Train aerodynamic force distributed measurement method and system

Abstract

The invention relates to the technical field of train measurement, and discloses a train aerodynamic force distributed measurement method, which comprises the following steps of: determining a wheel track supporting point position in a train head train model and installing a force sensor; force output signals in the X-axis direction, the Y-axis direction and the Z-axis direction are collected through a force sensor; calculating an X-axis resultant force, a Y-axis resultant force and a Z-axis resultant force based on the force output signals in the X-axis direction, the Y-axis direction and the Z-axis direction and the space coordinates of the force sensor, and calculating a resultant moment based on the space coordinates of the force sensor; constructing a multiple regression model, training the multiple regression model by taking the X-axis resultant force, the Y-axis resultant force, the Z-axis resultant force and the resultant moment as original data, and solving a regression coefficient matrix in the model to obtain a trained regression model; and inputting the X-axis resultant force, the Y-axis resultant force, the Z-axis resultant force and the resultant moment obtained in the wind tunnel test into the trained regression model to obtain the corrected X-axis resultant force, the corrected Y-axis resultant force, the corrected Z-axis resultant force and the corrected resultant moment.

Description

Technical Field

[0001] This invention relates to the field of train measurement technology, and in particular to a distributed measurement method and system for train aerodynamics. Background Technology

[0002] Currently, six-component box balances are widely used for centralized measurement in high-speed train dynamics testing. The principle is to simultaneously measure and process the loading forces at multiple points on the loading block during the test into six mechanical components: three translational forces and three axial moments. These components are then used to simulate and analyze the aerodynamics of the train during actual operation. Centralized measurement using box balances is a relatively mature technology in the field of aerodynamics and dynamics testing, with well-established design, calibration, and usage standards. In the field of high-speed train testing, the industry has clear specifications for the interpretation of centralized measurement data and error assessment, and the test results have good repeatability and comparability. Under ideal test conditions, the measured forces and moments can be guaranteed to have strong synchronicity, and it is insensitive to local disturbances in the test environment, such as airflow turbulence in wind tunnels and minor vibrations of the test bench.

[0003] However, as the continuous lightweighting, ultra-high speed, and complex operating environment of high-speed trains increasingly impact train performance, the shortcomings of the six-component box balance in high-speed train aerodynamics and dynamics testing, such as its testing accuracy and resistance to environmental interference (e.g., temperature variations), are becoming more pronounced. Furthermore, if the six-component box balance malfunctions during experiments, the entire system will fail to operate normally. Therefore, existing methods for measuring train aerodynamics suffer from weak interference resistance. Summary of the Invention

[0004] This invention provides a distributed measurement method and system for train aerodynamics to solve the problem of weak anti-interference capability in existing train aerodynamics measurement methods.

[0005] To achieve the above objectives, the present invention employs the following technical solution: In a first aspect, the present invention provides a distributed measurement method for train aerodynamic forces, comprising: Construct a train head car model for the target train and a track model for distributed measurement; Determine the wheel-rail support point positions in the train head car model, determine the sensor installation positions in the track model based on the wheel-rail support point positions, and install force sensors at the sensor installation positions; Place the train head car model on the track model, and align the wheel-rail center position in the train head car model with the position of the force sensor. The principle of wind tunnel testing was used to apply incoming airflows with different wind speeds and wind angles to the train head car model, and force output signals in the three directions of X-axis, Y-axis and Z-axis were collected by force sensors; The resultant force along the X-axis, Y-axis, and Z-axis is calculated based on the force output signals in the three directions of X, Y, and Z axes and the spatial coordinates of the force sensor. The resultant torque is also calculated based on the spatial coordinates of the force sensor. A multivariate regression model is constructed by using the resultant forces on the X-axis, Y-axis, and Z-axis as raw data to train the multivariate regression model, solving for the regression coefficient matrix in the model, and obtaining the trained regression model. The resultant forces and moments along the X, Y, and Z axes obtained from wind tunnel tests are input into the trained regression model to obtain the corrected resultant forces along the X, Y, and Z axes and the corrected moment.

[0006] Optionally, the number of force sensors is no less than 8, and each force sensor corresponds to 8 wheel-rail support points of the train head car model.

[0007] Optionally, the resultant force along the X-axis, Y-axis, and Z-axis is calculated based on the force output signals in the X, Y, and Z axes and the spatial coordinates of the force sensor, including: The force output signals in the X-axis direction are Fx1~Fx8 respectively; The force output signals in the Y-axis direction are Fy1~Fy8 respectively; The force output signals in the Z-axis direction are Fz1~Fz8 respectively; The calculation of the resultant force along the X-axis satisfies: Fx = Σ(Fx_i); The resultant force along the Y-axis is calculated to satisfy: Fy = Σ(Fy_i); The resultant force along the Z-axis is calculated to satisfy: Fz = Σ(Fz_i).

[0008] Optionally, the spatial coordinates of the force sensor include: the lateral center distance of the sensor, the longitudinal center distance of the sensor, the train distance, and the height difference between the sensor and the balance.

[0009] Optionally, the resultant torque is calculated based on the spatial coordinates of the force sensor, including: Based on the resultant force along the Y-axis, the resultant force along the Z-axis, the height difference between the sensor and the balance, and the lateral center distance of the sensor, the resultant moment in the X-axis direction is calculated, satisfying the following relationship: Mx=-Fy1·h-Fy2·h-Fy3·h-Fy4·h-Fy5·h-Fy6·h-Fy7·h-Fy8·h+Fz1·d / 2-Fz2·d / 2+Fz3·d / 2-Fz4·d / 2+Fz5·d / 2-Fz6·d / 2+Fz7·d / 2-Fz8·d / 2; The resultant moment in the Y-axis direction is calculated based on the resultant force along the X-axis, the resultant force along the Z-axis, the height difference between the sensor and the balance, the train's fixed distance, and the longitudinal center distance of the sensor. The calculation satisfies the following relationship: My=Fx1·h+Fx2·h+Fx3·h+Fx4·h+Fx5·h+Fx6·h+Fx7·h+Fx8·h-Fz1·(L+e) / 2-Fz2·(L+e ) / 2-Fz3·(Le) / 2-Fz4·(Le) / 2+Fz5·(Le) / 2+Fz6·(Le) / 2+Fz7·(L+e) / 2+Fz8·(L+e) / 2; Based on the resultant force along the X-axis, the resultant force along the Y-axis, the transverse center distance of the sensors, the longitudinal center distance of the sensors, and the train's fixed distance, the resultant moment in the Z-axis direction is calculated, satisfying the following relationship: Mz=-Fx1·d / 2+Fx2·d / 2-Fx3·d / 2+Fx4·d / 2-Fx5·d / 2+Fx6·d / 2-Fx7·d / 2+Fx8·d / 2+Fy1·(L+e) / 2+ Fy2·(L+e) / 2+Fy3·(Le) / 2+Fy4·(Le) / 2-Fy5·(Le) / 2-Fy6·(Le) / 2-Fy7·(L+e) / 2-Fy8·(L+e) / 2; In the formula, d represents the lateral center distance of the sensor, e represents the longitudinal center distance of the sensor, L represents the train's fixed distance, and h represents the height difference between the sensor and the balance.

[0010] Optionally, the decoupling matrix is ​​obtained by solving the least squares method.

[0011] Optionally, the regression coefficient matrix in the model can be solved, including: A multi-source, multi-order regression approach was used to systematically calibrate and decouple the resultant forces along the X, Y, and Z axes. The calculation process satisfies the following relationship: ; In the formula, C j,pqr The coefficients are represented by P, q, and r, which represent the powers of the input variables in the polynomial regression, respectively. i,corrected Let Fx represent the resultant force along the X-axis, Fy represent the resultant force along the Y-axis, and Fz represent the resultant force along the Z-axis.

[0012] Secondly, embodiments of this application provide a distributed aerodynamic measurement system for a train, including a processor and a memory; Memory, used to store computer programs; When a processor executes a program stored in memory, it implements any of the steps of the method described in the first aspect.

[0013] Beneficial effects: The distributed aerodynamic measurement method for trains provided by this invention sets up multiple independent sensors, so the failure of a single sensor will not cause the entire system to fail. The remaining sensor data can still be partially reconstructed through algorithms, which significantly enhances the system's robustness. The distributed layout makes it easy to implement targeted shielding, heat insulation or temperature compensation measures for each sensor or its local area, effectively reducing the impact of environmental airflow interference and temperature unevenness. Attached Figure Description

[0014] Figure 1 This is a flowchart of a preferred embodiment of the train aerodynamic distributed measurement method of the present invention; Figure 2 This is a schematic diagram of the installation of sensors, trains, and other equipment for aerodynamic measurement according to a preferred embodiment of the present invention. Detailed Implementation

[0015] The technical solution of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms "an" or "a" and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms "connected" or "linked" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up," "down," "left," "right," etc., are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship also changes accordingly.

[0017] Please see Figure 1 This application provides a distributed measurement method for train aerodynamic forces, comprising: Construct a train head car model for the target train and a track model for distributed measurement; Determine the wheel-rail support point positions in the train head car model, determine the sensor installation positions in the track model based on the wheel-rail support point positions, and install force sensors at the sensor installation positions; Place the train head car model on the track model, and align the wheel-rail center position in the train head car model with the position of the force sensor. Using the principle of wind tunnel testing, different wind speeds and wind angles are applied to the train head car model, and force output signals in the X, Y and Z axes are collected by force sensors; The resultant force along the X-axis, Y-axis, and Z-axis is calculated based on the force output signals in the three directions of X, Y, and Z axes and the spatial coordinates of the force sensor. The resultant torque is also calculated based on the spatial coordinates of the force sensor. A multivariate regression model is constructed by using the resultant forces on the X-axis, Y-axis, and Z-axis as raw data to train the multivariate regression model, solving for the regression coefficient matrix in the model, and obtaining the trained regression model. The resultant forces and moments along the X, Y, and Z axes obtained from wind tunnel tests are input into the trained regression model to obtain the corrected resultant forces along the X, Y, and Z axes and the corrected moment.

[0018] Optionally, the number of force sensors is no less than 8, and each force sensor corresponds to 8 wheel-rail support points of the train head car model.

[0019] Optionally, the resultant force along the X-axis, Y-axis, and Z-axis is calculated based on the force output signals in the X, Y, and Z axes and the spatial coordinates of the force sensor, including: The force output signals in the X-axis direction are Fx1~Fx8 respectively; The force output signals in the Y-axis direction are Fy1~Fy8 respectively; The force output signals in the Z-axis direction are Fz1~Fz8 respectively; The calculation of the resultant force along the X-axis satisfies: Fx = Σ(Fx_i); The resultant force along the Y-axis is calculated to satisfy: Fy = Σ(Fy_i); The resultant force along the Z-axis is calculated to satisfy: Fz = Σ(Fz_i).

[0020] Optionally, the spatial coordinates of the force sensor include: the lateral center distance of the sensor, the longitudinal center distance of the sensor, the train distance, and the height difference between the sensor and the balance.

[0021] Optionally, the resultant torque is calculated based on the spatial coordinates of the force sensor, including: Based on the resultant force along the Y-axis, the resultant force along the Z-axis, the height difference between the sensor and the balance, and the lateral center distance of the sensor, the resultant moment in the X-axis direction is calculated, satisfying the following relationship: Mx=-Fy1·h-Fy2·h-Fy3·h-Fy4·h-Fy5·h-Fy6·h-Fy7·h-Fy8·h+Fz1·d / 2-Fz2·d / 2+Fz3·d / 2-Fz4·d / 2+Fz5·d / 2-Fz6·d / 2+Fz7·d / 2-Fz8·d / 2; The resultant moment in the Y-axis direction is calculated based on the resultant force along the X-axis, the resultant force along the Z-axis, the height difference between the sensor and the balance, the train's fixed distance, and the longitudinal center distance of the sensor. The calculation satisfies the following relationship: My=Fx1·h+Fx2·h+Fx3·h+Fx4·h+Fx5·h+Fx6·h+Fx7·h+Fx8·h-Fz1·(L+e) / 2-Fz2·(L+e ) / 2-Fz3·(Le) / 2-Fz4·(Le) / 2+Fz5·(Le) / 2+Fz6·(Le) / 2+Fz7·(L+e) / 2+Fz8·(L+e) / 2; Based on the resultant force along the X-axis, the resultant force along the Y-axis, the transverse center distance of the sensors, the longitudinal center distance of the sensors, and the train's fixed distance, the resultant moment in the Z-axis direction is calculated, satisfying the following relationship: Mz=-Fx1·d / 2+Fx2·d / 2-Fx3·d / 2+Fx4·d / 2-Fx5·d / 2+Fx6·d / 2-Fx7·d / 2+Fx8·d / 2+Fy1·(L+e) / 2+ Fy2·(L+e) / 2+Fy3·(Le) / 2+Fy4·(Le) / 2-Fy5·(Le) / 2-Fy6·(Le) / 2-Fy7·(L+e) / 2-Fy8·(L+e) / 2; In the formula, d represents the lateral center distance of the sensor, e represents the longitudinal center distance of the sensor, L represents the train's fixed distance, and h represents the height difference between the sensor and the balance.

[0022] Optionally, the decoupling matrix is ​​obtained by solving the least squares method.

[0023] Optionally, the regression coefficient matrix in the model can be solved, including: A multi-source, multi-order regression approach was used to systematically calibrate and decouple the resultant forces along the X, Y, and Z axes. The calculation process satisfies the following relationship: ; In the formula, C j,pqr The coefficients are represented by P, q, and r, which represent the powers of the input variables in the polynomial regression, respectively. i,corrected Let Fx represent the resultant force along the X-axis, Fy represent the resultant force along the Y-axis, and Fz represent the resultant force along the Z-axis.

[0024] In the above embodiments, during ground loading tests, when a load is applied only in one direction (e.g., longitudinal), non-zero outputs also appear in other directions (lateral and vertical), indicating significant inter-channel coupling interference. This phenomenon may originate from the local structural torque effect during loading, causing additional responses from each sensor at different degrees of freedom. If the output values ​​in each direction are simply superimposed in the resultant force calculation, a large systematic error will be introduced. To correct this coupling error, this study uses the measured values ​​in all three directions as input independent variables and the theoretical loading value in a single direction as the target dependent variable, employing a multivariate multi-order regression method for system calibration and decoupling.

[0025] Regression analysis results show that when the regression order is increased to 3, the proportion of samples with a mean squared error of no more than 0.5 reaches 99.78%. This indicates that the corrected model containing 455 regression coefficients can effectively correct 99.78% of the test data. To verify the effectiveness of the method, a set of typical test data was selected and substituted into the model for comparison: before correction, the test value was 5.3059, the theoretical value was 4.8958N, and the relative deviation was 8.376%; after correction, the output value was 5.0153, and the relative deviation was reduced to 2.44%. This is significantly better than the unprocessed results, proving that the proposed multivariate regression decoupling method has good engineering applicability and accuracy improvement effect.

[0026] Example 1 The following is combined Figure 2 Taking the use of an eight-sensor distributed measurement system in the FD wind tunnel to measure the aerodynamics of the lead car of a 1:20 scale model of a train as an example, this paper details the specific implementation of the present invention.

[0027] Step 1: Setting up the measuring device: Prepare a 1:20 scale model of a high-speed train with a blunt nose, including a lead car and an intermediate car. The lead car weighs approximately 23 kg.

[0028] A specially designed foundation structure was installed on the floor of the FD wind tunnel test section. This foundation, located beneath the eight wheel-rail positions of the lead car, has eight precision-machined mounting platforms. A high-precision inclinometer was used to level the entire foundation.

[0029] Eight custom-designed three-dimensional force sensors (range: 30N in X / Z direction, 60N in Y direction) were rigidly fixed to their respective mounting platforms using hexagon socket head cap screws. The sensor model is a custom version based on T521G-0005.

[0030] Eight track-mounted top covers are bolted to the top of their respective sensors. The top surfaces of these top covers simulate the track plane and will eventually be pieced together to form a continuous track path.

[0031] The train head car model was hoisted above the foundation, and its position was precisely adjusted to ensure that the centers of the eight wheels of the head car were accurately aligned with the centers of the eight upper cover plates (tracks) below. Then, using a high-strength, fast-curing structural adhesive, each wheel was firmly bonded to the corresponding upper cover plate track surface. This step established a deterministic force transmission path from the train's aerodynamic shape being affected by wind to the sensors sensing the force.

[0032] The intermediate car exists only as an aerodynamic interference device, supported on the foundation by adjusting the screw, and maintaining a certain gap with the lead car.

[0033] Step 2: Preload Verification and System Calibration With the wind tunnel not running, apply a 1kg standard weight (generating a 9.8N vertical force) to the center of the top of the lead car.

[0034] The output values ​​of eight sensors in the Y direction are read simultaneously and summed to obtain the measured vertical resultant force. The recorded result should be in good agreement with the theoretical value of 9.8N (the measured value in the actual case is 9.7N) to preliminarily verify the effectiveness of the force transmission path.

[0035] A more comprehensive static loading system calibration was performed. Up to 30 different load conditions were applied to the loading sleeve (simulating the vehicle body) using weights and pulleys on a ground loading test bench (or directly on a pre-installed wind tunnel model). These included unidirectional forces (X, Y, Z), combined forces, unidirectional moments (Mx, My, Mz), and combined moments. Each load condition was repeated multiple times.

[0036] For each calibration condition, record the original output matrix of the eight sensors in three directions.

[0037] A third-order multiple regression model is established. For example, taking the target "total longitudinal force Fx" as an example, the raw output values ​​of eight sensors are used as input features to construct a combined feature matrix containing constant, linear, quadratic, and cubic terms. Using data from all calibration conditions, the regression coefficients for Fx are obtained through the least squares method. Similarly, the regression coefficient vectors for Fy, Fz, Mx, My, and Mz are solved.

[0038] Step 3: Dynamic Aerodynamic Testing and Data Processing Maintain the model's state and start the wind tunnel. Set the test conditions, for example: wind direction angle β = 0°, 5°, 15°; wind speed V = 30m / s, 40m / s, 50m / s.

[0039] Under each stable operating condition, voltage signals from eight sensors in three directions are simultaneously acquired at high speed (sampling frequency > 2000 Hz).

[0040] Original data correction: The 24-dimensional original data vector collected in real time is substituted into the six pre-calibrated regression coefficient models (corresponding to Fx, Fy, Fz, Mx, My, Mz) to calculate the six corrected total loading components.

[0041] Output results: Output the curves and statistical values ​​(such as mean and standard deviation) of the six components of the aerodynamic force of the locomotive (Fx, Fy, Fz, Mx, My, Mz) over time.

[0042] This application also provides a distributed aerodynamic measurement system for trains, including a processor and a memory; Memory, used to store computer programs; The processor, when executing a program stored in memory, implements any of the steps described in the distributed measurement method for train aerodynamics.

[0043] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A distributed measurement method for train aerodynamics, characterized in that, include: Construct a train head car model for the target train and a track model for distributed measurement; Determine the wheel-rail support point positions in the train head car model, determine the sensor installation positions in the track model based on the wheel-rail support point positions, and install force sensors at the sensor installation positions; Place the train head car model on the track model, and align the wheel-rail center position in the train head car model with the position of the force sensor. Using the principle of wind tunnel testing, different wind speeds and wind angles are applied to the train head car model, and force output signals in the X, Y and Z axes are collected by force sensors; The resultant force along the X-axis, Y-axis, and Z-axis is calculated based on the force output signals in the three directions of X, Y, and Z axes and the spatial coordinates of the force sensor. The resultant torque is also calculated based on the spatial coordinates of the force sensor. A multivariate regression model is constructed by using the resultant forces on the X-axis, Y-axis, and Z-axis as raw data to train the multivariate regression model, solving for the regression coefficient matrix in the model, and obtaining the trained regression model. The resultant forces and moments along the X, Y, and Z axes obtained from wind tunnel tests are input into the trained regression model to obtain the corrected resultant forces along the X, Y, and Z axes and the corrected moment.

2. The distributed measurement method for train aerodynamics according to claim 1, characterized in that, The number of force sensors is no less than 8, and each force sensor corresponds to 8 wheel-rail support points of the train head car model.

3. The distributed measurement method for train aerodynamics according to claim 1, characterized in that, The resultant forces along the X, Y, and Z axes are calculated based on the force output signals in the X, Y, and Z directions and the spatial coordinates of the force sensor. This includes: The force output signals in the X-axis direction are Fx1~Fx8 respectively; The force output signals in the Y-axis direction are Fy1~Fy8 respectively; The force output signals in the Z-axis direction are Fz1~Fz8 respectively; The calculation of the resultant force along the X-axis satisfies: Fx = Σ(Fx_i); The resultant force along the Y-axis is calculated to satisfy: Fy = Σ(Fy_i); The resultant force along the Z-axis is calculated to satisfy: Fz = Σ(Fz_i).

4. The distributed measurement method for train aerodynamics according to claim 1, characterized in that, The spatial coordinates of the force sensor include: the lateral center distance of the sensor, the longitudinal center distance of the sensor, the train distance, and the height difference between the sensor and the balance.

5. The distributed measurement method for train aerodynamics according to claim 4, characterized in that, Calculation of resultant torque based on spatial coordinates of a force sensor includes: Based on the resultant force along the Y-axis, the resultant force along the Z-axis, the height difference between the sensor and the balance, and the lateral center distance of the sensor, the resultant moment in the X-axis direction is calculated, satisfying the following relationship: Mx=-Fy1·h-Fy2·h-Fy3·h-Fy4·h-Fy5·h-Fy6·h-Fy7·h-Fy8·h+Fz1·d / 2-Fz2·d / 2+Fz3·d / 2-Fz4·d / 2+Fz5·d / 2-Fz6·d / 2+Fz7·d / 2-Fz8·d / 2; The resultant moment in the Y-axis direction is calculated based on the resultant force along the X-axis, the resultant force along the Z-axis, the height difference between the sensor and the balance, the train's fixed distance, and the longitudinal center distance of the sensor. The calculation satisfies the following relationship: My=Fx1·h+Fx2·h+Fx3·h+Fx4·h+Fx5·h+Fx6·h+Fx7·h+Fx8·h-Fz1·(L+e) / 2-Fz2·(L+e ) / 2-Fz3·(Le) / 2-Fz4·(Le) / 2+Fz5·(Le) / 2+Fz6·(Le) / 2+Fz7·(L+e) / 2+Fz8·(L+e) / 2; Based on the resultant force along the X-axis, the resultant force along the Y-axis, the transverse center distance of the sensors, the longitudinal center distance of the sensors, and the train's fixed distance, the resultant moment in the Z-axis direction is calculated, satisfying the following relationship: Mz=-Fx1·d / 2+Fx2·d / 2-Fx3·d / 2+Fx4·d / 2-Fx5·d / 2+Fx6·d / 2-Fx7·d / 2+Fx8·d / 2+Fy1·(L+e) / 2+ Fy2·(L+e) / 2+Fy3·(Le) / 2+Fy4·(Le) / 2-Fy5·(Le) / 2-Fy6·(Le) / 2-Fy7·(L+e) / 2-Fy8·(L+e) / 2; In the formula, d represents the lateral center distance of the sensor, e represents the longitudinal center distance of the sensor, L represents the train's fixed distance, and h represents the height difference between the sensor and the balance.

6. The distributed measurement method for train aerodynamics according to claim 1, characterized in that, The decoupling matrix is ​​obtained by solving the least squares method.

7. The distributed measurement method for train aerodynamics according to claim 6, characterized in that, Solving for the regression coefficient matrix in the model includes: A multi-source, multi-order regression approach was used to systematically calibrate and decouple the resultant forces along the X, Y, and Z axes. The calculation process satisfies the following relationship: ； In the formula, C j,pqr The coefficients are represented by P, q, and r, which represent the powers of the input variables in the polynomial regression, respectively. i,corrected Let Fx represent the resultant force along the X-axis, Fy represent the resultant force along the Y-axis, and Fz represent the resultant force along the Z-axis.

8. A distributed aerodynamic measurement system for trains, characterized in that, Including processor and memory; Memory, used to store computer programs; A processor, when executing a program stored in memory, implements the steps of the method described in any one of claims 1-7.

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