CN112115558B - Steam turbine cascade molded line parameterized reconstruction method based on crowd searching algorithm - Google Patents
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Abstract
The invention discloses a steam turbine blade grid profile parameterization reconstruction method based on a crowd search algorithm, which divides a steam turbine blade profile into a front edge arc curve, a tail edge arc curve, a suction side curve and a pressure side curve, and gives coordinate equations of the four curves; obtaining coordinate expressions of polygon control vertexes for describing the pressure side curve and the suction side curve according to the geometric relationship, and obtaining circle center coordinate points of tail edges of front and rear edges; bringing the coordinate points into coordinate equations of four curves to form a parameterized expression of the blade profile; and (3) finding out parameters of the three-time Bezier curve parameterized expression of the prototype blade through an SOA optimization algorithm, and further obtaining the three-time Bezier curve and circular arc curve parameterized expression of the prototype blade profile. The method can realize parameterization expression of the blade profile according to the basic geometrical parameters of the turbine blade, and can be fused with an SOA algorithm to realize intelligent reconstruction of the turbine blade profile, and the method for reconstructing the blade profile has high convergence speed and more stable convergence result.
Description
Technical Field
The invention belongs to the technical field of turbine cascade molded line design, and particularly relates to a steam turbine cascade molded line parameterized reconstruction method based on a crowd searching algorithm.
Background
The turbine blade is a core component for thermal power conversion of thermal power, nuclear power and marine turbines, the current turbine is often operated under extremely variable working conditions, the blade of the turbine blade bears local large steam force impact, flow removal flutter, backflow corrosion, blowing thermal deformation and the like, and certain high-power single-cylinder turbine blades bear the erosion effect of high-humidity steam, so that the performances of the whole turbine, such as efficiency, power, safety, reliability, service life and the like, are directly influenced. Therefore, developing the optimal design of the turbine blade has very important significance for ensuring the economy, the reliability and the safety of the turbine.
The parameterized modeling and the molded line reconstruction of the turbine blade are the core links of the blade optimization design. Geometrical parameters of the turbine blade profile such as camber line, chord length, blade profile bent angle, inlet and outlet blade profile angle, installation angle and the like directly determine the aerodynamic performance and structural strength of the blade, and directly influence the wet steam loss and erosion damage characteristics of the turbine stage of the wet steam area. There are two common methods of blade shaping: (1) Determining a camber line of a blade profile, giving thickness distribution of the blade, and constructing the blade profile through an envelope curve; (2) And selecting control points on the pressure surface and the suction surface of the blade profile, and constructing the blade profile through coordinates or curvature of the points. The blade forming method is difficult to realize parameterized modeling and difficult to apply to blade optimization design.
Disclosure of Invention
The invention aims at overcoming the defects of the technology, and provides a steam turbine cascade molded line parameterization reconstruction method based on a crowd searching algorithm, which has higher profile curve curvature change smoothness, better curve shape control capability, fewer control parameters and is convenient for giving parameterized expressions.
In order to achieve the purpose, the steam turbine cascade line parameterized reconstruction method based on the crowd searching algorithm comprises the following steps:
step one: the turbine blade profile comprises a leading edge arc curve DE, a trailing edge arc curve GH, a suction side curve GD and a pressure side curve HE, coordinate equations of the pressure side curve HE and the suction side curve GD are described based on three-time Bezier curves, the leading edge arc curve DE and the trailing edge arc curve GH are represented by the circular curve equations, and coordinate equations of four curves are given;
step two: determining the intersection point of the string and the forehead lineThe coordinate system origin O is defined, the forehead line is the coordinate system Y axis, the straight line perpendicular to the origin O is the X axis, and the polygon control vertex H, W describing the pressure side curve HE and the suction side curve GD is obtained according to the geometric relationship 1 、W 2 、E、G、U 1 、U 2 D, and the center coordinate point O of the leading edge and the trailing edge 1 And a trailing edge tail edge circle center coordinate point O 2 ；
Will D, E, G, H, U 1 、U 2 、W 1 、W 2 The coordinate points of the four curves in the first step are brought into the coordinate equation of the four curves to form a parameterized expression of the blade profile, and the parameterized expression comprises 8 geometric variables B and gamma p 、r 1 、r 2 、β 1 、β 2 、And 12 parameters composed of 4 Bezier curve shape control variables;
step three: and (3) finding out 12 parameters of the parameterized expression of the cubic Bezier curve of the prototype blade through an SOA optimization algorithm, and further obtaining the parameterized expression of the cubic Bezier curve and the circular arc curve of the prototype blade molded line.
Further, in the first step:
the pressure side curve HE is composed of polygon control vertices H, W 1 、W 2 And E, describing a cubic Bezier curve formed by the components, wherein the coordinate parameter equation is as follows:
the suction side curve GD is composed of polygon control vertexes G, U 1 、U 2 And D, describing a cubic Bezier curve formed by the components, wherein the coordinate parameter equation is as follows:
wherein, t represents the auxiliary parameter of the coordinate parameter equation of the cubic Bezier curve, t E [0,1], x represents the abscissa of the rectangular coordinate system, and y represents the ordinate of the rectangular coordinate system;
the expressions of the leading edge arc curve DE and the trailing edge arc curve GH are expressed by respective circular curve equations, respectively:
(x-x 1 ) 2 +(y-y 1 ) 2 ＝r 1 2
in the formula ,r1 Represents the radius of the arc of the front edge, r 2 Represents the radius of the trailing edge arc, x 1 Is the center o of the front edge arc 1 X, x 2 Is the circle center o of the trailing edge arc 2 Is y 1 Is the center o of the front edge arc 1 Is y 2 Is the circle center o of the trailing edge arc 2 Is defined by the vertical coordinate of (c).
Further, in the second step:
centre of circle O 1 、O 2 The coordinates of (a) are:
the coordinate points of the polygon control vertices D, E, G, H of the pressure side curve HE and the suction side curve GD are:
U 1 、U 2 、W 1 、W 2 the coordinate points are:
in the formula ,xM 、x N The transverse directions of the intersection points M, N of two tangent lines of the cubic Bezier curve in FIG. 1Coordinates k GM 、k HN 、k MD 、k NE Slopes of a tangent GM, a tangent HN, a tangent MD, and a tangent NE of the bezier curve in fig. 1, respectively;
b represents leaf width, gamma p Indicating the angle of installation beta 1 Representing geometric inlet angle beta 2 The geometric steam outlet angle is represented by the formula,representing the leading edge wedge,/->And h (i) (i=1, 2,3, 4) represents 4 Bezier curve shape control parameters.
Further, the specific process of the third step is as follows:
step 1: determining the population scale, the space dimension, the maximum iteration number, the parameter value range of the parameterized expression and the position of an initialized searcher of the searcher population;
step 2: and calculating an fitness function value of each searcher, wherein the fitness function is the mean square error of the function value of the blade profile parameterization equation and the coordinate value of the prototype blade, and the specific expression is as follows:
in the formula ,fmse Is a fitness function; x is x i Is the abscissa, y of the coordinate point of the ith prototype blade i The ordinate of the coordinate point of the ith prototype blade; x is x Bezier (t)、y Bezier (t) is a profile equation parameterized by the blade;is x Bezier An inverse function of (t); />When x=x i A value of time;
step 3: comparing the current fitness value in the individual with the individual extremum, and updating the individual extremum if the current fitness value of the individual is smaller than the individual extremum; then finding out the history optimal extremum of the current population, and if the history optimal extremum is smaller than the global optimal solution, updating the global optimal solution;
step 4: determining the search direction of searcher individual i in jAnd search step a ij (t); wherein, each step t calculates the search direction +.f for each searcher i in each dimension>And search step a ij (t), and a ij (t)≥0，After determining the search direction and the search step length, the search direction and the search step length are determined according to x ij (t+1)＝x ij (t)+Δx ij (t+1)(Δx ij (t+1)＝a ij (t)d ij (t)) updating the position of each searcher, and calculating the fitness value;
step 5: stopping searching if the maximum iteration number or the global optimal fitness value is smaller than the fitness setting precision, otherwise, turning to the step 2;
step 6: and optimizing the blade profile control parameters to obtain the optimal values of 12 parameters of the control blade profile, and further obtaining the cubic Bezier curve and circular arc curve parameterized expression of the prototype blade profile.
Further, the space dimension in the step 1 is the same as the number of parameters of the three-time Bezier curve parameterized expression of the prototype blade.
Further, in the step 1, the maximum iteration number is less than 1000, the four control variable value ranges of the Bezier curve are between 0 and 1, and the position of the initialized searcher is a random number in the 12 parameter ranges.
Further, in the step 4,
the search direction is
The direction of Liji is
The direction of the lithe is
The direction of the pre-movement is
Wherein ω represents an inertial weight,a random number between 0 and 1, sign () being a sign function; />The method is used for searching the historical optimal position of the individual up to the present and searching the collective historical optimal position of the neighborhood of the individual.
Further, in the step 5,
search step a ij (t) is derived from uncertainty reasoning and has the expression:δ ij the Gaussian membership function parameter is;
wherein ,
ω＝(t max -t)/t max
in the formula ,representing the positions of the minimum and maximum function values in the same population; t is the current iteration number, t max Is the maximum number of iterations.
Further, in the step 5, the fitness setting precision is that the global optimal fitness value is smaller than 0.01mm.
Compared with the prior art, the invention has the following advantages: the parameterized reconstruction method of the turbine blade grid profile based on the crowd searching algorithm can realize parameterized expression of the blade profile according to the basic geometrical parameters of the turbine blade, can arbitrarily modify the geometrical parameters of the blade profile to regenerate the blade profile model, is convenient to use, is simple in shape control modification, can be fused with the crowd Searching (SOA) intelligent optimization algorithm to realize intelligent reconstruction of the turbine blade profile, has high convergence speed and more stable convergence result, and lays a solid foundation for intelligent optimization design of the turbine blade; therefore, the invention not only can be used for quick and high-precision molded line reconstruction of the turbine blade, but also can provide powerful support for intelligent optimization design of the turbine through-flow part and the optimization operation of extreme working conditions.
Drawings
FIG. 1 is a three-time Bezier curve depiction of blade geometry and profile;
FIG. 2 is a flow of optimization for leaf pattern reconstruction based on a crowd Search (SOA) algorithm;
FIG. 3 is a Dykas leaf pattern reconstruction based on SOA;
FIG. 4 is a graph of Dykas turbine blade profile as a function of geometric parameters;
fig. 5 is a Dykas leaf profile reconstruction fitness curve based on SOA and PSO.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples.
A steam turbine cascade molded line parameterization reconstruction method based on a crowd searching algorithm comprises the following steps:
step one: the turbine blade profile comprises four curves (see fig. 1) of a leading edge arc curve DE, a trailing edge arc curve GH, a suction side curve GD and a pressure side curve HE, coordinate equations of the pressure side curve H and the suction side curve GD are described based on cubic Bezier (Bezier) curves, the leading edge arc curve DE and the trailing edge arc curve GH are represented by circular curve equations, and the coordinate equations of the four curves are given.
The pressure side curve HE is composed of polygon control vertices H, W 1 、W 2 And E, describing a cubic Bezier curve formed by the components, wherein the coordinate parameter equation is as follows:
the suction side curve GD is composed of polygon control vertexes G, U 1 、U 2 And D, describing a cubic Bezier curve formed by the components, wherein the coordinate parameter equation is as follows:
wherein, t represents the auxiliary parameter of the coordinate parameter equation of the cubic Bezier curve, t E [0,1], x represents the abscissa of the rectangular coordinate system, and y represents the ordinate of the rectangular coordinate system;
the expressions of the leading edge arc curve DE and the trailing edge arc curve GH are expressed by respective circular curve equations, respectively:
(x-x 1 ) 2 +(y-y 1 ) 2 ＝r 1 2
in the formula ,r1 Represents the radius of the arc of the front edge, r 2 Represents the radius of the trailing edge arc, x 1 Is the center o of the front edge arc 1 X, x 2 Is the circle center o of the trailing edge arc 2 Is y 1 Is the center o of the front edge arc 1 Is y 2 Is the circle center o of the trailing edge arc 2 Is the ordinate of (2);
step two: defining the intersection point of the chord line and the forehead line as the origin O of the coordinate system, wherein the forehead line is the Y axis of the coordinate system, and the straight line perpendicular to the origin O of the forehead line is XThe polygon control peak H, W describing the pressure side curve HE and the suction side curve GD can be obtained according to the geometrical relationship of the shaft 1 、W 2 、E、G、U 1 、U 2 D, and the center coordinate point O of the leading edge and the trailing edge 1 And a trailing edge tail edge circle center coordinate point O 2 ；
Centre of circle O 1 、O 2 The coordinates of (a) are:
the coordinate points of the polygon control vertices D, E, G, H of the pressure side curve HE and the suction side curve GD are:
U 1 、U 2 、W 1 、W 2 the coordinate points are:
in the formula ,xM 、x N The abscissa, k, of the intersection M, N of two tangents to the cubic Bezier curve in FIG. 1, respectively GM 、k HN 、k MD 、k NE Slopes of a tangent GM, a tangent HN, a tangent MD, and a tangent NE of the bezier curve in fig. 1, respectively;
b represents leaf width, gamma p Indicating the angle of installation beta 1 Representing geometric inlet angle beta 2 The geometric steam outlet angle is represented by the formula,representing the leading edge wedge,/->Representing trailing edge wedge angle, h (i) (i=1, 2,3, 4) represents 4 Bezier curve shape control parameters;
will D, E, G, H, U 1 、U 2 、W 1 、W 2 The coordinate points of the four curves in the first step are brought into the coordinate equation of the four curves to form a parameterized expression of the blade profile, and the parameterized expression comprises 8 geometric variables B and gamma p 、r 1 、r 2 、β 1 、β 2 、And 12 parameters composed of 4 Bezier curve shape control variables;
step three: 12 parameters of a parameterized expression of a three-time Bezier curve of a prototype blade are found through an SOA optimization algorithm, so that errors of a constructed parameterized model and a blade design line are guaranteed to reach constraint conditions, the flow of the optimization algorithm is shown in a figure 2, and the specific process is as follows:
step 1: determining the population scale, the space dimension (12 parameters of a prototype blade three-time Bezier curve parameterized expression, namely 12 dimensions), the maximum iteration times, the parameter value range of the parameterized expression and the position of an initialized searcher of the searcher population;
the maximum iteration times are less than 1000 times, the value range of four control variables of the Bezier curve is between 0 and 1, and the position of the initial searcher is a random number in 12 parameter ranges;
step 2: and calculating an fitness function value of each searcher, wherein the fitness function is the mean square error of the function value of the blade profile parameterization equation and the coordinate value of the prototype blade, and the specific expression is as follows:
in the formula ,fmse Is a fitness function; x is x i Is the abscissa, y of the coordinate point of the ith prototype blade i Is the ordinate of the coordinate point of the ith prototype blade; x is x Bezier (t)、y Bezier (t) is a profile equation parameterized by the blade;is x Bezier An inverse function of (t); />When x=x i A value of time;
step 3: comparing the current fitness value in the individual with its individual extremum (i.e., fitness value), and updating the individual extremum if the current fitness value of the individual is less than its individual extremum; then finding out the history optimal extremum of the current population, and if the history optimal extremum is smaller than the global optimal solution, updating the global optimal solution;
step 4: determining the search direction of searcher individual i in jAnd search step a ij (t); wherein, each step t calculates the search direction +.f for each searcher i in each dimension>And search step a ij (t), and a ij (t)≥0，After determining the search direction and the search step length, the search direction and the search step length are determined according to x ij (t+1)＝x ij (t)+Δx ij (t+(Δx ij (t+1)＝a ij (t)d ij (t)) updating the position of each searcher, and calculating the fitness value;
the search direction is
The direction of Liji is
The direction of the lithe is
The direction of the pre-movement is
Wherein ω represents an inertial weight,a random number between 0 and 1, sign () being a sign function; />Searching the historical optimal position of the individual up to the present and searching the collective historical optimal position of the neighborhood of the individual;
search step a ij (t) is derived from uncertainty reasoning and has the expression:δ ij the Gaussian membership function parameter is;
wherein ,
ω＝(t max -t)/t max
in the formula ,representing the positions of the minimum and maximum function values in the same population; t is the current iteration number, t max Is the maximum number of iterations.
Step 5: stopping searching if the maximum iteration number or the global optimal fitness value is smaller than the fitness setting precision, otherwise, turning to the step 2;
the adaptability setting precision is that the global optimal adaptability value is smaller than 0.01mm;
step 6: and optimizing the blade profile control parameters to obtain the optimal values of 12 parameters of the control blade profile, and further obtaining the cubic Bezier curve and circular arc curve parameterized expression of the prototype blade profile.
The "+.s" above are X.
By varying any of the 12 parameters described above, different blade profiles can be reconstructed.
Taking Dykas turbine blade as an example, the blade profile is represented by 20 coordinate points of a pressure side and a suction side, wherein the blade width B and the installation angle gamma p Radius r of arc of front and rear edges 1 and r2 Four geometric control variables are known. In order to realize the parameterized design of the turbine blade profile, the process of the invention is still required to complete the optimization solving of the other 8 control parameters of the parameterized expression. The steam turbine cascade profile parameterization reconstruction method based on the crowd search algorithm provided by the invention is used for reconstructing the Dykas steam turbine cascade profile, as shown in figure 3. It can be seen that after the blade design parameters are determined through iterative optimization by the SOA algorithm, the parameterized model curve can be well matched with 20 coordinate points of the suction side and the pressure side, and the accuracy of the reconstructed Dykas blade profile curve meets the requirements. The design parameters for deriving Dykas blade profiles are shown in the following table:
and (4) controlling other variables to be unchanged, and any one geometrical parameter variable is modified to generate a map of the Dykas turbine blade profile along with the geometrical parameters, as shown in figure 4. FIG. 5 shows a Dykas leaf reconstruction fitness curve with iteration number based on a crowd Search (SOA) algorithm and a Particle Swarm (PSO) algorithm, wherein the adaptation convergence value of the SOA is obviously lower than that of the PSO, the convergence accuracy is higher, and the initial convergence speed is high; meanwhile, PSO faces the problem of parameter selection, and SOA only needs to give the scale and the evolution times of the searcher, so that the difficulty of parameter selection does not exist, and the method has great potential in intelligent optimization of leaf type parameters.
Claims (9)
1. A steam turbine cascade molded line parameterization reconstruction method based on a crowd searching algorithm is characterized by comprising the following steps of: the method comprises the following steps:
step one: the method comprises the steps that a turbine blade profile comprises a leading edge arc curve DE, a trailing edge arc curve GH, a suction side curve GD and a pressure side curve HE, coordinate equations of the pressure side curve H and the suction side curve GD are described based on three-time Bezier curves, the leading edge arc curve DE and the trailing edge arc curve GH are represented by the circular curve equation, and coordinate equations of four curves are given;
step two: defining the intersection point of the chord line and the forehead line as the origin O of the coordinate system, wherein the forehead line is the Y axis of the coordinate system, the straight line perpendicular to the origin O of the forehead line is the X axis, and obtaining polygon control vertexes H, W describing the pressure side curve HE and the suction side curve GD according to the geometric relationship 1 、W 2 、E、G、U 1 、U 2 D, and the center coordinate point O of the leading edge and the trailing edge 1 And a trailing edge tail edge circle center coordinate point O 2 ；
Will D, E, G, H, U 1 、U 2 、W 1 、W 2 The coordinate points of the four curves in the first step are brought into the coordinate equation of the four curves to form a parameterized expression of the blade profile, and the parameterized expression comprises 8 geometric variables B and gamma p 、r 1 、r 2 、β 1 、β 2 、And 12 parameters composed of 4 Bezier curve shape control variables;
step three: and (3) finding out 12 parameters of the parameterized expression of the cubic Bezier curve of the prototype blade through an SOA optimization algorithm, and further obtaining the parameterized expression of the cubic Bezier curve and the circular arc curve of the prototype blade molded line.
2. The steam turbine cascade line parameterized reconstruction method based on the crowd searching algorithm of claim 1, wherein the method comprises the following steps: in the first step:
the pressure side curve HE is composed of polygon control vertices H, W 1 、W 2 And E, describing a cubic Bezier curve formed by the components, wherein the coordinate parameter equation is as follows:
the suction side curve GD is composed of polygon control vertexes G, U 1 、U 2 And D, describing a cubic Bezier curve formed by the components, wherein the coordinate parameter equation is as follows:
wherein, t represents the auxiliary parameter of the coordinate parameter equation of the cubic Bezier curve, t E [0,1], x represents the abscissa of the rectangular coordinate system, and y represents the ordinate of the rectangular coordinate system;
the expressions of the leading edge arc curve DE and the trailing edge arc curve GH are expressed by respective circular curve equations, respectively:
(x-x 1 ) 2 +(y-y 1 ) 2 ＝r 1 2
in the formula ,r1 Represents the radius of the arc of the front edge, r 2 Represents the radius of the trailing edge arc, x 1 Is the center o of the front edge arc 1 X, x 2 Is the circle center o of the trailing edge arc 2 Is y 1 Is the center o of the front edge arc 1 Is y 2 Is the circle center o of the trailing edge arc 2 Is defined by the vertical coordinate of (c).
3. The steam turbine cascade line parameterized reconstruction method based on the crowd searching algorithm of claim 1, wherein the method comprises the following steps: in the second step,:
centre of circle O 1 、O 2 The coordinates of (a) are:
the coordinate points of the polygon control vertices D, E, G, H of the pressure side curve HE and the suction side curve GD are:
U 1 、U 2 、W 1 、W 2 the coordinate points are:
in the formula ,xM 、x N The abscissa, k, of the intersection M, N of two tangents to the cubic Bezier curve in FIG. 1, respectively GM 、k HN 、k MD 、k NE Slopes of a tangent GM, a tangent HN, a tangent MD, and a tangent NE of the bezier curve in fig. 1, respectively;
b represents leaf width, gamma p Indicating the angle of installation beta 1 Representing geometric inlet angle beta 2 The geometric steam outlet angle is represented by the formula,representing the wedge angle of the front edge,And h (i) (i=1, 2,3, 4) represents 4 Bezier curve shape control parameters.
4. The steam turbine cascade line parameterized reconstruction method based on the crowd searching algorithm of claim 1, wherein the method comprises the following steps: the specific process of the third step is as follows:
step 1: determining the population scale, the space dimension, the maximum iteration number, the parameter value range of the parameterized expression and the position of an initialized searcher of the searcher population;
step 2: and calculating an fitness function value of each searcher, wherein the fitness function is the mean square error of the function value of the blade profile parameterization equation and the coordinate value of the prototype blade, and the specific expression is as follows:
in the formula ,fmse Is a fitness function; x is x i Is the abscissa, y of the coordinate point of the ith prototype blade i Is the ordinate of the coordinate point of the ith prototype blade; x is x Bezier (t)、y Bezier (t) is a profile equation parameterized by the blade;is x Bezier An inverse function of (t);when x=x i A value of time;
step 3: comparing the current fitness value in the individual with the individual extremum, and updating the individual extremum if the current fitness value of the individual is smaller than the individual extremum; then finding out the history optimal extremum of the current population, and if the history optimal extremum is smaller than the global optimal solution, updating the global optimal solution;
step 4: determining the search direction of searcher individual i in jAnd search step a ij (t); wherein, each step t calculates the search direction +.f for each searcher i in each dimension>And search step a ij (t), and a ij (t)≥0，/>After determining the search direction and the search step length, the search direction and the search step length are determined according to x ij (t+1)＝x ij (t)+Δx ij (t+(Δx ij (t+1)＝a ij (t)d ij (t)) updating each searcher's position, calculatingA fitness value;
step 5: stopping searching if the maximum iteration number or the global optimal fitness value is smaller than the fitness setting precision, otherwise, turning to the step 2;
step 6: and optimizing the blade profile control parameters to obtain the optimal values of 12 parameters of the control blade profile, and further obtaining the cubic Bezier curve and circular arc curve parameterized expression of the prototype blade profile.
5. The steam turbine cascade line parameterized reconstruction method based on the crowd searching algorithm of claim 4, wherein the method comprises the following steps: and the space dimension in the step 1 is the same as the number of parameters of the three Bezier curve parameterized expressions of the prototype blade.
6. The steam turbine cascade line parameterized reconstruction method based on the crowd searching algorithm of claim 4, wherein the method comprises the following steps: in the step 1, the maximum iteration number is less than 1000, the four control variable value ranges of the Bezier curve are between 0 and 1, and the position of the initialized searcher is a random number in 12 parameter ranges.
7. The steam turbine cascade line parameterized reconstruction method based on the crowd searching algorithm of claim 4, wherein the method comprises the following steps: in the step 4 of the above-mentioned process,
the search direction is
The direction of Liji is
The direction of the lithe is
The direction of the pre-movement is
Wherein ω represents an inertial weight,a random number between 0 and 1, sign () being a sign function; />The method is used for searching the historical optimal position of the individual up to the present and searching the collective historical optimal position of the neighborhood of the individual.
8. The steam turbine cascade line parameterized reconstruction method based on the crowd searching algorithm of claim 4, wherein the method comprises the following steps: in the step 5 of the above-mentioned process,
search step sizeDerived from uncertainty reasoning, the expression is: />δ ij The Gaussian membership function parameter is;
wherein ,
ω＝(t max -t)/t max
in the formula ,representing the positions of the minimum and maximum function values in the same population; t is the current iteration number, t max Is the maximum number of iterations.
9. The steam turbine cascade line parameterized reconstruction method based on the crowd searching algorithm of claim 4, wherein the method comprises the following steps: in the step 5, the fitness setting precision is that the global optimal fitness value is smaller than 0.01mm.
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