Physical constraint enhanced airborne equipment degradation trajectory characterization and task dynamic regulation method

Abstract

The application discloses a physical constraint enhanced airborne equipment degradation trajectory characterization and task dynamic regulation method, comprising the following steps: adaptively sampling sample points on the constraint boundary of a flight envelope; establishing a local differential geometry framework at each sample point; calculating a constraint tightness tensor under the geometry framework of the sample point, which is used to evaluate the motion trend and state of the current aircraft under the definition of the limit constraint; and using the global constraint tightness tensor in flight envelope monitoring to protect the flight envelope. The application aims at analyzing and describing the problem that the existing flight envelope protection technology cannot quantify the coupling effect of the constraint boundary curvature in the intersection region where multiple constraints are active at the same time, the safety margin of the aircraft in the "corner point" region is overestimated, and the existing technology only monitors the distance from the current state to the boundary and cannot identify the hidden risk that "the front envelope is rapidly narrowing", leading to the problem of sudden multiple violations in high-speed maneuvering.

Description

Technical Field

[0001] This invention relates to the field of aircraft flight control and trajectory planning technology, and more specifically, to a method for characterizing the decay trajectory of airborne equipment and dynamically controlling the mission with enhanced physical constraints. Background Technology

[0002] Flight envelope protection technology is a core mechanism for ensuring the safe operation of aircraft. Its main purpose is to ensure that aircraft remain within safe operating boundaries when faced with multiple physical and system constraints such as altitude, speed, angular rate, and power. With the increasing demands of high-dynamic missions and the increasing complexity of flight environments, aircraft often need to perform high-speed maneuvers under extreme conditions close to safety boundaries.

[0003] Traditional first-order monitoring methods calculate static distances based on scalars, measuring the shortest Euclidean distance from the state point to the constraint boundary. However, the boundaries of the intersection regions ("corner points") where these constraint boundaries (such as stall, height loss, and insufficient power) are active are not smooth. Traditional first-order monitoring will produce derivative singularities in these places, leading to significant deviations in the safety margin calculation.

[0004] In traditional flight envelope algorithms, the envelope boundary is typically defined by a set of functions. Composed of, among which It is the state vector of the aircraft, and the most common method is to use a function. The derivative tells the system which direction it should move to before hitting the boundary, and which direction it should move to avoid danger. At this point, the function... derivative Its main function is to act as a "risk avoidance compass". However, when two constraints intersect at a "corner point", if the boundary is not smooth, the derivative will be "uncomputable" at that point, especially when considering regions with overlapping constraints.

[0005] For example, for composite boundary functions with overlapping constraints. ,exist place ( and of), Defined as:

[0006]

[0007] That is when Approaching from region 1, Defined as ,when Approaching from region 2, Defined as ,when This results in the directional derivative at that point not being unique, meaning that at the "corner point"... The absence of a directional derivative at a singularity makes it impossible to calculate a unique normal vector and assess the maneuver state space of the current state. This situation leads to a severe overestimation of the aircraft's operational margin. The aircraft may be operating in a rapidly contracting narrow passage. Although the maneuver space appears ample based on the static distance calculated from the distance envelope constraint, the envelope boundary is actually closing rapidly, and the "maneuver margin" may be almost zero in the next instant. Such an aircraft exhibits poor flight stability.

[0008] In summary, existing flight envelope protection technologies and condition monitoring architectures have the following significant drawbacks when dealing with complex, high-dimensional, nonlinear constraints:

[0009] 1. Lack of geometric perception: Traditional methods are mostly based on first-order distance (absolute distance from the state point to the boundary) for monitoring, which cannot identify "corner" regions caused by the interweaving of multiple physical constraints. In these regions, due to the coupling effect of boundary curvature, the available maneuver space will narrow sharply, leading to an overestimation of the safety margin.

[0010] 2. Lagging status monitoring: Existing technology has difficulty identifying the trend risk of "the envelope ahead is narrowing" and cannot predict sudden multiple defaults during high-speed maneuvers.

[0011] 3. Health status decoupling: The flight envelope is usually a static boundary defined based on the design state, which fails to couple the performance degradation trajectory of airborne equipment (such as power system and control system) in real time, resulting in the failure of protection mechanisms when the equipment is damaged. Summary of the Invention

[0012] The purpose of this invention is to provide a method for characterizing the decay trajectory of airborne equipment and dynamically controlling the mission with enhanced physical constraints, so as to solve the problems in the background art.

[0013] The technical solution to achieve the purpose of this invention is as follows:

[0014] A method for characterizing the decay trajectory of airborne equipment and dynamically controlling the mission with enhanced physical constraints includes:

[0015] Step 1: Adaptively sample points on the constraint boundary of the flight envelope;

[0016] Step 2: Establish a local differential geometry framework at each sampling point;

[0017] Step 3: Calculate the constraint tightness tensor within the differential geometry framework of the sampling points to evaluate the current motion trend and state of the aircraft under the defined constraints.

[0018] Step 4: Use the global constraint tightness tensor in flight envelope monitoring to perform flight envelope protection.

[0019] Furthermore, step 1 specifically includes:

[0020] Step 1-1, Define the safety envelope, including: defining the aircraft's state vector. ,definition One safety constraint, namely A set of original boundary conditions, denoted as . The security constraints include constraints on discrete envelopes and piecewise linear envelopes.

[0021] Steps 1-2: Constructing continuously differentiable boundary functions: The analytical reconstruction method of single-constraint boundaries based on third-order B-splines is used to process and map the original boundary conditions, generating boundary functions that satisfy at least second-order continuous differentiability. The global security zone is defined as follows: ;

[0022] Steps 1-3, based on boundary functions Constructing a global cohesion function And define new safe flight zones for aircraft. The global condensation function and the safe flight area are:

[0023] ;

[0024] ;

[0025] in Sensitivity factor; increase Reduce the buffer band, reduce Increase the buffer zone;

[0026] Steps 1-4, Adaptive Feature Sampling: At the analytical boundary Uniform sampling is performed on the data to obtain the basic point set. .

[0027] Furthermore, the construction of continuously differentiable boundary functions in steps 1-2 specifically includes:

[0028] Step 1-2-1: Within the controlled two-dimensional state space of the aircraft, the physical effective range is delineated according to the envelope monitoring requirements, and axial discretization is performed to construct a two-dimensional structured observation grid covering the entire flight state.

[0029] Step 1-2-2: Extract discrete coordinates representing the physical boundary limits from the aerodynamic database to obtain a discrete set of physical boundary points;

[0030] Steps 1-2-3: For any intersection point in the two-dimensional structured observation grid, calculate the minimum geometric metric from it to the discrete physical boundary point set, and assign a symbolic value with negative inside and positive outside based on the topological inclusion relationship between the intersection point and the safety envelope, directly generating the normalized safety margin truth value at the intersection point, and obtaining the distance field truth matrix.

[0031] Steps 1-2-4: Construct a B-spline distance field function with the state vector as the joint independent variable. Using the calculated true value matrix of the distance field, inversely calculate the control vertex weight matrix of the B-spline distance field function to generate a boundary function that is at least second-order continuously differentiable.

[0032] Furthermore, the state vector includes flight speed and pitch angle, and the safety constraints include:

[0033] ;

[0034] ;

[0035] in, The current flight speed is a scalar value. The pitch angle, For the weight of the aircraft, air density, For wing area, The maximum lift coefficient, The maximum design normal overload factor allowed by the aircraft airframe structure. For pitch angle The monotonic pneumatic mechanism function.

[0036] Furthermore, the B-spline distance field function in steps 1-2-4 is:

[0037]

[0038] in Let M be the weight matrix of the two-dimensional spline control vertices to be solved, M be the total velocity coordinates of the two-dimensional structured observation grid under all flight conditions, N be the total pitch coordinates of the two-dimensional structured observation grid under all flight conditions, and p and q be the index variables of the double summation of M+3 and N+3. , These are the third-order B-spline basis functions corresponding to velocity and pitch angle, respectively. , Using the Cox-deBoor algorithm for velocity axis parameters and pitch axis parameters The solution is obtained recursively.

[0039] Boundary functions that satisfy the condition of being twice continuously differentiable include:

[0040] ;

[0041] ;

[0042] in and These are the control vertex weight matrices corresponding to the stall boundary and structural overload mechanism constraints, respectively. , These are the maximum and minimum flight speeds. , These are the maximum and minimum pitch angles. This indicates that the aircraft is within a safe airspeed range that meets aerodynamic lift requirements. This indicates that the actuator is within the safe overload range that does not exceed the allowable strength of the structure.

[0043] Furthermore, step 2 specifically includes:

[0044] Step 2-1, for a certain sampling point Calculate vector This vector uniquely and smoothly represents the vector formed by... The analytical boundary normal vector is formed by coupling the original boundary conditions; the contribution factor is defined. ,but Represent as ,when Approaching 1 indicates that the first The constraint is in a dominant and active state;

[0045] Step 2-2, construct the diagonal weight matrix The weights in the matrix are preset values. Weighted norm-based normalization is then applied to the analytical boundary normal vectors, resulting in:

[0046] ;

[0047] Steps 2-3, based on The unique weighted normalized normal vector at the point is used to solve the orthogonal complement tangent space, and SVD decomposition is performed to obtain the tangent space basis matrix.

[0048] Furthermore, steps 2-3 specifically include:

[0049] Step 2-3-1: Construct the matrix to be decomposed based on the normal vector. ;

[0050] Step 2-3-2, SVD decomposition implementation: For Perform singular value decomposition ;

[0051] Step 2-3-3: Extract the basis vectors to obtain the tangent space basis matrix.

[0052] .

[0053] Furthermore, step 3 specifically includes:

[0054] For global cohesion function and sampling points Calculate and define the weighted Hessian matrix. ,

[0055]

[0056]

[0057] in, It is a diagonal weight matrix;

[0058] Using the basis matrix of the tangent space Will Projected to In the tangent space, we obtain the global constraint compactness tensor:

[0059]

[0060] in The global constraint tightness tensor characterizes the anisotropic ensemble contraction pressure perceived by the aircraft as it moves on a currently safe and popular surface, induced by all constraints.

[0061] Furthermore, the global constraint tightness tensor is used in flight envelope monitoring to perform flight envelope protection, specifically including:

[0062] global constraint tightness tensor Perform eigenvalue decomposition:

[0063]

[0064] in Indicates the first The principal curvatures characterize the degree of bending of the constraint boundary in that characteristic direction. Indicates the first One principal direction, representing the principal axis direction of curvature change;

[0065] The largest eigenvalue among n-1 eigenvalues The corresponding principal axis direction indicates the undesirable direction; minimum eigenvalue The corresponding main axis direction indicates the optimal escape route;

[0066] based on Determine the flight risk level and implement flight envelope protection.

[0067] Furthermore, based on Determining the flight risk level includes:

[0068] This is a high-risk direction; if you proceed in this direction, the available space for maneuver will quickly disappear.

[0069] Medium risk, the width of the passage ahead remains unchanged;

[0070] Low risk, and the potential for growth is expanding.

[0071] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0072] (1) Achieving high-fidelity fully analytical manifold reconstruction of multi-physical constraint envelope constraints. This invention abandons the traditional discrete three-dimensional lookup table (LUT) or airborne nonlinear numerical iterative optimization that heavily relies on flight envelope monitoring. By introducing a high-order continuous mathematical analytical operator (analytical reconstruction of single-constraint boundaries based on third-order B-splines), the heterogeneous multi-mechanism physical constraints of multiple constraints (aerodynamic stall, structural overload, etc.) are transformed into a continuous implicit analytical field in the parameter domain, enabling the airborne computer to instantly output the fully analytical single-constraint distance measure through pure algebraic direct solution under limited computing power;

[0073] (2) Constructing a front-end protection mechanism based on a virtual "escape" within the security domain, this invention breaks through the traditional protection algorithm which must enter at the state point or cross the limit physical red line ( The hysteresis defect of hard cutoff control is only triggered when this condition is met. This invention creatively addresses this issue within the safe and feasible region (i.e., satisfying...). In the conventional flight zone, a preset equipotential surface threshold is introduced as a virtual hazard soft "enveloping line". When the aircraft's state approaches this specific equipotential surface, the protective mode is instantly triggered and the local differential geometry framework is activated, artificially constructing a defense mechanism before touching the real hard envelope line;

[0074] (3) Achieving advanced maneuvering pressure sensing through topological geometric feature extraction of non-boundary equipotential surfaces: This invention focuses on the triggering virtual equipotential surfaces ( It performs second-order differential geometric feature extraction, rather than strictly solving hard boundaries. The geometric characteristics at the location; the present invention utilizes the algebraic extension characteristics of the implicit analytical distance field in the whole space to directly solve for the danger perception normal vector of the virtual soft envelope at this location and the local principal curvature representing the compactness tensor; the design completely abandons the traditional "boundary orthogonal projection root-finding" iteration, and utilizes the continuous inward characteristics of the equipotential surface in space with distance, so that the system can analyze and predict the contraction and compression pressure of the available motorized pipeline ahead in the deep safety zone. Attached Figure Description

[0075] Figure 1 This is a flowchart of the general method for dynamic control proposed in this invention.

[0076] Figure 2 This is a flowchart of the method of the present invention that combines a PHM system and an alarm monitoring system. Detailed Implementation

[0077] Example 1

[0078] This embodiment addresses the problem that existing flight envelope protection technologies cannot quantify the coupling effect of constraint boundary curvature in intersection regions where multiple constraints are active simultaneously, leading to an overestimation of the safety margin of the aircraft in the "corner" region. Furthermore, existing technologies only monitor the distance from the current state to the boundary and cannot identify the hidden risk of "the forward envelope is narrowing rapidly," resulting in sudden multiple violations during high-speed maneuvers. This embodiment analyzes and describes the problem and provides a solution.

[0079] This embodiment provides a method for characterizing the decay trajectory of airborne equipment and dynamically controlling missions with enhanced physical constraints. It primarily adds second-order features to first-order monitoring. By defining a constraint tightness tensor for the geometric envelope constraints and performing eigenvalue decomposition, it can correspond to the decay rate of the aircraft's available maneuverability. In the "corner" region where multiple constraints overlap, the decomposition results of the above eigenvalues ​​often show multiple eigenvalues ​​being large positive values. This means that the boundaries are simultaneously squeezing inward in multiple dimensions, allowing the system to determine that "maneuverability space has instantly disappeared" and forcibly execute avoidance actions. Furthermore, this second-order curvature recognition mechanism can detect "dead-end" effects earlier than traditional first-order distance monitoring, guiding the aircraft system to maneuver in the direction of minimum (or even negative) eigenvalues. This achieves a technological leap from passive over-limit defense to active geometric perception, and can even buy a few seconds of warning time for redundant system switching. Figure 1 The method specifically includes:

[0080] Step 1, adaptive sampling, is to collect sample points that accurately reflect the geometry, curvature features and high-risk areas on the constrained boundaries of the flight envelope.

[0081] To obtain a more comprehensive basic framework for the geometric flight envelope, the specific implementation method is as follows:

[0082] Step 1-1, Define the safety envelope: defined as the state vector of the aircraft. ,definition One safety constraint condition can be defined A set of original boundary conditions. In practical engineering, constraints usually exist in the form of discrete envelopes and piecewise linear envelopes, denoted as the original boundary condition set. .

[0083] Steps 1-2: Constructing continuously differentiable boundary functions: To facilitate subsequent analysis of the constrained boundary functions, the original boundary conditions are processed and mapped (analytical reconstruction of single-constraint boundaries based on third-order B-splines) to generate boundary functions that at least satisfy second-order continuous differentiability. The system's global security zone is defined as follows: .

[0084] Steps 1-3: Construct a global condensation function: when multiple "smooth boundaries" are present. When they intersect, their intersection lines (intersection points / corner points of the envelopes) will exhibit singularities in their derivatives, making it impossible to analyze local features. In this multi-constraint superposition region, the shrinkage of the safety margin is caused by the combined effect of multiple constraint boundaries. Therefore, to address this situation, a global function should be constructed. :

[0085]

[0086] in As a sensitivity factor, and defining a new safe flight zone (inside the envelope) for the aircraft as follows:

[0087]

[0088] By adjusting The value can directly change the new safe zone. The degree of conservatism, among which increasing It can reduce the buffer zone, which is suitable for situations where the aircraft is in good condition and environmental interference is minimal. In such cases, the system allows the aircraft to approach its physical limits to achieve higher maneuverability; on the other hand, it reduces... The buffer band can be increased, at which point the new analytical boundary is formed. It will shrink significantly into the safe zone, forcing the system to reserve more physical redundancy.

[0089] Steps 1-4, Adaptive Feature Sampling: First, at the analytical boundary... Uniform sampling is performed on the data to obtain the basic point set. .

[0090] Step 2: Establish a local differential geometric framework at each sampling point to provide a "coordinate system" and "metric" for the subsequent construction of the constraint compactness tensor field. The specific implementation is as follows:

[0091] Step 2-1, define the active constraint set for a given sampling point. ,calculate This vector uniquely and smoothly represents the vector formed by... The analytical boundary normal is formed by the coupling of the original constraints. The contribution factor is defined. ,So It can also be expressed as ,when Approaching 1 indicates that the first The physical constraints are in a dominant and active state.

[0092] Step 2-2, performing weighted norm-based normalization: Unlike the standard Gram-Schmidt orthogonalization, which yields a standard basis for normal vectors, this method is not applicable in aircraft engineering scenarios. Different constraints may have different requirements for the normal vector basis. For example, the gradient direction for exceeding roll angle limits and the gradient direction for ground contact are treated equally in orthogonalization, causing the normal space basis to fail to reflect the engineering semantics of "which violation directions are more fatal." Specifically, a diagonal weight matrix is ​​constructed for the defined engineering priorities. ,

[0093] Perform weighted norm-based normalization of the normal vector:

[0094]

[0095] Unlike standard normalization, this process ensures that when the aircraft approaches multiple boundaries simultaneously, the normal vector... Will due to The gain effect automatically aligns to the "most fatal" default direction.

[0096] Steps 2-3, implement SVD decomposition: based on The unique weighted normal vector at a given location (the normal space is always one-dimensional) is used to solve for the orthogonal complement tangent space. The specific implementation is as follows:

[0097] Step 2-3-1, Construct the matrix to be decomposed: Define the matrix ;

[0098] Step 2-3-2, SVD decomposition implementation: For Perform singular value decomposition ;

[0099] Step 2-3-3, Basis Vector Extraction: Sampling Points tangent space basis The last part of the matrix Column vector composition:

[0100] .

[0101] Step 3, calculate the constraint tightness tensor at the above sampling points. Under the geometric framework, a constraint tightness tensor is defined to evaluate the current motion trend and state of the aircraft under the defined constraints. Specifically, the implementation is as follows:

[0102] Define the global constraint compactness tensor It is used to evaluate the local space contraction tendency and maneuvering pressure of an aircraft under a comprehensive constraint definition, targeting the global condensation function. and sampling points Calculate and define the weighted Hessian matrix. for:

[0103]

[0104] Among them It is the diagonal weight matrix from step 2. .

[0105] Using the basis matrix of the tangent space Will Projected to The tangent space at a point is specifically manifested as:

[0106]

[0107] in It is called the global constraint compactness tensor, which characterizes the anisotropic ensemble contraction pressure perceived by the aircraft as it moves on a currently safe and popular surface, induced by all constraints.

[0108] Step 4: Apply the global constraint tightness tensor to flight envelope monitoring.

[0109] Based on the above description of the global constraint compactness tensor, the global constraint compactness tensor... yes A symmetric matrix of dimension, for Perform eigenvalue decomposition:

[0110]

[0111] Among them, eigenvalues Indicates the first The principal curvatures characterize the degree of bending of the constraint boundary in that characteristic direction. No. The principal directions characterize the main axis directions of curvature changes. Flight risk assessment based on eigenvalues ​​is shown in Table 1.

[0112] Table 1 Flight Risk Assessment Table

[0113]

[0114] Eigenvalue decomposition transforms the compactness tensor into engineering-readable information of "most dangerous direction - degree of danger" and "safest direction - degree of looseness": the largest eigenvalue. Quantify the abruptness of the contraction of the anterior envelope, its principal direction. Indicates the direction that cannot be reached; minimum eigenvalue The information, including its direction, indicates the optimal escape route and directly drives alarm levels, flight control gain scheduling, pilot displays, and ground maintenance decisions.

[0115] Compared with existing technologies, this invention does not simply monitor the static distance between the flight state and the safety boundary. Instead, it extracts the second-order geometric features of the boundary by constructing a constraint compactness tensor field based on the original discrete constraint boundary. This invention provides a method for constructing a constraint compactness tensor field, transforming the motion planning problem of an aircraft within a safety envelope in a high-dimensional, nonlinear environment with complex constraints into a state-space problem. The concept of hypersurface is used, and a constraint tightness tensor field is constructed by localizing geometric features. This is used to describe the constraint tightness at the current moment of flight in a quantitative form. This is to solve the problem of the aircraft's ability to assess its geometric perception of the safety boundary in real time during flight, and to generate trajectory planning and safety decisions with geometric safety assurance.

[0116] Example 2

[0117] This embodiment uses examples to illustrate... The case where the state variables are flight speed and pitch angle will be explained in detail.

[0118] The airborne system acquires the three-axis aerodynamic velocity components of the aircraft in the body coordinate system in real time, using the Euclidean norm formula. As one of the state variables, in the transition mode of eVTOL or the climb phase of a fixed-wing aircraft, the coupling of flight speed and pitch angle constitutes the most sensitive region in the flight envelope.

[0119] On the one hand, defining the aerodynamic stall boundary and defining the velocity. With pitch angle The analytical relationship is as follows (the larger the pitch angle (the steeper the climb), the different the minimum level flight speed required to maintain lift):

[0120]

[0121] It is one of the defined constraint boundaries, where The current flight speed is a scalar value. The pitch angle, For the weight of the aircraft, air density, For wing area, This is the maximum lift coefficient. and Dynamic variables are used as state variables.

[0122] On the other hand, the structural overload mechanism constraint is defined, and the structural overload boundary restricts the maximum load of the aircraft under high dynamic pressure or severe pitch maneuvering conditions, as follows:

[0123]

[0124] The maximum design normal overload factor (constant) allowed by the aircraft airframe structure. For pitch angle The monotonic aerodynamic principle function, when It maps the boundary line between the maximum allowable overload speed of the structure, when This indicates that the aircraft is overloaded and exceeds its limits, posing a risk of structural disintegration.

[0125] In practical engineering applications, relying solely on mechanistic formulas often fails to capture complex aerodynamic interferences in transition modes. Therefore, the following implementation steps are used to reconstruct the constraint boundaries (i.e., in two-dimensional state space). The data-driven implicit analytic manifold reconstruction process (constructing analytic surfaces on top of each other), i.e., the reconstruction of the envelope implicit analytic manifold, includes:

[0126] This implementation uses a discrete set of boundary points as a physical reference at the ground end. By calculating the symbolic distance field from this point to a two-dimensional structured grid, the unstructured aerodynamic limit truth is analytically isomorphically mapped to the control weights of a tensor product B-spline surface. The specific control method in this embodiment includes:

[0127] 1. Construction of a fully state-space structured mesh.

[0128] Within the controlled two-dimensional state space of the aircraft, the physical effective range is delineated according to the envelope monitoring requirements, and axial discretization is performed independently to construct a two-dimensional structured observation grid covering the entire flight state.

[0129] Define the discrete coordinate set of the velocity axis as: Define the discrete coordinate set of the pitch angle axis as .

[0130] 2. High-fidelity discrete physical boundary extraction.

[0131] Discrete coordinates characterizing physical boundary limits (such as stall critical points) are extracted from publicly available high-fidelity aerodynamic databases, accurately mapping the real physical limits that include complex aerodynamic interference effects:

[0132] .

[0133] 3. Symbolic dimensionality reduction of physical truth values ​​and direct acquisition of weight coefficients.

[0134] For any intersection point in the two-dimensional structured mesh Calculate its distance to the set of discrete physical boundary points. The minimum geometric metric is used, and a symbolic assignment of negative inside and positive outside is performed based on the topological inclusion relationship between the intersection point and the safety envelope, directly generating the normalized safety margin truth value at the intersection point. The specific implementation is as follows:

[0135] For any intersection point on a pre-constructed two-dimensional structured mesh in the state space Traverse the extracted high-fidelity discrete physical boundary point set Using the Euclidean distance operator in metric space, the minimum absolute geometric distance from the grid intersection to the real physical boundary is calculated. :

[0136]

[0137] Based on the topological inclusion relationship between grid intersections and the safety envelope, a symbolic assignment of negative inner values ​​and positive outer values ​​is performed to directly generate the normalized safety margin truth value at that grid point. For any intersection point on a two-dimensional structured mesh Its normalized safety margin true value The algebraic definition of:

[0138]

[0139] in

[0140]

[0141] Through the above mapping, the originally scattered unstructured aerodynamic limit values ​​are successfully upgraded to a continuous scalar range field truth matrix covering the entire two-dimensional state space:

[0142]

[0143] The true value of each item in this matrix Its size directly represents the safety margin of the aircraft at the current state point.

[0144] 4. Analysis of control weights based on tensor product B-spline surfaces.

[0145] To obtain the continuous and analytically differentiable single-constraint boundary field function directly from the airborne end, this step utilizes the ground-based calculated true range field matrix. Inversely, the control vertex weight matrix of the B-spline surface is calculated. The specific implementation of the equations for the two-dimensional analytic surface (signed distance field analytic surface) involves constructing a velocity-based... With pitch angle Two-dimensional B-spline distance field function with joint independent variables :

[0146]

[0147] in The elements of the two-dimensional spline control vertex matrix to be solved are: , The Cox-deBoor algorithm was used to apply the velocity axis parameters respectively. and pitch axis parameters The third-order B-spline basis functions obtained by recursion are, where , These are the normalized parameter domain variables, where , The specific implementation of the solution is as follows:

[0148] 1) Build speed The axis node vector is:

[0149]

[0150] in internal nodes It satisfies strict monotonically increasing, that is .

[0151] First, define the zeroth-order basis functions. ,in .

[0152] Next, define first-order basis functions. ,here The resulting boundary is continuous but not differentiable, meaning there are "bends" at the nodes, which still cannot meet the requirements for calculating the Hessian matrix.

[0153] Next, define second-order basis functions. ,here .

[0154] Finally, define the third-order basis functions. ,here .

[0155] Similarly, for constructing the pitch angle Axis node vector , can be obtained To obtain the analytic basis functions and ,in .

[0156] 2) Solve for the constructed range field function In .

[0157] Take discrete state quantities respectively: velocity Mapped to The above is recorded as ,Right now State variables Mapped to The above is recorded as ,Right now Substitute into the basis functions and middle, traverse all and Generate static basis matrices for velocity axes covering all nodes in the mesh. Static basis matrix of pitch angle axis Retrieve the high-fidelity discrete symbolic distance truth matrix generated in advance based on the topological distance between the state space grid point set and the real physical boundary. By analyzing the above elements The generated matrix is ​​denoted as ,So The specific expression is:

[0158]

[0159] in The static basis matrix of the velocity axis The generalized inverse, This is the generalized inverse of the static basis matrix of the pitch angle axis. This allows for the one-time offline demodulation of a constant matrix containing all unknown weights. It is then stored as an analytical geometric graph for use in airborne analytical range field functions. High-frequency real-time online reproduction. That is:

[0160]

[0161] in The parameters are known.

[0162] 3) Instantiation mapping and analytical field construction of multi-physics boundaries.

[0163] Based on the above-mentioned data-driven implicit analytic manifold reconstruction process, a general framework for full-state-space two-dimensional tensor product B-spline analytic reconstruction is established. For the two previously defined constraints—aerodynamic stall boundary and structural overload mechanism—corresponding analytic distance field functions are constructed, denoted as follows: as well as ,in

[0164]

[0165]

[0166] in and These are the weight matrices corresponding to the stall boundary and structural overload mechanism constraints, respectively, and can be seen through the implicit analytic manifold reconstruction process of the envelope. This indicates that the aircraft is within a safe airspeed range that meets aerodynamic lift requirements. This indicates that the actuator is within the safe overload range that does not exceed the allowable strength of the structure.

[0167] 4. Construction of global analytical condensation function based on composite bounds.

[0168] In the actual flight envelope, the safe flight feasible region is essentially the logical intersection of the above-mentioned multiple single-constraint feasible regions (i.e., it must simultaneously satisfy...). as well as When the stall boundary and overload boundary geometrically intersect in the state space, a non-smooth "corner" is generated at the intersection. At such corners, the local first derivative (normal gradient) undergoes a sudden abrupt change, causing the airborne flight control system to be unable to extract a valid second-order Hessian curvature tensor when approaching the corner, easily inducing severe chattering of the control actuators or control law divergence. To overcome the singularity of differentiation caused by multi-mechanism constraint interference, this invention constructs a global analytical condensation function covering the entire domain. :

[0169]

[0170] in As a sensitivity factor, and based on the mechanism of constructing a globally analytical condensation function, It must be strictly wrapped by as well as Within the feasible region jointly formed. According to The properties of which increase It can reduce the buffer zone, which is suitable for situations where the aircraft is in good condition and environmental interference is minimal. In such cases, the system allows the aircraft to approach its physical limits to achieve higher maneuverability; on the other hand, it reduces... The buffer band can be increased, at which point the new analytical boundary is formed. It will shrink significantly into the safe zone, forcing the system to reserve more physical redundancy.

[0171] 5. Analytical boundary adaptive feature sampling and local differential geometric framework construction.

[0172] For surface sampling points (satisfy Its two-dimensional composite gradient vector Based on the chain rule, direct instantiation expands to:

[0173]

[0174] in , , representing the contribution factor of each constraint.

[0175] Define a diagonal weight matrix for engineering priorities specific to the two-dimensional state axis. ,in Characterizing the penalty gain for airspeed default, The penalty gain characterizes the attitude angle violation, where the sampling point is... Unit normal vector The component analytical expression is instantiated as:

[0176]

[0177] On the other hand, for a state space that is 2-dimensional, the sampling points The unit normal vector is Tangent space basis matrix It actually contains only one column vector. And it must satisfy the analytic orthogonality constraint:

[0178]

[0179] therefore, .

[0180] 6. Parallel solution of global constraint compactness tensor in multi-physics bounded systems.

[0181] To further dynamically and quantitatively assess the local space contraction trend and maneuvering pressure of an aircraft moving along the boundary under dual-constraint interference, the constraint tightness tensor was executed. Instantiation computation, for For the independent variable velocity and pitch angle Solve for the second-order partial derivatives and construct the quadratic derivative. for:

[0182]

[0183] In the formula, the second-order analytic partial derivatives of each term are all at specific boundary sampling points. The scalar values ​​are directly substituted into the calculation, and the diagonal weight matrix in step 5 is also used. Construct the weighted Hessian matrix at the current point using the symmetry operator. ,in:

[0184]

[0185] Through matrix multiplication instantiation, the elements of this weighted second-order characteristic matrix are precisely expressed as:

[0186]

[0187] Using the basis matrix of the tangent space Will Projected to The tangent space at that point is specifically:

[0188] Due to the tangent space matrix It strictly degenerates into a one-dimensional standard basis vector containing only a single column, and therefore has a global compactness tensor. ,Right now

[0189]

[0190] Expanded to:

[0191]

[0192] It is important to note that the global constraint compactness tensor... In this example, a scalar is calculated, therefore the unique principal curvature can be directly obtained. With the main direction scalar The unique and precise quantification of the current aircraft along the safe tangential direction During maneuvering, the degree of curvature and contraction pressure of the complex boundary encountered.

[0193] On the other hand, combining the physical risk mapping of stall and overload instances: This indicates that the feasible region shrinks sharply inward, and the boundary along... The direction shows a strong "inward bulge". The system senses that the available maneuver space is rapidly disappearing. Continuing to advance along the current tangential direction will face a fatal deadlock with "no speed to prevent stall and no margin to prevent overload". This indicates that the channel width remains essentially unchanged; This indicates that the aircraft is escaping the corner interference zone of stall and overload, and is maneuvering towards a space with more suitable speed and attitude.

[0194] This embodiment applies the above method to an existing PHM system, and the instantiation flowchart is as follows: Figure 2 As shown, it includes:

[0195] The PHM (Health Management System) detects when the aircraft's hardware performance deteriorates or degrades, and then calculates and outputs... To ensure that the envelope constraint of the current aircraft state contracts inward as a whole, due to the sensitivity factor It does not need to change at high frequencies with the vibration of the aircraft's attitude, so it is achieved through external low-frequency input.

[0196] Airborne sensors collect current speed at high frequency and pitch angle The cubic B-spline polynomial matrix stored in the onboard memory is directly substituted. (here) (Originally obtained using the offline Cox-deBoor algorithm), constructing the corresponding analytical field based on different constraint boundaries, and combining... Instantly outputs the "safe distance" from the current point to the composite boundary. (Global cohesion function).

[0197] Virtual soft packet threshold triggering: where This is the minimum envelope constraint of the current aircraft state. Based on the previous definition of the range field, the safe zone is defined as follows: Dangerous areas are defined in , This indicates that the aircraft is already in a danger zone. Therefore, to prevent this from happening, and in accordance with engineering considerations, a virtual soft envelope threshold is set. For global resolution, a virtual soft-packet threshold is set. ,when Trigger the system to instantly obtain activity weight At the same time, the compactness tensor is obtained. , It can pinpoint the "root cause" of a dangerous situation in an aircraft. It can be used as a current aircraft maneuver pressure sensor when the aircraft is rushing at high speed toward the boundary interference blind spot. The sudden increase can be characterized by the rapid collapse of the maneuver space.

[0198] Based on the input and triggered state value point The remaining distance calculated instantaneously And the causal risk item (by (Confirmed) Packed into a standard data bus message, it is sent to the integrated display unit (IDU), which is independent of the control closed loop. As a black box peripheral, the IDU does not need to parse complex spatial curvature, but directly triggers the corresponding directional alarm action based on the received cause code.

[0199] After triggering the soft-coverage wire protection mode (i.e.) (At time) the principal curvature of the equipotential surface will be obtained A filter for command control is introduced as a dynamic damping penalty term to limit and attenuate cockpit commands.

[0200] This embodiment eliminates the reliance on the underlying high-order dynamic trend equations of traditional envelope protection systems. Heavy reliance on [the technology / mechanism]. The airborne system only needs to receive the purely analytical geometric feature set calculated in real time. This allows for monitoring and dynamic task adjustments, including:

[0201] 1. Boundary topology degradation based on PHM (Health Management Module) (Strategic Layer): When the Predictive Health Management Module (PHM) senses that the airborne equipment is in a period of performance degradation, it can dynamically reduce the sensitivity factor. This algebraic operation forces the global condensation field to undergo conservative contraction at the physical interference corner (greatly ensuring the safety of the flight area of ​​unhealthy system states), achieving the effect of adaptive contraction of the envelope under physical degradation.

[0202] 2. Severity assessment and handling under multiple constraint physical boundaries: When the state point approaches the zero level set ( When this happens, the system instantly obtains the activity weight. ( This allows for the rapid identification of risk constraints and enables risk management for the identified "risk items" (e.g., in the example). The system will send the "overload" cause code to the integrated display unit and trigger an alarm.

[0203] 3. Based on compactness tensor Overshoot prevention dynamic limiting: The system limits the local tangential compactness tensor (principal curvature). By introducing a command-controlled filter, when the aircraft rushes at high speed towards the boundary interference blind spot, The sudden increase can be characterized by the rapid collapse of the maneuver space. The filter uses this as a dynamic damping penalty term to limit and attenuate cockpit pilot commands.

[0204] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and incorporate common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the claims.

Claims

1. A method for characterizing the decay trajectory of airborne equipment and dynamically controlling the mission with enhanced physical constraints, characterized in that, include: Step 1: Adaptively sample points on the constraint boundary of the flight envelope; Step 2: Establish a local differential geometry framework at each sampling point; Step 3: Calculate the constraint tightness tensor within the differential geometry framework of the sampling points to evaluate the current motion trend and state of the aircraft under the defined constraints. Step 4: Use the global constraint tightness tensor in flight envelope monitoring to perform flight envelope protection.

2. The method for characterizing airborne equipment decay trajectory and dynamically controlling tasks with enhanced physical constraints according to claim 1, characterized in that, Step 1 specifically includes: Step 1-1, Define the safety envelope, including: defining the aircraft's state vector. ,definition One safety constraint, namely A set of original boundary conditions, denoted as . The security constraints include constraints on discrete envelopes and piecewise linear envelopes. Steps 1-2: Constructing continuously differentiable boundary functions: The analytical reconstruction method of single-constraint boundaries based on third-order B-splines is used to process and map the original boundary conditions, generating boundary functions that satisfy at least second-order continuous differentiability. The global security zone is defined as follows: ; Steps 1-3, based on boundary functions Constructing a global cohesion function And define new safe flight zones for aircraft. The global condensation function and the safe flight area are: ； ； in Sensitivity factor; increase Reduce the buffer band, reduce Increase the buffer zone; Steps 1-4, Adaptive Feature Sampling: at the analytical boundary Uniform sampling is performed on the data to obtain the basic point set. .

3. The method for characterizing airborne equipment decay trajectory and dynamically controlling tasks with enhanced physical constraints according to claim 2, characterized in that, Steps 1-2 involve constructing continuously differentiable boundary functions, specifically including: Step 1-2-1: Within the controlled two-dimensional state space of the aircraft, the physical effective range is delineated according to the envelope monitoring requirements, and axial discretization is performed to construct a two-dimensional structured observation grid covering the entire flight state. Step 1-2-2: Extract discrete coordinates representing the physical boundary limits from the aerodynamic database to obtain a discrete set of physical boundary points; Steps 1-2-3: For any intersection point in the two-dimensional structured observation grid, calculate the minimum geometric metric from it to the discrete physical boundary point set, and assign a symbolic value with negative inside and positive outside based on the topological inclusion relationship between the intersection point and the safety envelope, directly generating the normalized safety margin truth value at the intersection point, and obtaining the distance field truth matrix. Steps 1-2-4: Construct a B-spline distance field function with the state vector as the joint independent variable. Using the calculated true value matrix of the distance field, inversely calculate the control vertex weight matrix of the B-spline distance field function to generate a boundary function that is at least second-order continuously differentiable.

4. The method for characterizing airborne equipment decay trajectory and dynamically controlling tasks with enhanced physical constraints according to claim 3, characterized in that, The state vector includes flight speed and pitch angle, and the safety constraints include: ； ； in, The current flight speed is a scalar value. The pitch angle, For the weight of the aircraft, air density, For wing area, The maximum lift coefficient, The maximum design normal overload factor allowed by the aircraft airframe structure. For pitch angle The monotonic pneumatic mechanism function.

5. The method for characterizing airborne equipment decay trajectory and dynamically controlling tasks with enhanced physical constraints according to claim 4, characterized in that, The B-spline distance field function in step 1-2-4 is: in Let M be the weight matrix of the two-dimensional spline control vertices to be solved, M be the total velocity coordinates of the two-dimensional structured observation grid under all flight conditions, N be the total pitch coordinates of the two-dimensional structured observation grid under all flight conditions, and p and q be the index variables of the double summation of M+3 and N+3. , These are the third-order B-spline basis functions corresponding to velocity and pitch angle, respectively. , Using the Cox-deBoor algorithm for velocity axis parameters and pitch axis parameters The solution is obtained recursively. Boundary functions that satisfy the condition of being twice continuously differentiable include: ； ； in and These are the control vertex weight matrices corresponding to the stall boundary and structural overload mechanism constraints, respectively. , These are the maximum and minimum flight speeds. , These are the maximum and minimum pitch angles. This indicates that the aircraft is within a safe airspeed range that meets aerodynamic lift requirements. This indicates that the actuator is within the safe overload range that does not exceed the allowable strength of the structure.

6. The method for characterizing airborne equipment decay trajectory and dynamically controlling tasks with enhanced physical constraints according to claim 2, characterized in that, Step 2 specifically includes: Step 2-1, for a certain sampling point Calculate vector This vector uniquely and smoothly represents the vector formed by... The analytical boundary normal vector is formed by coupling the original boundary conditions; the contribution factor is defined. ,but Represent as ,when Approaching 1 indicates that the first The constraint is in a dominant and active state; Step 2-2: Construct the diagonal weight matrix The weights in the matrix are preset values. Weighted norm-based normalization is then applied to the analytical boundary normal vectors, resulting in: ； Steps 2-3, based on The unique weighted normalized normal vector at the point is used to solve the orthogonal complement tangent space, and SVD decomposition is performed to obtain the tangent space basis matrix.

7. The method for characterizing airborne equipment decay trajectory and dynamically controlling tasks with enhanced physical constraints according to claim 6, characterized in that, Steps 2-3 specifically include: Step 2-3-1: Construct the matrix to be decomposed based on the normal vector. ; Step 2-3-2, SVD decomposition implementation: For Perform singular value decomposition ; Step 2-3-3: Extract the basis vectors to obtain the tangent space basis matrix. 。 8. The method for characterizing airborne equipment decay trajectory and dynamically controlling tasks with enhanced physical constraints according to claim 7, characterized in that, Step 3 specifically includes: For global cohesion function and sampling points Calculate and define the weighted Hessian matrix. , in, It is a diagonal weight matrix; Using the basis matrix of the tangent space Will Projected to In the tangent space, we obtain the global constraint compactness tensor: in The global constraint tightness tensor characterizes the anisotropic ensemble contraction pressure perceived by the aircraft as it moves on a currently safe and popular surface, induced by all constraints.

9. The method for characterizing airborne equipment decay trajectory and dynamically controlling tasks with enhanced physical constraints according to claim 1, characterized in that, The global constraint tightness tensor is used in flight envelope monitoring to perform flight envelope protection, specifically including: global constraint tightness tensor Perform eigenvalue decomposition: in Indicates the first The principal curvatures characterize the degree of bending of the constraint boundary in that characteristic direction. Indicates the first One principal direction, representing the principal axis direction of curvature change; The largest eigenvalue among n-1 eigenvalues The corresponding principal axis direction indicates the undesirable direction; minimum eigenvalue The corresponding main axis direction indicates the optimal escape route; based on Determine the flight risk level and implement flight envelope protection.

10. The method for characterizing airborne equipment decay trajectory and dynamically controlling tasks with enhanced physical constraints according to claim 1, characterized in that, based on Determining the flight risk level includes: This is a high-risk direction; if you proceed in this direction, the available space for maneuver will quickly disappear. Medium risk, the width of the passage ahead remains unchanged; Low risk, and the potential for growth is expanding.

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