Hot upflow positioning method based on data driving

Abstract

The invention discloses a hot upflow positioning method based on data driving. For a long time, unmanned aerial vehicles are always indispensable in the industries of monitoring tasks, geographic surveying and mapping, target reconnaissance and the like. Flight endurance is a key limit for wide use of unmanned aerial vehicles. However, although researchers effort to modify and optimize the aerodynamic shape to reduce glider drag or replace battery reactants, use of these methods to increase flight endurance still has limitations. The invention aims to utilize the energy of the nature by collecting wind energy. According to the method, upflow estimation is considered, and then the position of the wind field is estimated through a sparse recognition algorithm of nonlinear dynamics. The thermal positioning is realized through the SINDy-based method and the characteristic of accurately identifying the mathematical physical specification model, so that the capability of identifying the hot upflow is improved, and the energy of the aircraft is increased.

Description

Technical Field

[0001] The invention relates to the field of data-driven thermal updraft positioning, and in particular to a data-driven thermal updraft positioning method. Background Art

[0002] There are two main sources of updrafts, one of which is topography. They form mainly around fixed ridges or tall structures and change position depending on the direction of incoming air currents. Flight tests have been conducted in air currents in front of mountains and buildings, providing evidence for the potential use of topographic updrafts. Another source of updrafts is uneven ground temperatures caused by clouds blocking the sun. Lighter air masses rise above the heated surface, causing the surrounding air to converge towards the center and create an updraft. Birds, including falcons and frigate birds, have been observed actively following such updrafts for aerial surveillance and hunting.

[0003] A key technical challenge that must be addressed before simulating unpowered flight of birds is the location of thermal cells. In order to estimate the center and parameters of thermal updrafts, an algorithm based on the centroid method is designed. The location of thermal updrafts can be determined by measuring the air velocity. In addition, the convergence of the updraft amplitude and radius is achieved by iteratively minimizing the least squares error.

[0004] The shape of the thermal updraft is generalized from a Gaussian distribution to an elliptical cross section. This generalization allows the estimation of the center position and other parameters. However, these methods require the storage of batches of data for solution and iteration, which consumes the memory space of the aircraft computer. To overcome this problem, two extended Kalman filters, which are commonly used in flight controllers, can be used to estimate the location of the thermal updraft, as well as the bearing and distance relative to the glider. In this algorithm, only the state vector and covariance matrix of the filter need to be stored for long-term use. A more complete thermal model is constructed using splines, and the model coefficients can also be estimated using Kalman filtering. Another innovative method involves the use of onboard cameras to remotely measure and estimate thermal updrafts under cumulus clouds. This method develops a Kalman filter to estimate the lifetime and intensity of thermals.

[0005] Multiple thermal updraft localization algorithms can provide more opportunities for global planning algorithms. However, identifying the parameters of individual thermal updrafts is very beneficial for localizing them in a small area, especially when the monitoring range of the glider is limited. In previous works, thermal updrafts are usually regarded as nonlinear models. Although deriving thermal updraft model parameters from first principles may pose difficulties, data-driven methods have helped researchers to reveal the physical laws. This motivates us to adopt Sparse Identification of Nonlinear Dynamics (SINDy) to address the challenge of estimating unknown parameters.

[0006] The core idea of ​​the SINDy algorithm is to use sparse regression technology to identify the nonlinear differential equations of the dynamic system from the measured data. It assumes that the dynamics of the system can be described by a linear combination of a few functions in a function library. Through the optimization algorithm, SINDy can select the functions that have the greatest impact on the system dynamics and determine their coefficients to build a concise and accurate mathematical model. This usually requires collecting observation data of the system, which usually includes a time series of the system state. Through the optimization algorithm, SINDy can select the functions that have the greatest impact on the system dynamics and determine their coefficients to build a concise and accurate mathematical model. Finally, based on the results of sparse regression, a mathematical model of the system is constructed. This model is usually a nonlinear differential equation that describes the dynamic behavior of the system.

[0007] The SINDy method has several advantages. First, it does not rely on prior knowledge, but learns the dynamics of the system from observational data. This makes it a powerful tool for dealing with complex systems, especially in the absence of detailed physical models. It is also interpretable. By deriving the kinetic equations, researchers can have a deeper understanding of the behavior and interactions of the system. This provides strong support for the interpretability of the system. Therefore, the SINDy method has been successfully applied in many fields, including dynamic systems, fluid mechanics, chemical reaction networks, etc. Its application in practical problems demonstrates its applicability for nonlinear dynamic modeling.

[0008] It has been demonstrated in the literature that it is possible to sample partial data from sensors under flow conditions to identify a range of mathematical physics canonical models, such as the Korteweg-de Vries (KdV) or Navier-Stokes equations. Several strongly nonlinear systems, such as the dynamics of an F8 fighter jet, can also be accurately identified. The SINDy algorithm is a data-driven algorithm with concise, real-time model identification capabilities.

[0009] The proposed method significantly improves the identification of thermal updrafts under observable conditions. This is achieved by the characteristics of the proposed SINDy-based method and its precise identification mathematical model. The errors in the parameter estimation process are negligible, which is superior to existing methods. Compared with traditional algorithms, the proposed method does not require the adjustment of algorithm parameters. In addition, it is found that certain parameters of the heat source can be accurately estimated under unobservable conditions. We validate the proposed method on a compact embedded hardware platform of an unmanned aerial vehicle through hardware-in-the-loop simulation. The method is feasible for real-time online applications. These results may provide promising progress for the precise localization of heat sources in autonomous flight. Summary of the invention

[0010] The purpose of the present invention is to address the deficiencies of the prior art and to propose a data-driven thermal updraft positioning method.

[0011] The object of the present invention is achieved through the following technical solution: A data-driven thermal updraft positioning method comprises the following steps:

[0012] Characterize thermals using mathematical models to reduce erroneous parameter estimates and strike a balance between environmental fidelity and computational cost;

[0013] According to the law of conservation of energy of the glider, the working principle of the net variometer is integrated to estimate the thermal updraft to solve the problem of airflow perception;

[0014] Constructing a state information matrix from the collected thermal updraft information, removing data with large estimated deviations from the thermal updraft information, and arranging the removed data in a matrix to form a column vector form;

[0015] The dynamic process is extracted from the heat source data through sparse identification of nonlinear dynamics (SINDy algorithm), and the low-dimensional dynamic model is reconstructed using the prior knowledge of high-dimensional measurement data; the parameter identification problem is formulated as a sparse regression problem and solved;

[0016] The solution of sparse regression is used as the identification parameter, and the solved parameters are further inversely deduced to solve the position of the thermal updraft.

[0017] Furthermore, the mathematical model uses a two-dimensional Gaussian model as an application object for parameter identification, and can also be characterized by this algorithm.

[0018] Furthermore, the use of mathematical models to characterize thermal airflows is specifically as follows: integrating mathematical models in a simulation platform, defining the required fixed-wing glider by modifying the aerodynamic coefficients in SIMULINK, and adding a thermal updraft physical model to the environment so that the environment can generate thermal updrafts. The thermal updraft physical model is as follows:

[0019]

[0020] Among them, w z represents thermal updraft, w represents the wind strength at the thermal center, and p n and p e Indicates the position of the heat source on the two-dimensional coordinate axis; x n and x e represents the real-time position recorded during the glider's flight, and R represents the range of the hot core; the model follows a circular bell curve.

[0021] Furthermore, the estimated thermal updraft estimates its speed and intensity through physical formulas and models, as shown in the following formula:

[0022]

[0023] Among them, x, y, z represent the position coordinates of the drone, Va represents the airspeed, and T BW represents the rotation matrix;

[0024] The absolute velocity obtained by the global positioning system GPS consists of the relative air velocity and wind speed; since the wind speed is necessary in the inertial coordinate system, the air speed vector is transformed; T BW is a rotation matrix that transforms the vector from the wind coordinate system to the body coordinate system, T IB Represents the rotation matrix of the vector from the body coordinate system to the inertial coordinate system; Va represents the speed in the heading direction, which is directly measured by the airspeed indicator; combined with the rotation matrix T estimated by the extended pitot tube BW , the above formula is used to obtain the representation of relative motion in the body coordinate system.

[0025] Furthermore, the state information matrix is ​​constructed from the collected thermal updraft information as follows: the estimated updraft is collected at a consistent sampling rate to determine the parameters of the thermal mode; wherein each data is represented by x(t m ) indicates that, assuming the number of collected data is t m , define and create the X matrix information as follows:

[0026]

[0027] Furthermore, the construction of the state information matrix includes: the key is to perform calculations in discrete time, apply the SINDy algorithm to the discrete dynamic system, and regard the spatiotemporal changes caused by the relative motion between the hot updraft and the glider as a nonlinear dynamic system, and the nonlinear dynamic system is expressed in the following discrete form:

[0028] x k+1 =F(x k );

[0029] Where x represents the state vector of the dynamic system to be solved.

[0030] Furthermore, the parameter identification problem is converted into a sparse regression problem for solution by minimizing the least squares error between the measured value and the estimated value Θ(X), as shown in the following formula:

[0031]

[0032] Among them, X represents the state matrix information, ξ represents the coefficient to be solved, and Θ represents the function library; the regularization term is added to the formula to improve the sparsity of the activation term coefficient. Although the convergence of the equation cannot be guaranteed, in order to avoid calculation errors in the optimization process, the sequential threshold least squares method or sparse regularized relaxation regression can be used to solve the equation.

[0033] Furthermore, the solution of sparse regression is used as the identification parameter, and the solved parameters are further processed. The formula is as follows:

[0034]

[0035] Among them, ξ 1 , 2 and i Used to represent the 1st, 2nd, and i-th elements of a column vector, p e and p n That is the location of the airflow.

[0036] The beneficial effects of the present invention are:

[0037] 1. This invention proposes a new method for online identification and location of heat sources. The SINDy algorithm is introduced and slightly modified to estimate parameters more accurately.

[0038] 2. Compared with previous methods of estimating a single thermal field, the recognition ability is significantly enhanced, enabling accurate search for updrafts. The performance and reliability of the SINDy algorithm integrated with the flight control system are verified. It can not only better avoid overfitting, but also achieve a good balance between data memory and calculation accuracy.

[0039] 3. The algorithm was tested in hardware-in-the-loop (HITL), which showed the feasibility of deploying the proposed algorithm in actual scenarios. This invention provides innovative ideas for promoting future autonomous flight technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Flowchart of SINDy, where (a) is step A: schematic diagram of thermal prior knowledge of unknown parameters, (b) is step B: schematic diagram of data collection, (c) is step C: schematic diagram of selecting candidate term base, (d) is step D: schematic diagram of solving sparse regression problem, and (e) is step E: schematic diagram of thermal updrafts identified by SINDy;

[0041] Figure 2 It is a three-dimensional flight trajectory diagram under observable conditions;

[0042] Figure 3 Schematic diagram of the mean absolute error (MAE) and standard deviation (Std) of the estimated SINDy, where (a)-(f) are the result diagrams of 6 cases respectively;

[0043] Figure 4 Schematic diagram of the thermal position estimation results obtained by SINDy;

[0044] Figure 5 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0045] The present invention will be described in detail below in combination with specific embodiments according to the accompanying drawings.

[0046] like Figure 5 As shown, a data-driven thermal updraft positioning method provided by an embodiment of the present invention includes the following steps:

[0047] Step S1. Add a heat source model in the simulation platform.

[0048] The experiments were conducted on RflySim, an advanced platform developed by the Reliable Flight Control Group. The core of RflySim is that it supports a customized high-fidelity simulation framework, which is implemented through specialized components such as the carefully designed simulator CopterSim. By using RflySim, researchers can efficiently design models, develop and verify control algorithms, and verify hardware systems, thereby reducing the time required for algorithm conception and deployment.

[0049] The construction of the environment is achieved by integrating mathematical models in the Rflysim platform. First, by modifying the aerodynamic coefficients in SIMULINK, define the fixed-wing glider you need. Then add a thermal updraft physical model to the environment so that the environment can generate thermal updrafts. The location of the heat source is determined by the take-off point of the glider. In this experiment, the take-off point of the glider is defined at the origin of the three-dimensional coordinate system. The added heat source model is as follows:

[0050]

[0051] Among them, w z represents thermal updraft, w represents the wind strength at the thermal center, and p n and p e Indicates the position of the heat source on the two-dimensional coordinate axis; x n and x e represents the real-time position recorded during the glider's flight, and R represents the range of the thermal core; the thermal model follows a circular bell curve.

[0052] Step S2. Set three heat source positions.

[0053] Three heat source positions are set in the global environment, which are (800, 100), (1000, 500), and (600, 800). Their coordinates are given in (east, north). The glider flies in the form of a "lawn mower" to ensure the observability of the heat source and avoid encountering unobjective situations during the flight.

[0054] Step S3. Start the thermal updraft estimation algorithm.

[0055] After the glider takes off, the thermal updraft estimation algorithm is started. The pitch, roll and yaw angles of the glider are extracted from the IMU module, and the orientation of the glider in the inertial coordinate system is extracted from the GPS. Based on this information, a state transformation matrix is ​​constructed to provide data for thermal updraft estimation.

[0056] Extract the flight airspeed from the pitot module and combine the above data to calculate the thermal updraft. Use physical formulas and models to estimate the speed and strength of the updraft. Estimate the thermal updraft using the aircraft airspeed estimated by PX4, as well as the pitch and yaw angles estimated by the IMU element. The calculation formula is as follows:

[0057]

[0058] Among them, x, y, z represent the position coordinates of the drone, Va represents the airspeed, and T BW Represents a rotation matrix.

[0059] The absolute velocity obtained by the Global Positioning System (GPS) consists of the relative air velocity and the wind speed. Since the wind speed is required in an inertial coordinate system, the vector is transformed. BW is a rotation matrix that transforms the vector from the wind coordinate system to the body coordinate system. Similarly, T IB Convert the vector from the body coordinate system to the inertial coordinate system. Va represents the velocity in the heading direction, which is directly measured by the airspeed indicator. Combined with the rotation matrix T estimated by the extended pitot tube BW , and the representation of relative motion in the body coordinate system is obtained.

[0060] Step S4: Constructing a state information matrix about the thermal updraft.

[0061] In the case of thermal identification, the key is the vertical airflow, so the column dimension of the matrix is ​​equal to 1. m ) indicates that, assuming the number of collected data is t m , define and create the X matrix information as follows:

[0062]

[0063] Determine the parameters of the thermal model to collect estimated updrafts at a consistent sampling rate.

[0064] Step S5: Eliminate elements with large estimation deviations.

[0065] If the collected airflow information is abnormal and needs further processing, such as the value of the updraft is greater than 5m / s, or a downdraft is generated, then the flight in this area should be terminated. The judgment condition is that the estimated value is less than -3m / s. These data should also be eliminated.

[0066] For the estimation algorithm, in order to ensure the neatness of the matrix, it is eliminated by the following formula:

[0067] w z >5m / sorw z <-3m / s

[0068] Step S6: Solve the sparse regression problem.

[0069] The sparse regression method is used to determine which functions in the function library have a significant impact on the system dynamics. This step usually involves an optimization problem, the goal is to minimize the error while making the number of selected functions as small as possible (i.e. sparsity). The goal of the present invention is to approximate the measured value, and the regression problem becomes:

[0070]

[0071] For most application scenarios, the solution of sparse regression is used as the identification parameter. However, in the embodiment of the present invention, the solved parameters need to be further processed. For the convenience of expression, ξ i Used to represent the i-th element of a column vector. The formula is as follows:

[0072]

[0073] In the identification case of the present invention, having preliminary knowledge about the system eliminates the need to consider scanning the candidate function library. This further reduces the training execution time. It is worth noting that before further extending the sparse regression to identify thermal updraft parameters, considering that the identified model is consistent with x e and x n The decoupling of x e ·x n item.

[0074] Step S7. Optimize the result of thermal updraft.

[0075] Solving the sparse regression problem involves inverse operations on the matrix, so when the matrix is ​​singular, the thermal position needs to be further optimized. For areas of thermal updrafts, if the estimated position differs from the area where the aircraft is flying by more than 300m, these estimated results cannot be taken into account. Regardless of the position in the east direction or the position estimated in the north direction, these anomalies should also be eliminated. The present invention optimizes thermal airflow positioning through the following formula:

[0076] |x e -p e |<300and|x n -p n |<300

[0077] Before executing the above steps, a continuous sequence of updrafts is collected. Once a sufficient number of updrafts are accumulated, the SINDy algorithm starts to run. The data is organized into a matrix and the logarithmic form of the matrix is ​​calculated. Then, a candidate function library is constructed according to the position of the aircraft. The present invention solves the coefficients of these candidate functions to minimize the substitution formula. Finally, the coefficients are converted into heat source parameters.

[0078] Before the actual flight test, hardware-in-the-loop simulation was performed to evaluate the performance of SINDy. Unlike SITL, the fixed-wing model in HITL runs in real time, synchronized with the actual clock, ensuring accurate results. Win10WSL was used as a cross-compilation environment to flash the firmware onto the Pixhawk4 autopilot hardware.

[0079] The SINDy algorithm is uploaded to the flight controller hardware environment. Pixhawk4 integrates powerful processors, sensor technology and NuttX real-time operating system, which can flexibly and reliably control the glider. At this stage, communication is established using cable signal lines, without virtual network transmission. CopterSim transmits sensor data (including barometer and magnetometer readings) to Pixhawk4 via serial communication. The PX4 firmware running on the flight controller estimates state information using filtering algorithms (such as EKF).

[0080] The state information is broadcast to the information bus. The controller subscribes to messages from the information bus, calculates control commands, and sends them back to CopterSim. In addition, a wireless data transmission module is equipped to transmit the glider's state and flight parameters to QGC for monitoring. When the glider deviates from the expected flight path or loses control, the operator can intervene. HITL facilitates the deployment and execution of control algorithms on real embedded systems and provides an indoor simulation environment for outdoor flight tests.

[0081] like Figure 1Figures (a) to (e) summarize the steps for final positioning based on the algorithm results. First, a series of data is calculated based on the above-mentioned method for estimating thermal updrafts, and then the estimated data is created in matrix form. The thermal updraft problem is further converted into a parameter identification problem, and the coefficients of the matrix are solved using the formula for solving the problem with sparse regression. Finally, based on Figure 1 The formula in Figure (e) converts the coefficient of thermal updraft into the location of the heat source.

[0082] In order to fully demonstrate the performance of SINDy, this paper verifies the results of our algorithm through an example.

[0083] The identification was evaluated in an observable flight mode. The glider’s flight trajectory was simulated using a lawnmower pattern, consisting mainly of irregular curves. This pattern was chosen to minimize the occurrence of straight and circular flights, thus ensuring relatively high observability of the parameters to be estimated. Figure 2 The flight trajectory consists of two parts, light blue and orange. The thick solid orange line represents the trajectory during the detection of updrafts, whose amplitude exceeds a certain threshold for a defined duration.

[0084] The estimated performance of the SINDy algorithm is summarized as follows Figure 3 The average absolute error is within 20 meters. From Case 1 to Case 6, the estimation accuracy of the SINDy algorithm is very high. Moreover, its standard deviation is acceptable. During the entire flight, SINDy performed six Figure 4 As shown, the true values ​​are represented by green and blue dashed lines, while the estimated values ​​obtained by the traditional method are represented by solid lines. In Case 1, the traditional method gradually converges and the 3σ error band tends to be stable in the late flight. Compared with the results of SINDy, the estimated heat source position is still biased.

[0085] In Case 2, there is a slight estimation error in the easting position, although the 3σ error band has remained stable. In both cases, the SINDy algorithm has almost no error in the heat positioning. This phenomenon is also observed in the last run when the algorithm is activated. The triangles and circles represent the easting and northing directions, respectively. For enhanced clarity and simplicity, the points in the plot are drawn at a fixed interval, which is lower than the frequency performed by SINDy.

[0086] Figure 4It shows that from Case 3 to Case 6, SINDy consistently outperforms traditional methods in position estimation. Regardless of estimating the east or north position of the heat source, the identification error of the traditional algorithm is several to dozens of times larger than that of the SINDy algorithm. In Case 3 and Case 4, SINDy showed a slight deviation in estimating the east position. However, in most cases, its estimated values ​​are consistent with the set values. It is worth noting that since SINDy needs to accumulate a specific number of physical quantities to calculate the information matrix, once the collected updrafts reach a predetermined threshold, SINDy can accurately locate the heat unit.

Claims

1. A data-driven thermal updraft positioning method, characterized in that: The steps include: Characterize thermals using mathematical models to reduce erroneous parameter estimates and strike a balance between environmental fidelity and computational cost; According to the law of conservation of energy of the glider, the working principle of the net variometer is integrated to estimate the thermal updraft to solve the problem of airflow perception; Constructing a state information matrix from the collected thermal updraft information, removing data with large estimated deviations from the thermal updraft information, and arranging the removed data in a matrix to form a column vector form; The dynamic process is extracted from the heat source data through the SINDy algorithm of sparse identification of nonlinear dynamics, and the low-dimensional dynamic model is reconstructed using the prior knowledge of high-dimensional measurement data; the parameter identification problem is formulated as a sparse regression problem and solved; The solution of sparse regression is used as the identification parameter, and the solved parameters are further inversely deduced to solve the position of the thermal updraft.

2. A data-driven thermal updraft positioning method according to claim 1, characterized in that: The mathematical model uses a two-dimensional Gaussian model as an application object for parameter identification, and can also be characterized by the SINDy algorithm.

3. A data-driven thermal updraft positioning method according to claim 2, characterized in that: The use of mathematical models to characterize thermal airflows is specifically as follows: integrating mathematical models in the simulation platform, defining the required fixed-wing glider by modifying the aerodynamic coefficients in SIMULINK, and adding a thermal updraft physical model to the environment so that the environment can generate thermal updrafts. The thermal updraft physical model is as follows: Among them, w z represents thermal updraft, w represents the wind strength at the thermal center, and p n and p e Indicates the position of the heat source on the two-dimensional coordinate axis; x n and x e represents the real-time position recorded during the glider's flight, and R represents the range of the hot core; the model follows a circular bell curve.

4. The method for locating thermal updrafts based on data drive according to claim 1, characterized in that: The estimated thermal updraft is estimated by using physical formulas and models to estimate its speed and intensity, as shown in the following formula: Among them, x, y, z represent the position coordinates of the drone, Va represents the airspeed, and T BW represents the rotation matrix; The absolute velocity obtained by the global positioning system GPS consists of the relative air velocity and wind speed; since the wind speed is necessary in the inertial coordinate system, the air speed vector is transformed; T BW is a rotation matrix that transforms the vector from the wind coordinate system to the body coordinate system, T IB Represents the rotation matrix of the vector from the body coordinate system to the inertial coordinate system; Va represents the speed in the heading direction, which is directly measured by the airspeed indicator; combined with the rotation matrix T estimated by the extended pitot tube BW , the above formula is used to get the expression of airspeed in the aircraft coordinate system.

5. The method for locating thermal updrafts based on data drive according to claim 1, characterized in that: The state information matrix constructed from the collected thermal updraft information is specifically: collecting the estimated updraft at a consistent sampling rate to determine the parameters of the thermal mode; wherein each data is represented by x(t m ) indicates that, assuming the number of collected data is t m , define and create the X matrix information as follows:

6. A data-driven thermal updraft positioning method according to claim 5, characterized in that: The state information matrix construction includes: applying the SINDy algorithm to a discrete dynamic system, considering the spatiotemporal changes caused by the relative motion between the hot updraft and the glider as a nonlinear dynamic system, wherein the nonlinear dynamic system is represented by the following discrete form: x k+1 =F(x k ); Among them, x represents the state vector of the dynamic system to be solved, and k represents the number of data.

7. The method for locating thermal updrafts based on data drive according to claim 1, characterized in that: The specific solution of converting the parameter identification problem into a sparse regression problem is: Among them, X represents the state matrix information, ξ represents the coefficient to be solved, and Θ represents the function library.

8. The data-driven thermal updraft positioning method according to claim 1, characterized in that: The solution of sparse regression is used as the identification parameter, and the solved parameters are further processed. The formula is as follows: Among them, ξ1, ξ2 and ξ i Used to represent the 1st, 2nd, and i-th elements of a column vector, p e and p n That is, the location of the airflow.

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