A method for evaluating residual carrying capacity based on numerical programming after specific impulse reduction

Abstract

The application discloses a kind of remaining carrying capacity evaluation methods based on numerical programming after specific impulse drop, use failure occurrence time, remaining thrust percentage and propellant leakage percentage as the characteristic quantity of characterizing specific impulse drop failure.By searching the fault adaptation range of rocket into target orbit and safe parking orbit under different characteristic quantity combination conditions offline, the position that the remaining carrying capacity after failure can send the load to is evaluated.Finally, the fault adaptation range is bound to the rocket offline, and according to the three quantities of failure occurrence time, remaining thrust percentage and propellant leakage percentage, the corresponding adaptation range of the failure is quickly found after the failure occurs, and the remaining carrying capacity evaluation is realized.

Description

Technical Field

[0001] This application relates to the technical field of launch vehicle control, and in particular to a method for evaluating remaining payload capacity based on numerical programming after specific impulse decline. Background Technology

[0002] A typical failure mode of liquid rockets during flight is thrust reduction, which can generally be attributed to two types: decreased flow rate per second (FPS) and decreased specific impulse. FPS reduction is relatively easy to understand in the equations of motion: with constant specific impulse, FPS and thrust are directly proportional, and the percentage decrease in FPS is the percentage decrease in thrust. However, the phenomenon of decreased specific impulse is more complex, involving the engine's operating mechanism, making it difficult to accurately assess the trend of specific impulse after thrust reduction—it may increase, decrease, or remain unchanged. A more realistic scenario is that propellant leakage occurs simultaneously with the decrease in FPS, meaning that more propellant is consumed while thrust decreases, thus equivalent to a decrease in specific impulse failure mode.

[0003] In order to make the most correct use of the remaining fuel after a rocket failure, it is necessary to quickly assess whether the rocket's remaining payload capacity can send the payload into the target orbit. If not, it is necessary to quickly assess whether the payload can be sent into a safe parking orbit. Summary of the Invention

[0004] This application proposes a numerical programming-based method for assessing remaining payload capacity after specific impulse descent. The method uses the failure time, remaining thrust percentage, and propellant leakage percentage as characteristic quantities to characterize specific impulse descent failures. By offline searching for the failure adaptation range under different combinations of characteristic quantities, the method assesses the location where the remaining payload capacity can deliver the payload after the failure. Finally, the failure adaptation range is offline-attached to the rocket. After a failure, based on the failure time, remaining thrust percentage, and propellant leakage percentage, the adaptation range corresponding to the failure is quickly found, thus achieving the remaining payload capacity assessment.

[0005] Firstly, a method for assessing remaining carrying capacity based on numerical programming after a decrease in specific impulse is provided, the method comprising:

[0006] Retrieve the remaining carrying capacity assessment set {(t)} k ,κ i ,τ i,max )|k=1,…,p; i=1,…n};

[0007] Based on the time t of the fault occurrence fault and thrust decrease percentage κ fault Based on the aforementioned remaining carrying capacity assessment set, the maximum percentage of fuel leakage that can be accommodated is determined.

[0008] Among them, in the remaining carrying capacity assessment set {(t k ,κ i ,τ i,max In the sequence |k=1,…,p;i=1,…n}, (t k ,κ i ,τ i,max ) represents the time t when the k-th fault occurs. k The remaining thrust percentage κ of the i-th element i Maximum fuel leakage percentage τ under certain conditions i,max ,(t k ,κ i ,τ i,max τ in ) i,max It is based on the time t of the kth failure. k The remaining thrust percentage κ of the i-th element i The constraints under the given conditions are obtained by searching and optimizing the objective function maxτ.

[0009] In this application, the method can be applied to situations where the flow rate decreases per second and there is a fuel leak.

[0010] In this application, the remaining thrust percentage is 100% in the absence of a fault.

[0011] In conjunction with the first aspect, in some implementations of the first aspect, the constraints include at least one of the following: specific impulse descent motion equation constraints, remaining fuel constraints, and target orbit terminal constraints.

[0012] In conjunction with the first aspect, in certain implementations of the first aspect, the constraints of the specific impulse descent motion equation satisfy: T=κ·dmI sp g0, where r, V, u, and g represent position, velocity, thrust direction, and gravitational vector, respectively; T is the thrust amplitude; dm is the flow rate per second; and I is the gravitational vector. sp τ is the specific impulse, g0 is the standard Earth gravitational acceleration, κ is the percentage of remaining thrust, and τ is the percentage of fuel leakage.

[0013] In conjunction with the first aspect, in some implementations of the first aspect, at the k-th fault occurrence time t k Under the condition, the percentage of the i-th remaining thrust κ i Under these conditions, the maximum percentage of fuel leakage τ i,max Obtained through the following methods:

[0014] Traverse the interval [τ] in the direction from j=1 to j=m. i,j ,τ i,j+1 ], j = 1, 2, ..., m and τ i,1 =0, in [τi,j ,τ i,j+1 Within the interval, a search is performed using the search optimization objective function maxτ as the objective function to obtain the maximum fuel leakage percentage τ. i,max If τ i,max =τ i,j+1 Then in the next interval [τ i,j+1 ,τ i,j+2 Continue searching within ]; if τ i,max <τ i,j+1 Then the output is the time t when the k-th fault occurs. k Under the condition, the percentage of the i-th remaining thrust κ i Maximum fuel leakage percentage τ under certain conditions i,max .

[0015] It should be understood that the above traversal interval [τ] i,j ,τ i,j+1 ], j = 1, 2, ..., m, its main purpose is to improve the computational convergence. During the research and development process, it was found that directly calculating the maximum fuel leakage percentage τ globally... i,max The search may fail to converge or take too long. Without considering convergence, or the maximum fuel leakage percentage τ... i,max Even with a relatively small actual range, the time t for the k-th failure can be obtained solely based on the existing constraints. k Under the condition, the percentage of the i-th remaining thrust κ i Maximum fuel leakage percentage τ under certain conditions i,max .

[0016] In conjunction with the first aspect, in some implementations of the first aspect, the remaining thrust percentage κ at the i-th position... i Under the given conditions, the flight trajectory corresponding to the maximum fuel leakage percentage obtained within the interval [τ1,τ2] is the flight trajectory at the (i+1)th remaining thrust percentage κ. i+1 The initial conjecture for the search within the interval [τ1,τ2] under the given conditions.

[0017] In conjunction with the first aspect, in some implementations of the first aspect, at the k-th fault occurrence time t k Under the condition, t k Time and t k The standard trajectory after time step is the initial conjecture for searching within the interval [τ1,τ2] under the condition of the remaining thrust percentage κ1.

[0018] In conjunction with the first aspect, in certain implementations of the first aspect, the determination of the maximum acceptable fuel leakage percentage... include:

[0019] Based on the time t of the fault occurrencefault The time interval in which the fault occurred [t] k ,t k+1 ], and the percentage decrease in thrust κ fault The thrust reduction percentage range [κ] i ,κ i+1 ], in the remaining carrying capacity assessment set {(t k ,κ i ,τ i,max In the case of |k=1,…,p;i=1,…n}, according to (t k ,κ i ,τ i,max ), (t k+1 ,κ i ,τ i,max ), (t k ,κ i+1 ,τ i+1,max ) and (t k+1 ,κ i+1 ,τ i+1,max The maximum fuel leakage percentage that can be accommodated is obtained by interpolation.

[0020] In conjunction with the first aspect, in some implementations of the first aspect, if the actual percentage of fuel leakage τ in the fault... fault <τ max fault If the actual fuel leakage percentage is [not specified], then the remaining carrying capacity is sufficient; Then the remaining carrying capacity is insufficient.

[0021] Secondly, a method for determining the remaining carrying capacity under conditions of decreased specific impulse is provided, including:

[0022] From t1→t p directional traversal of time series S t ={t1,t2,…,t p}, t1 <t2<…<t p Wherein, at the time t of the kth failure occurrence k Under the condition, from κ1→κ n Directional traversal of the remaining thrust percentage sequence S κ ={κ1,κ2,…,κ n},κ1>κ2>…>κ n To determine the remaining carrying capacity assessment set {(t k ,κ i ,τ i,max )|k=1,…,p; i=1,…n}, (t k ,κ i ,τ i,max) represents the time t when the k-th fault occurs. k The remaining thrust percentage κ of the i-th element i Maximum fuel leakage percentage τ under certain conditions i,max .

[0023] In conjunction with the second aspect, in some implementations of the second aspect, the remaining thrust percentage κ at the i-th position... i Under the given conditions, traverse the interval [τ] in the direction from j=1 to j=m. i,j ,τ i,j+1 ], j = 1, 2, ..., m and τ i,1 =0, in [τ i,j ,τ i,j+1 Within the interval, based on the constraints, a search is performed with the objective function maxτ as the objective function to obtain the maximum fuel leakage percentage τ. i,max If τ i,max =τ i,j+1 Then in the next interval [τ i,j+1 ,τ i,j+2 Continue searching within ]; if τ i,max <τ i,j+1 Then the output is the time t when the k-th fault occurs. k Under the condition, the percentage of the i-th remaining thrust κ i Maximum fuel leakage percentage τ under certain conditions i,max .

[0024] Thirdly, an electronic device is provided for performing the method as described in any of the implementations of the first to second aspects above.

[0025] Compared with the prior art, the solution provided in this application has at least the following beneficial technical effects:

[0026] (1) This invention proposes an equivalent mathematical model of the specific impulse drop fault in the equation of motion and an objective function for the lower boundary of the search adaptation range, which can more realistically reflect the impact of the engine specific impulse drop fault on the rocket's remaining payload capacity.

[0027] (2) The iterative planning method proposed in this invention, which sequentially traverses different remaining thrust percentages, can improve the calculation time of each planning and converge to the lower bound of the propellant leakage percentage corresponding to the remaining thrust percentage when the thrust failure is severe.

[0028] (3) The remaining payload capacity assessment method for liquid rocket specific impulse reduction failure proposed in this invention can combine the coupling relationship between specific impulse and flow rate per second of engine thrust reduction failure to form a motion equation constraint that is closer to the actual situation, thereby calculating a more accurate remaining payload capacity assessment boundary. Attached Figure Description

[0029] Figure 1 This application proposes a method for evaluating the remaining carrying capacity based on numerical programming after a decrease in specific impulse. Detailed Implementation

[0030] The present application will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0031] To assess whether the rocket's remaining payload capacity can deliver the payload to the target orbit or a safe parking orbit after a specific impulse descent failure, this application proposes a numerical programming-based method for evaluating the remaining payload capacity after specific impulse descent. By establishing an equivalent mathematical model of the specific impulse descent failure in the equation of motion, the failure is introduced into the trajectory planning problem. By iterating through different failure occurrence times t0, the percentage of remaining thrust κ that the rocket can insert into orbit, and the percentage of propellant leakage τ, the failure adaptation boundary is obtained.

[0032] This method first searches offline for the fault tolerance ranges under different combinations of characteristic quantities, identifying the possible locations where the rocket can reach the target orbit and safe parking orbit, and assesses the remaining payload capacity after a fault to deliver the payload. Finally, the fault tolerance ranges are offline-attached to the rocket. After a fault occurs, based on three quantities—fault occurrence time, remaining thrust percentage, and propellant leakage percentage—the corresponding tolerance range is quickly identified, enabling the assessment of remaining payload capacity. The specific implementation steps are as follows.

[0033] 1) Establish an equivalent mathematical model of the specific impulse descent fault in the equation of motion.

[0034] One manifestation of thrust reduction due to decreased specific impulse is the simultaneous decrease in flow rate per second and fuel leakage, equivalent to a reduction in total impulse. This results in a decrease in thrust acceleration and a shortened combustion time due to fuel leakage. To address thrust reduction caused by specific impulse, by introducing the remaining thrust percentage κ into the mass differential equation and thrust calculation equation, and considering the fuel leakage percentage τ, and incorporating it into the mass differential equation, an equivalent mathematical model of specific impulse reduction in the equations of motion is formed:

[0035]

[0036] T=κ·dmI sp g0

[0037] Where r, V, u, and g represent position, velocity, thrust direction, and gravitational vector, respectively; T is the thrust amplitude; dm is the flow rate per second; and I is the gravitational vector. sp ρ is the specific impulse, and g0 is the standard Earth gravitational acceleration.

[0038] 2) Propose an optimization objective function

[0039] Given the failure time and remaining thrust percentage κ during planning, the search aims to find the maximum tolerable fuel leakage percentage τ. Therefore, the optimization objective function is set as maxτ. In other words, the search should proceed in the direction that increases τ as much as possible.

[0040] 3) Fast convergence iterative programming for different remaining thrust percentages

[0041] Given the time of failure, iterate through the remaining thrust percentage sequence S. κ ={κ1,κ2,…,κ n}, where κ1>κ2>…>κ n The following uses the i-th remaining thrust percentage κ. i For example, in the i-th remaining thrust percentage κ i Under the condition of searching for τ i The maximum value.

[0042] The fuel leakage percentage needs to satisfy the equivalent mathematical model in step 1). In actual calculations, for multiple grid nodes on the rocket body, the solution to the above equivalent mathematical model is prone to non-convergence. In some embodiments provided in this application, m intervals are defined, where the j-th interval is [τ i,j ,τ i,j+1 ], j = 1, 2, ..., m, and τ i,1 =0. In the search for τ i During the process of maximizing τ, i The above intervals are traversed sequentially from smallest to largest (i.e., starting from the direction j=1→j=m) until τ is found in a certain interval. i If the value is different from the maximum endpoint value of the interval, then the subsequent intervals will not be traversed.

[0043] The following example uses the j-th interval. When in [τ] i,j ,τ i,j+1 When searching within an interval, set τ i ∈[τ i,j ,τ i,j+1 ]. Then, using the trajectory of the (j-1)th planning as the initial conjecture, in [τ i,j ,τ i,j+1 Within the range, the maximum fuel leakage percentage τ i Given the objective function, construct a nonlinear programming problem that satisfies the constraints of the specific impulse descent motion equations, remaining fuel constraints, and target trajectory terminal constraints.

[0044] maxτ i

[0045]

[0046] If τ i,max=τ i,j+1 Then, taking the trajectory of the j-th planning as the initial conjecture, calculate the τ corresponding to j = j + 1. i,max until τ i,max <τ i,j+1 At that time, we obtain κ. i The maximum percentage of fuel leakage that can be tolerated under certain conditions, τ i,max .

[0047] In one embodiment, numerical optimization methods (such as interior-point method, sequential quadratic programming, and Newton's method) are used to solve for the flight trajectory that satisfies all constraints, and the corresponding maximum fuel leakage percentage τ is obtained. i,max .

[0048] In another embodiment, in [τ i,j ,τ i,j+1 Solving for τ over an interval i,max At that time, τ can be set first. i,max =τ i,j+1 According to τ i,j The corresponding flight trajectory is used as an initial conjecture, and an attempt is made to plan the flight trajectory based on the constraints mentioned above. If the flight trajectory can be planned, it could mean that τ i,max The actual value may be greater than τ i,j+1 Then in the next interval [τ i,j+1 ,τ i,j+2 Continue the search. If a flight path cannot be planned, it could mean τ i,max The actual value may be less than τ i,j+1 Then in [τ i,j+1 ,τ i,j+2 The range was gradually narrowed down to further determine τ. i,max The accurate output value.

[0049] In some embodiments, in κ i (i=1,…,n-1) After the first calculation of the maximum fuel leakage percentage between [τ1,τ2], the corresponding flight trajectory is recorded as κ. i+1 The initial conjecture for the first solution. This helps improve the convergence of the algorithm during the traversal process. When i=1, the standard trajectory without faults is used as the initial conjecture.

[0050] 4) Fast convergence iterative planning for different failure occurrence times

[0051] Given a time series S of possible failures t ={t1,t2,…,t p}, where t1 <t2<…<t p At time t of the kth failure occurrence k Under the condition of t kTime and t k The standard trajectory (i.e., standard trajectory) after time step 1 is the initial conjecture for the first planning of κ1. Step 3) is executed to obtain the maximum fuel leakage percentage set {(κ i ,τ i,max )|i=1,…n}.

[0052] Iterate through t1 to t2 in sequence p This allows us to obtain the maximum fuel leakage percentage corresponding to the total failure time and thrust reduction percentage, and define the remaining carrying capacity assessment set as {(t k ,κ i ,τ i,max )|k=1,…,p; i=1,…n}.

[0053] In practical applications, the planning result of step 4) {(t} can be used to plan the result of step 4) {(t} k ,κ i ,τ i,max The sequence |k = 1, ..., p; i = 1, ..., n} is stored in the onboard computer. When a specific impulse drop fault occurs during flight, the onboard computer can determine the cause based on the fault occurrence time t. fault and thrust decrease percentage κ fault Determine the maximum percentage of fuel leakage that can be tolerated.

[0054] In some embodiments, the fault occurrence time t can be used as a reference. fault The time interval in which the fault occurred [t] k ,t k+1 ], and the percentage decrease in thrust κ fault The thrust reduction percentage range [κ] i ,κ i+1 In the remaining carrying capacity assessment set, according to (t) k ,κ i ,τ i,max ), (t k+1 ,κ i ,τ i,max ), (t k ,κ i+1 ,τ i+1,max ) and (t k+1 ,κ i+1 ,τ i+1,max The maximum fuel leakage percentage that can be accommodated is obtained by interpolation.

[0055] In one embodiment, if the actual percentage of fuel leakage during the fault... The remaining carrying capacity is sufficient. If the actual percentage of fuel leakage during the fault... If the remaining carrying capacity is insufficient, additional methods are required to complete the flight mission normally.

[0056] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope defined in the claims of the present invention.

Claims

1. A method for evaluating residual carrying capacity based on numerical programming after a decrease in specific impulse, characterized in that, The method includes: Retrieve the remaining carrying capacity assessment set {( t k , κ i , τ i,max )| k =1,…, p ; i =1,… n }; Based on the time of failure t fault and percentage decrease in thrust κ fault Based on the aforementioned remaining carrying capacity assessment set, the maximum percentage of fuel leakage that can be accommodated is determined. τ max fault ; Among them, in the remaining carrying capacity assessment set {( t k , κ i , τ i,max )| k =1,…, p ; i =1,… n }middle,( t k , κ i , τ i,max ) indicates the first k Time of occurrence of each fault t k , No. i Percentage of remaining thrust κ i Maximum fuel leakage percentage under certain conditions τ i,max , ( t k , κ i , τ i,max In ) τ i,max It is based on the first k Time of occurrence of each fault t k , No. i Percentage of remaining thrust κ i Given the constraints, the objective function is optimized through a search. get; In the k Time of occurrence of each fault t k Under the conditions, No. i Percentage of remaining thrust κ i Maximum fuel leakage percentage under certain conditions τ i,max Obtained through the following methods: from j =1 j =m traverses the interval in the direction of [ τ i,j , τ i,j+1 ], j =1, 2, …, m and τ i,1 =0, in [ τ i,j , τ i,j+1 Within the interval, the objective function is optimized by search. A search is performed for the objective function to obtain the maximum percentage of fuel leakage. τ i,max ,like τ i,max = τ i,j+1 Then in the next interval [ τ i,j+1 , τ i,j+2 Continue searching within [the search area]; if τ i,max < τ i,j+1 The output will be at the 1st position. k Time of occurrence of each fault t k Under the conditions, No. i Percentage of remaining thrust κ i Maximum fuel leakage percentage under certain conditions τ i,max .

2. The method according to claim 1, characterized in that, The constraint conditions include at least one of the following: specific impulse degradation equation constraint, remaining fuel constraint, and target orbit terminal constraint.

3. The method according to claim 2, characterized in that, The specific impulse descent motion equations are constrained to satisfy: , ,in r , V , u , g These represent position, velocity, thrust direction, and gravitational vector, respectively. T For thrust amplitude, dm For per second of data, I sp For the sake of the specific impulse, g 0 represents the standard Earth's gravitational acceleration. κ This represents the percentage of remaining thrust. τ Percentage of fuel leak.

4. The method according to claim 1, characterized in that, In the i Percentage of remaining thrust κ i Under the condition, in [ τ 1 , τ The flight trajectory corresponding to the maximum fuel leakage percentage obtained within the interval [2] is the flight path in the [2]th [interval]. i +1% remaining thrust κ i+1 Under the conditions, [ τ 1 , τ 2] Initial conjecture on the search within the interval.

5. The method according to claim 1, characterized in that, In the k Time of occurrence of each fault t k conditions, t k Time and t k The standard trajectory after a certain time is based on the remaining thrust percentage. κ 1 condition, [ τ 1 , τ 2] Initial conjecture on the search within the interval.

6. The method according to claim 1, characterized in that, The determination of the maximum acceptable fuel leakage percentage τ max fault ,include: Based on the time of failure t fault The time interval in which the fault occurred [ t k , t k+1 ], and the percentage decrease in thrust. κ fault The thrust reduction percentage range [ κ i , κ i+1 ], in the remaining carrying capacity assessment set {( t k , κ i , τ i,max )| k =1,…, p ; i =1,… n In}, according to ( t k , κ i , τ i,max ), ( t k+1 , κ i , τ i,max ), ( t k , κ i+1 , τ i+1,max )and( t k+1 , κ i+1 , τ i+1,max The maximum fuel leakage percentage that can be accommodated is obtained by interpolation. τ max fault .

7. A method for determining the remaining carrying capacity under conditions of decreasing specific impulse, characterized in that, including: from t 1 t p Traversing the time series in different directions S t ={ t 1, t 2,…, t p }, t 1< t 2<…< t p , among which, in the first k Time of occurrence of each fault t k Under the conditions, from κ 1 κ n Traverse the remaining thrust percentage sequence in the direction S κ ={ κ 1, κ 2,…, κ n }, κ 1> κ 2>…> κ n To determine the remaining carrying capacity assessment set {( t k , κ i , τ i,max )| k =1,…, p ; i =1,… n }, ( t k , κ i , τ i,max ) indicates the first k Time of occurrence of each fault t k , No. i Percentage of remaining thrust κ i Maximum fuel leakage percentage under certain conditions τ i,max ; In the i Percentage of remaining thrust κ i Under the conditions, from j =1 j =m traverses the interval in the direction of [ τ i,j , τ i,j+1 ], j =1, 2,…, m and τ i,1 =0, in [ τ i,j , τ i,j+1 Within the interval, based on the constraints, the objective function is optimized through a search. A search is performed for the objective function to obtain the maximum percentage of fuel leakage. τ i,max ,like τ i,max = τ i,j+1 Then in the next interval [ τ i,j+1 , τ i,j+2 Continue searching within [the search area]; if τ i,max < τ i,j+1 The output will be at the 1st position. k Time of occurrence of each fault t k Under the conditions, No. i Percentage of remaining thrust κ i Maximum fuel leakage percentage under certain conditions τ i,max .

8. An electronic device, characterized in that, The electronic device is used to execute the method according to any one of claims 1 to 7.

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