (14) 1 And a partially similar scale model m 2 Performing simulation analysis on the finite element model to obtain performance parameter simulation data sensitive to distortion parameters;
step 3.4, adopting a power-variable coefficient method to process the simulation data to obtain a full-similarity scale model similarity lawSimilarity law of partial similarity scale model>
8. The power station distortion model-based "performance driven-separation similarity" prediction method according to claim 7, wherein the specific process of step 3.4 is:
defining the exponent alpha according to the exponentiation coefficient method i,j Is thatA power function of (2):
obtaining r group alpha according to formula (14) i,j Is represented by the coefficient gamma in the formula (16) i And beta i Converting to a least squares problem:
solving by using Levenberg-Marquardt algorithm to obtain a plurality of groups of coefficients gamma in a formula (15) i And beta i The index alpha shown in formula (12) is determined i,j The method comprises the steps of carrying out a first treatment on the surface of the Combining the formula (12) to obtain a full-similarity scale model similarity lawSimilarity law of partial similarity scale model>
9. The power station distortion model-based "performance driven-separation similarity" prediction method according to claim 7, wherein the specific process of step 4 is:
obtaining natural frequency f and maximum deflection u of a condensing unit of the spherical condenser of the omega space solar power station according to a formula (12) max Is the predictive equation of:
wherein,respectively represent thickness distortion models m of condensing units 0 With respect to natural frequency f, maximum deflection u between prototypes of concentrator units max Corresponding predictive indices are:
the corresponding y= [ γ ] is obtained according to step 3.4 i ,β i ](i＝1,2,…,4)；
Obtaining a distortion model similarity law by combining the formula (12)The method comprises the following steps:
wherein diag () represents a diagonal matrix.
10. The power station distortion model-based "performance driven-separation similarity" prediction method according to claim 1, wherein the specific process of step 5 is:
establishing a distortion model m 0 Performing simulation analysis on the finite element model to obtain corresponding natural frequencyMaximum deflection
Scaled law according to distortion modelPredicting natural frequency f of prototype P (pre) Maximum deflection u max (pre) As shown in formula (21):
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