Adaptive Simulation Verification Method for RF Segment in RNP AR Flight Procedure

Abstract

This invention discloses an adaptive simulation verification method for RF segments in RNP AR flight procedures, comprising: S1. Flight procedure parsing: obtaining the approach procedure file and identifying the RF segments; S2. Initial sampling: random sampling to generate several sets of initial test cases; S3. Simulation execution: running a closed-loop simulation of FMS software and a six-DOF aircraft model in a simulation platform, recording the complete TSE sequence for each simulation; S4. TSE extraction and TDC calculation: for each RF segment, extracting the maximum TSE value within its corresponding time period and calculating the TSE distribution coverage rate (TDC); S5. Closed-loop optimization: forming an adaptive iterative loop of TDC evaluation, gap identification, surrogate model perturbation inversion, and geometrically guided directional sampling; until the TDC of all RF segments reaches a preset threshold. The verification results of this invention are more reliable, and the number of simulations required is significantly reduced while ensuring sufficient verification.

Description

Technical Field

[0001] This invention relates to a flight simulation verification method, and more particularly to an adaptive simulation verification method for the RF segment in an RNP AR flight procedure. Background Technology

[0002] RNP AR (Required Navigation Performance for Authorization Required) flight procedures are commonly used at airports with complex terrain. A key characteristic is the inclusion of small-radius RF segments (Radius-to-Fix legs, segments that turn around a center point to a designated location with a fixed radius, typically <6 NM). Because RF segments have high turning rates and rely entirely on GNSS (Global Navigation Satellite System) navigation, they are extremely sensitive to navigation errors and wind disturbances. Even minor deviations can be amplified by the Flight Management System (FMS) guidance law, leading to excessive TSE (Total System Error = Actual Aircraft Position – Desired Track Position), jeopardizing safety. Therefore, both RTCA DO-283B and the "Performance-based Navigation (PBN) Manual – Volume II: Implementation Guidance" require rigorous simulation verification for each RF segment to ensure that the TSE does not exceed 2 × RNP (Required Navigation Performance) with a 95% probability. This verification process is also the most complex and costly part.

[0003] Currently, laboratory validation of RNP AR flight procedures (such as approach procedures for plateau airports like Linzhi and Daocheng) mainly employs the following methods: Fixed-number Monte Carlo simulation: In accordance with RTCA DO-315B recommendations, random uniform sampling is performed within a preset disturbance parameter space (e.g., crosswind 0–30kt, GNSS error ±0.15NM), and no less than 998 simulations are performed (in engineering practice, 1000 to 1100 simulations are often used, such as 1030 simulations). The 95th percentile (P95) of the total systematic error (TSE) for each flight segment is then calculated.

[0004] Manual experience-based supplementary sampling method: Engineers run preliminary simulations (e.g., 500 times) and manually check the TSE histogram. If the high TSE interval (e.g., [0.18, 0.20] NM) is found to be sparse, extreme test scenarios are manually designed based on experience to supplement the simulation.

[0005] In the above method, the interaction between the simulation platform and the FMS is as follows: the flight simulation provides the FMS with a noisy "estimated position"; the FMS calculates the desired trajectory based on the flight plan and outputs guidance commands; the flight simulation executes the commands and updates the aircraft status, forming a closed loop. The entire process either relies on a fixed number of use cases or on manual intervention.

[0006] As can be seen from the above, the existing technology has the following prominent problems: 1. Low and uncontrollable verification efficiency: The fixed-number method results in a serious waste of computing power for simple programs, while for complex programs containing small-radius RF segments, even 10^30 runs may lead to inaccurate P95 estimation due to insufficient tail samples. The root cause is the lack of an objective and quantitative criterion for verification sufficiency to dynamically terminate the simulation.

[0007] 2. Coverage of high-risk areas relies on experience: RF segments (turning radii are often less than 6 NM) are extremely sensitive to navigation errors, and the most unfavorable GNSS error direction is strongly correlated with the segment's geometric characteristics (turning radius, azimuth). Manual sampling methods are inefficient, highly subjective, and produce unreproducible results, making it difficult to meet the airworthiness certification requirements for auditability of the verification process.

[0008] 3. Lack of automated closed-loop mechanism: Existing methods cannot automatically identify coverage gaps in the TSE distribution and intelligently generate perturbation combinations that can accurately excite the gaps, resulting in long verification cycles and high costs. Summary of the Invention

[0009] The technical problem to be solved by the present invention is to provide an adaptive simulation verification method for the RF segment in RNP AR flight procedures, which provides more reliable verification results and can significantly reduce the number of simulations required while ensuring the sufficiency of verification.

[0010] To address the aforementioned technical problems, this invention provides an adaptive simulation verification method for RF segments in RNP AR flight procedures, comprising the following steps: S1. Flight procedure parsing: Obtain the approach procedure file and identify the RF segments; S2. Initial sampling: Randomly sample and generate several sets of initial test cases; S3. Simulation execution: Run closed-loop simulation of FMS software and a six-DOF aircraft model in the simulation platform, recording the complete TSE sequence for each simulation; S4. TSE extraction and distribution coverage calculation: For each RF segment, extract the maximum TSE value within its corresponding time period and calculate the TSE distribution coverage (TDC); S5. Closed-loop optimization: Form an adaptive iterative loop for TSE distribution coverage evaluation, gap identification, surrogate model perturbation inversion, and geometrically guided directional sampling; until the TSE distribution coverage of all RF segments reaches a preset threshold.

[0011] Further, step S1 reads the ARINC 424 format approach procedure file, identifies the RF segments, extracts the turning radius and azimuth of each RF segment, and determines the turning direction through the vector cross product.

[0012] Furthermore, step S2 involves uniform random sampling within the range of GNSS horizontal error ±0.15 NM and crosswind 0 to 30 knots to generate multiple sets of initial test cases.

[0013] Furthermore, in step S4, the target TSE interval [0, 2×RNP] for airworthiness requirements is divided into multiple equal-width sub-intervals, and the TSE distribution coverage rate is set as the proportion of the number of sub-intervals covered by at least one simulation to the total number of sub-intervals. In step S5, when the TSE distribution coverage rate of all RF segments reaches the preset threshold, the verification is deemed sufficient, and the simulation is dynamically terminated.

[0014] Furthermore, the turning radius of the RF segment is less than 6 NM, the number of sub-sections is 20-40, and the preset threshold value is 95%.

[0015] Furthermore, step S5 trains a Gaussian process regression surrogate model based on historical data, with crosswind disturbance and GNSS wind direction error as inputs and the maximum TSE for a certain RF segment as output; and uses the surrogate model to search in the input disturbance space so that the TSE output predicted by the model falls into the target-uncovered area.

[0016] Furthermore, the number of sub-intervals is 20, and the width of the corresponding sub-interval is 0.01 NM. When the uncovered sub-intervals [0.18, 0.19) NM and [0.19, 0.20) NM are identified in step S5, the model searches in the input perturbation space through Bayesian optimization or gradient descent optimization algorithms so that the TSE output predicted by the model falls into the target uncovered interval [0.185, 0.195] NM.

[0017] Furthermore, in step S5, during the disturbance inversion process, directional sampling is performed by combining the turning radius and azimuth of the RF segment. Step S5 sets the direction pointing to the outside of the turn as the most unfavorable direction of GNSS error, and increases the sampling density of the neighborhood of this direction when generating supplementary use cases.

[0018] Furthermore, the number of supplementary test cases shall not exceed 30% of the number of initial test cases. When the number of initial test cases is 500, the number of supplementary test cases shall be 120.

[0019] Furthermore, step S5 also includes outputting an auditable verification report containing TSE distribution coverage, the 95th percentile value of TSE for each flight segment, and the worst-case scenario.

[0020] Compared with the prior art, the present invention has the following advantages: The adaptive simulation verification method for RF segments in RNP AR flight procedures provided by the present invention makes the verification results more reliable by precisely controlling the coverage based on TSE distribution, and can significantly reduce the number of simulations required while ensuring the sufficiency of verification. Attached Figure Description

[0021] Figure 1 This is a flowchart of the adaptive simulation verification process for the RF segment in the RNP AR flight procedure of this invention. Detailed Implementation

[0022] The present invention will now be further described with reference to the accompanying drawings and embodiments.

[0023] Figure 1 This is a flowchart of the adaptive simulation verification process for the RF segment in the RNP AR flight procedure of this invention.

[0024] Please see Figure 1 This invention proposes a closed-loop adaptive simulation verification method for the high-risk RF segment in RNP AR flight procedures. Its core lies in abandoning the verification mode driven by fixed number of runs or human experience, and instead constructing an automated verification closed loop using "TSE Distribution Coverage" (TDC) as the quantitative convergence criterion and "surrogate model perturbation inversion" as the intelligent sampling engine. Specifically, it includes the following steps: 1. Quantitative criteria for validation sufficiency based on TDC: The target TSE interval [0, 2×RNP] for airworthiness requirements is divided into multiple equal-width sub-intervals, such as 20-40 equal-width sub-intervals, preferably 20. The TSE distribution coverage rate (TDC) is defined as the proportion of sub-intervals covered by at least one simulation to the total number of sub-intervals. The calculation formula is: TDC = Number of covered sub-intervals within the target TSE interval [0, 2×RNP] / Total number of sub-intervals in the target interval. When the TDC of all RF segments reaches a preset threshold (e.g., 95%), the verification is deemed sufficient, and the simulation can be dynamically terminated.

[0025] 2. Building a closed loop of "perception-optimization-execution": a. Perception: Obtain historical "perturbation parameter → maximum TSE" data pairs through initial uniform sampling and simulation; b. Optimization: Use historical data to train a surrogate model (such as Gaussian process regression), learn the nonlinear mapping relationship between perturbation and TSE, and solve in reverse the typical perturbation combination that can make TSE fall precisely into the uncovered region; c. Execution: Generate and run supplementary test cases, and merge the new results into the historical dataset.

[0026] 3. RF segment geometry-guided directional resampling: During the disturbance inversion process, the most unfavorable direction of the GNSS error (i.e., the direction pointing outwards from the turn) is pre-determined by combining the turning radius and azimuth of the RF segment. When generating supplementary test cases, the sampling density of the neighborhood in this direction is increased, thereby efficiently stimulating high TSE scenarios with fewer simulations. Preferably, the number of supplementary test cases does not exceed 30% of the number of initial test cases.

[0027] 4. Adaptive iteration until convergence: Through a technical chain of "TDC assessment → uncovered gap identification → surrogate model perturbation inversion → geometrically guided directional sampling", a complete adaptive iterative loop is formed. This loop continues to run until the TDC of all RF segments meets the preset threshold, and finally outputs an auditable and verifiable report that includes TDC, P95 (TSE) and worst-case scenario.

[0028] Example: Verification of RWY22 RNP 0.1 procedure at Daocheng Yading Airport; 1. Program Analysis: Read the ARINC 424 format Daocheng approach procedure file and identify two RF segments. Extract the turning radius R1=4.2NM, start / end point, and azimuth θ1 of RF1; extract the turning radius R2=6.0NM and azimuth θ2 of RF2. Determine that RF1 is a left turn and RF2 is a right turn using the cross product.

[0029] 2. Initial sampling: Uniform random sampling was performed within the range of GNSS horizontal error ±0.15 NM and crosswind 0 to 30 knots to generate the initial 500 test cases.

[0030] 3. Simulation execution: Run the closed-loop simulation of the FMS software and the six-DOF aircraft model in the Simulink simulation platform, and record the complete TSE(t) sequence of each simulation.

[0031] 4. TSE Extraction and TDC Calculation: For each RF segment, extract the maximum TSE value within its corresponding time period. Divide the target TSE interval [0, 0.2] NM into 20 equal-width sub-intervals (each segment is 0.01 NM). In 500 simulations, the TSE value of RF1 covered 17 sub-intervals (TDC=85%), and RF2 covered 19 sub-intervals (TDC=95%).

[0032] 5. Closed-loop optimization: a. Since TDC=85%<95% for RF1, the system identifies the uncovered sub-intervals as [0.18, 0.19) NM and [0.19, 0.20) NM.

[0033] b. Based on 500 historical data, train a Gaussian process regression (GPR) surrogate model with inputs of (crosswind, GNSS eastward error, GNSS northward error) and output of the maximum TSE of RF1.

[0034] c. Using this surrogate model, an optimization algorithm (such as Bayesian optimization or gradient descent) is used to search the input perturbation space so that the model's predicted TSE output falls into the target uncovered interval [0.185, 0.195] NM. This process transforms the perturbation generation problem into a constrained inverse optimization problem, thereby accurately locating high-value test scenarios.

[0035] d. Considering that RF1 is a left turn and its most unfavorable GNSS direction is east, 120 sets of supplementary test cases are generated with this combination as the center, within the range of crosswind [25, 28] knots and GNSS eastward error [0.11, 0.14] NM.

[0036] 6. Results Output: After re-running the simulation, the TDC of RF1 improved to 96.3%, and the TDC of RF2 remained above 95%. The final 95th percentile of TSE = 0.182NM ≤ 0.2NM. A verification pass report is output, including auditable data such as the TDC of each RF segment and the worst-case scenario. If, after re-running the simulation, the TDC of RF1 is still less than 95%, repeat steps 5 and 6 until the TDC reaches the target requirement of >95%.

[0037] Compared with the prior art, the present invention has the following advantages and effects: 1. Significantly Improved Verification Efficiency: In a typical implementation (Daocheng Yading Airport RNP 0.1 procedure), after approximately 620 simulations, the method of this invention achieved a TDC of over 95% for all RF segments, and the 95th percentile of TSE stabilized at 0.182 NM, meeting airworthiness requirements. In contrast, using traditional fixed-number methods such as Monte Carlo simulations, after approximately 1030 simulations, the TDC was only 94.1%, and the tail interval [0.19, 0.20] NM was still not fully covered.

[0038] This data shows that the present invention can significantly reduce the number of simulations required while ensuring sufficient verification.

[0039] 2. More reliable coverage of high-risk areas: By using the TDC index and targeted supplementary sampling, it is ensured that the tail of the TSE distribution (close to 0.2NM) is fully stimulated, avoiding the risk of underestimation of P95 due to missing tail samples, and making the verification results more credible.

[0040] 3. Provide quantifiable evidence of adequacy: The TDC indicator directly and objectively measures the adequacy of verification, and supports the requirements of DO-283B regarding the provision of sufficient verification evidence in response to the audit requirements of airworthiness certification bodies for "verification adequacy".

[0041] 4. Fully automated and reproducible: No manual intervention is required. It is suitable for batch verification of RNP AR procedures for multiple airports. The verification process is transparent and the results are reproducible.

[0042] 5. The design of the TDC metric directly serves airworthiness compliance. Experimental and theoretical analyses show that when the TSE coverage (TDC) within the interval [0, 2×RNP] reaches 95%, the estimated P95 exhibits high stability, and its 95% confidence interval upper limit reliably guarantees ≤ 2×RNP. Conversely, if TDC < 95%, missing tail samples may lead to a systematic underestimation of P95, posing a safety hazard. Therefore, TDC ≥ 95% is an effective and quantifiable criterion for ensuring the adequacy of validation.

[0043] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications and improvements without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be defined by the claims.

Claims

1. An adaptive simulation verification method for RF segments in RNP AR flight procedures, characterized in that, Includes the following steps: S1. Flight Procedure Analysis: Obtain the approach procedure file and identify the RF segment; S2. Initial Sampling: Random sampling to generate several sets of initial test cases; S3. Simulation Execution: Run the closed-loop simulation of FMS software and a six-degree-of-freedom aircraft model in the simulation platform, and record the complete TSE sequence for each simulation; S4. TSE Extraction and Distribution Coverage Calculation: For each RF segment, extract the maximum TSE value within the corresponding time period and calculate the TSE distribution coverage. S5. Closed-loop optimization: Form an adaptive iterative loop of TSE distribution coverage assessment, uncovered gap identification, surrogate model perturbation inversion, and geometrically guided directional sampling; until the TSE distribution coverage of all RF segments reaches the preset threshold.

2. The adaptive simulation verification method for RF segments in RNP AR flight procedures as described in claim 1, characterized in that, Step S1 reads the ARINC 424 format approach procedure file, identifies the RF segments, extracts the turning radius and azimuth of each RF segment, and determines the turning direction through the vector cross product.

3. The adaptive simulation verification method for RF segments in RNP AR flight procedures as described in claim 1, characterized in that, Step S2 involves uniform random sampling within the range of GNSS horizontal error ±0.15 NM and crosswind 0 to 30 knots to generate multiple initial test cases.

4. The adaptive simulation verification method for RF segments in RNP AR flight procedures as described in claim 1, characterized in that, In step S4, the target TSE interval [0, 2×RNP] for airworthiness requirements is divided into multiple equal-width sub-intervals. The TSE distribution coverage rate is set as the proportion of the number of sub-intervals covered by at least one simulation to the total number of sub-intervals. In step S5, when the TSE distribution coverage rate of all RF segments reaches the preset threshold, the verification is deemed sufficient, and the simulation is dynamically terminated.

5. The adaptive simulation verification method for RF segments in RNP AR flight procedures as described in claim 4, characterized in that, The turning radius of the RF segment is less than 6 NM, the number of sub-sections is 20-40, and the preset threshold value is 95%.

6. The adaptive simulation verification method for RF segments in RNP AR flight procedures as described in claim 5, characterized in that, Step S5 trains a Gaussian process regression surrogate model based on historical data. The input is crosswind disturbance and GNSS wind direction error, and the output is the maximum TSE of a certain RF segment. The surrogate model is then used to search in the input disturbance space so that the TSE output predicted by the model falls into the target-uncovered area.

7. The adaptive simulation verification method for RF segments in RNP AR flight procedures as described in claim 6, characterized in that, The number of sub-intervals is 20, and the width of each sub-interval is 0.01 NM. When the uncovered sub-intervals [0.18, 0.19) NM and [0.19, 0.20) NM are identified in step S5, the model searches in the input perturbation space using Bayesian optimization or gradient descent optimization algorithms so that the model's predicted TSE output falls into the target uncovered interval [0.185, 0.195] NM.

8. The adaptive simulation verification method for RF segments in RNP AR flight procedures as described in claim 1, characterized in that, In step S5, during the disturbance inversion process, the turning radius and azimuth of the RF segment are combined to perform directional sampling. Step S5 sets the direction pointing to the outside of the turn as the most unfavorable direction of GNSS error, and increases the sampling density of the neighborhood of this direction when generating supplementary use cases.

9. The adaptive simulation verification method for RF segments in RNP AR flight procedures as described in claim 8, characterized in that, The number of supplementary test cases shall not exceed 30% of the number of initial test cases. When the number of initial test cases is 500, the number of supplementary test cases shall be 120.

10. The adaptive simulation verification method for RF segments in RNP AR flight procedures as described in claim 1, characterized in that, Step S5 also includes outputting an auditable and verifiable report containing TSE distribution coverage, the 95th percentile value of TSE for each flight segment, and the worst-case scenario.

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