CN114662388B - Method for solving variable-principal-star offset frequency strategy based on sequence genetic algorithm - Google Patents

Method for solving variable-principal-star offset frequency strategy based on sequence genetic algorithm Download PDF

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CN114662388B
CN114662388B CN202210282191.XA CN202210282191A CN114662388B CN 114662388 B CN114662388 B CN 114662388B CN 202210282191 A CN202210282191 A CN 202210282191A CN 114662388 B CN114662388 B CN 114662388B
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张佳锋
马晓珊
彭晓东
高辰
赵梦园
强丽娥
张玉珠
唐文林
杨震
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Abstract

The invention discloses a method for solving a variable-principal-satellite offset frequency strategy based on a sequence genetic algorithm, which is used for a space-based gravitational wave detector, wherein the space-based gravitational wave detector comprises a satellite formation formed by three satellites, and each satellite is respectively provided with two laser interference optical platforms which are arranged at an included angle of 60 degrees, and the method comprises the following steps: selecting a pre-established phase locking scheme corresponding to a main satellite by taking a certain laser interference optical platform of a certain satellite as the main satellite as an initial stage; according to a set target function, adopting a sequence genetic algorithm to solve the offset frequency planning results of different moments when the incremental constraint condition is met in the current stage until the incremental constraint condition is not met, adopting an epsilon criterion to select a main satellite and phase locking scheme in the next stage, and repeating the steps to obtain the offset frequency planning results of different moments in different stages; and outputting the main satellite sequence and the offset frequency planning result in different stages until the set solution termination time is reached, thereby obtaining the variable main satellite offset frequency strategy.

Description

Method for solving variable-principal-star offset frequency strategy based on sequence genetic algorithm
Technical Field
The invention relates to the technical field of computers, in particular to a method for solving a variable-principal-star offset frequency strategy based on a sequence genetic algorithm.
Background
In recent years, in the detection process of a space-based gravitational wave detector, heterodyne interference ranging is adopted to perform inter-satellite ranging due to the existence of a doppler shift phenomenon. The result of the inter-satellite distance measurement can be used for judging whether the gravitational wave is detected or not through a series of calculations. The core of heterodyne interference ranging is to calculate the beat frequency generated by the interference between the laser emitted by the remote satellite optical platform and the laser emitted by the local optical platform. Laser light emitted from a remote satellite optical platform is affected by Doppler frequency shift, so that beat frequency generated by interference is unstable. To ensure that the beat frequency falls within a reasonable range, an offset frequency is added to the optical phase-locked loop to solve the problem. At present, in space-based gravitational wave detection plans such as LISA, Taiji and the like, three satellites are generally adopted to form a satellite formation for gravitational wave detection. Each satellite is respectively provided with two laser interference optical platforms which are arranged at an included angle of 60 degrees and used for transmitting and receiving laser to the adjacent optical platform of the same satellite and the far-end optical platforms of other satellites. Each optical platform comprises a weak light phase-locked loop which is used for carrying out weak light phase-locked processing on the received laser at the far end and adding an artificially set offset frequency in the process.
Since the space-based gravitational wave detector is generally composed of a plurality of satellites, there are the following problems: 1. and 2, constructing a variable-master star phase-locked scheme, namely setting offset frequency in each optical phase-locked loop based on the selected phase-locked scheme, or called as an offset frequency strategy, and 3, adopting which algorithm to efficiently solve the corresponding offset frequency strategy. Since each time the phase-locked scheme and the offset frequency are changed, the detection process is interrupted, the phase-locked scheme should be designed to be as unchanged as possible, and the offset frequency added to each optical phase-locked loop should be kept unchanged for as long as possible under the condition that the beat frequency constraint is satisfied, i.e., the longer the duration, the better the duration.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for solving a variable-principal-star offset frequency strategy based on a sequence genetic algorithm.
In order to achieve the above object, the present invention provides a method for solving a variable-principal-satellite offset frequency strategy based on a sequence genetic algorithm, which is used for a space-based gravitational wave detector, wherein the space-based gravitational wave detector comprises a formation of satellites composed of three satellites, each satellite is respectively loaded with two laser interference optical platforms arranged at an included angle of 60 degrees, and the method comprises:
selecting a pre-established phase locking scheme corresponding to a main satellite by taking a certain laser interference optical platform of a certain satellite as the main satellite as an initial stage;
according to a set target function, adopting a sequence genetic algorithm to solve the offset frequency planning results of different moments when the incremental constraint condition is met in the current stage until the incremental constraint condition is not met, adopting an epsilon criterion to select a main satellite and phase locking scheme in the next stage, and repeating the steps to obtain the offset frequency planning results of different moments in different stages; and outputting the main satellite sequence and the offset frequency planning result in different stages until the set solution termination time is reached, thereby obtaining the variable main satellite offset frequency strategy.
As a modification of the above method, the laser interference optics platforms are arranged in a counter-clockwise direction, respectively A, B, C, D, E, F, with laser interference optics platforms A and B at a first satellite, laser interference optics platforms C and D at a second satellite, and laser interference optics platforms E and F at a third satellite.
As an improvement of the above method, the method specifically comprises:
step 1) taking a certain laser interference optical platform of a certain satellite as a main satellite as an initial stage, and selecting a pre-established phase locking scheme corresponding to the main satellite;
step 2) setting a target function, a genetic algorithm initialization parameter and solving termination time;
step 3) setting the starting time of the incremental constraint condition to be T1-1 and the ending time of the incremental constraint condition to be T2-T1;
step 4) constructing corresponding incremental constraint conditions according to the T1 and the T2 and a phase locking scheme;
step 5) searching an optimal solution meeting the constraint condition constructed in the step 4) by adopting a genetic algorithm;
step 6) judging whether the optimal solution is converged or not, if yes, turning to step 7); otherwise, turning to the step 5);
step 7) judging whether the optimal solution has a feasible solution, if so, saving the current offset frequency planning result and the main satellite and phase locking scheme adopted in the current stage, and turning to step 8); otherwise, judging whether T2 is equal to 1, if so, replacing other main satellites and phase locking schemes and transferring to the step 3); if T2 is not equal to 1, selecting the main star and the phase-locking scheme of the next stage by adopting an epsilon criterion, and turning to the step 9);
step 8), judging whether T2 is equal to the solution termination time, if so, turning to the step 10); otherwise, adding 1 to T2, and turning to step 4);
step 9), judging whether T2 is equal to the solution termination time, if so, entering step 10); otherwise, setting to assign T2 to T1, and turning to step 4);
and step 10) finishing the solution of the variable main satellite offset frequency strategy, and storing the main satellite sequence, the phase locking scheme and the offset frequency planning result of each stage.
As an improvement of the above method, the phase locking scheme of step 1) includes: an L1 phase-locked scheme with C as the primary satellite, an L2 phase-locked scheme with F as the primary satellite, and an L3 phase-locked scheme with a as the primary satellite, wherein,
after the phase locking of the L1 phase locking scheme, the laser frequencies are as follows:
Figure GDA0003799614250000031
wherein f is A 、f B 、f C 、f D 、f E And f F Respectively representing A, B, C, D, E and F laser frequency after laser phase locking of laser interference optical platform 0 Representing the initial frequency, set to be fixedFrequency, f BC (t)、f DE (t) and f AF (t) denotes the time-varying Doppler shift, Δ f, between the first satellite and the second satellite, between the second satellite and the third satellite, and between the third satellite and the first satellite, respectively AB 、Δf CD And Δ f EF Respectively representing the artificial offset frequency, deltaf, added between two optical platforms in the first satellite, the second satellite and the third satellite BC And Δ f DE Respectively representing the artificial offset frequency added between the two laser interference optical platforms B and C and between the two laser interference optical platforms D, E;
generated by the laser interference optical bench D: beat frequency between two laser interference optical stages D and E
Figure GDA0003799614250000032
Generated by the laser interference optical bench C: beat frequency between two laser interference optical platforms B and C
Figure GDA0003799614250000033
Generated by the laser interference optical stage a: beat frequency between A and F laser interference optical platforms
Figure GDA0003799614250000034
Generated by the laser interference optical bench F: beat frequency between A and F laser interference optical stages
Figure GDA0003799614250000035
Obtained according to the following formula:
Figure GDA0003799614250000036
the constraint conditions are as follows:
Figure GDA0003799614250000041
wherein LB represents the lower limit of the constraint and UB represents the upper limit of the constraint;
after the phase locking of the L2 phase locking scheme, the laser frequencies are as follows:
Figure GDA0003799614250000042
wherein, Δ f AF Representing the added artificial offset frequency between the A and F laser interference optical platforms;
generated by the laser interference optical stage E: beat frequency between two laser interference optical stages D and E
Figure GDA0003799614250000043
Generated by the laser interference optical bench F: beat frequency between A and F laser interference optical stages
Figure GDA0003799614250000044
Generated by the laser interference optical stage B: beat frequency between two laser interference optical platforms B and C
Figure GDA0003799614250000045
Generated by the laser interference optical stage C: beat frequency between two laser interference optical platforms B and C
Figure GDA0003799614250000046
Obtained according to the following formula:
Figure GDA0003799614250000047
the constraint conditions are as follows:
Figure GDA0003799614250000051
after the phase locking of the L3 phase locking scheme, the laser frequencies are as follows:
Figure GDA0003799614250000052
generated by the laser interference optical stage a: beat frequency between A and F laser interference optical platforms
Figure GDA0003799614250000053
Generated by the laser interference optical stage B: beat frequency between two laser interference optical platforms B and C
Figure GDA0003799614250000054
Generated by the laser interference optical bench D: beat frequency between two laser interference optical stages D and E
Figure GDA0003799614250000055
Generated by the laser interference optical stage E: beat frequency between two laser interference optical platforms D and E
Figure GDA0003799614250000056
Obtained according to the following formula:
Figure GDA0003799614250000057
the constraint conditions are as follows:
Figure GDA0003799614250000061
as an improvement of the above method, the objective function of step 2) includes: maximizing offset frequency duration, minimizing a number of primary star changes, and minimizing a number of offset frequency changes, and the priority of the objective function is maximizing offset frequency duration > minimizing a number of primary star changes > minimizing a number of offset frequency changes.
As a modification of the above method, the genetic algorithm initialization parameters of step 2) include the number of iterations and the population number.
As an improvement of the above method, the incremental constraint condition of step 4) specifically includes:
when the start time T1 and the end time T2 are determined, each time point from T1 to T2 satisfies the following equation for employing the phase-locked scheme L1:
LB＜＝Δf AB ＜＝UB
LB＜＝Δf CD ＜＝UB
LB＜＝Δf EF ＜＝UB
Figure GDA0003799614250000062
wherein T1- > T2 represents each time point from a start time T1 to an end time T2;
when the start time T1 and the end time T2 are determined, each time point from T1 to T2 satisfies the following equation for employing the phase-locked scheme L2:
LB＜＝Δf AB ＜＝UB
LB＜＝Δf CD ＜＝UB
LB＜＝Δf EF ＜＝UB
Figure GDA0003799614250000063
when the start time T1 and the end time T2 are determined, each time point from T1 to T2 satisfies the following equation for employing the phase-locked scheme L3:
LB＜＝Δf AB ＜＝UB
LB＜＝Δf CD ＜＝UB
LB＜＝Δf EF ＜＝UB
Figure GDA0003799614250000071
as a refinement of the above method, the epsilon criterion of step 7) satisfies the following equation:
Figure GDA0003799614250000072
wherein, P 1 Probability of selecting phase-locked scheme in last step, P 2 And P 3 To select the probabilities of the other two phase-locking schemes, P 2 ＝P 3 N is the number of last phase-locking scheme, epsilon is a set coefficient, 0<ε<1。
The utility model provides a system for solve variable main star frequency of excursion strategy based on sequence genetic algorithm for sky base gravitational wave detector, sky base gravitational wave detector includes the satellite formation that three satellites constitute, and every satellite loads two laser interference optical platforms that are placed at 60 contained angles respectively, the system includes: the system comprises an initial module and a variable main satellite offset frequency strategy output module; wherein,
the initial module is used for selecting a pre-established phase locking scheme corresponding to a main satellite by taking a certain laser interference optical platform of a certain satellite as the main satellite as an initial stage;
the variable-master satellite offset frequency strategy output module is used for solving offset frequency planning results at different moments when the phase meets the incremental constraint condition by adopting a sequence genetic algorithm according to a set target function until the incremental constraint condition is not met, selecting a master satellite and phase locking scheme at the next phase by adopting an epsilon criterion, and repeating the step to obtain the offset frequency planning results at different moments when the phase does not meet the incremental constraint condition; and outputting the main satellite sequence and the offset frequency planning result in different stages until the set solution termination time is reached, thereby obtaining the variable main satellite offset frequency strategy.
Compared with the prior art, the invention has the advantages that:
1. according to the invention, three different phase-locking schemes are constructed, and different main satellites are respectively adopted, so that the diversity of the phase-locking scheme selection is facilitated, and a better main satellite-variable offset frequency planning scheme is conveniently found;
2. aiming at the characteristics of the problem, the method adopted by the invention not only can realize multi-target planning, but also can avoid the complexity and the inefficiency of the traditional multi-target genetic algorithm;
3. the invention adopts the phase-locking scheme of replacing the main satellite, improves the diversity of the offset frequency planning, and avoids the singleness of the phase-locking scheme and the singleness of the offset frequency planning scheme when only one satellite is used as the main satellite.
Drawings
Fig. 1(a) -1 (c) are schematic diagrams of phase-locking schemes of three different main satellites according to the present invention, wherein fig. 1(a) is a phase-locking scheme L1, fig. 1(b) is a phase-locking scheme L2, and fig. 1(c) is a phase-locking scheme L3;
2(a) -2 (c) are simulated time series Doppler shift data for a base gravitational wave detector having an arm length of 300 kilometres per day; wherein fig. 2(a) shows the doppler shift between satellite 1 and satellite 2 over time; fig. 2(b) shows the doppler shift between satellite 2 and satellite 3 over time; FIG. 2(c) shows the Doppler shift between satellite 1 and satellite 3 over time;
FIG. 3 is a flowchart of a method for solving a variable principal satellite offset frequency strategy based on a sequence genetic algorithm according to the present invention.
Detailed Description
The invention aims to provide a method and a system for solving a variable master satellite offset frequency strategy by a sequence genetic algorithm, which comprises a plurality of alternative phase-locking schemes of different master satellites and the sequence genetic algorithm for solving the offset frequency strategy of the variable master satellite phase-locking scheme, so as to solve the problem of making the offset frequency strategy of the variable master satellite phase-locking scheme in the existing space gravitational wave detection.
In order to solve the problems, three phase-locking schemes of different main satellites are provided. The three schemes can appoint three laser interference optical platforms positioned at different satellites in advance as alternative main satellites. This phenomenon is increasingly severe over time due to the persistence of the doppler shift. Therefore, it is impossible to always fall the beat frequency within a reasonable range without changing the offset frequency. To cope with the above problem, the offset frequency needs to be changed after the beat frequency constraint cannot be satisfied. If the offset frequency of the current stage cannot satisfy the beat frequency constraint condition due to the lapse of time, the offset frequency can be adjusted in the following two ways: 1. and replacing the main satellite and establishing an offset frequency strategy suitable for the main satellite. 2. And (5) the main satellite is unchanged, and an offset frequency strategy is re-established according to the current situation. Since the phase-locking scheme is expensive to replace, the adjustment needs to be performed as much as possible in the 2 nd method. After the main satellite and the offset frequency are changed, the next stage of the offset frequency planning scheme is called to be entered.
The phase-locking scheme has three forms, namely a phase-locking scheme L1, a phase-locking scheme L2 and a phase-locking scheme L3. As shown in fig. 1(a), 1(b), and 1 (c).
Wherein f is A ，f B ，f C ，f D ，f E ，f F The laser frequencies after the respective laser phase locks are respectively represented. f. of BC (t)、f DE (t) and f AF (t) respectively represent the time-varying doppler shifts between three stars. Δ f AB 、Δf CD And Δ f EF Respectively, the artificial offset frequencies added between two optical platforms in the same satellite. Δ f BC 、Δf AF And Δ f DE Respectively, representing the artificial offset frequency added between two optical platforms between different satellites.
L1, L2, and L3 use the same phase-locked sequence, but use optical stage C, optical stage E, and optical stage a, respectively, as the primary optical stages.
The L1 phase-locked scheme uses the optical stage C as the main optical stage. After being influenced by Doppler shift and added with artificial shift frequency, the laser frequencies are respectively equal to L1 phase locking scheme
Figure GDA0003799614250000091
Wherein f is 0 The initial frequency of each laser is indicated, and the default value is 281 THz.
The beat frequency calculation formula is as follows
Figure GDA0003799614250000092
Beat frequency between two laser interference optical stages D and E
Figure GDA0003799614250000093
The superscript D indicates that the beat frequency is generated on the laser interference optical platform D; beat frequency between A and F laser interference optical stages
Figure GDA0003799614250000094
Superscripts A and F respectively represent beat frequencies generated on the laser interference optical platforms A and F; beat frequency between two laser interference optical platforms B and C
Figure GDA0003799614250000095
The superscript C indicates that the beat frequency is generated at the laser interference optical stage C.
The L2 phase-lock scheme employs optical stage E as the primary optical stage. After being influenced by Doppler shift and added with artificial shift frequency, the laser frequencies are respectively equal to L2 phase locking scheme
Figure GDA0003799614250000101
The beat frequency calculation formula is as follows
Figure GDA0003799614250000102
Beat frequency between two laser interference optical stages D and E
Figure GDA0003799614250000103
The superscript E indicates that the beat frequency is generated at the laser interference optical platform E; beat frequency between A and F laser interference optical platforms
Figure GDA0003799614250000104
The superscript F indicates that the beat frequency is generated on the laser interference optical platform F; beat frequency between two laser interference optical platforms B and C
Figure GDA0003799614250000105
Superscript B, C indicates that the beat frequencies are respectively generated at laser interference optics platform B, C.
The L3 phase-lock scheme employs optical platform a as the primary optical platform. After being influenced by Doppler shift and added with artificial shift frequency, the laser frequencies are respectively equal to L3 phase locking scheme
Figure GDA0003799614250000106
The beat frequency calculation formula is as follows:
Figure GDA0003799614250000107
beat frequency between two laser interference optical stages D and E
Figure GDA0003799614250000111
And
Figure GDA0003799614250000112
superscript D, E indicates that beat frequencies were generated at laser interference optical stage D, E, respectively; beat frequency between A and F laser interference optical stages
Figure GDA0003799614250000113
Superscript A indicates that the beat frequency is generated on the laser interference optical platform A; beat frequency between two laser interference optical platforms B and C
Figure GDA0003799614250000114
Superscript B indicates that the beat frequency is generated at the laser interference optical stage B.
The constraint for optical platform C as the dominant star, where LB represents the lower bound of the constraint and UB represents the upper bound of the constraint.
Figure GDA0003799614250000115
The constraint for optical platform E as the dominant star, where LB represents the lower bound of the constraint and UB represents the upper bound of the constraint.
Figure GDA0003799614250000116
The constraint for optical platform a as the primary star, where LB represents the lower bound of the constraint and UB represents the upper bound of the constraint.
Figure GDA0003799614250000121
The sequence genetic algorithm for solving the offset frequency strategy of the variable-master satellite phase-locking scheme comprises target function setting, master satellite sequence construction, incremental constraint condition setting and convergence judgment.
The solution to the problem for the sequence genetic algorithm has 3 objectives, namely, maximizing the offset frequency duration, minimizing the number of phase-locked scheme changes, and minimizing the number of offset frequency changes, respectively. The priority of the objective function is maximizing the offset frequency duration > minimizing the number of phase locking scheme changes > minimizing the number of offset frequency changes.
The objective function is shown by the following formula:
Figure GDA0003799614250000122
the main star sequence is constructed as follows: and when the planned offset frequency of the previous stage cannot meet the constraint condition of the current moment, selecting the main star of the next stage by adopting an epsilon criterion.
The incremental constraint is:
and when the main satellite of the phase locking scheme is determined, solving the problem by adopting a genetic algorithm. Since the doppler shift is time-varying, the optimization problem is constrained in an incremental constraint. Two parameters are required to build the incremental constraint, namely the start time T1 and the end time T2 of the constraint. Taking the phase-locking scheme L3 as an example, for T1 ═ T2 ═ 1, the constraint conditions are as follows:
Figure GDA0003799614250000123
when the genetic algorithm finds a set of Δ f AB 、Δf CD 、Δf EF 、Δf BC And Δ f AF After the solution of (2), the original constraint is extended. At this time, T1 is unchanged, and T2 ═ T2+ 1.
The constraints after the increment are as follows
Figure GDA0003799614250000131
If there is always a feasible solution, the above steps are repeated, so the constraint condition needs to be incrementally processed according to the initial time T1 and the termination time T2.
The epsilon criterion is:
in the case of offset frequency switching, it is necessary to consider whether the original phase-locking scheme is still adopted. For simplicity of the procedure, a selection is made, and therefore an epsilon criterion is constructed, which is shown in the following formula
Figure GDA0003799614250000132
Wherein, 0<ε<1 needs to be specified manually at the solver initialization. n represents the number of times a certain phase locking scheme is continuously employed. P 1 Representing the probability, P, that the last phase-locked scheme is still selected 2 And P 3 Representing the probability of using the other two phase locking schemes.
The criterion is preferably the last phase-locking scheme selected, the value of e is used to control the probability of continuing to use the last phase-locking scheme, the closer e is to 0, the greater the probability of using the last phase-locking scheme, otherwise the more the probability is to be chosen randomly, so as to ensure that the phase-locking scheme is changed as little as possible. Assume that the phase-locking scheme L1 is selected in the first phase of program operation and ε is set to 0, whichWhen n is 1, P 1 ＝1，P 2 ＝P 3 0. Therefore, the phase-locking scheme L1 is still selected in the next stage. Suppose that the phase-locking scheme L2 is selected in two consecutive stages during the program running process, and ε is set to 1, where n is 2, P 1 ＝1/2，P 2 ＝P 3 1/4. Therefore, the probability of still selecting the phase-locking scheme L2 at the next stage is 1/2, and the probabilities of selecting the other two phase-locking schemes are both 1/4.
Convergence determination
When the genetic algorithm is used for solving, whether the result of the algorithm reaches the optimal solution needs to be judged. The convergence determination is implemented as a loop of running solution steps until the longest duration of days has not changed.
The sequence genetic algorithm solving step specifically comprises the following steps:
step 1) randomly selecting a main star as an initial main star. And selecting the phase locking scheme corresponding to the main satellite as the current phase locking scheme, wherein the phase locking scheme comprises a phase locking scheme L1, a phase locking scheme L2 and a phase locking scheme L3.
And 2) setting a target function and initialization parameters of the genetic algorithm. The return value of the objective function is the maximum time that a set of offset frequencies can last given the chosen phase-locked scheme. The genetic algorithm parameters comprise iteration times and population number.
Step 3) set T1 to 1, T2 to T1. T1 represents the start time of the incremental constraint and T2 represents the end time of the incremental constraint.
Step 4) constructs constraints from the start time T1 and the end time T2 of the incremental constraints.
And 5) searching a group of offset frequency planning results meeting the constraint conditions established in the step 4) by adopting a genetic algorithm.
Step 6) judging the convergence or no solution of the solution result, and entering step 7) if the convergence or no solution exists; otherwise, return to step 5).
Step 7) if feasible solutions exist in the step 6), saving the current offset frequency planning result and the main satellite and phase locking scheme adopted in the current stage, and entering the step 8); otherwise, if T2 is equal to 1, the other master star is replaced and the phase locking scheme is restarted; if T2 is not equal to 1, then the master star and phase-locking scheme of the next stage is selected by using the e criterion, and the process goes to step 9).
Step 8) if T2 is the solution termination time, entering step 10); otherwise, set T2 to T2+1, go to step 4).
Step 9) if T2 is the solution termination time, entering step 10); otherwise, set T1 to T2, go to step 4).
And step 10) finishing the solving of the variable main satellite offset frequency strategy, and storing the main satellite sequence and the offset frequency values in each stage.
Wherein, the steps 3) -8) ensure that the duration of the offset frequency in the objective function in the sequence genetic algorithm is maximized and the change times of the offset frequency are minimized. The epsilon criterion ensures that the number of changes of the primary star in the objective function is minimized.
The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and examples.
Example 1
The 5-year (2190 days in total) analog time sequence doppler shift data of the existing base gravitational wave detector with the arm length of 300 kilometers per day is used as the doppler shift data of the current primary satellite shift frequency planning scheme, as shown in fig. 2(a) -2 (c). In fig. 2(a) -2 (c), the abscissa represents time in days, and the ordinate represents doppler shift in MHz. Wherein fig. 2(a) shows the doppler shift between satellite 1 and satellite 2 over time; fig. 2(b) shows the doppler shift between satellite 2 and satellite 3 over time; fig. 2(c) shows the doppler shift between satellite 1 and satellite 3 over time.
And programming constraint formulas of phase locking schemes of different main satellites for use in solving a subsequent variable main satellite offset frequency planning scheme.
Solving the problem by adopting a sequence genetic algorithm, wherein the solving steps are as follows:
step 1) randomly selecting a master satellite and phase locking scheme as an initial master satellite and phase locking scheme. As shown in fig. 3, the phase-locking scheme includes a phase-locking scheme L1, a phase-locking scheme L2, and a phase-locking scheme L3.
And 2) setting a target function and initialization parameters of the genetic algorithm. The return value of the objective function is the maximum time that a set of offset frequencies can last given the chosen primary star and phase lock scheme. The genetic algorithm parameters comprise iteration times and population number.
Step 3) setting T1 to 1 and T2 to T1. T1 represents the start time of the incremental constraint and T2 represents the end time of the incremental constraint.
Step 4) constructs constraints from the start time T1 and the end time T2 of the incremental constraints.
And 5) searching a group of offset frequency planning results meeting the constraint conditions established in the step 4) by adopting a genetic algorithm.
Step 6) judging the convergence or no solution of the solution result, and entering step 7) if the convergence or no solution exists; otherwise, return to step 5).
Step 7) if feasible solutions exist in the step 6), saving the current offset frequency planning result and the phase locking scheme adopted in the current stage, and entering the step 8); otherwise, if T2 is equal to 1, the other phase-locking schemes are replaced and restarted; if T2 is not equal to 1, then the phase-locking scheme of the next stage is selected by using the e criterion, and the process goes to step 9).
Step 8) if T2 is the solution termination time, entering step 10); otherwise, set T2 to T2+1, go to step 4).
Step 9) if T2 is the solution termination time, entering step 10); otherwise, set T1 to T2, go to step 4).
And step 10) solving the variable main satellite offset frequency strategy is finished, and a result is stored.
Wherein, the steps 3) to 8) ensure that the offset frequency duration in the objective function is maximized and the number of times of changing the offset frequency is minimized. The epsilon criterion ensures that the number of changes of the dominant star in the objective function is minimized.
The sequence genetic algorithm for solving the offset frequency strategy of the variable-master satellite phase-locking scheme comprises target function setting, master satellite sequence construction, incremental constraint condition setting and convergence judgment. The solution to the problem for the sequence genetic algorithm has 3 objectives, namely, maximizing the offset frequency duration, minimizing the number of phase-locked scheme changes, and minimizing the number of offset frequency changes, respectively. The priority of the objective function is maximizing the offset frequency duration > minimizing the number of phase locking scheme changes > minimizing the number of offset frequency changes.
The objective function is shown by the following formula:
Figure GDA0003799614250000161
the main star sequence is constructed as follows: and when the planned offset frequency of the previous stage cannot meet the constraint condition of the current moment, selecting the main star of the next stage by adopting an epsilon criterion.
The incremental constraint is:
and when the main satellite of the phase locking scheme is determined, solving the problem by adopting a genetic algorithm. Since the doppler shift is time-varying, the optimization problem is constrained in an incremental constraint. Two parameters are required to build the incremental constraint, namely the start time T1 and the end time T2 of the constraint. When T1 and T2 are determined, the constraints are as follows:
Figure GDA0003799614250000162
the "phase-locking scheme L1", the "phase-locking scheme L2", and the "phase-locking scheme L3" respectively represent incremental constraint condition construction formulas when different phase-locking schemes are adopted. T1- > T2 represents from time point T1 to time point T2. Each time point T1 through T2 needs to satisfy the above constraints.
Taking the phase-locking scheme L3 as an example, for T1 ═ T2 ═ 1, the constraint conditions are as follows:
Figure GDA0003799614250000171
when the genetic algorithm finds a set of Δ f AB 、Δf CD 、Δf EF 、Δf BC 、Δf AF And Δ f DE After the solution of (2), the original constraint is extended. At this time, T1 is unchanged, and T2 ═ T2+ 1.
The constraints after incrementing are as follows
Figure GDA0003799614250000172
If there is always a feasible solution, the above steps are repeated, so the constraint condition needs to be incrementally processed according to the initial time T1 and the termination time T2.
The epsilon criterion is:
in the case of offset frequency switching, it is necessary to consider whether the original phase-locking scheme is still adopted. For simplicity of the procedure, a selection is made, and therefore an epsilon criterion is constructed, which is shown in the following formula
Figure GDA0003799614250000181
Wherein, 0<ε<1 needs to be specified manually at the solver initialization. n represents the number of times a certain phase-locking scheme is successively applied. P 1 Representing the probability, P, that the last phase-locked scheme is still selected 2 And P 3 Representing the probability of using the other two phase locking schemes.
The criterion may preferably be the last phase-locking scheme selected, the value of e being used to control the probability of continuing to use the last phase-locking scheme, the closer e is to 0 the greater the probability of using the last phase-locking scheme, otherwise the more the probability is to be chosen randomly to ensure that as few changes to the phase-locking scheme as possible. Suppose that phase-locking scheme L1 is selected in the first stage of program operation, and ε is set to 0, when n is equal to 1, P 1 ＝1，P 2 ＝P 3 0. Therefore, the phase locking scheme L1 is still selected for the next stage. Suppose that the phase-locking scheme L2 is selected in two consecutive stages during the program running process, and ε is set to 1, where n is 2, P 1 ＝1/2，P 2 ＝P 3 1/4. Therefore, the probability of still selecting the phase-locking scheme L2 at the next stage is 1/2, and the other two schemes are selectedThe probability of the phase-lock scheme is 1/4.
Convergence determination
When the genetic algorithm is used for solving, whether the result of the algorithm reaches the optimal solution needs to be judged. The convergence determination is implemented as a loop of running solution steps until the longest duration of days has not changed.
For this example, the algorithmic solution results are as follows:
TABLE 1 results of solution
Figure GDA0003799614250000182
It can be seen from the results that for the 5-year time sequence doppler frequency shift data, the sequence genetic algorithm is adopted for solving, the main satellite needs to be changed 1 time, the offset frequency needs to be changed 3 times, and the total time sequence doppler frequency shift data is divided into 4 stages. Stage 1 is day 1 to day 1936, stage 2 is day 1937 to day 1996, stage 3 is day 1997 to day 2142, and stage 4 is day 2143 to day 2190.
The offset frequency is set as follows:
TABLE 2 offset frequency
Offset frequency unit (MHZ) Stage 1 Stage 2 Stage 3 Stage 4
Δf AB -18.28 -24.62 24.74 24.95
Δf CD 24.86 22.40 23.541 24.77
Δf EF 22.58 11.16 -24.70 -24.75
Δf BC -14.07 / / /
Δf AF -12.47 8.83 -13.84 -21.33
Δf DE / -10.43 -24.01 -24.71
Example 2
The embodiment 2 of the invention provides a system for solving a variable-principal satellite offset frequency strategy based on a sequence genetic algorithm, which is used for a space-based gravitational wave detector, wherein the space-based gravitational wave detector comprises a satellite formation formed by three satellites, each satellite is respectively provided with two laser interference optical platforms which are arranged at an included angle of 60 degrees, and the system is realized based on the method of the embodiment 1 and comprises the following steps: the system comprises an initial module and a variable main satellite offset frequency strategy output module; wherein,
the initial module is used for selecting a pre-established phase locking scheme corresponding to a main satellite by taking a certain laser interference optical platform of a certain satellite as the main satellite as an initial stage;
the variable-master satellite offset frequency strategy output module is used for solving offset frequency planning results at different moments when the phase meets the incremental constraint condition by adopting a sequence genetic algorithm according to a set target function until the incremental constraint condition is not met, selecting a master satellite and phase locking scheme at the next phase by adopting an epsilon criterion, and repeating the step to obtain the offset frequency planning results at different moments when the phase does not meet the incremental constraint condition; and outputting the main satellite sequence and the offset frequency planning result in different stages until the set solution termination time is reached, thereby obtaining the variable main satellite offset frequency strategy.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (9)

1. A method for solving a variable-principal satellite offset frequency strategy based on a sequence genetic algorithm is used for a space-based gravitational wave detector, the space-based gravitational wave detector comprises a satellite formation formed by three satellites, and each satellite is respectively provided with two laser interference optical platforms which are arranged at an included angle of 60 degrees, and the method comprises the following steps:
selecting a pre-established phase locking scheme corresponding to a main satellite by taking a certain laser interference optical platform of a certain satellite as the main satellite as an initial stage;
according to a set target function, adopting a sequence genetic algorithm to solve the offset frequency planning results of different moments when the incremental constraint condition is met in the current stage until the incremental constraint condition is not met, adopting an epsilon criterion to select a main satellite and phase locking scheme in the next stage, and repeating the steps to obtain the offset frequency planning results of different moments in different stages; and outputting the main satellite sequence and the offset frequency planning result in different stages until the set solution termination time is reached, thereby obtaining the variable main satellite offset frequency strategy.
2. The method for solving the variable dominant star offset frequency strategy based on the sequence genetic algorithm as claimed in claim 1, wherein the laser interference optical platforms are arranged in a counterclockwise direction, respectively A, B, C, D, E, F, wherein the laser interference optical platforms A and B are at a first satellite, the laser interference optical platforms C and D are at a second satellite, and the laser interference optical platforms E and F are at a third satellite.
3. The method for solving the variable prime star offset frequency strategy based on the sequence genetic algorithm according to claim 2, wherein the method specifically comprises:
step 1) taking a certain laser interference optical platform of a certain satellite as a main satellite as an initial stage, and selecting a pre-established phase locking scheme corresponding to the main satellite;
step 2) setting a target function, a genetic algorithm initialization parameter and solving termination time;
step 3) setting the starting time of the incremental constraint condition to be T1-1 and the ending time of the incremental constraint condition to be T2-T1;
step 4) constructing corresponding incremental constraint conditions according to the T1 and the T2 and a phase locking scheme;
step 5) searching an optimal solution meeting the constraint condition constructed in the step 4) by adopting a genetic algorithm;
step 6) judging whether the optimal solution is converged or not, if yes, turning to step 7); otherwise, turning to the step 5);
step 7) judging whether the optimal solution has a feasible solution, if so, saving the current offset frequency planning result and the main satellite and phase locking scheme adopted in the current stage, and turning to step 8); otherwise, judging whether T2 is equal to 1, if so, replacing other main satellites and phase locking schemes and transferring to the step 3); if T2 is not equal to 1, selecting the main star and the phase-locking scheme of the next stage by adopting an epsilon criterion, and turning to the step 9);
step 8), judging whether T2 is equal to the solution termination time, if so, turning to the step 10); otherwise, adding 1 to T2, and turning to step 4);
step 9), judging whether T2 is equal to the solution termination time, if so, entering step 10); otherwise, setting to assign T2 to T1, and turning to step 4);
and step 10) finishing the solution of the variable main satellite offset frequency strategy, and storing the main satellite sequence, the phase locking scheme and the offset frequency planning result of each stage.
4. The method for solving the frequency strategy of the variable master star offset based on the sequence genetic algorithm according to claim 3, wherein the phase locking scheme of the step 1) comprises: an L1 phase-locked scheme with C as the primary satellite, an L2 phase-locked scheme with F as the primary satellite, and an L3 phase-locked scheme with a as the primary satellite, wherein,
after the phase locking of the L1 phase locking scheme, the laser frequencies are as follows:
Figure FDA0003558226950000021
wherein f is A 、f B 、f C 、f D 、f E And f F Respectively representing A, B, C, D, E and F laser frequency after laser phase locking of laser interference optical platform 0 Representing the initial frequency, set to a fixed frequency, f BC (t)、f DE (t) and f AF (t) represents the time-varying Doppler shift, Δ f, between the first satellite and the second satellite, between the second satellite and the third satellite, and between the third satellite and the first satellite, respectively AB 、Δf CD And Δ f EF Respectively representing the artificial offset frequency, Δ f, added between two optical platforms in the first satellite, the second satellite and the third satellite BC And Δ f DE Respectively representing the artificial offset frequency added between the two laser interference optical platforms B and C and between the two laser interference optical platforms D, E;
generated by the laser interference optical stage D: beat frequency between two laser interference optical stages D and E
Figure FDA0003558226950000022
Generated by the laser interference optical stage C: beat frequency between two laser interference optical platforms B and C
Figure FDA0003558226950000023
Generated by the laser interference optical stage a: beat frequency between A and F laser interference optical platforms
Figure FDA0003558226950000024
Generated by the laser interference optical bench F: beat frequency between A and F laser interference optical stages
Figure FDA0003558226950000025
Obtained according to the following formula:
Figure FDA0003558226950000031
the constraint conditions are as follows:
Figure FDA0003558226950000032
wherein LB represents the lower limit of the constraint and UB represents the upper limit of the constraint;
after the phase locking of the L2 phase locking scheme, the laser frequencies are as follows:
Figure FDA0003558226950000033
wherein, Δ f AF Representing the added artificial offset frequency between the A and F laser interference optical platforms;
generated by the laser interference optical stage E: beat frequency between two laser interference optical stages D and E
Figure FDA0003558226950000034
Generated by the laser interference optical bench F: beat frequency between A and F laser interference optical stages
Figure FDA0003558226950000035
Generated by the laser interference optical stage B: beat frequency between two laser interference optical platforms B and C
Figure FDA0003558226950000036
Generated by the laser interference optical stage C: beat frequency between two laser interference optical platforms B and C
Figure FDA0003558226950000037
Obtained according to the following formula:
Figure FDA0003558226950000041
the constraint conditions are as follows:
Figure FDA0003558226950000042
after the phase locking is performed by the L3 phase locking scheme, the laser frequencies are as follows:
Figure FDA0003558226950000043
generated by the laser interference optical stage a: beat frequency between A and F laser interference optical stages
Figure FDA0003558226950000044
Generated by the laser interference optical stage B: beat frequency between two laser interference optical platforms B and C
Figure FDA0003558226950000045
Generated by the laser interference optical stage D: beat frequency between two laser interference optical stages D and E
Figure FDA0003558226950000046
Generated by the laser interference optical stage E: beat frequency between two laser interference optical stages D and E
Figure FDA0003558226950000047
Obtained according to the following formula:
Figure FDA0003558226950000048
the constraint conditions are as follows:
Figure FDA0003558226950000051
5. the method for solving the variable prime star offset frequency strategy based on the sequence genetic algorithm according to claim 3, wherein the objective function of the step 2) comprises: maximizing offset frequency duration, minimizing a number of primary star changes, and minimizing a number of offset frequency changes, and the priority of the objective function is maximizing offset frequency duration > minimizing a number of primary star changes > minimizing a number of offset frequency changes.
6. The method for solving the variable prime star offset frequency strategy based on the sequence genetic algorithm according to claim 3, wherein the genetic algorithm initialization parameters of the step 2) comprise iteration number and population number.
7. The method for solving the frequency-of-variation strategy based on the sequence genetic algorithm according to claim 4, wherein the incremental constraint conditions of the step 4) specifically include:
when the start time T1 and the end time T2 are determined, each time point from T1 to T2 satisfies the following equation for employing the phase-locked scheme L1:
LB＜＝Δf AB ＜＝UB
LB＜＝Δf CD ＜＝UB
LB＜＝Δf EF ＜＝UB
Figure FDA0003558226950000052
wherein T1- > T2 represents each time point from a start time T1 to an end time T2;
when the start time T1 and the end time T2 are determined, each time point from T1 to T2 satisfies the following equation for employing the phase-locked scheme L2:
Figure FDA0003558226950000061
when the start time T1 and the end time T2 are determined, each time point from T1 to T2 satisfies the following equation for employing the phase-locked scheme L3:
Figure FDA0003558226950000062
8. the method for solving the frequency strategy of the shifting of the variable prime star based on the sequence genetic algorithm according to claim 4, wherein the epsilon criterion of the step 7) satisfies the following formula:
Figure FDA0003558226950000063
wherein, P 1 Probability of selecting phase-locked scheme in last step, P 2 And P 3 To select the probabilities of the other two phase-locking schemes, P 2 ＝P 3 N is the number of last phase-locking scheme, epsilon is a set coefficient, 0<ε<1。
9. The utility model provides a system for solve variable main star frequency of excursion strategy based on sequence genetic algorithm for sky base gravitational wave detector, sky base gravitational wave detector includes the satellite formation that three satellites constitute, and every satellite loads two laser interference optical platforms that are 60 contained angles and place respectively, its characterized in that, the system includes: the system comprises an initial module and a variable main satellite offset frequency strategy output module; wherein,
the initial module is used for selecting a pre-established phase locking scheme corresponding to a main satellite by taking a certain laser interference optical platform of a certain satellite as the main satellite as an initial stage;
the variable-master satellite offset frequency strategy output module is used for solving offset frequency planning results at different moments when the phase meets the incremental constraint condition by adopting a sequence genetic algorithm according to a set target function until the incremental constraint condition is not met, selecting a master satellite and phase locking scheme at the next phase by adopting an epsilon criterion, and repeating the step to obtain the offset frequency planning results at different moments when the phase does not meet the incremental constraint condition; and outputting the main satellite sequence and the offset frequency planning result in different stages until the set solution termination time is reached, thereby obtaining the variable main satellite offset frequency strategy.
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