CN111783232B - Recyclable rocket return section self-adaptive optimization method based on cluster analysis - Google Patents
Recyclable rocket return section self-adaptive optimization method based on cluster analysis Download PDFInfo
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Abstract
The invention discloses a self-adaptive optimization method of a returnable rocket return section based on cluster analysis, which comprises the following steps: establishing a return track optimization problem model of a sub-level return section; solving a state transition matrix of the tail end constraint variable relative to the design variable; carrying out sensitivity division on data elements in the state transition matrix by using a clustering algorithm, and screening out data elements with higher sensitivity to form a state transition matrix M; screening linear constraint variables, linear design variables and corresponding linear state transition matrixes from M according to a set linearity criterion, and screening nonlinear constraint variables and nonlinear design variables from M; aiming at the linear parameters and the nonlinear parameters, different optimization methods are respectively utilized to obtain the optimal design variable values. The method can effectively process the complex landing constraint problem, has higher precision, convergence and calculation efficiency, reduces the dimensionality and complexity of the parameter space of the return section optimization problem, and has good adaptivity and expansibility.
Description
Technical Field
The invention belongs to the field of spacecraft flight control, and particularly relates to a recoverable rocket return section self-adaptive optimization method based on cluster analysis.
Background
In recent years, with the arrival of the commercial aerospace era, the vertical take-off and landing technology of the recoverable carrier rocket has become a research hotspot in the international aerospace field. At present, the vertical take-off and landing technology has become a feasible and most promising recyclable launch vehicle technology, which greatly reduces the cost of the launch mission of the spacecraft. The optimal track design of a first-sub-stage return section (hereinafter referred to as a return section) of the whole carrier rocket is used as a core key technology for vertical take-off and landing, is a systematic and integral track optimization problem, has mutual coupling and cross-linking relations among various complex constraints and design variables, and has very high requirement on landing precision.
The return section is an important basis for the whole detector orbit design and rocket overall design, comprises a plurality of flight sections, and has the advantages of high reentry speed, complex return process, large range and speed span, obvious flight environment change and strong disturbance factors of various factors. The return section track optimization not only needs to ensure the high-precision stable landing of the tail end, but also needs to comprehensively consider the constraints of dynamic pressure, overload, heat flux density, engine performance, tail end landing position, speed, attitude and the like of each flight section, so that relevant research needs to be carried out on the nonlinear problems of high-dimensional constraints and design variables under the multiple flight sections. Such systematic and global trajectory optimization problems need to be considered simultaneously and satisfied under a unified model, and should not be handled in a single stage. In summary, multi-phase synchronized planning is a key direction for future research. In recent years, many scholars at home and abroad respectively propose own optimization design methods for the optimization problem of the returnable carrier rocket return section, but most of the scholars have one of the following problems:
(1) the model is ideal and does not accord with the actual flight condition of the whole return track of the first sublevel of the carrier rocket;
(2) research is mainly focused on a single flight segment, namely a vertical landing segment;
(3) the first-level flight time is short, the design variables and the constraint variables considered are few, the adjusting capacity is limited, and the requirement of returning to the optimal track of a plurality of flight sections in the whole process cannot be met;
(4) the optimization problem needs to be reconstructed by combining a relevant algorithm aiming at different return tasks or different flight sections, the derivation process is complex, and the calculation is complex;
(5) adaptive optimization of the return trajectory and automatic allocation of the algorithm cannot be achieved.
Under high-dimensional parameter space (parameter space formed by complex constraint and design variables) and high dynamics, the traditional optimization method cannot meet the requirements from the aspects of precision, efficiency, optimality, adaptability and the like, and the situation of non-convergence is easy to occur, so that the self-adaptive trajectory optimization method which is more accurate and has stronger applicability needs to be developed.
Disclosure of Invention
The invention aims to provide a recoverable rocket return section self-adaptive optimization method based on cluster analysis aiming at the defect that the traditional optimization method cannot meet the optimization problem of the recoverable rocket return section from the aspects of precision, efficiency, optimality, adaptability and the like, can effectively process the complex landing constraint problem, has higher precision, convergence and calculation efficiency, reduces the dimensionality and complexity of the parameter space of the optimization problem of the return section, and has good adaptivity and expansibility.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a recoverable rocket return section self-adaptive optimization method based on cluster analysis comprises the following steps:
step 1, establishing a return track optimization problem model of a sub-level return section; the optimization problem model comprises flight segment division information, design variable information and constraint variable information of a return segment; wherein the constraint variable information comprises design variable constraint information, process constraint variable information and terminal constraint variable information;
the method is characterized by further comprising the following steps:
step 3, carrying out sensitivity division on data elements in the state transition matrix by using a clustering algorithm, and identifying and dividing data elements with higher sensitivity from the state transition matrix according to design requirements to form a state transition matrix M after preliminary dimension reduction;
step 4, screening linear constraint variables, linear design variables and corresponding linear state transition matrixes from the M according to a set linearity criterion, and screening nonlinear constraint variables and nonlinear design variables from the M;
step 5, aiming at the linear constraint variable, the linear design variable and the corresponding linear state transition matrix, the optimal design variable value is obtained by utilizing a linear search algorithm; aiming at nonlinear constraint variables and nonlinear design variables, the optimal design variable value is obtained by utilizing a direct optimization method in a nonlinear optimization method.
As a preferable mode, the step 1 includes the steps of:
step 11, dividing a return section into four flight sections, namely an attitude adjusting section, a power deceleration section, an atmosphere reentry section and a vertical landing section;
step 12, establishing a three-degree-of-freedom kinetic equation of a sub-level return track;
and step 13, determining an objective function, design variable information and constraint variable information of the sub-level track optimization.
As a preferred mode, the three-degree-of-freedom kinetic equation established in step 12 is:
wherein, x, y and z are respectively the coordinates of a sublevel in the x direction, the y direction and the z direction of the emission coordinate system; v is a sub-level velocity value; θ is the velocity dip of a sub-stage; σ is a yaw angle of one sub-order; m is a sub-level current quality;
the rates of change of x, y, z, V, theta, sigma and m respectively; r is the radius of the earth; r is the geocentric distance; p is the rated thrust of the engine on a sub-stage; epsilon n Is a variable thrust factor and is not less than 0 epsilon n Not more than 1, when n is 0, epsilon n Is the variable thrust factor of the power deceleration section, and is epsilon when n is 1 n A variable thrust factor for the vertical landing segment; i is sp Is the engine specific impulse; g is a radical of formula 0 Is sea level gravitational acceleration; g r ＝-μ/r 2 Mu is the gravitational constant; α is the angle of attack of one sub-step; beta is a sub-step sideslip angle; x q 、Y q 、Z q The aerodynamic force components of a sub-stage in the x direction, the y direction and the z direction of the speed coordinate system are respectively.
As a preferred mode, the objective function determined in step 13 is expressed by the following formula: min j ═ m (t) f ) Where J is the objective function, t f M (t) for landing time f ) Is the quality of a sub-level at the time of landing.
As a preferable mode, the design variable information determined in step 13 is:
X s ＝[t 1 t 2 t 3 t 4 α 1 α 2 β 1 β 2 ε 1 ε 2 ] T ，
wherein, X s For designing matrices of variables, t 1 Is the sliding time of a sub-level in the posture adjusting section, t 2 Is the flight time of a sub-stage in the dynamic deceleration section, t 3 Time of flight, t, for a sub-stage in the atmospheric reentry phase 4 Time of flight, α, for a sublevel in a vertical landing stage 1 Is the angle of attack, alpha, of a sub-stage in the power reduction section 2 Angle of attack, beta, of a sub-stage in a vertical landing leg 1 Is the sideslip angle, beta, of a sub-stage in the power reduction section 2 Is the sideslip angle, ε, of a sublevel in the vertical landing zone 1 Is an engine thrust factor, epsilon, of one sub-stage in the power reduction section 2 Is the engine thrust factor for a sub-stage at the vertical landing stage.
Preferably, the design variable constraint information includes angle of attack constraint information, sideslip angle constraint information, and engine thrust constraint information.
Preferably, the process constraint variable information includes one or more of a dynamic pressure limit condition, an overload limit condition, a startup ignition time interval condition of an engine connected with two power sections, and a terminal landing quality limit condition of a sub-stage.
As a preferable mode, the end constraint variable information includes: within the set precision range, the position of a sub-level landing reaches the designated position, the speed of the sub-level landing reaches the designated speed, and the posture of the sub-level landing is vertical.
As a preferable mode, in the step 3, a K-means clustering algorithm is adopted to perform sensitivity division on data elements in the state transition matrix.
As a preferred mode, when the K-means clustering algorithm is executed, the clustering center is initialized according to data experience returned to the task model in a sub-level mode.
Compared with the prior art, the method can effectively process the complex landing constraint problem, has higher precision, convergence and calculation efficiency, reduces the dimensionality and complexity of the parameter space of the return section optimization problem, and has good adaptivity and expansibility.
Drawings
FIG. 1 is a cross-sectional view of the return flight.
FIG. 2 is a flow chart of the present invention.
Fig. 3 is a graph of an optimization iteration process.
FIG. 4 is a cross-sectional comparison of the main parameters.
Detailed Description
The overall technical idea of the method is as follows:
firstly, a problem model which returns multiple flight sections, multiple constraints and multiple variables is established. Then, an adaptive optimization algorithm is provided through parameter characteristic analysis: solving a high-dimensional parameter space state transition matrix of the terminal constraint variable relative to the design variable, wherein the high-dimensional parameter space state transition matrix describes the sensitivity of the terminal constraint variable relative to the perturbation of the design variable; carrying out sensitivity division on data elements in the state transition matrix through a K-means clustering algorithm, screening out a linear constraint variable, a linear design variable and a linear state transition matrix according to a set linearity criterion, and screening out a nonlinear constraint variable and a nonlinear design variable; and finally, automatically distributing different optimization algorithms according to the linear and nonlinear characteristics of different parameters.
The invention is described in detail below with reference to the accompanying drawings:
1-Return multi-flight segment model establishment
A partitioning model of a sub-level return multi-flight section, a return trajectory dynamics model and an optimization problem model under multivariable multi-constraint are established.
1.1 one-substage Return Multi-flight segment partitioning
The trajectory optimization problem studied by the invention is only directed to the recovery process of a sub-stage of the launch vehicle, and therefore the ascension stage is not considered. The first-level return recovery comprises two modes of returning to an original field and not returning to the original field. After a typical first-level flight without returning to the original field is completed in the ascending stage, the returning process usually goes through a plurality of flight stages such as an attitude adjusting stage, a high-altitude reentry stage, a dynamic deceleration stage, an atmospheric reentry stage and a vertical landing stage. The return segment division also differs for different flight missions. Considering that the attitude adjusting section and the sliding section are basically outside the dense atmosphere, the pneumatic influence can be ignored, the attitude adjusting section is also in unpowered sliding, and the attitude is adjusted by a reverse thrust control system, so that the two flight sections are only influenced by the attractive force. The invention simplifies a return section division model, and divides the return section into four flight sections, namely an attitude adjusting section, a power deceleration section, an atmosphere reentry section and a vertical landing section. The return flight profile is shown in fig. 1.
1.2 establishment of kinetic model
When the mass center motion of the carrier rocket in the first-sub-level return process is researched, a three-degree-of-freedom kinetic equation of the first-sub-level return track is deduced without considering the control and adjustment process of the attitude and the autorotation motion of the earth, and is expressed by the following differential equation set:
wherein, x, y and z are respectively the coordinates of a sublevel in the x direction, the y direction and the z direction of the emission coordinate system; v is a sub-level velocity value; θ is the velocity dip of a sub-stage; σ is a yaw angle of one sub-step; m is a sub-level current quality;
the rates of change of x, y, z, V, theta, sigma, m, respectively; r is the radius of the earth; r is the geocentric distance; p is the rated thrust of the engine on a sub-stage; epsilon n The n-th powered flight section (powered here refers to the thrust provided by the engine, the powered deceleration section is the first powered flight section, the vertical landing section is the second powered flight section, and the other two flight sections are unpowered) of the return section and the epsilon is more than or equal to 0 n Epsilon is not more than 1, n is 0 n Is the variable thrust factor of the power deceleration section, and is epsilon when n is 1 n A variable thrust factor for the vertical landing segment; i is sp Is the engine specific impulse; g 0 Is HaipingSurface acceleration of gravity; g r ＝-μ/r 2 Mu is the gravitational constant; α is the angle of attack of one sub-step; beta is a sub-step sideslip angle; x q 、Y q 、Z q The aerodynamic force components of a sub-stage in the x-direction, the y-direction and the z-direction of the velocity coordinate system are respectively.
X q 、Y q 、Z q The definition is as follows:
in the formula, S M A reference area (constant) for a first sublevel feature of the launch vehicle; p is the local atmospheric density of the earth,
ρ 0 is sea level atmospheric density, h 0 Is a reference height (constant); c x 、C y 、C z Respectively drag, lift and lateral force coefficients, and C z ＝-C y Defined as follows:
in the formula, C x0 、
Is a constant.
1.3 optimization problem description
And the sub-stage return segment trajectory optimization refers to adjusting each design variable to enable the aircraft to meet flight process constraints and to softly land at a set landing point by taking the minimum fuel consumption as a target.
1.3.1 objective function
In order to optimize the launch capacity of the launch vehicle and to have enough fuel for the guidance and correction maneuver, the performance index of the whole process of a sub-stage return section is the minimum fuel consumption, namely the maximum end landing quality, so the objective function of the trajectory optimization is
minJ＝-m(t f ) (4)
Where J is the objective function, t f M (t) for landing time f ) Is the quality of a sub-level at the time of landing.
1.3.2 design variables
Design variables of each flight segment:
adjusting the posture section: unpowered sliding is realized, the attack angle is adjusted to 0 degrees by a reverse thrust control system so as to meet the ignition attitude requirement of an engine, and the design variables are as follows: coasting time t 1 。
A power deceleration section: the engine is started to decelerate, the speed of the engine entering the atmosphere again is reduced, the attack angle and the sideslip angle are controlled simultaneously, and main design variables are as follows: time of flight t 2 Thrust factor epsilon of engine 1 Angle of attack alpha 1 Angle of sideslip beta 1 。
An atmosphere reentry section: the flight is designed according to an attack angle of 0 degrees in the stage, pneumatic deceleration is completely adopted, and the design variables are as follows: time of flight t 3 。
Vertical landing segment: the secondary ignition of the engine starts the engine to decelerate to a first-level landing, and the main design variables are as follows: time of flight t 4 Thrust factor epsilon of engine 2 Angle of attack alpha 2 Angle of sideslip beta 2 。
The flight time of each flight segment and the thrust coefficients of the dynamic deceleration segment and the vertical landing segment can be obtained by direct optimization. The attack angle and the sideslip angle of the dynamic deceleration section and the vertical landing section are optimized by designing discrete points, and the attack angle and the sideslip angle can be obtained by a linear interpolation method between the discrete points. The program expressions of the attack angle and the sideslip angle of the power deceleration section are as follows:
the program expressions of the attack angle and the sideslip angle of the vertical landing segment are as follows:
according to the designed flight program, the following variables are selected as design variables:
X s ＝[t 1 t 2 t 3 t 4 α 1 α 2 β 1 β 2 ε 1 ε 2 ] T (7)
1.3.3 constraints
A sub-stage may be limited in the return process by various complex constraints, including mainly design variable constraints, process constraints, and precision landing constraints.
(1) Controlling constraints
The control constraints mainly include angle of attack, sideslip angle, and engine thrust constraints.
In the formula, p is 1,2,3 and 4 respectively represent an attitude adjusting section, a power descending section, an atmosphere reentry section and a vertical landing section.
The minimum and maximum values of the angle of attack, sideslip angle and thrust of each flight segment, respectively.
Is a variable in the amount of time,
respectively, the start time and the end time of each flight segment.
Is shown in the time interval
With a continuous first derivative.
(2) Process constraints
The return process needs to take into account dynamic pressure and overload limits.
In the formula,
is the thrust component under the velocity system; n is max The maximum overload that the arrow body can bear; q. q.s max The upper dynamic pressure limit.
Meanwhile, in consideration of the working performance of the engine, the starting ignition time of the engine in two adjacent power sections needs to have a certain interval
Δt≥Δt min (10)
In the formula,. DELTA.t min The lower limit of the engine shutdown ignition time interval of two adjacent power sections.
In addition, a sub-stage has undergone multiple flight phases before landing in the vertical landing zone, with limited propellant remaining to ensure that the tip landing mass is greater than the structural mass
m(t f ) (p＝4) ≥m dry (11)
In the formula, m dry Is a sub-level structural mass, namely the lower limit of the residual mass in the flight process.
The connection condition between each flight segment is
(3) Tip precision landing constraint
The landing of the tail end of the vertical landing segment requires that the position and the speed of a sub-level are required to reach the specified target and precision, and the posture of the vertical landing segment is ensured to be vertical. In the research of the invention, geodetic longitude, geodetic latitude and altitude are adopted as terminal position constraints, relative speed is used as speed constraint, and ballistic inclination is used as attitude constraint.
In the formula of lambda f ,B f ,H f ,V f ,θ f Respectively calculating the geodetic longitude, the geodetic latitude, the altitude, the relative speed and the ballistic inclination angle of the landing point by ballistic integral; lambda [ alpha ] f ,B f ,H f ,V f ,θ f Respectively including geodetic longitude, geodetic latitude, altitude, relative speed and trajectory inclination of a target landing point; zeta λ ,ζ B ,ζ H ,ζ V ,ζ θ Respectively the corresponding tip landing accuracy.
For convenience of representation, the process inequality constraint is denoted as F and the terminal precise landing constraint is denoted as G in the following study f ＝[λ f -λ f ,B f -B f ,H f -H f ,V f -V f ,θ f -θ f ] T 。
2 Algorithm design
Under the condition of considering various complex constraints and design variables, a self-adaptive optimization algorithm strategy is provided, namely an algorithm distribution strategy based on cluster analysis. The high-dimensional parameter space state transition matrix obtained by finite difference approximation is further processed, high-sensitivity data elements in the matrix and corresponding design variables are automatically identified and divided through a clustering analysis method, then the terminal constraint variables and the design variables are divided into linear parameters and nonlinear parameters through a linearity criterion, and finally different optimization algorithms are distributed to the linear parameters and the nonlinear parameters. The algorithm is simple in logic, the dimensionality of the high-dimensional parameter space optimization problem is reduced, and self-adaptive distribution of the optimization algorithm is achieved. For specific details, see the following sections.
2.1 high-dimensional parametric space state transition matrix solution
For optimization problems in a high-dimensional parameter space, it is necessary to analyze the main design variables that affect the end-constraint variables. Each element in the state transition matrix represents the sensitivity of the constraint variable to the perturbation of the design variable, so that the elements in the state transition matrix are subjected to parameter identification to obtainInfluencing a constraint variable
Varying principal design variables
Thereby through adjustment
So that
Aiming at a predetermined target.
To make the problem generic, design variables are taken into account
Constraint of equality
(n is 10, m is 5 in the optimization problem model of the invention), and a nonlinear functional relationship exists between the n and the m
G f ＝f(X s ,t) (14)
The state transition matrix between the end constraint and the design variable is
In the formula,
represents X s The corresponding design variables in (1);
to end constraint G f For design variable X s The state transition matrix of (a), describes the sensitivity of the constraint variables to perturbation of the design variables. At present, two common methods are used for solving the state transition matrix, one is to calculate the display expression of the state transition matrix, and the display expression is in the area of the track productSynchronously solving in a center division manner; and the other method adopts a numerical difference method to approximately solve. A sub-level return section dynamic model is complex, and the terminal constraint and the design variable have no displayed functional relation, so that the analytic form of a state relation matrix cannot be obtained. The invention adopts finite difference approximate formula to solve in the calculation
The respective elements of (a):
when the calculation is performed by the expression (16),
is composed of
If the deviation is too large, convergence and calculation accuracy are affected, if the deviation is too small, calculation errors are caused, and according to numerical simulation experience, a small deviation (1% in the invention) between 0.1% and 1% of design variable intervals is generally adopted. Thus, the state transition matrix can be obtained by numerical simulation calculation.
2.2 Cluster analysis of State transition matrix data elements
For different return tasks, the state transition matrix changes due to changes of flight segment tasks or design variables, so that a method capable of automatically identifying matrix elements is necessary, and manual participation can be avoided. The cluster analysis is an important data analysis method in statistics and is widely applied to the fields of pattern recognition, machine learning, data analysis, image processing and the like; the data are automatically divided into a plurality of clusters according to a certain similarity measurement criterion, the whole division is an unsupervised process, and finally the data similarity in the same cluster is enabled to be as high as possible and the data among the clusters are separated as independent as possible. The invention adopts a classic K-means clustering algorithm to cluster the data elements in the state transition matrix. The clustering process of the K-means clustering algorithm on the matrix data elements is briefly introduced below by combining the state transition matrix in the high-dimensional parameter space.
(1) First, the state is transferred to the matrix
The element in (1) is subjected to min-max standardization, and the original element data is subjected to linear transformation to enable the result to fall into [0, 1%]In the interval, if the normalized matrix is A, the corresponding element in A is
(2) In the parameter space
In (1), let normalized matrix A ═ A 1 ,...,A i ,...,A m ] T Each A is known i Containing n data elements, i.e. A i ＝(A i1 ,...,A ij ,...,A in ) The data elements need to be classified into p classes. In the research of the invention, data elements are divided into two types, namely a high-sensitivity parameter and a low-sensitivity parameter, the initial iteration frequency is set as b to be 0, and two clustering centers are selected for initialization
(3) For A i Solving Euclidean distances from any data element to p cluster centers:
in A i Center and cluster center
Data elements that are close together are grouped into corresponding clusters, i.e. if
Just holdA ij Division into clusters
In (1).
(4) Computing new cluster centers from data elements in each cluster
Wherein A is ij Is a class
Data element of (1), N p Is as
The number of data elements in the list.
(5) When in use
And (4) time-lapse representing algorithm convergence, namely, the value of the clustering center is kept unchanged after iterative updating, and epsilon is an iteration stop threshold. Otherwise, let b be b +1, go to step (3), and continue the iteration.
The K-means clustering algorithm is simple and efficient, is easy to realize, and simulation shows that the K-means clustering algorithm can be iterated to a convergence value for 5-10 times. However, research shows that the selection of the clustering center influences the convergence and efficiency of clustering, and the random selection of the initial clustering center also brings great uncertainty to the algorithm. Therefore, when the state transition matrix is subjected to cluster division, the accuracy of the parameter sensitivity clustering result can be improved by reasonably selecting the clustering center. The method is based on prior information guidance, a clustering center is initialized according to a large number of data experiences of a sub-level returned task model, the clustering effect at the initial stage of iteration is improved, data elements are guided to be accurately clustered, and meanwhile constraint is reasonably applied in the clustering process to improve the clustering performance.
At this moment, high-sensitivity data elements in the state transition matrix are automatically screened out through clustering analysis, and therefore local intervals are obtained
The main design variables affecting the constraint variables in the range, denoted
And the preliminary dimension reduction of the problem model is realized. Recording the state transition matrix after the preliminary dimension reduction as M, then
In the formula,
to represent
The corresponding design variables in (1); p is a radical of n The number of variables, and p, is designed for the post-clustering principal n ＜n，
Next, the variables will be designed
And calculating a change value of the output constraint variable when the design variable is changed in the design interval by using a shooting method as input, wherein a corresponding change matrix is defined as a difference matrix and is marked as N. Dividing the element in the matrix N by the element at the corresponding position of M to obtain a matrix C, wherein C is the number of the elements ik ＝N ik /M ik Wherein the meaning of each element is a multiple of the change of the end constraint variable as the design variable changes within the design interval and the local interval. Deviation in the present invention
A design interval of 1% of design variables is taken, namely, the local deviation is expanded by 100 times to the design interval. Define the linearity index l (in the present study, linearity indexThe symbol l ═ 0.9,1.1]X 100), if the position of the high-sensitivity data element obtained by the cluster analysis is within the range of the linear index of the value of the corresponding main element in C, it indicates that a global linear relationship exists between the design variable and the constraint variable corresponding to the main data element, so that the linear parameters existing in the design variable and the constraint variable and the corresponding linear state transition matrix (marked as Q) can be screened out, thereby decoupling the linear parameters from the nonlinear parameters is realized, and the dimension reduction is performed on the optimization problem again.
2.3 optimization problem reconstruction and optimization Algorithm adaptive Allocation
Through the clustering analysis, the sensitivity and the linearity of the parameters are automatically classified, the parameter decoupling of the terminal constraint variable and the design variable is realized, and the complexity and the dimensionality of the optimization problem are reduced. Then, according to the linear and nonlinear characteristics of the parameters, the corresponding optimization algorithm can be allocated to the self-adaptation. Recording design variables
Wherein,
the variables are designed for the linear parameters,
and optimizing design variables for the nonlinear parameters after dimension reduction. Constraint of memory equation
Wherein,
the variables are constrained for the linear parameters and,
and (5) constraining variables for the tail ends of the nonlinear parameters after dimension reduction. For linear parameters, there are linear search algorithms such as newton iteration, quasi-newton iteration, differential correction methods, etc. Notably, the linear search algorithm can enhance the solution in the optimizationThe robustness of. The invention adopts a differential correction method to carry out iterative solution, which is essentially a Newton iterative approach expectation value algorithm, namely an iterative target practice method, and the constraint variables are finally converged to the expectation value by continuously adjusting the design variables, so that the method has sufficient adaptability and robustness. Through the analysis of sensitivity and linearity
Relative to X 1s Linear state transition matrix Q of
To be generic, the constraint variables are solved using a least squares strategy
And iterative design variables
Under the condition of unequal degrees of freedom, and increasing the iteration factor mu increases the precision and convergence of the iteration, then
Wherein mu is an iteration factor, and mu is more than 0 and less than or equal to 1. It is worth noting that theoretically, parameters with strict linear relation can be converged to expected values through one iteration, the defined linear parameters are measured through the linearity index l and are not strict linear, and simulation shows that the constraint variables need to be iterated for 5-10 times when converging to the expected accuracy.
For nonlinear design variables after dimensionality reduction
The method can be optimized by direct optimization method such as Sequence Quadratic Programming (SQP), interior point method, pseudo-spectral method, etc., so as to make nonlinear terminal constraint variable
Constraint of sum inequality
Convergence to the required accuracy, objective function
Can pass through the pair
Differential iterative correction sum pair
And optimizing and searching to obtain the optimal index. The invention optimizes the original optimization problem through a Genetic Algorithm (GA) to obtain an initial value solution.
2.4 algorithm summary
The general flow of the invention is shown in fig. 2, and mainly comprises three aspects of state transition matrix solving, cluster analysis, problem reconstruction and algorithm distribution; the three parts are progressive layer by layer, the state transition matrix is an algorithm basis, the clustering analysis is a core link, and the problem reconstruction and the algorithm distribution are key parts.
The self-adaptive optimization algorithm starts from the solution of a state transition matrix, high-sensitivity data elements in the matrix are identified and extracted through a clustering analysis algorithm, then linear analysis is further carried out by combining a difference matrix, linear and nonlinear parameters are accurately identified and analyzed to obtain a linear state transition matrix, and finally different optimization algorithms are distributed according to different parameter characteristics. It is worth noting that once the flight segment is divided, the number of the design variables and the design variable interval are determined, the linear state transition matrix is a constant matrix, and does not need to be updated in the differential correction calculation process, so that the operation efficiency is greatly improved. In a word, the algorithm has the greatest advantages that manual participation is not needed in the whole process, the algorithm is simple and efficient, and automatic identification and classification of parameters and automatic allocation of the optimization algorithm can be accurately realized.
3 simulation verification
Calculating a state transition matrix according to a finite difference approximation formula
The state transition matrix min-max is then normalized to obtain the normalized matrix A, as shown in Table 1. Performing cluster analysis on the data elements in A to obtain high-sensitivity elements, as shown by the rough oblique elements in A, corresponding to the elements in the state transition matrix in Table 1
Shown in bold diagonal elements. And analyzing the sensitivity of the constraint variables to the design variables to obtain main design variables influencing the constraint variables, namely the design variables corresponding to the rough diagonal elements.
It can be seen that within the local deviation range, the terminal landing longitude λ is affected f The main design variable of the variation is the sideslip angle beta of the power-down section 1 Affecting the terminal landing latitude B f The main design variable that varies is the time of flight t of the attitude adjustment segment 1 Affecting tip landing height H f The main design variables of the change are the flight time t of the attitude adjusting section and the atmosphere reentry section 1 、t 3 Influencing tip landing velocity V f The main design variable that varies is the time of flight t of the vertical landing leg 4 And thrust factor ε 2 Affecting tip landing velocity dip theta f The main design variable that varies is the time of flight t of the vertical landing leg 4 Wherein t is 1 And t 4 Is a coordinated control variable, t 1 While being the main control variables for B and H, t 4 While being the main control quantities for V and theta.
TABLE 1 State transition matrix and corresponding normalization matrix
The clustering analysis described above yields the main design of the variables that affect the end constraintVariables of
And a state transition matrix M after preliminary dimension reduction, will
As input, using a target practice calculation
And outputting the change value of the constraint variable when the design variable is changed in the whole range to obtain a global difference matrix N, wherein the matrixes M and N are shown in a table 2. Dividing N by the corresponding element in M yields the matrix C, and it can be found that λ varies by a factor of 100 when the design variable range varies f ,B f ,H f The corresponding coarse diagonal elements have values within the linearity range, and V f ,θ f The corresponding coarse skew element is not within the linearity range. Thus, the screen yields a linear design variable t 1 ,t 3 ,β 1 And a linear constraint variable λ f ,B f ,H f And a linear state transition matrix Q.
TABLE 2 Primary dimensionality reduction State transition matrix M, Difference matrix N, matrix C
The linear state transition matrix Q is expressed as
Thus lambda f -λ f ,B f -B f ,H f -H f Correction amount of (1) and t 1 ,t 3 ,β 1 Has the following relationship between the adjustment amounts
T is obtained by parameter sensitivity and linearity analysis 1 ,t 3 ,β 1 And λ f -λ f ,B f -B f ,H f -H f Linear partial derivative matrix, i.e. differential correction matrix, between, correcting t by successive iterations 1 ,t 3 ,β 1 So that lambda is f ,B f ,H f Converge to a desired value lambda f ,B f ,H f Design variables and constraint variables are correspondingly reduced by three dimensions when the optimization is carried out by using a nonlinear optimization algorithm. In the reconstruction of the optimization problem,
the self-adaptive optimization algorithm (abbreviated as AOA) designed by the invention is compared with the SQP algorithm in the prior art for verification analysis. The tip landing position accuracy for both methods is shown in table 3. It can be seen that the accuracy of the tip landing position (including longitude, latitude and altitude) iteratively corrected by AOA is higher than that obtained by the SQP method. The terminal landing speed and the speed inclination angle obtained by the two methods both meet the precision requirement, and the effect is equivalent. The AOA method is proved to have good convergence and precision.
TABLE 3 tip precision landing comparison
As can be seen from FIG. 3, the number of optimized iterations of the SQP algorithm is 43, and the number of optimized iterations of the AOA algorithm is 16, which is only 37.2% of the SQP algorithm. Meanwhile, the terminal landing mass obtained from AOA was 22582kg, and that obtained from SQP was 22136 kg. Therefore, the AOA method is superior to the SQP algorithm in computational efficiency and optimality.
Fig. 4(a) - (h) give cross-sections of the main parameters. Fig. 4(a) - (b) show the profiles of overload and dynamic pressure. It can be seen that both methods yield results that satisfy all constraints, and that fig. 4(c) - (g) give profile curves for the main parameters of end landing. In the vertical landing stage, the longitude and latitude are almost kept unchanged, and a sub-stage reaches the area above the target landing point and mainly adjusts the altitude, the speed and the speed inclination angle. Fig. 4(g) shows a comparison of the mass profiles of the two methods. The slope of the curve of the mass profile represents the mass-second consumption of the engine. In the attitude adjusting section and the atmosphere reentry section, the quality is kept unchanged because the engine is shut down. In the power descending section and the vertical landing section, the mass curves of the two methods are almost parallel, which shows that the thrust factor of the engine obtained by optimization is approximately equal in size. However, the engine start-up time periods of the AOA method at the two power stages are 80.2s and 35.4s, respectively, while the engine start-up time periods of the SQP method at the two power stages are 87.6s and 31.4s, respectively, the AOA method consumes 12918kg of fuel mass, and the SQP method consumes 13264kg of fuel. The AOA method takes 398.5s for the whole return process, and the SQP method takes 396.2s for the whole return process. For such a free time optimization problem, the AOA method guarantees the optimality of engine ignition timing and fuel consumption.
In conclusion, the invention has the following advantages:
(1) a systematic and integral track optimization problem model of a plurality of flight sections of the whole return section of a first sub-stage of the carrier rocket is established, and is considered and satisfied simultaneously under a unified model.
(2) On the basis of a high-dimensional parameter space state transition matrix, accurate identification and positioning of high-sensitivity data elements in the state transition matrix are successfully realized on the basis of a K-means clustering algorithm, and linear and nonlinear parameters and a linear partial derivative matrix are screened out through linearity analysis; and finally, different optimization algorithms are distributed according to the linear and nonlinear characteristics of different design variables and constraint variables, so that the method has good precision, convergence, calculation efficiency and optimality.
(3) The method has the advantages that main design variables influencing the change of the constraint variables can be obtained in the clustering analysis process, reference is provided for the adjustment design of the nominal track, the complexity and the dimensionality of the optimization problem are reduced through sensitivity and linearity analysis, and the decoupling of the linear parameters and the nonlinear parameters is realized.
(4) The method realizes the automation of parameter identification and classification and the self-adaptation of algorithm allocation, basically does not need manual participation, has good reliability, accuracy and expansibility, and has reference significance for other types of high-dimensional optimization problems.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (10)
1. A recoverable rocket return section self-adaptive optimization method based on cluster analysis comprises the following steps:
step 1, establishing a return track optimization problem model of a sub-level return section; the optimization problem model comprises flight segment division information, design variable information and constraint variable information of a return segment; wherein the constraint variable information comprises design variable constraint information, process constraint variable information and terminal constraint variable information;
the method is characterized by further comprising the following steps:
step 2, solving a state transition matrix of the terminal constraint variable relative to the design variable;
step 3, carrying out sensitivity division on data elements in the state transition matrix by using a clustering algorithm, and identifying and dividing data elements with higher sensitivity from the state transition matrix according to design requirements to form a state transition matrix M after preliminary dimension reduction;
step 4, screening linear constraint variables, linear design variables and corresponding linear state transition matrixes from the M according to a set linearity criterion, and screening nonlinear constraint variables and nonlinear design variables from the M;
step 5, aiming at the linear constraint variable, the linear design variable and the corresponding linear state transition matrix, the optimal design variable value is obtained by utilizing a linear search algorithm; aiming at nonlinear constraint variables and nonlinear design variables, the optimal design variable value is obtained by utilizing a direct optimization method in a nonlinear optimization method.
2. The adaptive optimization method for returnable rocket return segments based on cluster analysis according to claim 1, wherein said step 1 comprises the steps of:
step 11, dividing a return section into four flight sections, namely an attitude adjusting section, a power deceleration section, an atmosphere reentry section and a vertical landing section;
step 12, establishing a three-degree-of-freedom kinetic equation of a sub-level return track;
and step 13, determining an objective function, design variable information and constraint variable information of the sub-level track optimization.
3. The adaptive optimization method for returnable rocket return segments based on cluster analysis according to claim 2, wherein the three-degree-of-freedom dynamical equation established in the step 12 is:
wherein, x, y and z are respectively the coordinates of a sublevel in the x direction, the y direction and the z direction of the emission coordinate system; v is a sub-level velocity value; θ is the velocity dip of a sub-stage; σ is a yaw angle of one sub-order; m is a sub-level current quality;
the rates of change of x, y, z, V, theta, sigma and m respectively; r is the radius of the earth; r is the geocentric distance; p is the rated thrust of the engine on the first sub-stage; epsilon n Is a variable thrust factor and is not less than 0 epsilon n Not more than 1, when n is 0, epsilon n Is the variable thrust factor of the power deceleration section, and is epsilon when n is 1 n A variable thrust factor for the vertical landing segment; i is sp Is the engine specific impulse; g 0 Is sea level gravitational acceleration; g r ＝-μ/r 2 Mu is the gravitational constant; α is the angle of attack of one sub-step; beta is a sub-step sideslip angle; x q 、Y q 、Z q The aerodynamic force components of a sub-stage in the x-direction, the y-direction and the z-direction of the velocity coordinate system are respectively.
4. A method for adaptive optimization of returnable rocket return segments based on cluster analysis according to claim 2 or 3, wherein said objective function determined in step 13 is represented by the following formula: min j ═ m (t) f ) Where J is the objective function, t f For landing time, m (t) f ) Is the quality of a sub-level at the time of landing.
5. The adaptive optimization method for returnable rocket return sections based on cluster analysis according to claim 2 or 3, wherein the design variable information determined in step 13 is:
X s ＝[t 1 t 2 t 3 t 4 α 1 α 2 β 1 β 2 ε 1 ε 2 ] T ，
wherein, X s For designing matrices of variables, t 1 Is the sliding time of a sub-level in the posture adjusting section, t 2 Is the flight time of a sub-stage in the dynamic deceleration section, t 3 Time of flight, t, for a sub-stage in the atmospheric reentry phase 4 Time of flight, α, for a sublevel in a vertical landing stage 1 Is the angle of attack, alpha, of a sub-stage in the power reduction section 2 Angle of attack, beta, of a sub-stage in a vertical landing leg 1 Is a sideslip angle, beta, of a sub-stage in the power reduction section 2 Is the sideslip angle, ε, of a sub-stage in the vertical landing zone 1 Engine thrust factor, ε, of one sub-stage in the power reduction section 2 Is the engine thrust factor for a sub-stage at the vertical landing stage.
6. The cluster analysis-based adaptive optimization method for returnable rocket return segments according to claim 2, wherein the design variable constraint information comprises angle of attack constraint information, sideslip angle constraint information, and engine thrust constraint information.
7. The adaptive optimization method for returnable rocket return segments based on cluster analysis as claimed in claim 2, wherein said process constraint variable information comprises one or more of dynamic pressure limiting condition, overload limiting condition, engine start-up ignition time interval condition of two connected power segments, and end landing quality limiting condition of a sub-stage.
8. The cluster analysis-based adaptive optimization method for returnable rocket return segments according to claim 2, wherein the end constraint variable information comprises: within the set precision range, the position of a sub-level landing reaches the designated position, the speed of the sub-level landing reaches the designated speed, and the posture of the sub-level landing is vertical.
9. The adaptive optimization method for recoverable rocket return sections based on cluster analysis according to claim 1, wherein in step 3, the data elements in the state transition matrix are sensitivity-partitioned by using a K-means clustering algorithm.
10. The adaptive recoverable rocket return section optimization method based on cluster analysis of claim 9, wherein the K-means clustering algorithm is performed by initializing a clustering center based on data experience of a sub-level return task model.
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