Flutter test flight real-time safety monitoring method based on structural response model

Abstract

The invention relates to the technical field of aviation, in particular to a flutter test flight real-time safety monitoring method based on a structural response model. The time domain safety monitoring threshold curve is constructed through the simulation structure response of the model to serve as a reference value to monitor the flutter flight test structure safety, the reference index problem of the structure time domain response is solved, and the timeliness and reliability of safety monitoring are effectively improved.

Description

Technical Field

[0001] The invention relates to the field of aviation technology, and in particular to a real-time safety monitoring method for flutter flight test based on a structural response model. Background Art

[0002] Aircraft flutter flight test is an important part of verifying the aeroelastic design of aircraft. It is a flight test that must be conducted for new aircraft and aircraft with major structural modifications. It is also a flight test subject specified in China's civil aircraft airworthiness standards and national military standards. As a Class I flight test risk subject in my country, flutter flight test has the characteristics of high flight test risk. If flutter occurs during the flight test, the consequences are often catastrophic. At the same time, as a key subject of the aircraft speed right envelope expansion flight test, it is crucial to the entire flight test progress of the aircraft.

[0003] During the flutter flight test, the evaluation of the flutter characteristics of the aircraft is generally carried out by testing the response of the structure under excitation. The frequency and damping of each main structural mode are obtained by calculating the excitation and response data, and the structural safety is evaluated by the change of the damping value and its compliance with the relevant standard requirements. At present, real-time safety monitoring uses the telemetry data of the aircraft's measured response to draw the structural response curve in the ground monitoring system, and monitors the time domain change of the curve. This method lacks a comparison value of the measured response curve value, especially the threshold value of time domain monitoring, and the real-time process relies heavily on the experience of monitoring engineers. On the other hand, the current quasi-real-time data processing technology uses the telemetry of the structural response and excitation signal on the ground safety monitoring system receiver to perform a complete modal data processing after excitation to obtain the main structural damping value. Although the problem of evaluation indicators is solved, there are problems such as lag in emergency situations, and missing points and jumping points when the telemetry signal is poor. How to improve the timeliness, reliability and efficiency of real-time safety monitoring in flutter flight tests is an important engineering issue at present. Summary of the invention

[0004] Purpose of the invention: To provide a real-time safety monitoring method for flutter flight test based on structural response model, so as to effectively monitor the structural response in aircraft flutter flight test.

[0005] Technical solution:

[0006] A real-time safety monitoring method for flutter flight test based on a structural response model, comprising:

[0007] S110: When the aircraft reaches a preset flight state, an excitation signal is injected into the aircraft's servo to control the movement of the aircraft's rudder surface and perform structural excitation;

[0008] S120: Transmitting the aircraft structure response measured by the acceleration sensor to the ground safety monitoring system through the flight test telemetry system, and the ground safety monitoring system receives the telemetered measured aircraft structure response;

[0009] S130: according to the current flight state of the aircraft, using the same excitation as the excitation signal to simulate under the aircraft structure response model to obtain a simulated structural response, and loading the simulated structural response into the ground safety monitoring system, and forming a safety threshold curve according to the simulated structural response;

[0010] S140: The monitoring screen of the ground safety monitoring system synchronously draws the measured aircraft structure response and safety threshold curve;

[0011] S150: Determine whether the measured aircraft structure response exceeds the safety threshold curve;

[0012] S160: If the measured aircraft structure response does not exceed the safety threshold curve, return to step 110 to enter the next excitation signal or set the next preset flight state and execute the planned excitation signal.

[0013] S170: If the measured aircraft structural response exceeds the safety threshold curve, emergency measures are taken to terminate the excitation signal on the aircraft, exit the current preset flight state to the safe flight state, and immediately return to the field for structural inspection.

[0014] Furthermore, in S110, an excitation signal is injected into the aircraft's steering gear to control the movement of the aircraft's control surface and perform structural excitation, which specifically includes:

[0015] Generate an excitation signal through an electronic device, inject the excitation signal into the test interface of the aircraft servo controller, inject symmetric excitation signal and antisymmetric excitation signal into the left and right symmetrical rudder surfaces respectively, and control the symmetrical or antisymmetric movement of the symmetrical rudder surfaces of the aircraft. For some aircraft with a single rudder, only one excitation signal needs to be injected.

[0016] Furthermore, in S110, an excitation signal is injected into the aircraft's steering gear to control the movement of the aircraft's control surface and perform structural excitation, which specifically includes:

[0017] First, a symmetrical excitation signal is input to the left and right servos of the aircraft at the same time. After the symmetrical excitation signal input is completed, an anti-symmetrical excitation signal is input to the left and right servos of the aircraft at the same time. Alternatively, an anti-symmetrical excitation signal is input to the left and right servos of the aircraft at the same time. After the anti-symmetrical excitation signal input is completed, a symmetrical excitation signal is input to the left and right servos of the aircraft at the same time.

[0018] Further, in S110, the frequency range of the excitation signal covers the main modal frequency of the aircraft control surface and the main modal frequency of the aircraft main wing structure to which the aircraft control surface is connected.

[0019] Furthermore, S120 also includes: sending the excitation signal and an excitation starting point synchronization signal representing the excitation start time to the ground safety monitoring system through the telemetry system.

[0020] Furthermore, in S120, the frequency measurement range of the acceleration sensor should cover the main frequencies of dangerous modes obtained by numerical simulation of aircraft flutter.

[0021] Further, in S130, a safety threshold curve is formed according to the simulated structural response, specifically including:

[0022] It is formed by multiplying the upper contour line value and the lower contour line value of the simulated structural response by the safety factor, and the safety factor is generally greater than 1 and less than 2.

[0023] Further, in S130, a safety threshold curve is formed according to the simulated structural response, specifically including:

[0024] During the simulation calculation, the key modal damping value of the aeroelastic system is adjusted to an expected value of not less than 0.03, and the simulated structural response of the key position of the structure under the implemented excitation is obtained by simulation. The upper contour line and the lower contour line of the simulated structural response are used as the safety threshold curve.

[0025] According to a second aspect of the present disclosure, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the computer program implements the real-time safety monitoring method for flutter flight testing based on a structural response model provided according to the first aspect.

[0026] It should be understood that the content described in this section is not intended to identify the key or important features of the embodiments of the present disclosure, nor is it intended to limit the scope of the present disclosure. Other features of the present disclosure will become easily understood through the following description.

[0027] Beneficial effects:

[0028] The time-domain safety monitoring threshold curve is constructed through the simulated structural response of the model as a reference value to monitor the structural safety of the flutter flight test, solve the reference indicator problem of the structural time-domain response, and effectively improve the timeliness and reliability of safety monitoring. This method can timely judge the abnormality of the structural response in the aircraft flutter flight test and improve the safety of the flutter flight test. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The accompanying drawings are used to better understand the present solution and do not constitute a limitation of the present disclosure.

[0030] Figure 1 A flow chart of a real-time safety monitoring method for flutter flight test based on a structural response model provided in an embodiment of the present disclosure;

[0031] Figure 2 A data flow diagram of a real-time safety monitoring method for flutter flight testing based on a structural response model provided by an embodiment of the present disclosure;

[0032] Figure 3 An example diagram of a safety monitoring threshold curve formed based on a model simulation structural response provided in an embodiment of the present disclosure;

[0033] Figure 4 An example diagram of a security monitoring software screen that synchronously displays a measured structural response and a security monitoring threshold curve provided by an embodiment of the present disclosure. DETAILED DESCRIPTION

[0034] The following is a description of exemplary embodiments of the present disclosure in conjunction with the accompanying drawings, including various details of the embodiments of the present disclosure to facilitate understanding, which should be considered as merely exemplary. Therefore, it should be recognized by those of ordinary skill in the art that various changes and modifications may be made to the embodiments described herein without departing from the scope and spirit of the present disclosure. Similarly, for the sake of clarity and conciseness, descriptions of well-known functions and structures are omitted in the following description.

[0035] Both new and modified aircraft must undergo flutter flight tests to confirm that the aircraft does not have aeroelastic instability. Aircraft flutter flight tests are the final step in verifying aircraft flutter design. Aircraft flutter flight tests are characterized by high risks. Flutter of the aircraft may cause structural damage or even disintegration of the aircraft. Real-time safety monitoring is an important part of flutter flight tests. In addition to the traditional telemetry data safety monitoring of flight parameters such as altitude, speed, and fuel volume, the actual measurement of aircraft structural response parameters is an important part. However, in traditional flutter flight structural safety monitoring, there is no reference threshold value for time domain response data. It relies on the response rules of previous sorties and the experience of monitoring personnel. Although quasi-real-time data processing can obtain structural modal information as a structural safety evaluation indicator through identification algorithms, due to reasons such as telemetry signal jumps and loss points, the accuracy of the results is often poor, and the identification results need to be obtained after the entire excitation signal ends, which is time-consuming and cannot be timely.

[0036] The present invention constructs a time-domain safety monitoring threshold curve through the simulated structural response of the model as a reference value to monitor the structural safety of the flutter flight test, solves the reference index problem of the structural time-domain response, and effectively improves the timeliness and reliability of safety monitoring.

[0037] In this regard, the present application provides a structural response safety monitoring method applied to a flutter flight test, comprising:

[0038] When the aircraft reaches a preset flight state, an excitation signal is injected into the aircraft's servo to control the movement of the aircraft's rudder surface and perform structural excitation;

[0039] The aircraft structural response measured by the acceleration sensor is transmitted to the ground safety monitoring system through the flight test telemetry system, and the ground safety monitoring system receives the telemetered measured aircraft structural response;

[0040] At the same time, according to the current flight state of the aircraft, the simulated structural response of the aircraft structural response model under the same excitation as the excitation signal is loaded into the ground safety monitoring system; and a safety threshold curve is formed according to the simulated structural response;

[0041] The monitoring screen of the ground safety monitoring system synchronously draws the measured aircraft structural response and safety threshold curve, so as to realize the real-time safety monitoring of the structure of the aircraft under the preset flight state.

[0042] Figure 1 A flow chart of a real-time safety monitoring method for flutter test flight based on a structural response model provided in an embodiment of the present disclosure is provided. The method can be applied to electronic devices, which can be devices with data processing capabilities such as servers and computers, and the present disclosure does not limit this.

[0043] like Figure 1 As shown in FIG. 1 , the real-time safety monitoring method for flutter flight test based on the structural response model includes:

[0044] S110: When the aircraft reaches a preset flight state, an excitation signal is injected into the aircraft's servo to control the movement of the aircraft's control surface and perform structural excitation.

[0045] The flight status includes the flight altitude and flight speed. Reaching the preset flight status means that the aircraft used for the test reaches the preset flight altitude and maintains stable level flight at the preset flight speed.

[0046] Injecting an excitation signal into the aircraft's servo to control the movement of the aircraft's control surface and perform structural excitation, specifically includes: generating an excitation signal through an electronic device, injecting the excitation signal into a test interface of the aircraft's servo controller, injecting symmetric excitation signals and antisymmetric excitation signals into the left and right symmetrical control surfaces respectively, controlling the symmetric or antisymmetric movement of the aircraft's symmetrical control surfaces. For some aircraft with a single-direction rudder, only one excitation signal needs to be injected.

[0047] In some possible embodiments, a symmetrical excitation signal may be input to the left and right steering gears of the aircraft at the same time, and after the symmetrical excitation signal input is completed, an anti-symmetrical excitation signal may be input to the left and right steering gears of the aircraft at the same time. Alternatively, an anti-symmetrical excitation signal may be input to the left and right steering gears of the aircraft at the same time, and after the anti-symmetrical excitation signal input is completed, a symmetrical excitation signal may be input to the left and right steering gears of the aircraft at the same time.

[0048] The symmetric excitation signals have the same phase and the same or similar amplitude, while the antisymmetric excitation signals have opposite phases and the same or similar amplitude.

[0049] In some implementations, the frequency range of the excitation signal covers the main modal frequencies of the aircraft control surface and the main modal frequencies of the aircraft main wing structure to which the aircraft control surface is connected.

[0050] For example, the frequency of the antisymmetric main structural mode of the aircraft wing is within 25Hz, and the excitation signals injected into the left and right ailerons can be two-way linear sine sweep signals with a sweep range of 1Hz to 30Hz. The two signals have opposite phases and the same amplitude and do not exceed 1°. The duration of the antisymmetric excitation signal does not exceed 60 seconds.

[0051] S120. Transmitting the aircraft structure response measured by the acceleration sensor to the ground safety monitoring system through the flight test telemetry system, and the ground safety monitoring system receives the telemetered measured aircraft structure response.

[0052] The measured aircraft structural response is obtained by arranging acceleration sensors on the aircraft wing and rudder surfaces. The frequency measurement range of the acceleration sensors should cover the main frequencies of dangerous modes obtained by numerical simulation of aircraft flutter. The telemetry system is a device that sends and receives via radio, and sends the excitation signal and acceleration signal measured on the aircraft to the ground safety monitoring system. The ground safety monitoring system is generally composed of computer hardware and monitoring software. The monitoring software includes a monitoring screen for real-time display of the measured structural response transmitted by the telemetry system.

[0053] In some implementations, in order to subsequently synchronously draw the measured response and simulated response curves, the excitation signal and the characteristic parameters representing the excitation start time (excitation start point synchronization signal) are generally also sent to the ground security monitoring system through the telemetry system.

[0054] S130, according to the current flight state of the aircraft, using the same excitation as the excitation signal to simulate under the aircraft structure response model to obtain a simulated structural response, and loading the simulated structural response into the ground safety monitoring system, and forming a safety threshold curve according to the simulated structural response. The current flight state includes: when performing structural excitation, the pressure altitude, correction speed, and fuel volume of the aircraft are the main parameters that affect the flutter characteristics of the aircraft.

[0055] In some implementations, the aircraft structure response model includes: a dynamic response model constructed based on test flight data identification, and an aeroelastic response calculation model formed based on an aircraft structure finite element model.

[0056] In some implementations, a safety threshold curve is formed based on a simulated structural response, specifically comprising: forming a safety threshold curve based on an upper contour line value and a lower contour line value of the simulated structural response multiplied by a safety factor, wherein the safety factor is generally greater than 1 and less than 2.

[0057] In some implementations, a safety threshold curve is formed based on the simulated structural response, specifically including: during the simulation calculation, by adjusting the key modal damping value of the aeroelastic system to an expected value of not less than 0.03, the simulated structural response of the key position of the structure under the implemented excitation is obtained by simulation, and the upper contour line and the lower contour line of the simulated structural response are used as the safety threshold curve.

[0058] S140, the monitoring screen of the ground safety monitoring system synchronously draws the measured aircraft structure response and safety threshold curve,

[0059] The measured aircraft structural response and the safety threshold curve have the same time domain length and the same starting point; the number of acquisition points of the measured aircraft structural response and the number of numerical points of the formed safety threshold curve are the same; the drawn measured aircraft structural response and the safety threshold curve are displayed in the same coordinates.

[0060] S150. Determine whether the measured aircraft structural response exceeds the safety threshold curve. The measured aircraft structural response exceeding the safety threshold curve means that a portion of the measured response curve values ​​of the structure is greater than the value of the upper boundary line or a portion is less than the value of the lower boundary line.

[0061] Among them, the upper boundary line of the safety threshold curve is used as the upper limit of the structural response safety, and the lower boundary line of the safety threshold curve is used as the lower limit of the structural response safety.

[0062] S160: If the measured aircraft structure response does not exceed the safety threshold curve, return to step 110 to enter the next excitation signal or set the next preset flight state and execute the planned excitation signal.

[0063] In some embodiments, each preset flight state has multiple sets of excitation signals, which are used to excite different rudder combinations to obtain the modal information of interest of each order of the structure; if all the excitation signals of a preset flight state are successfully completed, the next preset state is entered for structural excitation according to the test flight mission plan.

[0064] S170: If the measured structural response exceeds the safety threshold curve, emergency measures will be taken, such as: terminating the excitation signal on the aircraft, exiting the current preset flight state to a safe flight state, and immediately returning to the field for structural inspection.

[0065] Figure 2 A data flow diagram of a real-time safety monitoring method for flutter flight testing based on a structural response model provided in an embodiment of the present disclosure.

[0066] refer to Figure 2 The measured aircraft structural response, flight status signal, excitation signal, and excitation starting point synchronization signal of the aircraft after being excited under a preset state are transmitted to the ground receiving antenna of the telemetry system via radio signals. After the signal is parsed by the telemetry server, the flight status signal (including: altitude and speed information of the aircraft during the excitation action) and the excitation signal are transmitted to the aircraft structural response model for simulation response calculation to obtain the simulated structural response, and the calculated simulated structural response is transmitted to the safety monitoring computer. At the same time, the measured aircraft structural response signal and the excitation starting point synchronization signal are transmitted to the safety monitoring computer of the safety monitoring system. The safety monitoring computer forms a safety monitoring threshold curve based on the simulated structural response through the monitoring software, and displays it synchronously with the measured excitation signal to realize visual structural response personnel monitoring.

[0067] In some implementations, before the flutter flight mission is executed, the simulated structural response signal corresponding to the aircraft can be calculated based on the preset flight state and excitation signal that the aircraft is about to execute in the mission execution plan, forming a structural response signal library classified and stored according to the aircraft flight state and excitation signal, so as to facilitate timely calling of the simulated structural response signal during real-time tasks.

[0068] Figure 3 An example diagram of a safety monitoring threshold curve formed based on a model simulation structural response provided in an embodiment of the present disclosure.

[0069] In some embodiments, reference Figure 3 , an example of forming a safety monitoring threshold curve based on model simulation structural response, including:

[0070] S210 , an excitation signal used in the simulation, an example of which uses an excitation signal with a range of 0.1 Hz to 5 Hz, an amplitude of 0.2°, and a duration of 30 s.

[0071] S220, a simulated response signal at a certain position, at a certain height and speed, obtained by calculating the aircraft structure response model, under the excitation of the S210 excitation signal.

[0072] S230 , forming an upper contour line and a lower contour line of the simulation response signal through the positions of the local maximum points and minimum points of the curve.

[0073] S240 , the upper contour line and the lower contour line of the simulated response signal are multiplied by the selected coefficient 1.5 to form the upper threshold boundary and the lower threshold boundary of the response.

[0074] In this example, it is obvious that the response contains two structural modal information. When monitoring the measured structural response signal, the safety monitoring personnel should pay attention to whether the two bulges exceed the upper and lower boundary values ​​of the threshold.

[0075] Figure 4An example diagram of a security monitoring software screen that synchronously displays a measured structural response and a security monitoring threshold curve provided by an embodiment of the present disclosure.

[0076] Some embodiments, see Figure 4 , is an example of the measured response of a certain position structure of the aircraft displayed in the safety monitoring screen when the aircraft reaches the preset state and the aileron is subjected to anti-symmetric excitation. It can be seen that the response contains 4 obvious bulges, indicating that the measured response signal contains 4 structural modal information. In the monitoring operation, attention is paid to whether the peak of each bulge exceeds the upper boundary and the lower boundary of the safety threshold. In the example, the peak response of the response does not exceed the upper boundary and the lower boundary of the relevant safety threshold, so it is safe.

[0077] The program code for implementing the method of the present disclosure may be written in any combination of one or more programming languages. These program codes may be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that the program code, when executed by the processor or controller, enables the functions / operations specified in the flow chart and / or block diagram to be implemented. The program code may be executed entirely on the machine, partially on the machine, partially on the machine and partially on a remote machine as a stand-alone software package, or entirely on a remote machine or server.

[0078] In order to provide interaction with the user, the security monitoring screen described herein can be implemented on a computer of the security monitoring system, which has: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and a pointing device (e.g., a mouse or a trackball), through which the user can provide input to the computer. Other types of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and the input from the user can be received in any form (including acoustic input, voice input, or tactile input).

[0079] The techniques described herein may be implemented in a computing system that includes back-end components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes front-end components (e.g., a user computer with a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, or front-end components. The components of the system may be interconnected by any form or medium of digital data communication (e.g., a communications network). Examples of communications networks include: a local area network (LAN), a wide area network (WAN), and the Internet.

[0080] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps recorded in this disclosure can be executed in parallel, sequentially or in different orders, as long as the desired results of the technical solutions disclosed in this disclosure can be achieved, and this document does not limit this.

[0081] The above specific implementations do not constitute a limitation on the protection scope of the present disclosure. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

Claims

1. A real-time safety monitoring method for flutter test flight based on structural response model, characterized in that: include: S110: When the aircraft reaches a preset flight state, an excitation signal is injected into the aircraft's servo to control the movement of the aircraft's rudder surface and perform structural excitation; S120: Transmitting the aircraft structure response measured by the acceleration sensor to the ground safety monitoring system through the flight test telemetry system, and the ground safety monitoring system receives the telemetered measured aircraft structure response; S130: according to the current flight state of the aircraft, using the same excitation as the excitation signal to simulate under the aircraft structure response model to obtain a simulated structural response, and loading the simulated structural response into the ground safety monitoring system, and forming a safety threshold curve according to the simulated structural response; S140: The monitoring screen of the ground safety monitoring system synchronously draws the measured aircraft structure response and safety threshold curve; S150: Determine whether the measured aircraft structure response exceeds the safety threshold curve; S160: If the measured aircraft structure response does not exceed the safety threshold curve, return to step 110 to enter the next excitation signal or set the next preset flight state and execute the planned excitation signal. S170: If the measured aircraft structural response exceeds the safety threshold curve, emergency measures are taken to terminate the excitation signal on the aircraft, exit the current preset flight state to the safe flight state, and immediately return to the field for structural inspection.

2. The method according to claim 1, characterized in that In S110, an excitation signal is injected into the aircraft's steering gear to control the movement of the aircraft's control surface and perform structural excitation, which specifically includes: Generate an excitation signal through an electronic device, inject the excitation signal into the test interface of the aircraft servo controller, inject symmetric excitation signal and antisymmetric excitation signal into the left and right symmetrical rudder surfaces respectively, and control the symmetrical or antisymmetric movement of the symmetrical rudder surfaces of the aircraft. For some aircraft with a single rudder, only one excitation signal needs to be injected.

3. The method according to claim 1, characterized in that In S110, an excitation signal is injected into the aircraft's steering gear to control the movement of the aircraft's control surface and perform structural excitation, which specifically includes: First, a symmetrical excitation signal is input to the left and right servos of the aircraft at the same time. After the symmetrical excitation signal input is completed, an anti-symmetrical excitation signal is input to the left and right servos of the aircraft at the same time. Alternatively, an anti-symmetrical excitation signal is input to the left and right servos of the aircraft at the same time. After the anti-symmetrical excitation signal input is completed, a symmetrical excitation signal is input to the left and right servos of the aircraft at the same time.

4. The method according to claim 1, characterized in that: In S110, the frequency range of the excitation signal covers the main modal frequency of the aircraft control surface and the main modal frequency of the aircraft main wing structure to which the aircraft control surface is connected.

5. The method according to claim 1, characterized in that S120 also includes: sending the excitation signal and the excitation starting point synchronization signal representing the excitation start time to the ground safety monitoring system through the telemetry system.

6. The method according to claim 1, characterized in that In S120, the frequency measurement range of the acceleration sensor should cover the main frequencies of the dangerous modes obtained by the numerical simulation of aircraft flutter.

7. The method according to claim 1, characterized in that In S130, a safety threshold curve is formed according to the simulated structural response, specifically including: It is formed by multiplying the upper contour line value and the lower contour line value of the simulated structural response by the safety factor, and the safety factor is generally greater than 1 and less than 2.

8. The method according to claim 1, characterized in that: In S130, a safety threshold curve is formed according to the simulated structural response, specifically including: During the simulation calculation, the key modal damping value of the aeroelastic system is adjusted to an expected value of not less than 0.03, and the simulated structural response of the key position of the structure under the implemented excitation is obtained by simulation. The upper contour line and the lower contour line of the simulated structural response are used as the safety threshold curve.

Images