Non-contained failure safety analysis method based on cylindrical projection and Monte Carlo

Abstract

The present invention discloses a non-contained failure safety analysis method based on cylindrical projection and Monte Carlo, which relates to the technical field of aircraft special risk analysis and assessment. The method comprises the following steps: discretizing the outline of a model of a key aircraft component obtained after a qualitative safety analysis to characterize the component's geometric shape; analyzing the cylindrical projection and boundary extraction method when debris impacts the component, and obtaining the component's danger window by extracting the component projection boundary; generating random numbers using the Monte Carlo method to simulate the debris motion trajectory, judging the component failure status and whether the aircraft is in catastrophic danger based on the relationship between the debris motion trajectory and the danger window of the key component, and finally calculating the aircraft's catastrophic danger probability; thereby providing relevant methodological support for the airworthiness certification of non-contained failures during the aircraft development process. The method can achieve accurate and efficient calculation of the aircraft's catastrophic danger probability.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft special risk analysis and assessment, and in particular to a non-contained failure safety analysis method based on cylindrical projection and Monte Carlo. Background Art

[0002] Uncontained failure refers to a failure in which high-energy fragments that fall off the rotor of an aircraft engine or auxiliary power unit during high-speed rotation cannot be contained by the casing due to factors such as fatigue, posing a threat to the aircraft. Uncontained failure is a typical special risk that affects aircraft safety. High-energy uncontained fragments are very likely to penetrate critical systems or components such as the aircraft fuselage, wings, and fuel tanks, leading to multiple risks such as cabin depressurization, control failure, fuel tank leakage and fire, and may even cause a catastrophic accident to the aircraft.

[0003] Although the "Engine Airworthiness Standards" have required that the design of the engine must be containment of the rotor blades, and engine manufacturers are also committed to using new materials, new processes and new structures to improve the structural strength of the rotor and the containment of the casing, service experience has shown that uncontained failures will still occur. Therefore, it is necessary to consider uncontained failures when designing aircraft to minimize the damage caused by uncontained failures to the aircraft.

[0004] Major foreign aviation powers have been conducting research on the issue of uncontained failures since the 1960s. The research areas include analysis of statistical data on uncontained accidents, research on safety analysis methods, and research on protection technologies for uncontained failures. They have also developed analytical tools for evaluating uncontained failures, and their effectiveness has been demonstrated through analysis of small general business jets and general twin-engine aircraft. However, due to technological blockades, existing materials only introduce the functions of the software without explaining its specific implementation methods.

[0005] Domestic research on non-contained failures started late, with traceable literature dating back to the early 21st century. Relevant research work mainly focused on the analysis and research of relevant airworthiness clauses, non-contained failure cases and data statistical analysis, and research on safety analysis methods for non-contained failures.

[0006] In the research on safety analysis methods for non-contained failures, most qualitative safety analysis methods are based on functional hazard analysis and fault tree analysis. There are two main types of research on quantitative safety analysis methods. The first is the formula method, which solves the catastrophic hazard probability of the aircraft by constructing a hazard probability calculation model. This method has the following defects: the input of the calculation model is the dispersion risk angle and translation risk angle of the key components, but the use of the dispersion risk angle and translation risk angle to represent the danger window of the key components is not accurate and is larger than the actual danger window; an approximate calculation is used, and the mean probability of failure of the key components by single debris impact is used as the triggering probability of the minimum cut set; it is assumed that at most only one minimum cut set is triggered in each non-contained event, which is inconsistent with the actual situation. In addition, the accuracy analysis of the model constructed after adopting this assumption has not been carried out, making it difficult to ensure the accuracy and credibility of the calculation results;

[0007] The second is the Monte Carlo method in the CATIA environment, which involves analyzing failed components through a collision detection module in the CATIA environment and using the Monte Carlo method to calculate the probability of catastrophic failure of the aircraft. However, the drawback is that the collision detection efficiency is relatively low, especially since the Monte Carlo method requires a large number of simulations to obtain more accurate results, which results in a longer analysis time. Summary of the Invention

[0008] In order to solve the above technical problems, the present invention provides a non-inclusive failure safety analysis method based on cylindrical projection and Monte Carlo, which includes the following steps:

[0009] S1. For the minimum cut set obtained after safety characterization, discretize the outlines of the key components that constitute the minimum cut set and determine the three-dimensional coordinates of each discrete point. The key components are those whose failure will hinder the aircraft's continued safe flight and landing.

[0010] S2. Projecting the discrete points of the key component's outline onto a cylindrical surface based on the characteristics of non-contained failures and the attribute information of the fragments, where the attribute information of the fragments includes the type of fragment, the number of fragments, and the rotation direction of the rotor that generated the fragments;

[0011] S3. Expand the cylinder to obtain a discrete point set corresponding to each projection point of the cylinder on the plane, and use a discrete point set boundary extraction method to extract the boundary to obtain the danger window of the key component;

[0012] S4. Calculate the probability of catastrophic hazards occurring in aircraft based on Monte Carlo simulation method.

[0013] The technical solution further defined in the present invention is:

[0014] Furthermore, in step S1, the outline discretization of key components includes the following steps:

[0015] S1.1. Import the digital prototype of the aircraft into the 3D modeling software;

[0016] S1.2. Identify the key components in the affected area and export the key component models separately;

[0017] S1.3. Subdivide the key component model to obtain triangular facets that fit the outline of the key component model;

[0018] S1.4. Each vertex of the triangular face is a discrete point of the outline of the key component model, and the vertex coordinate data of each triangular face is derived.

[0019] In the aforementioned non-contained failure safety analysis method based on cylindrical projection and Monte Carlo, in step S1.3, the accuracy is set when the key component model is tessellated. The parameters for the accuracy setting are the chord height and the step length. The chord height refers to the maximum distance from the surface of the original key component model to the triangular facets after tessellation. The smaller the chord height and the smaller the step length, the more triangular facets are required to fit the outline of the key component model, the better the effect of the triangular facets fitting the outline of the key component model, and the larger the exported data file.

[0020] The aforementioned non-contained failure safety analysis method based on cylindrical projection and Monte Carlo, in step S2, the method of projecting the discrete points of the key component outline onto the cylindrical surface includes the following steps:

[0021] S2.1. Determine the radius and height of the cylinder based on the specific failure model;

[0022] S2.2. Analyze the range of the debris center of mass trajectory and the process of debris flying out of the rotor based on the characteristics of non-contained failure, and consider the range of the intersection of the debris center of mass trajectory and the cylindrical surface when the debris impacts a point in space, that is, the projection of the point in space on the cylindrical surface;

[0023] S2.3. Project each discrete point of the key component's outer contour onto the cylindrical surface to obtain the projection area of ​​the discrete point of the key component's outer contour on the cylindrical surface.

[0024] In the aforementioned non-contained failure safety analysis method based on cylindrical projection and Monte Carlo, in step S2.1, the cylinder is considered to be the surface on which the engine case is located, and the center of the cylinder is considered to be the rotation center of the engine rotor. When fragments are thrown from the rotor, different fragment failure models have different flying angles, corresponding to different impact areas. The relationship between the cylinder radius and the cylinder height within the impact area is expressed by the following formula:

[0025]

[0026] Where H represents the surface height, R represents the cylinder radius, and θ represents the flying angle of the failure model.

[0027] The aforementioned non-containment failure safety analysis method based on cylindrical projection and Monte Carlo, in step S3, the cylindrical expansion method includes the following steps

[0028] S3.1.1. Cut the cylinder along a generatrix and unfold it into a plane;

[0029] S3.1.2. Establish a plane rectangular coordinate system and convert the spatial coordinates of each projection point on the cylinder into plane coordinates according to the expansion method;

[0030] S3.1.3. The discrete point set corresponding to each projection point on the cylinder is obtained based on the coordinate transformation formula.

[0031] In the aforementioned non-contained failure safety analysis method based on cylindrical projection and Monte Carlo, in step S3, the boundary of the discrete point set in the plane domain is extracted using the Delaunay triangulation method or the Alpha-Shape algorithm. The extraction of the boundary of the discrete point set in the plane domain using the Delaunay triangulation method includes the following steps S3.2.1, establishing a super triangle containing the entire discrete point set as the initial mesh;

[0032] S3.2.2. Insert the discrete points sequentially into the most recently updated mesh. Find the triangle in the mesh whose circumcircle contains the insertion point, i.e., the influencing triangle of the insertion point. Delete the common edges of the influencing triangles to form a Delaunay cavity. Connect the insertion point to the vertices of the Delaunay cavity to form a new Delaunay mesh.

[0033] S3.2.3. Repeat step 2 until all discrete points are inserted.

[0034] S3.2.4. Delete redundant triangles in the mesh. If a node in a triangle does not belong to the original point set, the triangle is considered redundant.

[0035] S3.2.5. After removing the redundant triangles, the final result is a Delaunay triangulation mesh;

[0036] S3.2.6. Extract the boundary of the Delaunay triangulation mesh as the boundary of the discrete point set. For each Delaunay edge in the mesh, if it is shared by two triangles in the mesh, then the Delaunay edge is not a boundary of the mesh. Conversely, if a Delaunay edge appears in only one triangle, then the Delaunay edge is part of the mesh boundary.

[0037] S3.2.7. After the boundary of the discrete point set is determined, calculate the area of ​​the figure enclosed by the boundary. If the coordinates of the n boundary points extracted are A i (xi ,y i , z i )(i=1,2,…,n), then the area of ​​the figure enclosed by the boundary of the discrete point set is calculated by the following formula:

[0038]

[0039] Where O is the origin of the plane coordinate system, and n represents the number of boundary points.

[0040] In the aforementioned non-contained failure safety analysis method based on cylindrical projection and Monte Carlo, in step S3, when the Alpha-Shape algorithm is used to extract the boundary of the discrete point set in the plane domain, a circle with a radius of α is rolled outside the discrete point set, and the rolling trace is the boundary of the discrete point set.

[0041] In the aforementioned non-contained failure safety analysis method based on cylindrical projection and Monte Carlo, in step S4, the generated random numbers are used to simulate the failure model of the non-contained failure and the trajectory of the debris after it flies out of the rotor. If the trajectory of the debris passes through the critical component danger window, the component is considered to have failed due to the impact of the debris;

[0042] In a non-containment event, multiple key components may fail. Based on the combined failure of key components, it is determined whether a minimum cut set is triggered, which in turn leads to a catastrophic hazard for the aircraft. This completes the simulation process of a non-containment event.

[0043] The convergence value of the ratio of the number of aircraft catastrophic hazards to the total number of simulations can be used as the probability of non-contained failure leading to aircraft catastrophic hazards.

[0044] In the aforementioned non-contained failure safety analysis method based on cylindrical projection and Monte Carlo, in step S4, the solution to the probability of catastrophic hazard of the aircraft includes the following steps:

[0045] S4.1. Clarify under what non-inclusive model the analysis object needs to verify its airworthiness compliance;

[0046] S4.2. Define the number of Monte Carlo simulations N and initialize the number of aircraft catastrophic hazards occurring n = 0;

[0047] S4.3. Randomly determine the engine rotor that exploded;

[0048] S4.4. The trajectory of the debris is determined based on the impact area of ​​the debris, and the probability of the debris flying in all directions is evenly distributed;

[0049] S4.5. Determine the impact failure status of each component based on whether the debris trajectory passes through the critical component's danger window;

[0050] S4.6. Determine whether the failure of a combination of key components will lead to a catastrophic aircraft event;

[0051] S4.7. If a catastrophic aircraft top event occurs, determine whether this event has led to a catastrophic aircraft hazard based on the corresponding risk factors;

[0052] S4.8. If a catastrophic event occurs, record this simulation, n = n + 1; repeat steps S4.3 to S4.7, and continue with the next uncontained event simulation until all simulations are complete, n = N;

[0053] S4.9. Calculate the probability of catastrophic hazard to the aircraft P = n / N.

[0054] The beneficial effects of the present invention are:

[0055] (1) The present invention uses a cylindrical projection method based on the position, size, and other collective parameters of rotor debris and aircraft components to automatically obtain the danger window of each component under different types of debris. Compared with the traditional solution using approximate formulas, this method avoids the tedious calculation process, is more intuitive and clear, and has higher accuracy.

[0056] (2) In the present invention, the Monte Carlo simulation method is used to randomly generate the flight trajectory of the debris. According to the component danger window, it is judged whether the key components will be hit by the debris, and then it is determined whether the debris will cause catastrophic danger. The probability of catastrophic danger can be obtained through multiple simulations. This method can effectively avoid the inherent defects of the current use of fault tree analysis for rotor non-contained failure, such as the non-independence of basic events and the conservative calculation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is the overall flow chart of the present invention;

[0058] Figure 2 Schematic diagram of the process of acquiring discrete point data of the outline of key components in the first embodiment of the present invention;

[0059] Figure 3 Schematic diagram of a cylindrical surface within the debris impact area in Example 1 of the present invention;

[0060] Figure 4 This is a diagram showing the range of debris centroid trajectories in Example 1 of the present invention;

[0061] Figure 5 This is a schematic diagram of one-third of the wheel fragments flying out of the projection plane in the first embodiment of the present invention;

[0062] Figure 6 Schematic diagram of the projection of a spatial point on a cylindrical surface in the first embodiment of the present invention;

[0063] Figure 7 This is a schematic diagram of the cylindrical surface expansion in the first embodiment of the present invention;

[0064] Figure 8 This is a view of the cylindrical surface on the XOZ plane in Example 1 of the present invention;

[0065] Figure 9 1. It is a cylindrical projection and a partial enlarged view of the spherical component in the second embodiment of the present invention;

[0066] Figure 10 Schematic diagram of cylindrical expansion and boundary extraction results of the spherical component projection in the second embodiment of the present invention;

[0067] Figure 11 This is a diagram showing the relative positions of key components and the cylindrical surface in Example 3 of the present invention;

[0068] Figure 12 This is a schematic diagram of the cylindrical expansion and boundary extraction results of the projection area of ​​the key component in Example 3 of the present invention. DETAILED DESCRIPTION

[0069] Example 1: This example provides a non-contained failure safety analysis method based on cylindrical projection and Monte Carlo, such as Figure 1 As shown, the following steps are included

[0070] S1. For the minimum cut set obtained after qualitative safety analysis, the components that constitute the minimum cut set are critical components, which represent components whose failure will hinder the continued safe flight and landing of the aircraft. In view of the fact that critical components have various shapes, it is difficult to project them directly onto the cylinder (or the surface where the engine casing is located). Therefore, the outline of the critical components is discretized. The projection of spatial points onto the cylinder is relatively easy to achieve. The projection area of ​​the discrete points of the component outline on the cylinder is approximately the projection of the component on the cylinder. Therefore, the discrete points of the component outline are extracted in the 3D modeling software. Taking the CATIA environment as an example, the coordinate data of the discrete points of the key component outline can be obtained using the digital prototype of the aircraft. The process is as follows: Figure 2 shown.

[0071] Based on the results of the qualitative safety analysis, the key components in the area affected by the analyzed rotor debris were identified, and the key component models were exported using the aircraft digital prototype in the assembly design module of the CATIA software. Then, the "Tessellation" tool was used in the STL rapid prototyping module to perform surface fitting and coloring on the outline of the key component model, obtaining triangular facets that fitted the surface of the component model. The vertices of the triangular facets can be considered as discrete points of the component model outline. Finally, the point cloud output tool "STL export" was used to output the coordinate data of each vertex of the triangular facet. The export format can be selected as ".asc". The exported discrete point data of the component outline can be used for subsequent projection processes.

[0072] When performing surface subdivision on a component model in the CATIA environment, you can set the precision. The parameters for precision setting are chord height and step length. Chord height refers to the maximum distance from the surface of the original component model to the triangular facets after surface subdivision. The smaller the chord height and the smaller the step length, the more triangular facets are required to fit the component outline, and the better the effect of the triangular facets fitting the outline of the three-dimensional solid model. At the same time, the larger the exported data file, in order to make the number of triangular facets fit the component outline better and not make the exported data file too large, which will greatly increase the subsequent calculation amount, it is necessary to reasonably select the parameter value according to the actual specific situation and requirements when setting the precision.

[0073] S2. An analytical approach to solving the problem of non-contained failure using the cylindrical projection method is presented. Combining the characteristics of non-contained failure, a cylindrical projection method is proposed when debris impacts components to achieve projection of components on the cylindrical surface.

[0074] The traditional cylindrical projection method is to project a space point onto the cylindrical surface along the direction pointing to the center of the cylinder. The safety analysis process of non-contained failure can use the cylindrical projection method, such as Figure 3 As shown in Figure 1, the cylinder can be regarded as the surface where the engine casing is located (it is not unique, but only used as a reference surface), and the center of the cylinder can be regarded as the rotation center of the engine rotor. When the fragments are thrown out from the rotor, different fragment failure models have different flying angles, corresponding to different impact areas. Therefore, the relationship between the cylinder radius R and the cylinder height H in the impact area can be expressed by formula (1):

[0075]

[0076] Where θ represents the flying angle of the failure model, which is 6° for one-third wheel fragmentation and 10° for medium fragmentation or optional models.

[0077] Uncontained failure is complex. We cannot simply assume that fragments are thrown directly outward from the rotor's center of rotation and ignore the size of the fragments. Therefore, we cannot directly use the cylindrical projection method to project the component outline onto the cylindrical surface. We need to study the cylindrical projection method when fragments impact the component based on the characteristics of uncontained failure.

[0078] When fragments fall off and fly out of the rotor, they are not necessarily within the rotor's rotation plane. The trajectory circle of the center of mass of the fragment may undergo a certain deflection, and then the fragment flies out from a certain point on the trajectory circle along the tangent direction of that point. The different flight paths of the fragments form the impact area of ​​the fragments. The maximum angle range that the trajectory circle can be deflected is the fragment's flying angle.

[0079] like Figure 4As shown in the figure, the debris center of mass trajectory circle in the rotor rotation plane rotates around the Z axis at a certain angle, and any position may be used as the center of mass trajectory of the debris when it flies out; the debris center of mass trajectory forms a part of the sphere after rotation, and the radius of the sphere is the radius of the debris center of mass trajectory R c , θ is the angular range within which the debris center-of-mass trajectory can be deflected, which is determined by the failure model; the plane where the center-of-mass trajectory circle lies when the debris falls off from the rotor is the debris's ejection plane, and the intersection of the ejection plane and the spherical surface is the debris center-of-mass trajectory before it is thrown out of the rotor.

[0080] Considering that when fragments fall off the rotor, they fly out along the tangent direction of the center of mass trajectory in the direction of rotor rotation, and rotate around their center of gravity but do not roll when flying out of the casing, the influence of fragment size cannot be ignored.

[0081] Here we take the failure model of one-third of the wheel fragments as an example for analysis. Figure 5 As shown in the figure, in the debris ejection plane, the fragments fly out in the tangent direction of their center of mass trajectory. Since the fragments rotate around their center of mass (center of gravity) to form a circular surface when flying out, and the circular surface motion forms a sweeping path, the sweeping path width is the maximum size of the fragments. For a certain spatial component, if part or all of it is located on the debris sweeping path, the component will be hit by the fragments and fail. For other failure models, the fragment flying process is similar, the difference is that the width of the debris sweeping path is different, and the width of each fragment sweeping path depends on the maximum size of the fragment.

[0082] For a discrete point on the component outline, the process of generating a projection on the cylindrical surface is as follows: Figure 6 shown.

[0083] Assume that the rotor of a certain stage of the engine rotates clockwise, and the spatial point P is located in the influence area of ​​the rotor fragment of this stage. When the center of mass of the fragment is at point T1, the fragment flies out along the tangential direction. At this time, the inner boundary of the fragment sweep path will pass through point P. The inner boundary of the sweep path is ray T1P, and T1″ is the tangent point of the circular surface formed by the inner boundary of the sweep path and the rotation of the rotor itself. After the fragment breaks away from the rotor and flies out, the intersection point of the center of mass orbit and the cylindrical surface is point Q1; when the center of mass of the fragment is at point T2, the fragment flies out along the tangential direction. At this time, the fragment The outer boundary of the fragment's sweeping path will pass through point P. The outer boundary of the sweeping path is ray T2P, T2′ is the tangent point of the outer boundary of the sweeping path and the circular surface formed by the rotation of the rotor itself, and the intersection of the center of mass orbit and the cylindrical surface after the fragment breaks away from the rotor and flies out is point Q2. It is easy to know that when the center of mass of the fragment flies out at any point on the arc T1T2, the sweeping path of the fragment can pass through point P in space, and the intersection range of the center of mass orbit of the fragment and the cylindrical surface is arc Q1Q2. Therefore, it can be considered that the projection of the spatial point P on the cylindrical surface is arc Q1Q2.

[0084] To determine the projection of the spatial point P on the cylinder, it is necessary to calculate the coordinates of points Q1 and Q2. Taking the calculation of the coordinates of point Q2 as an example, according to the motion trajectory of the fragment, it is necessary to first calculate the coordinates of point T2′ when the outer boundary of the fragment sweeping path passes through point P. Then the coordinates of point T2 can be determined, and the motion trajectory of the fragment after being thrown out can be determined, and the intersection with the cylinder is point Q2.

[0085] First, calculate the coordinates of point T2′ according to the above analysis process:

[0086] When the center of mass of the debris is located at point T2, the outer boundary of the sweep path passes through point P in space. If T is any point in the debris ejection plane (except point O and point P), the debris ejection plane can be expressed by formula (2):

[0087]

[0088] Among them, point O is the center of the cylinder, that is, the origin of the space coordinate system; is the vertical axis of the spatial rectangular coordinate system.

[0089] For point T2′, considering its influence on different projection planes and the trajectory of the center of mass of the debris, its distribution area is a part of the sphere. The spherical equation is shown in formula (3):

[0090] x 2 +y 2 +z 2 =(R c +D / 2) 2 (3)

[0091] Among them, R c is the radius of the debris center of mass trajectory; D is the maximum size of the debris, that is, the width of the debris sweep path.

[0092] By combining equations (2) and (3), we can determine the trajectory of point T2′ in the projection plane. And because point T2′ is the tangent point, equation (4) is satisfied.

[0093]

[0094] The coordinates of point T2′ can be solved by combining equations (2), (3) and (4).

[0095] Next, you need to calculate the coordinates of point T2:

[0096] After analysis, it can be seen that points T2′, T2 and O are collinear, so the coordinates of point T2 can be calculated using the straight line OT2′ and the center of mass trajectory equation. Combined with the rotor rotation direction, the only possible tangent point can be determined as the coordinates of point T2.

[0097] Finally, the coordinates of point Q2 are calculated:

[0098] The center of mass of the debris flies out along the tangent direction of the trajectory at point T2 and intersects the cylinder at point Q2. The coordinates of point Q2 can be calculated using formula (5):

[0099]

[0100] At this point, the coordinates of point Q2 can be obtained. Similarly, the coordinates of point Q1 can be solved, and the arc Q1Q2 can be determined. The projection of the spatial point P on the cylinder is obtained. The projection is also represented by discrete points, that is, points of reasonable density are inserted between points Q1 and Q2 to represent the arc Q1Q2.

[0101] For each discrete point of the component's outer contour, the above projection method is used to obtain the projection area of ​​the component on the cylindrical surface.

[0102] S3. Analyze the cylindrical surface expansion process and determine the method for converting the coordinates of the projection points on the cylindrical surface into plane coordinates; extract the boundaries of each projection point in the plane to obtain the danger window of key components.

[0103] The analysis process is as follows Figure 7 As shown, the cylindrical surface is unfolded along the intersection line of the positive half plane of YOZ and the cylindrical surface (a generatrix of the cylindrical surface), and a plane rectangular coordinate system is established. The midpoint of the left boundary after the cylinder is unfolded is used as the origin of the plane coordinate system, and the plane X′O′Y′ is parallel to the plane XOY.

[0104] According to the cylindrical expansion method, for the space point P(x p ,y p ,z p ), whose projection point on the cylinder is Q(x q ,y q ,z q ), the two-dimensional coordinate corresponding to the projection point after expansion is marked as Q′(x′ q ,y′ q ,z′ q ), it is easy to know that y′ q =y q ; So we only need to consider x′ q The value of .

[0105] The view of the cylindrical surface in the ZOX plane is as follows Figure 8 As shown, rotate the Z axis counterclockwise around point O in the positive direction, and When the rotation ends in the same direction, the angle is recorded as α, and its value can be calculated by formula (6)

[0106]

[0107] It can be seen that the horizontal coordinate x' of point Q' on plane X'O'Y' is q =Rα, so the plane coordinates of the point Q′ corresponding to the projection point Q on the cylinder after the cylinder is expanded can be determined.

[0108] After obtaining the plane coordinates of the projection points of each discrete point on the outline of the key component, it is necessary to use the boundary extraction method of the discrete point set to obtain its danger window, which can be achieved by using Delaunay triangulation or Alpha-Shape algorithm.

[0109] Delaunay triangulation is a triangulation standard that satisfies the maximization of minimum angle characteristics and empty circle characteristics. Its implementation steps are:

[0110] Step 1: Create a super triangle containing the entire point set as the initial mesh;

[0111] Step 2: Insert the data points into the most recently updated mesh in sequence, find the triangle whose circumcircle contains the insertion point (called the influencing triangle of the point), delete the common edges of the influencing triangle to form a Delaunay cavity, and connect the insertion point with the Delaunay cavity vertex to form a new Delaunay mesh;

[0112] Step 3: Loop through step 2 until all discrete points are inserted;

[0113] Step 4: Delete redundant triangles in the mesh. That is, if a node in a triangle does not belong to the original point set, delete the triangle. The final result is a Delaunay triangulation mesh.

[0114] After obtaining the Delaunay triangulation of the discrete point set, the boundary of the triangular mesh is extracted as the boundary of the discrete point set. The idea is: for each Delaunay edge in the mesh, if it is shared by two triangles in the mesh, then the Delaunay edge is not the boundary of the mesh; conversely, if a Delaunay edge only appears in one triangle, then the Delaunay edge constitutes part of the mesh boundary.

[0115] After the boundary of the discrete point set is determined, the area of ​​the figure enclosed by the boundary can be calculated. If the coordinates of the n boundary points extracted are A i (xi,y i , z i )(i=1,2,…,n), then the area of ​​the figure enclosed by the boundary of the discrete point set can be calculated by formula (7)

[0116]

[0117] Where O is the origin of the plane coordinate system and n is the number of boundary points.

[0118] Determining whether a fixed point is inside the polygon enclosed by a boundary is a traditional problem in computer vision. Methods such as the ray method, the angle sum test method, and the area method can be used, which will not be discussed here.

[0119] The Alpha-Shape algorithm can also be used to extract edges from a bunch of unordered point sets in a plane. The algorithm principle is: suppose there is a point set V, its Alpha-Shape is a polygon determined by the point set V and the radius parameter α; imagine that there is a circle with a radius of α rolling outside the point set, and the trace of the circle rolling is the boundary of the point set V; it is easy to know that if α is very small, the circle will roll to the inside of the point set V, and each point is considered to be a boundary point of the discrete point set; if α is very large (α→∞), the extracted boundary is the convex hull of the point set.

[0120] To determine whether a point in the point set V is a boundary point, the following conditions can be used: draw a circle with a radius of α through any two points in the point set V. If the circle does not contain other points in the point set, then these two points are boundary points; otherwise, they are not boundary points, and the line segment connecting the two points is the boundary segment.

[0121] The Alpha-Shape algorithm is currently widely used. MATLAB also has a built-in alphaShape function for generating Alpha-Shape polygons for discrete point sets. The object it returns is used as input to the area function and inShape function to calculate the area of ​​the Alpha-Shape polygon and determine whether a certain point is inside the Alpha-Shape shape, respectively. We will not go into details here.

[0122] From the above analysis, we can see that Delaunay triangulation can obtain the convex hull of a discrete point set in a plane. If the ideal boundary of the key component is the concave hull of the point set, large errors will occur. The effect of the boundary extracted by the Alpha-Shape algorithm depends on the radius parameter α. Therefore, in practical applications, a reasonable choice should be made based on the density of discrete points to obtain more accurate boundary extraction results.

[0123] S4. After obtaining the danger window of each key component, the Monte Carlo method is used to generate random numbers to simulate the trajectory of debris movement. The relationship between the trajectory and the danger window of the key component is used to determine the component failure situation and whether the aircraft is in catastrophic danger. Finally, the probability of catastrophic danger to the aircraft is calculated.

[0124] The Monte Carlo method is used to calculate the probability of catastrophic hazard of an aircraft, which includes the following steps:

[0125] S4.1. Clarify under what non-inclusive model the analysis object needs to verify its airworthiness compliance;

[0126] S4.2. Define the number of Monte Carlo simulations N and initialize the number of aircraft catastrophic hazards n = 0;

[0127] S4.3. Randomly determine the engine rotor that exploded;

[0128] S4.4. The trajectory of the debris is determined based on the impact area of ​​the debris, and the probability of the debris flying in all directions is evenly distributed;

[0129] S4.5. Determine the impact failure status of each component based on whether the debris trajectory passes through the critical component's danger window;

[0130] S4.6. Determine whether the failure of a combination of key components will lead to a catastrophic aircraft event;

[0131] S4.7. If a catastrophic aircraft top event occurs, determine whether this event has led to a catastrophic aircraft hazard based on the corresponding risk factors;

[0132] S4.8. If a catastrophic event occurs, record the current simulation (n = n + 1). Continue with the next uncontained event simulation, i.e., repeat steps S4.3 to S4.7 until all simulations are complete (n = N).

[0133] S4.9. Calculate the probability of catastrophic hazard to the aircraft P = n / N.

[0134] To further illustrate the present invention, the safety analysis method for non-contained failures provided by the present invention is described in detail below in conjunction with Example 2 and Example 3, but they should not be understood as limiting the scope of protection of the present invention.

[0135] Example 2: A spherical component within the HPT rotor influence area of ​​a certain aircraft's right engine is analyzed to calculate the probability of failure of the component due to impact by a single optional model. It is known that the HPT rotor rotates in the positive direction (right-hand rule). The relevant parameter settings required for the analysis are shown in Table 1.

[0136] Table 1

[0137]

[0138] The outer contour of the spherical component is discretized and then projected onto the cylindrical surface. Only three special states in the projection process are considered. The projection results are as follows: Figure 9 shown.

[0139] State 1 is the intersection of the debris center of mass orbit and the cylindrical surface when the inner boundary of the debris sweeping path hits the points of the component's outer contour; State 2 is the intersection of the center of mass and the cylindrical surface when the center of mass of the debris flies out and just passes through the points of the component's outer contour; State 3 is the intersection of the debris center of mass orbit and the cylindrical surface when the outer boundary of the debris sweeping path hits the points of the component's outer contour. It is easy to see that any state from State 1 to State 3 constitutes part of the component's projection on the cylindrical surface, that is, the area on the right side of the figure is the projection of the component on the cylindrical surface.

[0140] After the cylinder is unfolded, the plane of the component projection area is displayed as follows Figure 10 As shown in (a), the Alpha-Shape algorithm is used to Figure 10 The boundary of the discrete point set in (a) is extracted, and the extraction result is as follows Figure 10 As shown in (b) in .

[0141] The area of ​​the figure enclosed by the extracted boundary is calculated, and the result is 0.0262. The ratio of this to the area after the cylinder is expanded is the probability of the component being hit and failing by a single optional model, which is 0.0059.

[0142] If the two parameters in the formula method are used to represent the critical component's danger window, the measured flying risk angle of the spherical component is (88.94°, 91.06°), and the translation risk angle is (62.36°, 74.04°), so the probability of component failure can be calculated as 0.0069. This shows that using the flying risk angle and the translation risk angle to represent the actual danger window of the component is not accurate enough, resulting in the traditional formula method calculating the probability of catastrophic danger to the aircraft being too high.

[0143] Example 3: Consider evaluating the uncontained design of a certain type of civil transport aircraft. This aircraft uses a layout with two engines suspended under the wings. Each engine has 20 rotor stages, including a three-stage low-pressure compressor, an 11-stage high-pressure compressor, a two-stage high-pressure turbine, and a four-stage low-pressure turbine. Since the analysis process used for each rotor stage is similar, only the probability of a catastrophic hazard occurring in the aircraft after the triple-option model is generated due to an uncontained failure of a certain HPC stage.

[0144] The minimum cut set of the rotor influence area and its related information are shown in Table 2. The HPC rotor rotates in the positive direction, and the relevant parameter settings required for analysis are shown in Table 1.

[0145] Table 2

[0146]

[0147] After discretizing the outline of each key component, cylindrical projection is performed on each discrete point to obtain the projection area of ​​the key component on the cylindrical surface. The relative positions of each key component and the cylindrical surface in the HPC rotor influence area are as follows: Figure 11As shown, the projections of the key components on the cylindrical surface are not shown here.

[0148] After analyzing the cylindrical projection area according to the coordinate transformation method when the cylindrical surface is expanded, the corresponding plane discrete point set is obtained, such as Figure 12 As shown in (a) in the figure, the Alpha-Shape algorithm is used to extract the boundaries of the projection area of ​​each key component to determine the danger window corresponding to each key component. The results are shown in Figure 12 As shown in (b) in .

[0149] The Monte Carlo method is used to analyze the implementation steps of non-contained engine rotor failure, and the probability of triple one-third wheel disk fragments causing catastrophic danger to the aircraft can be calculated. When the number of simulations reaches 107, the convergence value of the simulation results is 0.0276.

[0150] A similar process can be used to analyze the probability of catastrophic damage to the aircraft when the remaining rotors produce triple-one-third wheel fragments. After calculating the average value, it can be determined whether the aircraft meets the airworthiness requirements under the triple-one-third wheel fragment failure model.

[0151] Thus, from the description of Examples 1 to 3, it can be seen that based on the collective parameters of the rotor fragments and aircraft components, such as the position and size, the cylindrical projection method can be used to automatically obtain the danger window of each component under different types of debris. Compared with the traditional solution using approximate formulas, this method avoids the tedious calculation process, is more intuitive and clear, and has higher accuracy.

[0152] At the same time, the Monte Carlo simulation method is used to randomly generate the flight trajectory of debris. According to the component danger window, it is judged whether the key components will be hit by the debris, and then it is determined whether the debris will cause catastrophic danger. The probability of catastrophic danger can be calculated through multiple simulations. This method can effectively avoid the inherent defects of the current use of fault tree analysis for rotor non-contained failure, such as the non-independence of basic events and conservative calculation results.

[0153] In addition to the above embodiments, the present invention may also have other implementations. Any technical solution formed by equivalent replacement or equivalent transformation falls within the scope of protection required by the present invention.

Claims

1. A non-contained failure safety analysis method based on cylindrical projection and Monte Carlo, characterized by: The following steps are included S1. For the minimum cut set obtained after safety characterization, discretize the outlines of the key components that constitute the minimum cut set and determine the three-dimensional coordinates of each discrete point. The key components are those whose failure will hinder the aircraft's continued safe flight and landing. S2. Projecting the discrete points of the key component's outline onto a cylindrical surface based on the characteristics of non-contained failures and the attribute information of the fragments, where the attribute information of the fragments includes the type of fragment, the number of fragments, and the rotation direction of the rotor that generated the fragments; S3. Expand the cylinder to obtain a discrete point set corresponding to each projection point of the cylinder on the plane, and use a discrete point set boundary extraction method to extract the boundary to obtain the danger window of the key component; S4. Determine the probability of catastrophic hazards occurring in aircraft based on Monte Carlo simulation method; In step S3, the boundary of the discrete point set in the plane domain is extracted using the Delaunay triangulation method. The boundary of the discrete point set in the plane domain is extracted using the Delaunay triangulation method, which includes the following steps: S3.2.

1. Create a super triangle containing the entire discrete point set as the initial mesh; S3.2.

2. Insert the discrete points sequentially into the most recently updated mesh. Find the triangle in the mesh whose circumcircle contains the insertion point, i.e., the influencing triangle of the insertion point. Delete the common edges of the influencing triangles to form a Delaunay cavity. Connect the insertion point to the vertices of the Delaunay cavity to form a new Delaunay mesh. S3.2.

3. Repeat step 2 until all discrete points are inserted. S3.2.

4. Delete redundant triangles in the mesh. If a node in a triangle does not belong to the original point set, the triangle is considered redundant. S3.2.

5. After removing the redundant triangles, the final result is a Delaunay triangulation mesh; S3.2.

6. Extract the boundary of the Delaunay triangulation mesh as the boundary of the discrete point set. For each Delaunay edge in the mesh, if it is shared by two triangles in the mesh, then the Delaunay edge is not a boundary of the mesh. Conversely, if a Delaunay edge appears in only one triangle, then the Delaunay edge is part of the mesh boundary. S3.2.

7. After the boundary of the discrete point set is determined, calculate the area of ​​the figure enclosed by the boundary. If the coordinates of the n boundary points extracted are A i (x i ,y i , z i ), i = 1, 2, ..., n, then the area of ​​the figure enclosed by the boundary of the discrete point set is calculated by the following formula: Where O is the origin of the plane coordinate system, and n represents the number of boundary points.

2. The non-contained failure safety analysis method based on cylindrical projection and Monte Carlo according to claim 1, characterized in that: In step S1, the outline discretization processing of key components includes the following steps: S1.

1. Import the digital prototype of the aircraft into the 3D modeling software; S1.

2. Identify the key components in the affected area and export the key component models separately; S1.

3. Subdivide the key component model to obtain triangular facets that fit the outline of the key component model; S1.

4. Each vertex of the triangular face is a discrete point of the outline of the key component model, and the vertex coordinate data of each triangular face is derived.

3. The non-contained failure safety analysis method based on cylindrical projection and Monte Carlo according to claim 2, characterized in that: In the step S1.3, the precision is set when the key component model is tessellated. The parameters for the precision setting are the chord height and the step length. The chord height refers to the maximum distance from the surface of the original key component model to the triangular facets after tessellation. The smaller the chord height and the smaller the step length, the more triangular facets are required to fit the outline of the key component model, and the better the effect of the triangular facets fitting the outline of the key component model. At the same time, the larger the exported data file is.

4. The non-contained failure safety analysis method based on cylindrical projection and Monte Carlo according to claim 1, characterized in that: In step S2, the method of projecting the discrete points of the key component outline onto the cylindrical surface includes the following steps: S2.

1. Determine the radius and height of the cylinder according to the preset failure model; S2.

2. Analyze the range of the debris center of mass trajectory and the process of debris flying out of the rotor based on the characteristics of non-contained failure, and consider the range of the intersection of the debris center of mass trajectory and the cylindrical surface when the debris impacts a point in space, that is, the projection of the point in space on the cylindrical surface; S2.

3. Project each discrete point of the key component's outer contour onto the cylindrical surface to obtain the projection area of ​​the discrete point of the key component's outer contour on the cylindrical surface.

5. The non-contained failure safety analysis method based on cylindrical projection and Monte Carlo according to claim 4, characterized in that: In step S2.1, the cylinder is considered as the curved surface of the engine casing, and the center of the cylinder is considered as the rotation center of the engine rotor. When fragments are thrown out of the rotor, different fragment failure models have different flying angles, corresponding to different impact areas. The relationship between the cylinder radius and the cylinder height within the impact area is expressed by the following formula: Where H represents the surface height, R represents the cylinder radius, and θ represents the flying angle of the failure model.

6. The non-contained failure safety analysis method based on cylindrical projection and Monte Carlo according to claim 1, characterized in that: In step S3, the method for cylindrical expansion includes the following steps: S3.1.

1. Cut the cylinder along a generatrix and unfold it into a plane; S3.1.

2. Establish a plane rectangular coordinate system and convert the spatial coordinates of each projection point on the cylinder into plane coordinates according to the expansion method; S3.1.

3. The discrete point set corresponding to each projection point on the cylinder is obtained based on the coordinate transformation formula.

7. The non-contained failure safety analysis method based on cylindrical projection and Monte Carlo according to claim 1, characterized in that: In step S4, the generated random numbers are used to simulate the failure model of non-contained failure and the trajectory of the debris after it flies out of the rotor. If the trajectory of the debris passes through the critical component danger window, it is considered that the component has failed due to the impact of the debris. In a non-containment event, multiple key components may fail. Based on the combined failure of key components, it is determined whether a minimum cut set is triggered, which in turn leads to a catastrophic hazard for the aircraft. This completes the simulation process of a non-containment event. The convergence value of the ratio of the number of aircraft catastrophic hazards to the total number of simulations is taken as the probability that non-contained failure will lead to catastrophic hazards for the aircraft.

8. The non-contained failure safety analysis method based on cylindrical projection and Monte Carlo according to claim 7, characterized in that: In step S4, the calculation of the probability of catastrophic hazard of the aircraft includes the following steps: S4.

1. Clarify under what non-inclusive model the analysis object needs to verify its airworthiness compliance; S4.

2. Define the number of Monte Carlo simulations N and initialize the number of aircraft catastrophic hazards occurring n = 0; S4.

3. Randomly determine the engine rotor that exploded; S4.

4. The trajectory of the debris is determined based on the impact area of ​​the debris, and the probability of the debris flying in all directions is evenly distributed; S4.

5. Determine the impact failure status of each component based on whether the debris trajectory passes through the critical component's danger window; S4.

6. Determine whether the failure of a combination of key components will lead to a catastrophic aircraft event; S4.

7. If a catastrophic aircraft top event occurs, determine whether this event has led to a catastrophic aircraft hazard based on the corresponding risk factors; S4.

8. If a catastrophic event occurs, record this simulation, n = n + 1; repeat steps S4.3 to S4.7, and continue with the next uncontained event simulation until all simulations are complete, n = N; S4.

9. Calculate the probability of catastrophic hazard to the aircraft P = n / N.

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