Flight Complex Stability Assessment Method and Early Warning System Based on Safety Boundaries and Energy Management

Abstract

This invention relates to the field of flight control technology, and particularly to a method for assessing complex flight stability based on safety boundaries and energy management. The method includes: defining energy parameters; constructing kinematic equations based on the aircraft's descent process; defining equilibrium energy; constructing static boundaries based on approach phase characteristics, including a static upper boundary and a static lower boundary; extracting the aircraft's trend baseline; correcting the static boundaries to construct dynamic boundaries; and providing early warning of energy allocation anomalies based on the constructed dynamic boundaries and a preset warning mechanism, outputting the warning result. This invention innovatively integrates physical constraints and data-driven technology, enabling the boundary function to achieve smooth dynamic adjustment based on flight altitude and adapt to changing flight environments. Simultaneously, the warning mechanism based on temporal logic can trigger responses in advance at the risk nascent stage, providing pilots with sufficient operational time, resulting in stronger environmental adaptability and system stability.

Description

Technical Field

[0001] This invention belongs to the field of flight control technology, and in particular relates to a method for evaluating complex flight stability based on safety boundaries and energy management. Background Technology

[0002] The rapid development of the global air transport industry continues to drive the growth of air traffic volume. Against this backdrop, flight safety remains the bottom line for civil aviation operations. Statistics from the International Civil Aviation Organization (ICAO) reveal a crucial phenomenon: although the approach and landing phase accounts for only about 4% of the entire flight time, it accounts for 49.1% of the probability of flight accidents. Unstable approaches are widely considered one of the main factors inducing serious safety incidents such as Controlled Flight Into Land (CFIT) and runway deviation. Therefore, summarizing the main causes and development trends of unsafe events during the approach phase helps to achieve early risk prediction.

[0003] The current civil aviation regulatory system relies primarily on threshold monitoring of individual flight parameters to determine stable approaches. However, focusing on a single parameter is insufficient to comprehensively reflect the dynamic changes in an aircraft's energy state. First, a situation may arise where all monitored parameters are within safe limits, but the pilot reacts to an abnormal energy state perception, leading to an unstable approach assessment. Second, the interrelationships between different parameters are often overlooked in the evaluation, potentially causing discrepancies between the assessment results and the pilot's actual operational decisions. Stable approaches require all relevant parameters to simultaneously meet stability standards, but pilots sometimes exhibit cognitive biases, leading to insufficient awareness of the potential hazards of unstable approaches and a failure to strictly adhere to stable approach requirements. Summary of the Invention

[0004] The purpose of this invention is to provide a flight complexity stability assessment method based on safety boundaries and energy management, aiming to solve the problem that focusing on only a single parameter is insufficient to fully represent the dynamic changes in the aircraft's energy state.

[0005] This invention is implemented as follows: a flight complexity stability assessment method based on safety boundaries and energy management, the method comprising:

[0006] Define energy parameters, construct kinematic equations based on the aircraft descent process, and define equilibrium energy;

[0007] Static boundaries are constructed based on the characteristics of the entry phase. The static boundaries include a static upper boundary and a static lower boundary.

[0008] The trend baseline of the aircraft is extracted using a linear fitting method, and the static boundary is corrected to construct the dynamic boundary.

[0009] Based on the constructed dynamic boundary and the preset early warning mechanism, an abnormal energy distribution is predicted, and the early warning result is output.

[0010] Preferably, in the step of defining energy parameters, constructing kinematic equations based on the aircraft's descent process, and defining the equilibrium energy, the following steps are defined: x The horizontal distance traveled. h The geometric height from the horizontal plane. γ Where is the flight path angle, W is gravity, T is thrust, D is drag, L is lift, and TAS is vacuum speed. V W For wind speed, the kinematic equation is expressed as: ; Where m is the mass of the aircraft and g is the acceleration due to gravity. t For flight time, V Wx This represents the horizontal decomposition of wind speed. V Wh This represents the decomposition of wind speed in the vertical direction.

[0011] Preferably, the total energy of an aircraft per unit mass is expressed as: .

[0012] Preferably, the equilibrium energy is the difference between the aircraft's potential energy and kinetic energy, expressed as: ; If, over a short period of time, the mass of the aircraft and TAS are considered constant, then the rate of change of equilibrium energy is expressed as: .

[0013] Preferably, in the step of constructing static boundaries based on the characteristics of the approach phase, the runway threshold is taken as the key node, and safety constraints are constructed based on the principle of energy conservation. When the aircraft arrives at the runway threshold, its total energy must meet the requirements for safe landing. Based on this, the safe lower limit of energy altitude is derived. The total energy of the aircraft arriving at the runway threshold is expressed as: ; The total energy at the runway entrance. The speed allowed at the runway threshold, This refers to the permitted height at the runway entrance.

[0014] Preferably, a height attenuation function is introduced to dynamically adjust the static boundary. The height attenuation function is expressed as: ; in, The stable altitude is based on the airport elevation of 1000 feet. The current position is high.

[0015] Preferably, the dynamically adjusted static boundary is represented as follows: ; For static boundaries, To establish a trend baseline that is highly fitted to the global energy. This represents the minimum energy corresponding to the lower limit of energy fluctuation. This represents the maximum energy corresponding to the upper limit of energy fluctuation.

[0016] Preferably, the step of extracting the trend baseline of the aircraft using a linear fitting method and correcting the static boundary to construct the dynamic boundary includes extracting the residual of the trend baseline, whereby the residual is expressed as: ; This represents the residual between the actual energy level and the trend baseline. This indicates the actual energy level at the current moment. This indicates the energy height of the current trend baseline.

[0017] The residuals are standardized to obtain the standardized residuals;

[0018] Feature extraction is performed on the standardized residuals, and a dynamic boundary is constructed based on the extracted residual features.

[0019] Preferably, the dynamic boundary is represented as: ; Among them, Q 0.05 and Q 0.95 To capture the fluctuation range of the residuals, 1.5 is used as a safety margin. and These are the dynamic upper boundary and the dynamic lower boundary, respectively. It is an energy altitude descent curve fitted based on actual flight data.

[0020] Preferably, the early warning mechanism includes:

[0021] Equilibrium energy triggers tightening boundary mechanism: if the rate of change of equilibrium energy within the window If the difference from the standard value is greater than 0.15 rad and lasts for 2 seconds, an energy distribution imbalance is determined, which will trigger the tightening boundary formula: ; This represents the dynamic upper boundary after the equilibrium energy triggers tightening. This represents the dynamic lower boundary after the equilibrium energy triggers tightening;

[0022] At the same time, tighten the dynamic boundary and provide early warning of abnormal energy distribution;

[0023] Balanced energy triggering mechanism: If the window has balanced energy If the difference from the mean is greater than 0.15 rad and lasts for 2 seconds, it is determined that the energy distribution is unbalanced, and the dynamic boundary is tightened to provide an early warning of abnormal energy distribution.

[0024] The flight complexity stability assessment method based on safety boundaries and energy management provided by this invention not only overcomes the limitations of single threshold assessment by integrating multi-dimensional parameters, but also accurately identifies potential energy imbalance risks under the condition that the parameters meet the standards. It innovatively integrates physical constraints and data-driven technology, enabling the boundary function to be smoothly and dynamically adjusted according to flight altitude, and to adapt to the ever-changing flight environment. At the same time, the early warning mechanism based on time-series logic can trigger a response in advance at the risk bud stage, allowing pilots sufficient operation time, and exhibits stronger environmental adaptability and system stability overall. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the forces acting on an aircraft during descent, provided as an embodiment of the present invention. Figure 2 A schematic diagram of the equilibrium energy change rate curve provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the main flight display interface of a certain aircraft model provided in an embodiment of the present invention; Figure 4 A schematic diagram of the trend baseline and static boundary provided for embodiments of the present invention; Figure 5a This is a schematic diagram of the mean and standard deviation of residuals within a window provided in an embodiment of the present invention; Figure 5b This is a schematic diagram of the energy height descent gradient within a window provided in an embodiment of the present invention; Figure 6 A schematic diagram of the 5% and 95% quantiles of the residuals within the window provided in an embodiment of the present invention; Figure 7 A schematic diagram of data-driven dynamic boundaries provided for embodiments of the present invention; Figure 8 This is a schematic diagram of the time-series visualization results and output tag positioning provided in an embodiment of the present invention; Figure 9 A schematic diagram illustrating the descent rate and safety boundary provided in an embodiment of the present invention; Figure 10 A schematic diagram of the speedometer and safety boundary provided in an embodiment of the present invention; Figure 11 This is a schematic diagram of energy height and dynamic boundary provided for an embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0027] This invention will include defining core energy parameters such as energy altitude and kinetic-potential ratio, and establishing a model describing the dynamic evolution of energy state. This invention can provide solid theoretical support for the early identification of unstable approaches and provide data-driven decision-making basis for optimizing energy control strategies of key airborne equipment such as autothrottle and flight guidance systems. This has significant theoretical value and broad engineering application prospects for improving flight safety under complex and variable weather conditions.

[0028] The International Civil Aviation Organization (ICAO) has clear regulations for stable approaches: aircraft must strictly follow the prescribed glide path, maintain speed within a specified range, and the rate of vertical descent must not exceed 1000 feet per minute. Adjustments to critical configurations must be completed before reaching the stable approach point. However, in actual flight, pilot maneuvers can lead to loss of energy control. When a pilot reduces thrust to decrease kinetic energy, if the pitch angle is not adjusted in time, the rate of potential energy decay may significantly exceed the rate of kinetic energy decay, resulting in a chain reaction affecting parameters such as altitude, speed, glide angle, and vertical speed.

[0029] The energy state of an aircraft is essentially a comprehensive reflection of its kinetic and potential energy. Independent analysis of these two types of energy is insufficient to effectively capture their dynamic synergistic relationship. Therefore, this research proposes the concepts of "energy altitude" and "balance energy." "Energy altitude" converts kinetic energy into an equivalent altitude and then superimposes it with the actual geometric altitude to form a comprehensive energy index with unified dimensions. "Balance energy" quantifies the degree of equilibrium in the distribution of kinetic and potential energy, as shown in the following formula:

[0030] Balanced energy = Equivalent height after kinetic energy conversion - Actual geometric height

[0031] When the equilibrium energy approaches zero, it indicates that the distribution of kinetic and potential energy is in an ideal state. If the equilibrium energy exceeds 50 meters, it is considered that there is excess kinetic energy, and the excess kinetic energy needs to be converted into potential energy by increasing the pitch angle.

[0032] like Figure 1 The diagram shown is a force diagram illustrating the motion of an aircraft descending according to an embodiment of the present invention. The method includes:

[0033] S100 defines the energy parameters, constructs kinematic equations based on the aircraft's descent process, and defines the equilibrium energy.

[0034] In this step, the energy parameters are defined as follows: For stability assessment during the final approach phase of an aircraft, traditional methods often employ a dual-parameter independent monitoring mode of "speed-altitude," which has significant limitations. Due to the strong coupling characteristics of flight parameters during the approach phase, speed and altitude can be correlated through the conversion of kinetic and potential energy. External disturbances often act on both speed and altitude simultaneously, making it difficult to accurately capture the essential characteristics of the energy state through assessment using only a single or dual parameter. Therefore, this invention defines "energy altitude" and "equilibrium energy" as assessment parameters to achieve synergistic analysis of kinetic and potential energy, providing a quantitative basis for multi-dimensional energy state assessment.

[0035] Definition of Energy Altitude: The stability of an aircraft during the final approach phase is essentially a manifestation of the dynamic balance between kinetic and potential energy. Traditional research often analyzes kinetic and potential energy independently, which fails to reflect their synergistic relationship. Therefore, this invention utilizes the concept of "unified control of total energy" to convert kinetic energy into equivalent altitude. Adding the equivalent altitude to the actual altitude yields "energy altitude," which physically represents the aircraft's total energy as equivalent to an equivalent altitude consisting solely of gravitational potential energy, providing a direct and intuitive characterization of the aircraft's total energy reserves through a single parameter.

[0036] The forces and key parameters of an aircraft's descent, such as Figure 1 As shown, x The horizontal distance covered (m) is the distance traveled. h It represents the geometric height (m) above the horizontal plane. γ The flight path angle (the angle between the flight path and the horizontal plane) is rad. W is gravity (N), T is thrust (N), D is drag (N), and L is lift. TAS is the velocity in vacuum (m / s). V W The value represents wind speed (m / s). The solid green line represents the trajectory, TOD represents the top of descent, and CG represents the center of gravity.

[0037] Considering the aircraft as a point mass, its kinematic equations can be expressed as: (1) m is the mass of the aircraft (kg), and g is the acceleration due to gravity (9.81 m / s²). t The flight time is in seconds. V Wx This represents the horizontal decomposition of wind speed. V Wh This represents the decomposition of wind speed in the vertical direction.

[0038] We can obtain: (2)

[0039] Total energy of the aircraft It can be represented as kinetic energy. and gravitational potential energy sum: (3)

[0040] To achieve dimensional uniformity, the total energy is represented by the equivalent form of "height". Assuming all the total energy is converted into potential energy, the total energy per unit mass can be obtained as follows: (4)

[0041] Energy altitude can reflect the total energy reserve status of an aircraft through a single parameter (equivalent altitude). If the energy altitude is too high, it indicates that there is excess total energy, which may lead to an excessively high touchdown speed; if the energy altitude is too low, it means that there is insufficient total energy, which may result in risks such as poor disturbance immunity.

[0042] The combined effect of thrust and track angle on total energy is determined below using the rate of change of total energy:

[0043] Total energy change rate

[0044] Differentiating formula (4) yields: (5) because Substituting it into (5) gives: (6) Because the descent angle is small during aircraft descent, the ILS approach rule is defined as 3 degrees. Therefore, it can be considered that... Therefore, formula (6) can be written as: (7) Substituting formula (2) into (7) yields: (8) During normal flight, the weight change of an aircraft mainly comes from the reduction in fuel. Therefore, the mass of an aircraft remains almost constant over short periods of time. mg Considered a constant, available Characterizes the rate of change of kinetic energy (m / s). γ (or sin) γ The potential energy change rate (rad) is represented by this parameter. This parameter reveals the synergistic effect of thrust and track angle on total energy. The total energy is directly controlled by changing the thrust, while the track angle is controlled by changing the thrust. γ Adjust the distribution ratio of kinetic energy and potential energy.

[0045] Definition of balanced energy:

[0046] The balanced distribution of kinetic and potential energy during flight is a key factor determining approach operational margin. Traditional single-parameter monitoring methods struggle to accurately quantify the dynamic distribution relationship between kinetic and potential energy. To address this challenge, this invention proposes a concept of "balanced energy," starting with "energy conversion efficiency." By quantitatively analyzing the degree of balance in kinetic and potential energy distribution, it provides pilots with an intuitive and real-time reference for energy allocation, contributing to improved safety and accuracy in approach operations.

[0047] Balanced Energy B e Defined as the difference between potential energy and kinetic energy, it is expressed as: (9) Differentiating both sides simultaneously, we obtain the equilibrium energy change rate: (10) Will Substituting into the above equation, we get: (11) The aircraft's mass and TAS are constant over a short period of time; their effects are ignored. It can be represented as: (12)

[0048] Based on a standard 3° glide slope, 150 knots airspeed, and windless operating conditions, Figure 2 A comparative plot of the measured equilibrium energy change rate curves under standard conditions during the aircraft's final 1000-foot approach phase is presented. Observation reveals that the standard curve maintains a stable and regular trend throughout, while the measured data responds in real-time to the dynamic changes in the energy change rate. Equilibrium energy change rate. The fluctuation frequency is higher than that of traditional parameters such as speed and altitude, which can detect abnormal energy distribution in advance and provide pilots with more timely decision-making basis.

[0049] S200 constructs static boundaries based on the characteristics of the entry stage. The static boundaries include a static upper boundary and a static lower boundary.

[0050] In this step, the safety boundary function serves as a key constraint in the evaluation system, and its design is crucial. This invention leverages fundamental theories of flight mechanics, combined with civil aviation regulations and standards, to construct a dynamic boundary function. This function, through multi-parameter collaborative coupling and adaptive adjustment mechanisms, accurately establishes the safety boundary of the aircraft's energy state, providing a reliable basis for approach stability assessment.

[0051] The final approach phase carries an extremely high risk factor throughout the flight, imposing stringent requirements on the design of the safety boundary function. The International Civil Aviation Organization (ICAO) clearly defines the stability altitude in document DOC 8168: under Instrument Weather Conditions (IMC), the stability altitude is 1000 feet above airport elevation; under Visual Weather Conditions (VMC), it is reduced to 500 feet. Airlines may also develop equivalent criteria based on aircraft performance characteristics and actual operating environments.

[0052] A stable approach requires the following criteria to be met before reaching a stable altitude: Horizontal and vertical paths must be precisely controlled, and deviations from the glide path and glide slope must not exceed one point (as indicated by the glide slope deviation scale and indicators on the main flight display). Figure 3 Complete the landing configuration transition, ensuring the landing gear is fully deployed and the flaps are properly adjusted; engine thrust must be maintained stably within a specific range to guarantee the target speed, which is usually higher than the idle thrust; the flight speed should converge to the target value, generally controlled within the range of -5 to +10 knots of the Vapp speed reference.

[0053] In an IMC environment, due to the pilot's limited perception of the external environment, adjustments must be completed before reaching an altitude of 500 feet. If any criterion is not met, the crew must execute a go-around procedure unless a rapid assessment determines that only minor corrections are required (thrust adjustment ≤ 5%, track angle correction ≤ 1°).

[0054] The core objectives of the final approach are to maintain a stable airspeed, a 3° glide slope, and a reasonable energy state to achieve a safe touchdown. The energy state during this phase must adhere to a "double decrease" principle—total energy continuously decreases with decreasing altitude, and the distribution of kinetic and potential energy must remain balanced. Therefore, the design of the boundary functions must focus on core parameters such as energy altitude and equilibrium energy, while also considering dynamic stability requirements and practical constraints.

[0055] Static boundaries are the "bottom-line constraints" of the safety envelope, and their design must strictly adhere to civil aviation regulations and flight mechanics principles to ensure the safety of the energy state under ideal conditions. According to the relevant requirements of the Flight Standards Department of the Civil Aviation Administration of China, the target approach speed (Vapp) serves as the core reference, and the actual flight speed must be precisely maintained within the range of -5 to +10 knots of Vapp. From the perspective of ensuring pilot operational margin and go-around energy reserves, the descent rate during the final approach phase must be controlled below 1000 feet per minute to allow pilots sufficient adjustment time.

[0056] In the final approach phase, setting the energy altitude boundary is a crucial step in ensuring a safe landing. Using the runway threshold as the key node, safety constraints are constructed based on the principle of energy conservation. When the aircraft arrives at the runway threshold, its total energy must meet the requirements for a safe landing; based on this, a safe lower limit for energy altitude is derived. This provides a guarantee for a smooth landing from an energy perspective, ensuring that the aircraft has adequate energy reserves at the end of the approach.

[0057] (13) in, The total energy at the runway entrance. The speed allowed at the runway threshold, This refers to the permitted height at the runway entrance.

[0058] The initial safety envelope is based on the static energy boundary defined by the physical model. To match the operational logic of "the lower the altitude, the stricter the energy control" during the approach phase, an altitude decay function is introduced. Dynamically adjust static boundaries: (14) In the formula, The stable altitude is based on the airport elevation of 1000 feet. The current position is high. The range is as follows: (15) This is a trend baseline that is highly fitted to the global energy. The minimum energy corresponding to the lower limit of energy height fluctuation: if the speed is less than 5 knots below the standard, the height corresponding to the equivalent potential energy is less than 20 meters. The maximum energy corresponding to the upper limit of energy height fluctuation: when the speed exceeds the standard by 10 knots, the height corresponding to the equivalent potential energy is 42 meters.

[0059] The steps to obtain the trend baseline that is highly fitted to the global energy are as follows:

[0060] Using a univariate linear regression model, the trend baseline is assumed to be: ;

[0061] Where 'a' is the slope (representing the rate of decrease in energy level) and 'b' is the intercept (representing the initial energy level). The optimal parameters 'a' and 'b' are solved by minimizing the sum of squared residuals using the least squares method.

[0062] Formula (15) represents a comparison between a stable altitude of 1000 feet and the current actual flight altitude. In higher airspace, the flight trajectory is less affected by obstacles. Therefore, the upper boundary of the energy altitude is relatively wide, which can accommodate the natural fluctuations of energy during normal flight. As the aircraft trajectory continues to descend, the tolerable fluctuations at the lower boundary of the altitude continue to narrow exponentially. This function design enables a smooth transition of the boundary, effectively avoiding judgment biases that may be caused by sudden changes in the boundary.

[0063] Figure 4 Trend baseline Its static boundaries. The initial position of the upper static boundary is 42 meters above the trend line, and the initial position of the lower static boundary is 20 meters below the trend line. Over time, the upper boundary gradually approaches the trend baseline, while the lower boundary contracts to 15.2 meters (50 feet) within 30 seconds and remains parallel to the trend baseline after 30 seconds. The range change trend between the upper and lower static boundaries can be divided into two parts: a dynamic narrowing phase before 30 seconds and a parallel descent phase after 30 seconds, providing a reference framework for monitoring the energy altitude range during aircraft approach.

[0064] The S300 uses a linear fitting method to extract the aircraft's trend baseline and corrects the static boundary to construct the dynamic boundary.

[0065] In this step, the static boundary defines the energy range under ideal conditions. However, in real-world operations, complex and variable weather conditions are frequently encountered, making it difficult for the static boundary to adapt to dynamic energy fluctuations. Therefore, this invention uses Fast Access Recorder (QAR) data from an international airport between 2015 and 2020 as the research object, deeply mines key information, and proposes a dynamic boundary correction strategy that combines energy altitude with equilibrium energy. It also utilizes sliding window statistical techniques to capture data characteristics and combines trend analysis to optimize the safety envelope profile, enabling the boundary setting to better adapt to complex environmental conditions and improving the environmental adaptability and practical application value of the assessment system.

[0066] Data preprocessing: To accurately analyze the characteristics of energy data, the study used a linear fitting method to extract a trend baseline. This effectively separates long-term trends from short-term fluctuations in the data. This is achieved by calculating the residuals. This data processing method can intuitively present the short-term deviation of energy levels from the ideal trend. It avoids the interference of trend factors in quantile calculations, ensuring the accuracy of subsequent analysis. The residual formula is as follows: (16) Z-score standardization of the residuals eliminates the influence of differences in the dimensions of different parameters, allowing for comparative analysis of all parameters on a uniform scale. This lays the foundation for subsequent construction of a dynamic boundary correction model. The standardization method is as follows: (17) In the formula, X represents any parameter that is standardized. Represents the standardized parameters. μ X and σ X represents the mean and standard deviation of parameter X, respectively.

[0067] Dynamic boundary correction method

[0068] (1) The following features are extracted using a sliding window with a length of 5 seconds: residual mean μ res The average level of energy fluctuations within the window reflects short-term fluctuations and is used for anomaly detection.

[0069] residual standard deviation σ res Standard deviation measures the dispersion of energy fluctuations; a larger standard deviation indicates more severe fluctuations.

[0070] Energy height decline rate β Ensure the descent rate meets the energy gradient requirements for a stable approach. (18) In the formula, The energy level at the final moment, The initial energy level. For the final moment, This is the initial time.

[0071] The extracted data is shown in the figure. Figure 5a The residual mean and standard deviation are shown at different times, while Figure 5b It shows the rate of decrease in energy altitude and flight altitude at different times.

[0072] Dynamic boundary adjustment rules: The 5% and 95% quantiles of the residuals within the window are calculated based on the residual quantiles, using the following formula: (19)

[0073] Among them, Q 0.05 and Q 0.95 To capture the typical fluctuation range of the residuals, 90% of the data was covered. Formula 1.5 σres This provides a 1.5 times safety margin for the residuals, preventing false alarms. T,upper and E T,lowerThese are the static upper boundary and the static lower boundary, respectively. E T,tre It is an energy altitude descent curve fitted based on actual flight data. Dynamic margin is as follows: Figure 6 As shown.

[0074] S400 performs early warning of energy distribution anomalies based on the constructed dynamic boundary and the preset early warning mechanism, and outputs the early warning results.

[0075] In this step, the equilibrium energy triggers a tightening boundary mechanism: if the rate of change of the equilibrium energy within the window... If the difference from the standard value is greater than 0.15 rad and lasts for 2 seconds, it is determined that the energy distribution is unbalanced. At this time, the tightening boundary formula (20) will be triggered, and the dynamic boundary will be tightened to give an early warning of abnormal energy distribution.

[0076] Balanced energy triggering mechanism: If the window has balanced energy If the difference from the mean is greater than 0.15 rad and lasts for 2 seconds, an energy distribution imbalance is determined, and the dynamic boundary is tightened to provide an early warning of abnormal energy distribution. Figure 7 The pink area. The formula is as follows: (20) This mechanism improves the accuracy of early warnings by focusing boundary adjustments on energy distribution rather than fluctuation amplitude through continuous anomaly identification of balanced energy.

[0077] The effects of the present invention are illustrated by the following experiments:

[0078] Comparative experiment:

[0079] 1. Mixed boundary method:

[0080] This invention uses approach data from a B777 flight at an international airport on April 5, 2015, as the experimental sample. The data comprehensively records various flight parameters during the final approach phase, covering core indicators such as airspeed, rate of descent, N1 speed, and energy altitude, with a time resolution of once per second. The data includes various disturbances such as normal weather conditions, weak turbulence, and slight wind shear, fully demonstrating the typical characteristics of energy fluctuations during approach. No sensor malfunctions or missing key data were found in the data, and the sampling frequency and accuracy of important parameters such as airspeed and altitude strictly comply with ICAO standards.

[0081] The data preprocessing steps are as follows: outliers caused by sensor noise are removed using the 3σ criterion; Z-score standardization is performed on core parameters such as energy height and equilibrium energy to ensure the consistency of model input; continuous data in the range of 415-1415 feet is extracted, focusing on the key stage below the stable height.

[0082] Figure 8 The time-series visualization of the experimental data shows the relationship between energy level and dynamic and static boundaries. In the figure, the blue curve represents the measured energy level, the solid black line represents the dynamic upper boundary, the solid red line represents the dynamic lower boundary, the dashed red line represents the static lower boundary, and the dashed yellow line represents the static upper boundary. Labels are color-coded: yellow areas indicate a state of alert (label 1), and red areas indicate a state of warning (label 2). As can be seen from the figure, the energy level briefly exceeded the dynamic upper boundary at 48:45, triggering a yellow alert; subsequently, at 48:58, it remained below the dynamic lower boundary for 3 consecutive seconds and exceeded the static boundary, triggering a red warning. The visualization results intuitively reflect the evolution of the energy state from fluctuation to imbalance, providing crucial evidence for anomaly localization.

[0083] In the verification of the alert state (Label 1), at 48 minutes and 45 seconds, due to turbulence, the energy altitude momentarily exceeded the dynamic upper boundary, and the early warning system quickly triggered an alert, promptly transmitting the energy fluctuation signal to the pilot. From 48 minutes and 55 seconds to 48 minutes and 56 seconds, the energy altitude remained below the dynamic lower boundary for two consecutive seconds, and the system maintained the alert state. This design allows the pilot reasonable reaction time, precisely matching the minimum reaction cycle of human operation. Entering the warning state (Label 2) stage, from 48 minutes and 58 seconds to 48 minutes and 59 seconds, the energy altitude fell below the static boundary for two consecutive seconds, triggering a warning alarm. At 49 minutes and 01 seconds, due to the abnormal situation that had occurred for three consecutive seconds, the system issued another warning. It is noteworthy that the warning time was completely synchronized with the pilot's operation. At 48 minutes and 58 seconds, the pilot increased the engine thrust from 58% to 60%, fully verifying the high degree of consistency between the warning logic and the actual operation in the time sequence. Subsequent data showed that after 49 minutes and 10 seconds, the energy altitude returned to the dynamic envelope range, and the warning label automatically reset to 0. This process demonstrates that the early warning mechanism can not only respond accurately when anomalies occur, but also quickly return to normal monitoring after the energy status returns to normal, effectively avoiding the combined risks of false alarms and missed alarms, and ensuring the continuous and stable operation of the system.

[0084] Output tag analysis ; Output Tag Analysis (Continued) ; 2. Traditional evaluation model:

[0085] To deeply verify the sophistication and practicality of the hybrid boundary method, comparative experiments were conducted with the traditional single-parameter threshold method and a purely data-driven model lacking physical constraints. Through multi-dimensional index comparison and scenario-based verification, the performance differences of different methods in energy state assessment were systematically analyzed.

[0086] Single-parameter thresholding method:

[0087] The single-parameter threshold method is currently the mainstream method for assessing stability approach in civil aviation, monitoring only two independent numerical parameters: speed and descent rate. Experimental data shows that... Figure 9 , Figure 10 During the approach, the flight maintained a stable speed of 145-152 kt and a descent rate of -720 to -944 ft / min, which is considered a "stable approach" by traditional methods (label 0).

[0088] Comparative analysis revealed that during the period from 48 minutes and 58 seconds to 49 minutes and 01 seconds, traditional parameters showed that all aircraft indicators were within the normal range. However, the energy boundary function constructed in this invention clearly showed that the energy altitude continuously exceeded both the dynamic lower boundary and the static boundary during this period (see...). Figure 8 This contradictory phenomenon exposes the inherent flaws of the traditional single-parameter threshold method: this method only judges whether a single parameter meets the standard in isolation, and cannot identify the potential risks caused by the interaction between parameters. In stark contrast, the multi-parameter fusion method proposed in this invention, by comprehensively considering the dynamic relationship between energy parameters, can more accurately reveal the true state of energy, effectively making up for the shortcomings of traditional methods.

[0089] Compared to a purely data-driven model without physical constraints:

[0090] Pure data-driven models, which rely solely on Fast Access Recorder (QAR) data to train dynamic boundaries, exhibit significant limitations due to the lack of embedded physical constraints from flight mechanics. The experimental data visualization results are as follows... Figure 11 Display, comparison Figure 8 The model exhibited several boundary anomalies during the approach: at 34 and 52 seconds, the dynamic boundary contracted unreasonably, with the lower dynamic boundary abnormally higher than the energy altitude trend line while the upper dynamic boundary fell below it, causing normal fluctuations in flight parameters to be incorrectly flagged as abnormal. Furthermore, at the critical stage of the approach's final 67 seconds, below 500 feet, the boundary unexpectedly expanded, with the lower dynamic boundary falling below the static boundary, completely failing to meet the stringent energy accuracy requirements at low altitudes. More seriously, facing a severe energy imbalance between 48 minutes 58 seconds and 49 minutes 01 seconds, the model failed to trigger any warning signals, ultimately resulting in a significant missed risk, clearly highlighting the negative impact of missing physical constraints on model reliability.

[0091] This invention innovatively integrates an altitude decay function with physical constraints, ensuring from a theoretical foundation that the boundary function conforms to the principles of flight mechanics while dynamically adjusting according to actual flight altitude. The altitude decay function gradually tightens the boundary as altitude decreases, while physical constraints define the scientific boundaries of energy changes. Together, these ensure the rigor of the assessment system. In contrast, purely data-driven models, overly reliant on historical data training and lacking the underlying support of physical laws, cannot accurately identify the intrinsic relationship between altitude and energy changes. This makes their constructed dynamic boundaries difficult to match the needs of real-world flight scenarios, ultimately leading to warning failures under complex energy fluctuations, highlighting the indispensability of physical constraints in flight safety assessments.

[0092] This invention addresses the limitations of traditional flight energy state assessment methods by proposing and constructing a hybrid boundary method, aiming to improve the stability and adaptability of energy management during flight approach. The main research conclusions are as follows:

[0093] 1. The shortcomings of traditional methods are obvious: Experimental data show that traditional static boundary relies on a single parameter for evaluation and cannot fully reflect the flight energy state; pure data models lack physical constraints and have weak generalization ability in complex scenarios. Both are difficult to meet the requirements of high-precision energy assessment.

[0094] 2. Significant advantages of the hybrid boundary method: The proposed hybrid boundary method breaks through the constraints of single threshold assessment by integrating multi-dimensional parameters (airspeed, altitude, descent rate, energy change rate, etc.), and can accurately identify potential energy imbalance risks under the condition that the parameters meet the standards. At the same time, it innovatively integrates physical constraints and data-driven technology, enabling the boundary function to be smoothly and dynamically adjusted according to the flight altitude, adapting to the changing flight environment and showing stronger environmental adaptability and system stability.

[0095] 3. Outstanding innovation in stability assessment system: The stability assessment system based on energy management has two core innovations: First, it uses energy height and equilibrium energy as core assessment parameters to clarify the mechanism of the "kinetic energy-potential energy" coupling effect on approach stability; second, it designs a dynamic boundary function that combines physical constraints and data-driven characteristics, and achieves dynamic boundary adaptation through a height decay mechanism to make up for the shortcomings of traditional static boundaries.

[0096] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A flight complexity stability assessment method based on safety boundaries and energy management, characterized in that, The method includes: Define energy parameters, construct kinematic equations based on the aircraft descent process, and define equilibrium energy; Static boundaries are constructed based on the characteristics of the entry phase. The static boundaries include a static upper boundary and a static lower boundary. The trend baseline of the aircraft is extracted using a linear fitting method, and the static boundary is corrected to construct the dynamic boundary. Based on the constructed dynamic boundary and the preset early warning mechanism, an abnormal energy distribution is predicted, and the early warning result is output.

2. The flight complexity stability assessment method based on safety boundaries and energy management according to claim 1, characterized in that, In the step of defining energy parameters, constructing kinematic equations based on the aircraft descent process, and defining the equilibrium energy, the following steps are defined: x The horizontal distance traveled. h The geometric height from the horizontal plane. γ Where is the flight path angle, W is gravity, T is thrust, D is drag, L is lift, and TAS is vacuum speed. V W For wind speed, the kinematic equation is expressed as: ; Where m is the mass of the aircraft and g is the acceleration due to gravity. t For flight time, V Wx This represents the horizontal decomposition of wind speed. V Wh This represents the decomposition of wind speed in the vertical direction.

3. The flight complexity stability assessment method based on safety boundaries and energy management according to claim 2, characterized in that, The total energy of an aircraft per unit mass is expressed as: 。 4. The flight complexity stability assessment method based on safety boundaries and energy management according to claim 3, characterized in that, The equilibrium energy is the difference between the aircraft's potential energy and kinetic energy, expressed as: ; If, over a short period of time, the mass of the aircraft and TAS are considered constant, then the rate of change of equilibrium energy is expressed as: 。 5. The flight complexity stability assessment method based on safety boundaries and energy management according to claim 1, characterized in that, In the step of constructing static boundaries based on the characteristics of the approach phase, the runway threshold is taken as the key node. Based on the principle of energy conservation, safety constraints are constructed. When the aircraft arrives at the runway threshold, its total energy must meet the requirements for safe landing. Based on this, the safe lower limit of energy altitude is derived. The total energy of the aircraft arriving at the runway threshold is expressed as: ; The total energy at the runway entrance. The speed allowed at the runway threshold, This refers to the permitted height at the runway entrance.

6. The flight complexity stability assessment method based on safety boundaries and energy management according to claim 5, characterized in that, it introduces... The height decay function dynamically adjusts the static boundary. The height decay function is expressed as: ; in, The stable altitude is based on the airport elevation of 1000 feet. The current position is high.

7. The flight complexity stability assessment method based on safety boundaries and energy management according to claim 6, characterized in that, The dynamically adjusted static boundary is represented as follows: ; For static boundaries, To establish a trend baseline that is highly fitted to the global energy. This represents the minimum energy corresponding to the lower limit of energy fluctuation. This represents the maximum energy corresponding to the upper limit of energy fluctuation.

8. The flight complexity stability assessment method based on safety boundaries and energy management according to claim 1, characterized in that, The steps of extracting the trend baseline of the aircraft using a linear fitting method and correcting the static boundary to construct the dynamic boundary include extracting the residuals of the trend baseline, which are expressed as: ; This represents the residual between the actual energy level and the trend baseline. This indicates the actual energy level at the current moment. This indicates the energy height of the current trend baseline. The residuals are standardized to obtain the standardized residuals; Feature extraction is performed on the standardized residuals, and a dynamic boundary is constructed based on the extracted residual features.

9. The flight complexity stability assessment method based on safety boundaries and energy management according to claim 8, characterized in that, Dynamic boundaries are represented as: ; Among them, Q 0.05 and Q 0.95 To capture the fluctuation range of the residuals, 1.5 is used as a safety margin. and These are the dynamic upper boundary and the dynamic lower boundary, respectively. It is an energy altitude descent curve fitted based on actual flight data.

10. The flight complexity stability assessment method based on safety boundaries and energy management according to claim 9, characterized in that, The early warning mechanism includes: Equilibrium energy triggers tightening boundary mechanism: if the rate of change of equilibrium energy within the window If the difference from the standard value is greater than 0.15 rad and lasts for 2 seconds, an energy distribution imbalance is determined, which will trigger the tightening boundary formula: ; This represents the dynamic upper boundary after the equilibrium energy triggers tightening. This represents the dynamic lower boundary after the equilibrium energy triggers tightening; At the same time, tighten the dynamic boundary and provide early warning of abnormal energy distribution; Balanced energy triggering mechanism: If the window has balanced energy If the difference from the mean is greater than 0.15 rad and lasts for 2 seconds, it is determined that the energy distribution is unbalanced, and the dynamic boundary is tightened to provide an early warning of abnormal energy distribution.

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