A train traction and braking performance prediction method

Abstract

The application discloses a kind of train traction and brake performance prediction method, comprising: constructing dynamic model and curve model;Select PSO, GA or LSTM to obtain basic resistance parameters by processing idle stage data;Using sliding window average method to process traction stage and brake stage data to obtain train acceleration data, according to the transformation relationship of ATO current corresponding traction force and brake force, train acceleration data, basic resistance parameters and dynamic model, obtain the full traction force and brake force data of train;Using sliding window Z score processing technology to process full traction force and brake force data;According to full traction force data and using subsection particle swarm algorithm or weighted genetic algorithm to obtain traction characteristic curve parameters;According to full brake force data, fully connected neural network and balanced loss fitting to obtain brake characteristic curve parameters;According to traction characteristic curve parameters, brake characteristic curve parameters and curve model, obtain the traction characteristic curve and brake characteristic curve of train.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of urban rail transit. More particularly, it relates to a train traction and braking performance prediction method. BACKGROUND

[0002] With the rapid development of urban rail transit, the traction and braking performance of urban rail trains has become increasingly important in ensuring train safety, improving operational efficiency, and optimizing passenger experience. Traction performance directly affects the train's start-up, acceleration, and smooth running, while braking performance determines the response speed and accuracy of the train during deceleration, stopping, and emergency braking. In order to cope with the increasingly complex operating environment and growing traffic demand, traditional traction and braking control systems have been unable to meet the requirements of modern urban rail trains for high efficiency, safety, energy saving, and other aspects.

[0003] The traction and braking performance of urban rail trains is influenced by a variety of factors, including train load, speed, track conditions, air resistance, and external environment. These factors exhibit complex nonlinear relationships, especially under high-speed operating conditions of the train, making the distribution of traction and braking forces more difficult to control. Existing physical models or experience-based control strategies are unable to accurately capture these nonlinear characteristics, resulting in problems such as excessive train energy consumption, inaccurate braking distance, or decreased ride comfort. In addition, modern urban rail trains typically use a multi-mode braking system that combines electric braking and mechanical braking. How to optimize the distribution of braking force under different operating conditions and balance energy consumption and safety is also a major technical challenge.

[0004] Based on this background, the present application proposes a train traction and braking performance prediction method that combines big data, machine learning, and deep learning technologies. By dynamically analyzing real-time train operation data, an intelligent prediction model is constructed to predict the demand for traction and braking force under different speeds, loads, and environmental conditions. This method is not only suitable for traction and braking performance optimization during the design phase of the train, but also provides accurate performance evaluation and control schemes for the train during actual operation, effectively improving the reliability, economy, and safety of train operation. SUMMARY

[0005] The present application aims to provide a train traction and braking performance prediction method to solve at least one of the problems in the prior art.

[0006] To achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0007] The present application provides a train traction and braking performance prediction method, comprising:

[0008] S1, acquire train operation data, construct a dynamics model including train basic resistance, train additional resistance, train traction force and braking force, and a curve model; the train operation data includes coasting stage data, traction stage data and braking stage data;

[0009] S2, process the coasting stage data by using a particle swarm optimization algorithm, a genetic algorithm or a long-short sequence neural network method to obtain train basic resistance parameters;

[0010] S3, process the traction stage data and the braking stage data by using a sliding window average method to obtain train acceleration data, and obtain full traction force data and full braking force data of the train according to an ATO current corresponding traction force conversion relationship, an ATO current corresponding braking force conversion relationship, the train acceleration data, the basic resistance parameters and the dynamics model;

[0011] S4, clean up abnormal values and noises in the full traction force data and the full braking force data by using a sliding window Z-score processing technology, and output smooth full traction force data and full braking force data;

[0012] S5, process the smooth full traction force data by using a particle swarm algorithm or a weighted genetic algorithm to obtain traction characteristic curve parameters; and process the smooth full braking force data by using a fully connected neural network and a balanced loss to fit to obtain braking characteristic curve parameters;

[0013] S6, obtain train traction characteristic curve and braking characteristic curve according to the traction characteristic curve parameters, the braking characteristic curve parameters and the curve model.

[0014] Optionally, the dynamics model is

[0015]

[0016] wherein M is the mass of the train; a(v x ) is the acceleration of the train when the train speed is v x ; F(v x ) is the traction force or braking force when the train speed is v x ; f base (v x ) is the unit basic resistance when the train speed is v x ; W(x) is the total additional resistance of the train at position x; k1, k2 and k3 are basic resistance parameters of the train; wherein k3 is the friction resistance of the train, k2 is the resistance coefficient of the train, and k1 is the aerodynamic resistance coefficient of the train; W i is the slope additional resistance; w i is the unit slope additional resistance; g is the acceleration of gravity, and w r is the unit curve additional resistance; R is the curve radius of the line; and A is an empirical constant; F(vfront ) is the braking force of the train at speed v front , v front , F back and v x are the speeds of the train at the corresponding front, back, x positions, F front is the braking force of the train at the corresponding position front; F back is the braking force of the train at the corresponding position back.

[0017] Optionally, the curve model is

[0018]

[0019] wherein F(v) is the traction force when the running speed of the train is v; v is the running speed of the train; K1 is the maximum traction force constant of the train; m, n, p and q are the constant coefficients of each term of the traction characteristic curve fitting of the train in the constant torque zone; B(v) is the braking force when the running speed of the train is v; K2 is the maximum braking force constant of the train; o, l and h are the constant coefficients of each term of the braking characteristic curve fitting; the traction characteristic curve of the train is divided into a constant work zone and a constant torque zone according to the running characteristics; when the running speed of the train is less than v 转 , the train works in the constant torque zone, and the maximum traction force of the train is constant; when the running speed of the train increases until exceeds v 转 , the train enters the constant torque zone, and the traction power of the train remains unchanged in the constant torque zone; v 终 is the maximum speed of traction under the current speed level; when the running speed of the train is less than v 转折 , the maximum braking force of the train is constant; when the running speed of the train increases until exceeds v 转折 , the train speed and the maximum value power present a quadratic linear relationship, and v 终点 is the maximum speed of braking under the current speed level.

[0020] Optionally, the S2 further comprises

[0021] S21, when the basic resistance parameter range of the train is known, performing preliminary analysis, rapid calibration or parameter initialization task, and obtaining the basic resistance parameter of the train by processing the data in the coasting stage by using a particle swarm optimization algorithm;

[0022] S22, when it is necessary to accurately identify the basic resistance parameter of the train under multiple speed and load working conditions, obtaining the basic resistance parameter of the train by processing the data in the coasting stage by using a genetic algorithm;

[0023] S23, when the basic resistance parameter of the train is dynamically changed, or the basic resistance parameter under the future speed change needs to be predicted, a long-short sequence neural network method is used to process the data in the idle running stage to obtain the basic resistance parameter of the train.

[0024] Optionally, the specific formula for processing the data in the idle running stage by using the particle swarm optimization algorithm is

[0025]

[0026] wherein w start_PSO and w end_PSO are the inertia weight when the POS algorithm starts to explore and ends to explore respectively; f mean is the average fitness of the population using the POS algorithm, f min_PSO is the current optimal fitness using the POS algorithm, f is the fitness of the current individual, and F is the traction or braking force of the train.

[0027] The specific formula for processing the data in the idle running stage by using the genetic algorithm is

[0028]

[0029] wherein f(k) is the fitness value, F predicted is the resistance value calculated by identifying the parameters following the GA optimization process, F actual is the actually measured resistance value; v jdata is the train speed of the j data th data point; is the weight of the individual i indiv ; f indiv is the fitness value of the individual i avg , f min_GA is the average fitness of the population using the GA algorithm, f start_GA is the optimal fitness of the population using the GA algorithm, and f is the fitness of the current individual; w end_GA is the initial value of the inertia weight when the GA algorithm explores; and w para is the end value of the inertia weight when the GA algorithm explores.

[0030] The specific formula for processing the data in the idle running stage by using the long-short sequence neural network method is

[0031]

[0032] wherein is the mean value of the parameters k1, k2 and k3 in each round of iteration; is the standard deviation of the parameters k1, k2 and k3 in each round of iteration; is the i samp th parameter in the jsamp the value in the sample; n num is the number of samples; is the average value of the i para th parameter; a is a weight coefficient for balancing the MSE loss and the parameter constraint loss, L MSE is the mean square error, L constraint is the constraint error.

[0033] Optionally, the processing of the traction phase data and the braking phase data by using the sliding window average method to obtain the train acceleration data comprises calculating the train acceleration in the window row by row and smoothing the train acceleration in the window, and the specific formula is

[0034]

[0035] wherein, represents the speed of the last row of the current window; represents the speed of the first row of the current window; and is the average acceleration in the window i win ; is the acceleration calculated for the current row; is the acceleration corresponding to each row in the window; and N is a preset number of rows.

[0036] Optionally, the conversion relationship between the ATO current and the traction force and the conversion relationship between the ATO current and the braking force are

[0037]

[0038] wherein, F all (v x ) is the full traction force or the full braking force when the train speed is v x , a all (v x ) is the acceleration of the full traction force or the acceleration of the full braking force when the train speed is v x , I(v x ) is the ATO current when the train speed is v x , I all is the ATO current of the full traction force or the full braking force; the ATO current when the train has no traction force or the ATO current when the train has no braking force is 4; and g is the acceleration of gravity.

[0039] The calculation formula of the smoothed full traction force data or the full braking force data is

[0040]

[0041] wherein, is the speed vx Full traction or braking force at that time The speed at which outliers and noise are cleaned up is v x The acceleration at full traction force or full braking force.

[0042] Optionally, a sliding window Z-score processing technique is used to clean up outliers and noise in the full traction force and full braking force data, outputting smooth full traction force and full braking force data. This further includes applying Z-score processing to the acceleration data in the constant power region of the full traction force data, and using automatic Z-score processing of the acceleration data in the constant power and constant torque regions using a sliding window. For the acceleration data of the full braking force, local weighted regression, outlier interpolation, and moving average + spline interpolation are used for processing, with the specific formulas as follows:

[0043]

[0044] in, The i-th tractive acceleration data obtained from the conversion acc acceleration The Z-score of the data; μ is the mean of the full traction acceleration data; σ is the standard deviation; W is the window size; Represents the j-th element within the window. win-acc One acceleration data point; For the i-th win The mean of the data within each window; σ iwin For the i-th win The standard deviation of the data within each window; Indicates the kth data-point The Z-scores for each data point; τ is the threshold for the Z-scores; For the k-th node within the sliding window data-point One acceleration data point; W' is the number of non-outliers within the window; D represents the current acceleration data. With the acceleration data to be estimated a d The distance between them, each acceleration data For the acceleration data to be estimated, a d weight Calculated using a cubic weighting function; abnormal acceleration data Apply interpolation to replace it with adjacent acceleration data. and A reasonable valuation at a given point in time. Above, based on neighboring points The data is interpolated from the current acceleration data; The moving average acceleration data is in the sliding window. For the j-th value after outlier handling nor One acceleration; Sner (v inter ) is a spline function; v inter is the to-be-solved interpolation point velocity data, v ner is the velocity of the interpolation adjacent point; b ner , c ner , d ner , and e ner are spline coefficients fitted according to data points and continuity conditions, respectively.

[0045] Optionally, the full traction data after smoothing is processed by the particle swarm algorithm or the weighted genetic algorithm to obtain the traction characteristic curve parameters, including

[0046] When performing preliminary analysis, rapid calibration, or parameter initialization tasks, the particle swarm algorithm is used to process the full traction data after smoothing to obtain the traction characteristic curve parameters; the specific formula for processing the full traction data after smoothing by the particle swarm algorithm is

[0047]

[0048] wherein, represents the velocity of particle i particle at time t, is the individual optimal position of particle i particle , g best is the global optimal position, w is the inertia weight, c1 and c2 are learning factors, and r1 and r2 are random numbers between 0 and 1; represents the position of particle i particle at time t; is the actual full traction value, is the predicted value; is the second derivative of the fitted curve; λ is the weight coefficient of the penalty term; x1 and x n are the upper limit and the lower limit of the turning point position of the curve, respectively; is used to ensure that the penalty is not increased when the second derivative is negative, and the penalty is increased when the second derivative is positive;

[0049] When it is necessary to identify the traction characteristic curve parameters of the train under multiple speed and load conditions, the genetic algorithm is used to process the full traction data after smoothing to obtain the traction characteristic curve parameters; the specific formula for processing the full traction data after smoothing by the genetic algorithm is

[0050]

[0051] wherein, α is a random number between 0 and 1, pa1 and pa2 are the first parent individual and the second parent individual, respectively, ch1 and ch2 are the first child individual and the second child individual, respectively; x′ indiv is the individual xindiv The gene value after mutation.

[0052] Optionally, the loss function for processing the smooth full braking force data by using the full connection neural network and the balanced loss is

[0053] Loss=MSE+λ1x transition value constraint+λ2x transition slope constraint+λ3x(k penalty +a penalty +b penalty +c penalty )

[0054] Wherein, λ1, λ2 and λ3 are respectively the first control weight, the second control weight and the third control weight; the transition value constraint is the value of v 转折 , the transition slope constraint is the slope when v 转折 , k penalty is the range constraint of K2, a penalty is the range constraint of o, b penalty is the range constraint of l, and c penalty is the range constraint of h.

[0055] The beneficial effects of the present application are as follows:

[0056] The present application discloses a train traction and braking performance prediction method, which effectively reduces the prediction error and improves the safety and energy saving of train operation, and is suitable for the design and actual operation evaluation of urban rail trains. Compared with the physical model of the train controller modeling, the present application is more accurate and efficient in predicting the train traction and braking performance, and the present application can also evaluate the predicted results. BRIEF DESCRIPTION OF DRAWINGS

[0057] The specific embodiments of the present application will be further described in detail below with reference to the accompanying drawings.

[0058] Figure 1 A flow chart of the train traction and braking performance prediction method is shown.

[0059] Figure 2 A basic resistance-speed curve diagram showing the basic resistance parameter results of the train obtained by processing the idling stage data by using the particle swarm algorithm, genetic algorithm and long-short sequence neural network method is shown.

[0060] Figure 3aA traction force-speed curve diagram showing full traction force data without cleaning outliers and noise.

[0061] Figure 3b A traction force-speed curve diagram showing full traction force data after cleaning outliers and noise.

[0062] Figure 4a A braking force-speed curve diagram showing full braking force data without cleaning outliers and noise.

[0063] Figure 4b A braking force-speed curve diagram showing full braking force data after cleaning outliers and noise.

[0064] Figure 5a A traction force-speed curve diagram showing the traction characteristic curve parameters obtained by processing the smoothed full traction force data using a particle swarm algorithm.

[0065] Figure 5b A traction force-speed curve diagram showing the traction characteristic curve parameter results obtained by processing the smoothed full traction force data using a weighted genetic algorithm.

[0066] Figure 6 A braking force-speed curve diagram showing the braking characteristic curve parameter results fitted by a fully connected neural network and an equalization loss. DETAILED DESCRIPTION

[0067] In order to more clearly illustrate the present application, the present application will be further described below in conjunction with embodiments and drawings. In the drawings, similar components are denoted by the same reference numerals. It should be understood by those skilled in the art that the specific descriptions below are illustrative rather than limiting, and should not limit the scope of protection of the present application.

[0068] The urban rail train traction and braking performance prediction method provided by the present application uses actual urban rail train operation data and line data to construct a simulation test environment, and realizes the construction and solution of the model under the Python platform.

[0069] In one embodiment, as shown in Figure 1 A train traction and braking performance prediction method includes the following steps:

[0070] S1, obtain train operation data, and construct a dynamics model including train basic resistance, train additional resistance, train traction force and braking force, and a curve model; the train operation data includes data in the coasting stage, data in the traction stage and data in the braking stage;

[0071] S2, basic resistance parameters of the train are obtained by processing the data in the coasting phase by using a particle swarm optimization (PSO) algorithm, a genetic algorithm (GA), or a long short-term memory (LSTM) method, and the basic resistance parameters are used to calculate basic resistance corresponding to different speeds of the train;

[0072] S3, train acceleration data are obtained by processing the data in the traction phase and the data in the braking phase by using a sliding window average method, and full traction force data and full braking force data of the train are obtained according to a conversion relationship between ATO current and traction force, a conversion relationship between ATO current and braking force, the train acceleration data, the basic resistance parameters, and a dynamics model;

[0073] S4, abnormal values and noise in the full traction force data and the full braking force data are cleaned by using a sliding window Z-score processing technique, and smooth full traction force data and smooth full braking force data are output;

[0074] S5, traction characteristic curve parameters are obtained by processing the smooth full traction force data by using a particle swarm algorithm or a weighted genetic algorithm, and braking characteristic curve parameters are obtained by fitting the smooth full braking force data by using a fully connected neural network and a balanced loss;

[0075] S6, the traction characteristic curve and the braking characteristic curve of the train are obtained according to the traction characteristic curve parameters, the braking characteristic curve parameters, and a curve model.

[0076] Further, the present application further includes S7, the performance of the train is evaluated according to the basic resistance corresponding to different speeds of the train, the traction characteristic curve, and the braking characteristic curve, so as to provide a reference for performance evaluation and optimization of the train.

[0077] The present application discloses a method for predicting the traction and braking performance of a train, which effectively reduces the prediction error and improves the safety and energy saving of train operation, and is suitable for the design and actual operation evaluation of a city train. Compared with the physical model of the train controller, the present application is more accurate and efficient in predicting the traction and braking performance of the train, and the present application can also evaluate the prediction results.

[0078] In one embodiment, step S1 further includes

[0079] S11, single mass point dynamics model of urban rail train, in urban rail transit, the train generally adopts the power dispersion marshalling mode to ensure good consistency of train traction and braking. Therefore, when modeling the dynamics of urban rail transit trains, a single mass point model can be used, and the dynamics model formula is as follows:

[0080]

[0081] wherein M is the mass of the train; a(v x ) is the acceleration of the train when the train speed is v x , the unit is m / s 2 ; F(v x ) is the traction or braking force when the train speed is v x , the unit is KN; f base (v x ) is the unit basic resistance when the train speed is v x , the unit is KN / N; W(x) is the total additional resistance of the train at position x, the unit is KN; k1, k2 and k3 are basic resistance parameters of the train; wherein k3 is the friction resistance of the train, k2 is the resistance coefficient of the train, and k1 is the aerodynamic resistance coefficient of the train; W i is the slope additional resistance, the unit is KN; w i is the additional resistance of the unit slope, the unit is N / KN; g is the acceleration of gravity, w r is the additional resistance of the unit curve, the unit is N / KN; R is the curve radius of the line, the unit is m; A is an empirical constant, usually taken as 600; F(v front ) is the braking force of the train at speed v front , v front , F back and v x are the speeds of the train at the corresponding front, back and x positions, F front is the braking force of the train at the corresponding position front; D back is the braking force of the train at the corresponding position back.

[0082] S12, train traction characteristic curve, according to the running characteristics, it is divided into constant power zone and constant torque zone; when the train running speed is less than v 转 , it works in the constant torque zone, and the maximum traction force of the train is constant; in the constant power zone, when the train running speed increases until exceeds v 转 , it enters the constant torque zone, and the traction power of the train remains unchanged in the constant torque zone, v 终 is the maximum speed of traction under the current speed level; the direction of the braking force is opposite to the driving direction of the train, and the effect is opposite to the traction force. The braking characteristic curve of the train, when the train running speed is less than v 转折At the same time, the maximum braking force of the train remains constant; as the train speed increases until it exceeds v... 转折 Afterwards, the train speed and the maximum power exhibit a quadratic linear relationship, v 终点 This is the maximum braking speed at the current speed level. The braking force output can be adjusted according to the actual needs of the train during operation. The specific formula for the traction-braking characteristic curve is as follows:

[0083]

[0084]

[0085] Where F(v) is the traction force when the train is running at speed v; v is the train's running speed; K1 is the train's maximum traction force constant; m, n, p, and q are the constant coefficients of each term in the fitting of the train's traction characteristic curve in the constant torque region; B(V) is the braking force when the train is running at speed v; K2 is the train's maximum braking force constant; o, l, and h are the constant coefficients of each term in the fitting of the braking characteristic curve.

[0086] In one embodiment, step S2 analyzes the actual operation data during the coasting phase, and processes the data using particle swarm optimization, genetic algorithm, and long and short sequence neural network methods to obtain the train's basic resistance parameters, accurately calculating the basic resistance at different speeds; for example... Figure 2 The figure shows the basic resistance-speed curves obtained by processing the coasting phase data using particle swarm optimization, genetic algorithm, and long and short sequence neural network methods. The horizontal axis represents the train speed in km / h, and the vertical axis represents the basic resistance of the train in kN. The root mean square error (RMSE) is used to judge the parameter fitting effect. As shown in the figure, the RMSE of the three algorithms is less than 0.035, and the maximum error of the resistance curve is 1%.

[0087] In one embodiment, step S2 includes

[0088] S21. When the range of the train's basic resistance parameters is known, and the task of performing preliminary analysis, rapid calibration, or parameter initialization requires quick results, the particle swarm optimization algorithm is used to process the data during the coasting phase to obtain the train's basic resistance parameters.

[0089] Specifically, PSO updates the position and velocity of particles by iteration to approach the optimal solution gradually. In the prediction of train resistance parameters, PSO is used to find three parameters k1, k2, k3 in the resistance formula. In order to enhance the global search and local search ability of PSO, this paper introduces an adaptive inertia weight adjustment mechanism. In the standard algorithm of PSO, the inertia weight w is an important parameter to control the velocity of particles. The larger the inertia weight, the more the algorithm tends to global search, while the smaller the weight, the more the algorithm focuses on local search. In order to dynamically balance the two, the inertia weight w is dynamically adjusted with the fitness value

[0090]

[0091] where g is the acceleration of gravity, usually 9.81; Q is a preset value, usually 1000 for the conversion between KN and N; v is the speed of the train, M is the mass of the train; w start_PSO and w end_PSO are the inertia weights when the POS algorithm starts to explore and ends the exploration, respectively; f mean is the average fitness of the population using the POS algorithm, f min_PSO is the current optimal fitness using the POS algorithm, f is the fitness of the current individual, and F is the traction or braking force of the train;

[0092] S22, when it is necessary to accurately identify the basic resistance parameters of the train under various speed and load conditions, a genetic algorithm is used to process the data in the idle stage to obtain the basic resistance parameters of the train;

[0093] Specifically, the train resistance parameter identification method based on GA iteratively optimizes the fitness function and constantly updates the individual parameters to ultimately obtain the optimal solution. The tournament selection method is used to select individuals with higher fitness for breeding, crossover and mutation operations are used, diversity is introduced, and the weight is updated adaptively to ensure the accuracy of the identification result:

[0094]

[0095] where f(k) is the fitness value, F predicted is the resistance value calculated by identifying the parameters following the GA optimization process, F actual is the actual measured resistance value; is the train speed of the th data point, and the smaller the value of the fitness function, the more adaptive the individual to the solution space of the current problem; is the weight of individual i indiv ; is the fitness value of individual i indiv , f avg is the average fitness of the population using the GA algorithm, f min_GAFor the population optimal fitness of the GA algorithm, f is the fitness of the current individual; w start_GA is the initial value of the inertia weight when the GA algorithm explores; w end_GA is the end value of the inertia weight when the GA algorithm explores.

[0096] S23, when the basic resistance parameters of the train are dynamically changing, or the basic resistance parameters under the future speed change need to be predicted, a long-short sequence neural network method is used to process the data in the coasting phase to obtain the basic resistance parameters of the train.

[0097] Specifically, the train resistance parameters change with speed in a complex nonlinear relationship, and LSTM can learn historical speed and acceleration data to predict resistance parameters k1, k2 and k3. In the training process of LSTM, the model will output different resistance prediction values according to the parameter values k1, k2 and k3 of each iteration. In order to avoid the influence of noise in the model training process and ensure the stability of the prediction results, the parameter values predicted by LSTM are optimized by mean and mean square deviation. In order to ensure that the prediction results of the LSTM model are reasonable in physical sense, a parameter constraint loss is added to the loss function. The total loss function includes mean square error (MSE) loss: used to calculate the error between the predicted acceleration and the true acceleration; constraint loss is used to limit the value range of k1, k2 and k3, and ensure that the parameters meet the physical requirements.

[0098]

[0099] wherein, is the mean value of parameters k1, k2 and k3 in each round of iteration; is the standard deviation of parameters k1, k2 and k3 in each round of iteration; is the value of the i para th parameter in the j samp th sample; n num is the number of samples; is the average value of the i para th parameter; a is the weight coefficient, used to balance the MSE loss and the parameter constraint loss, L MSE is the mean square error, L constraint is the constraint error.

[0100] In summary, the three-dimensional particle swarm algorithm with self-adaptive inertia weight, the genetic algorithm with self-adaptive weight, and the LSTM algorithm with mean square deviation and multi-objective loss function are used for parameter identification of the basic resistance of the train, and the basic resistance of the urban rail train is predicted. The three methods provided can adapt to different running environments and different running data, and accurately predict the basic resistance of the train.

[0101] In one embodiment, step S3 performs data preprocessing on the ATO (Automatic Train Operation) running curve data of the actual train, and the acceleration calculation adopts a sliding window average method to obtain more stable and smooth acceleration results. The method includes two steps: row-by-row acceleration calculation and window acceleration smoothing processing, and the specific formula is as follows

[0102]

[0103] wherein, represents the speed of the last row of the current window (the i win th row of the window); represents the speed of the first row of the current window;△t is a fixed time interval; is the average acceleration in the window i win th window; is the acceleration calculated for the current row; is the acceleration corresponding to each row in the window;N is a preset number of rows, for example, N = 5, which means that the acceleration is taken once every 5 rows.

[0104] In one embodiment, the current range of the ATO simulation output is generally selected to be 0-20 mA, but only the range of 4-18 mA is used as a linear set value, and the value is 0 to 100% of the set value. The output in the range of 0-2 mA is considered invalid. The range of 2-4 mA is used for a set value of 0% (0% set value means that the train is idling and should not produce any acceleration or deceleration), and the range of 18-20 mA is used for a set value of 100%. The full traction force data and the full braking force data of the train are obtained according to the ATO current corresponding traction force conversion relationship, the ATO current corresponding braking force conversion relationship, the train acceleration data and the dynamics model;

[0105] The conversion relationship between the ATO current and the traction force and the conversion relationship between the ATO current and the braking force are

[0106]

[0107] wherein, F all (v x ) is the full traction force or the full braking force when the train speed is v x , a all (v x ) is the acceleration of the full traction force or the acceleration of the full braking force when the train speed is v x , I(v x ) is the ATO current when the train speed is v x .all 4 represents the ATO current at full traction or full braking force (18mA or -18mA), 4 represents the ATO current when the train has no traction or no braking force; g represents the acceleration due to gravity.

[0108] The formula for calculating the smooth full traction force data or full braking force data is as follows:

[0109]

[0110] in, The speed at which outliers and noise are cleaned up is v x Full traction or braking force at that time (corresponding to ATO current of 18mA or -18mA), The speed at which outliers and noise are cleaned up is v x The acceleration under full traction or full braking force (corresponding to ATO current of 18mA or -18mA).

[0111] In one embodiment, step S4 employs a sliding window Z-score processing technique to clean up outliers and noise in the full traction force and full braking force data, outputting smooth full traction force and full braking force data. This further includes applying Z-score processing to the acceleration data in the constant power region of the full traction force data, and using automatic sliding window Z-score processing to process the acceleration data of the full traction force in the constant power and constant torque regions. For the acceleration data of the full braking force, local weighted regression, outlier interpolation, and moving average + spline interpolation are used for processing. The specific formulas are as follows:

[0112]

[0113] in, The i-th tractive acceleration data obtained from the conversion acc acceleration The Z-score of the data; μ is the mean of the full traction acceleration data; σ is the standard deviation; W is the window size; Indicates the first in the window One acceleration data point; For the i-th win The mean of the data within each window; For the i-th win The standard deviation of the data within each window; Indicates the kth data-point The Z-scores for each data point; τ is the threshold for the Z-scores; For the k-th node within the sliding window data-point One acceleration data point; W' is the number of non-outliers within the window; D represents the current acceleration data. With the acceleration data to be estimated a ddistance between them, usually using Euclidean distance as the non-anomalous data points within the window; each acceleration data For the acceleration data a d to be estimated is calculated by a cubic weight function; anomalous acceleration data is replaced by adjacent acceleration data by applying interpolation and a reasonable estimate of the current acceleration data at a given time point is interpolated based on the data of adjacent points ; is the moving average acceleration data in the sliding window, is the j nor th acceleration after outlier processing; S ner (v inter ) is a spline function; v inter is the speed data of the interpolation point to be solved, v ner is the speed of the interpolation adjacent point; b ner , c ner , d ner and e ner are spline coefficients fitted according to the data points and continuity conditions respectively.

[0114] Specifically, Figure 3a show the traction force-speed curve diagram without cleaning the outliers and noise of the full traction force data, Figure 3b show the traction force-speed curve diagram after cleaning the outliers and noise of the full traction force data.

[0115] Figure 3a and Figure 3b After comparison, it is shown that the curve of Figure 3b has less noise and is more smooth, which is suitable for realizing parameter identification of the traction characteristic curve. Figure 3a and Figure 3b The abscissa is speed, unit: km / h; the ordinate is traction force, unit: KN. As Figure 4a show the braking force-speed curve diagram without cleaning the outliers and noise of the full traction force data; Figure 4b show the braking force-speed curve diagram after cleaning the outliers and noise of the full traction force data. Figure 4a and Figure 4b After comparison, it is shown that the curve of Figure 4b has less noise and is more smooth, which is suitable for realizing parameter identification of the braking characteristic curve. Figure 4a and Figure 4bThe abscissa of the graph is the speed, in km / h; the ordinate is the braking force, in KN. By combining various data optimization processing techniques such as sliding window Z-score, abnormal values and noise are cleaned up, and smooth data to be identified is output, so as to ensure the accuracy of the data and provide good input data for subsequent basic resistance, traction and braking performance prediction.

[0116] In one embodiment, the full traction data and full braking force data after cleaning up abnormal values and noise are analyzed, and a particle swarm algorithm or a weighted genetic algorithm is selected to identify the traction characteristic curve parameters, and a fully connected neural network (FNN) and an equalization loss are used to fit the braking characteristic curve parameters.

[0117] In order to accurately predict the traction curve of the train, such as Figure 5a and Figure 5b The particle swarm optimization algorithm (PSO) and the genetic algorithm (GA) are used to optimize the key parameters of the traction in the curve model. Figure 5a A traction-speed curve graph showing the traction characteristic curve parameters obtained by processing the smoothed full traction data using the particle swarm algorithm. Figure 5b A traction-speed curve graph showing the traction characteristic curve parameter results obtained by processing the smoothed full traction data using the weighted genetic algorithm. The RMSE of the identification results of the two algorithms is less than 1%. Figure 5a and Figure 5b The abscissa of the graph is the speed, in km / h; the ordinate is the traction force, in KN.

[0118] In one embodiment, when performing preliminary analysis, rapid calibration or parameter initialization tasks, the particle swarm algorithm is used to process the smoothed full traction data to obtain the traction characteristic curve parameters; the specific formula for processing the smoothed full traction data using the particle swarm algorithm is

[0119]

[0120] wherein, represents the position of particle i particle at time t, is the individual optimal position of particle i particle , g best is the global optimal position, w is the inertia weight, c1 and c2 are learning factors, and r1 and r2 are random numbers between 0 and 1; represents the position of particle i particle at time t; is the actual full traction force value, is the predicted value; is the second derivative of the fitted curve; λ is the weight coefficient of the penalty term; x1 and x n are the upper and lower limits of the turning point position of the curve, respectively. to ensure that no penalty is added when the second derivative is negative (i.e., concave). When the second derivative is positive (convex), the penalty is increased.

[0121] Specifically, the basic idea of the piecewise swarm optimization (PSO) algorithm is to find the optimal solution by simulating the cooperative search behavior of individuals in a swarm in the search space. The straight line and curve parts of the traction characteristic curve are predicted respectively. In the PSO algorithm, each individual (i.e., particle) represents a potential solution, and its goodness is evaluated according to the fitness function. The algorithm updates the state of the particle by adjusting its velocity and position, gradually approaching the optimal solution. The fitness function of the algorithm is based on the residual sum of squares (RSS), i.e., the error between the fitted value and the actual value; to ensure the smoothness and concavity of the curve, a curvature penalty term is introduced, which increases the penalty when the second derivative of the fitted curve is positive (i.e., the curve is convex), so that the algorithm generates a concave curve. Dynamic weights and learning factors are used, and in each iteration, the inertia weight and learning factor are dynamically adjusted according to the number of iterations. The inertia weight gradually decreases from the initial value of 0.9 to 0.4, and the learning factor is also linearly adjusted with the number of iterations. This dynamic adjustment mechanism helps to explore a larger search space in the early stage, and converges to the global optimal solution in the later stage.

[0122] In one embodiment,

[0123] When it is necessary to identify the traction characteristic curve parameters of the train under various speed and load conditions, a genetic algorithm is used to process the smoothed full traction data to obtain the traction characteristic curve parameters; the specific formula for processing the smoothed full traction data using the genetic algorithm is

[0124]

[0125] where α is a random number between 0 and 1, pa1 and pa2 are the first and second parent individuals respectively, ch1 and ch2 are the first and second child individuals respectively; x' is the gene value after mutation of the individual x; σ is the standard deviation, used to control the amplitude of mutation. indiv indiv is the gene value after mutation of the individual x.

[0126] ​Specifically, genetic algorithm (GA) is an optimization algorithm that simulates the biological evolution process, and uses selection, crossover and mutation operations to evolve individuals in the population, so as to gradually approach the optimal solution. GA algorithm has global search ability and can handle nonlinear complex optimization problems. Similar to PSO, the fitness function of GA is also based on the sum of squared residuals, and contains a turning point penalty and a curvature penalty term. In order to ensure that the constant K in the low speed interval and the polynomial curve in the high speed interval are continuous at the turning point, the turning point penalty term is introduced, which requires that the difference between K and the value of the polynomial at this point is less than 1, otherwise the difference will be squared. The curvature penalty is also used to optimize the generation of concave curves. In each generation of GA, first, the roulette wheel selection operation is used to select individuals with higher fitness for breeding. Then, uniform crossover operation is performed, that is, the gene information of two parent individuals is combined into a new individual through random weight. In addition, the parameters of each individual are randomly fine-tuned through Gaussian mutation operation to increase the diversity of the population. The mutation rate is set to 0.1 to ensure moderate diversity.

[0127] In one embodiment, in order to accurately predict the braking force curve of the train, a fully connected neural network (FNN) is used to identify the parameters of the train braking force model. As shown in Figure 6 The fully connected neural network and the balanced loss fit the braking force-velocity curve of the braking characteristic curve parameter result. The abscissa is the speed, the unit is km / h, and the ordinate is the braking force, the unit is KN. According to Figure 6 The RMSE of the fully connected neural network and the balanced loss fitting the key braking parameters is less than 0.8%.

[0128] Specifically, we designed a neural network containing multiple hidden layers, which outputs 4 key parameters: K2, o, l, h. The model fits the braking force curve of the train at different speeds through training.

[0129] Extract the speed (speed) and brake force (brake force) data. In order to adapt to the input of the neural network, the speed data is converted into a tensor, and the correspondence between the brake force and the speed is maintained. The designed fully connected neural network contains three hidden layers, each followed by a ReLU activation function. The input of the network is the speed, and the output is the parameters K2, o, l, h of the brake force model.

[0130] In order to ensure the fitting accuracy of the model in each speed interval, a custom loss function is defined, which not only considers the mean square error (MSE), but also adds constraints for smooth transition at the speed turning point (v=85km / h). These constraints include:

[0131] ①k and polynomial f+gv+hv 2The values at the turning points are to be equal.

[0132] ②Smooth transition of the slope, that is, the slope should be consistent when v=85.

[0133] ③Constraints on parameters K2, o, l and h to be within a reasonable range.

[0134] The model is trained using the Adam optimizer, with a learning rate set to 0.07, and the training process is performed for a total of 1000 epochs. In each epoch, the parameters K2, o, l, h output by the neural network are used to calculate the braking force curve, and the loss function is used to perform gradient backpropagation and parameter update according to the difference between the actual and predicted braking forces.

[0135] The loss function for smoothing the full braking force data using a fully connected neural network and a balanced loss is

[0136] Loss=MSE+λ1×transition value constraint+λ2×transition slope constraint+λ3×(k penalty +a penalty +b penalty +c penalty )

[0137] Where θ1, λ2 and λ3 are the first control weight, the second control weight and the third control weight respectively; transition value constraint is the value of v 转折 , transition slope constraint is the slope of v 转折 , k penalty is the range constraint of K2, a penalty is the range constraint of o, b penalty is the range constraint of l, and c penalty is the range constraint of h.

[0138] The present application discloses a train traction and braking performance prediction method to solve the problem of the accuracy of train traction and braking performance prediction. The present application generates traction characteristic curves and braking characteristic curves according to train operation data, effectively reduces prediction errors, improves the safety and energy saving of train operation, and is suitable for the design and actual operation evaluation of urban rail trains. Compared with the physical model of the train controller modeling, the present application is more accurate and efficient in predicting the train traction and braking performance, and the present application can also evaluate the predicted results.

[0139] In one embodiment, step S7 verifies and evaluates the accuracy and effectiveness of the predicted traction characteristic curve and braking characteristic curve, and the proposed evaluation method includes

[0140] ①Error calculation and deviation point statistics.

[0141] Error calculation: Discretize the train's traction and braking characteristic curves of the prediction result, obtain multiple discrete points, and calculate the relative error of each discrete point compared with the reference curve.

[0142] Deviation point statistics: Set a deviation threshold (such as 2%), count the number of points whose error exceeds the threshold, and calculate the proportion of deviation points (set to not more than 1% or lower), which is considered to meet the prediction accuracy requirement.

[0143] ②Model simulation running curve comparison.

[0144] Using the curve model, combined with the line control strategy, considering the train and line conditions, the running curve is simulated to obtain the speed-time curve and speed-displacement curve; the obtained curve is compared with the reference model running curve or the actual running curve, and the prediction accuracy is within a certain threshold range (99%) to be considered to meet the prediction accuracy requirement.

[0145] The present application can evaluate the prediction result, effectively reduce the prediction error, improve the safety and energy saving of train operation, and is suitable for the design and actual operation evaluation of urban rail trains.

[0146] In the description of the present application, it should be noted that the orientation or position relationship indicated by the terms "upper", "lower" and the like is based on the orientation or position relationship shown in the drawings, and is only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore it cannot be understood as a limitation on the present application. Unless otherwise specified and limited, the terms "mounting", "connection", "connection" should be understood broadly, for example, it can be fixed connection, or detachable connection, or integral connection; it can be mechanical connection, or electrical connection; it can be directly connected, or indirectly connected through an intermediate medium, or the internal communication of two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0147] It is further noted that the terminology "first", "second" and the like used in the description of the application is merely intended to differentiate one entity or operation from another, without necessarily requiring or implying any actual such relationship or order between such entities or operations. Moreover, the use of the term "including", "containing" or any other variation thereof is intended to cover a non-exclusive inclusion, such that a process, method, article or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or even inherent to such process, method, article or apparatus. An element proceeded by "comprises... a", "has... a", "includes... a" or "contains... a", does not, without more constraints, preclude the existence of additional identical elements in the process, method, article or apparatus that comprises the element.

[0148] Obviously, the above-described embodiments of the present application are only examples for clearly illustrating the present application, and are not intended to limit the implementation manners of the present application. Based on the above description, other different forms of changes or variations can be made by those skilled in the art, and it is impossible to enumerate all the implementation manners here. Any obvious changes or variations derived from the technical solutions of the present application are still within the protection scope of the present application.

Claims

1. A method of predicting train traction and braking performance, characterized by, The method comprises the following steps: S1, acquiring train operation data, and constructing a dynamics model comprising train basic resistance, train additional resistance, train traction force and braking force, and a curve model; The train operation data comprises coasting stage data, traction stage data and braking stage data; S2, processing the coasting stage data by using a particle swarm optimization algorithm, a genetic algorithm or a long-short sequence neural network method to obtain train basic resistance parameters; S3, processing the traction stage data and the braking stage data by using a sliding window average method to obtain train acceleration data, and obtaining train full traction force data and full braking force data according to an ATO current corresponding traction force conversion relationship, an ATO current corresponding braking force conversion relationship, the train acceleration data, the basic resistance parameters and the dynamics model; S4, cleaning abnormal values and noises in the full traction force data and the full braking force data by using a sliding window Z-score processing technology, and outputting smoothed full traction force data and full braking force data; S5, processing the smoothed full traction force data by using a particle swarm algorithm or a weighted genetic algorithm to obtain traction characteristic curve parameters, and fitting the smoothed full braking force data by using a fully connected neural network and an equalization loss to obtain braking characteristic curve parameters; S6, obtaining train traction characteristic curve and braking characteristic curve according to the traction characteristic curve parameters, the braking characteristic curve parameters and the curve model; The curve model is Wherein, F(v) is the traction force when the train running speed is v; v is the train running speed; K1 is the maximum traction force constant of the train; m, n, p and q are the constant coefficients of each term of the traction characteristic curve fitting of the train in the constant torque area respectively; B(v) is the braking force when the train running speed is v; K2 is the maximum braking force constant of the train; o, l and h are the constant coefficients of each term of the braking characteristic curve fitting respectively; the traction characteristic curve of the train is divided into constant torque area and constant power area according to the running characteristics; when the train running speed is less than v 转 , it works in the constant torque area, and the maximum traction force of the train is constant; when the train running speed increases until it exceeds v 转 , it enters the constant torque area, and the traction power of the train remains unchanged in the constant torque area; v 终 is the maximum speed of traction under the current speed level; when the train running speed is less than v 转折 , the maximum braking force of the train is constant; When the train speed increases until v 转折 , the train speed and the maximum power present a quadratic linear relationship, v 终点 is the maximum speed of braking under the current speed level.

2. The method of claim 1, wherein, The dynamics model is where M is the train mass; a(v x ) is the train acceleration at the train speed v x ; F(v x ) is the traction or braking force at the train speed v x ; f base (v x ) is the unit basic resistance at the train speed v x ; W(x) is the total additional resistance of the train at the position x; k1, k2 and k3 are the basic resistance parameters of the train; wherein k3 is the friction resistance of the train, k2 is the resistance coefficient of the train, and k1 is the aerodynamic resistance coefficient of the train; W i is the additional resistance of the slope; w i is the unit additional resistance of the slope; g is the acceleration of gravity, w r is the unit additional resistance of the curve; R is the curve radius of the line; A is an empirical constant; F(v front ) is the braking force of the train at the speed v front ; v front , F back and v x are the speeds of the train at the corresponding front, back and x positions, respectively; F front is the braking force of the train at the corresponding position front; and F back is the braking force of the train at the corresponding position back.

3. The method of claim 2, wherein, The S2 further comprises S21, when the range of train basic resistance parameters is known, performing preliminary analysis, rapid calibration or parameter initialization tasks, and processing the coasting stage data by using a particle swarm optimization algorithm to obtain train basic resistance parameters; S22, when it is necessary to accurately identify the basic resistance parameters of the train under multiple speed and load conditions, processing the coasting stage data by using a genetic algorithm to obtain train basic resistance parameters; S23, when the train basic resistance parameters are dynamically changing, or it is necessary to predict the basic resistance parameters under future speed changes, processing the coasting stage data by using a long-short sequence neural network method to obtain train basic resistance parameters.

4. The method of claim 3, wherein, The specific formula for processing the coasting stage data by using the particle swarm optimization algorithm is where w start_PSO and w end_PSO are the inertia weights at the beginning and end of the exploration of the POS algorithm, respectively; f mean is the average fitness of the population using the POS algorithm, f min_PSO is the current optimal fitness using the POS algorithm, f is the fitness of the current individual, F is the traction or braking force of the train; and Q is a preset value. The specific formula for processing the coasting stage data by using the genetic algorithm is Where f(k) is the fitness value, F predicted The drag value F is calculated based on the parameters identified during the GA optimization process. actual This is the actual measured resistance value; For the j-th data Train speed at each data point; For individual i indiv The weights; For individual i indiv fitness value, f avg f is the average fitness of the population using the GA algorithm. min_GA The optimal fitness of the population using the GA algorithm is given by f, where f is the fitness of the current individual; w start_GA The initial value of the inertia weight during the GA algorithm exploration; w end_GA This represents the final value of the inertial weights during the GA algorithm's exploration. The specific formula for processing the coasting stage data by using the long-short sequence neural network method is where, is the mean of parameters k1, k2 and k3 in each round of iteration; is the standard deviation of parameters k1, k2 and k3 in each round of iteration; is the value of the i para th parameter in the j samp th sample; n num is the number of samples; is the mean of the i para th parameter; a is the weight coefficient to balance the MSE loss and the parameter constraint loss, L MSE is the mean square error, L constraint is the constraint error.

5. The method of claim 4, wherein, The processing of the traction stage data and the braking stage data by using the sliding window average method to obtain train acceleration data comprises calculating train acceleration in the window row by row and smoothing the train acceleration in the window, and the specific formula is wherein, represents the speed of the last row of the current window; represents the speed of the first row of the current window; and is the average acceleration within the window i win is the acceleration calculated for the current row; is the acceleration corresponding to each row within the window; andN is a predetermined number of rows.

6. The method of claim 5, wherein, The conversion relationship between the ATO current and the traction force and the conversion relationship between the ATO current and the braking force are wherein F all (v x ) is the full traction force or full braking force when the train speed is v x a all (v x ) is the acceleration of the full traction force or full braking force when the train speed is v x I(v x ) is the ATO current when the train speed is v x I all is the ATO current for the full traction force or full braking force; the ATO current when the train has no traction force or the ATO current when the train has no braking force is 4; g is the acceleration due to gravity; The calculation formula of the smoothed full traction force data or the full braking force data is wherein, is the speed for cleaning outliers and noise v x is the full traction or braking force at the time t, is the acceleration of the full traction force or the acceleration of the full braking force at the time t, x is the full traction force at the time t.

7. The method of claim 6, wherein, The Z-score processing technology with a sliding window is used to clean up abnormal values and noises in the full traction force data and the full braking force data, and output smooth full traction force data and full braking force data, further comprising Z-score processing of acceleration data of the full traction force in the constant power region, and automatic Z-score processing of acceleration data of the full traction force in the constant power region and the constant torque region with a sliding window; the acceleration data of the full braking force is processed by local weighted regression, interpolation of abnormal values, and moving average + spline interpolation method, and the specific formula is as follows in, The i-th tractive acceleration data obtained from the conversion acc acceleration The Z-score of the data; μ is the mean of the full traction acceleration data; σ is the standard deviation; W is the window size; Represents the j-th element within the window. win-acc One acceleration data point; For the i-th win The mean of the data within each window; For the i-th win The standard deviation of the data within each window; Indicates the kth data-point The Z-scores for each data point; τ is the threshold for the Z-scores; For the k-th node within the sliding window data-point One acceleration data point; W' is the number of non-outliers within the window; D represents the current acceleration data. With the acceleration data to be estimated a d The distance between them, each acceleration data For the acceleration data to be estimated, a d weight Calculated using a cubic weighting function; abnormal acceleration data Apply interpolation to replace it with adjacent acceleration data. and A reasonable valuation at a given point in time. Above, based on neighboring points The data is interpolated from the current acceleration data; The moving average acceleration data is in the sliding window. For the j-th value after outlier handling nor One acceleration; S ner (v inter ) is a spline function; v inter For the velocity data of the interpolation points to be solved, v ner b is the velocity of the nearest interpolated point; ner c ner d ner and e ner The spline coefficients are obtained by fitting the data points and the continuity condition, respectively.

8. The method of claim 7, wherein, The particle swarm algorithm or the weighted genetic algorithm is used to process the smooth full traction force data to obtain the traction characteristic curve parameters, comprising When performing preliminary analysis, rapid calibration or parameter initialization tasks, the particle swarm algorithm is used to process the smooth full traction force data to obtain the traction characteristic curve parameters; the specific formula for processing the smooth full traction force data by the particle swarm algorithm is wherein, represents the position of particle i particle at time t, is the individual optimal position of particle i particle , g best is the global optimal position, w is the inertia weight, c1 and c2 are learning factors, and r1 and r2 are random numbers between 0 and 1; represents the position of particle i particle at time t; is the actual value of the traction force, is the predicted value; is the second derivative of the fitting curve; λ is the weight coefficient of the penalty term; x1 and x n are the upper and lower limits of the turning point position of the curve, respectively; is used to ensure that the penalty is not increased when the second derivative is negative, and the penalty is increased when the second derivative is positive; When it is necessary to identify the traction characteristic curve parameters of the train under multiple speed and load conditions, the genetic algorithm is used to process the smooth full traction force data to obtain the traction characteristic curve parameters; the specific formula for processing the smooth full traction force data by the genetic algorithm is wherein a is a random number between [0, 1], pa1 and pa2 are the first parent individual and the second parent individual respectively, ch1 and ch2 are the first child individual and the second child individual respectively; x' indiv is the gene value of the individual x indiv after mutation.

9. The method of claim 8, wherein, The loss function for processing the smooth full braking force data by the fully connected neural network and the balanced loss is Loss = MSE + λ1 x transition value constraint + λ2 x transition slope constraint + λ3 x (k penalty + a penalty + b penalty + c penalty ) where λ1, λ2, and λ3 are the first control weight, the second control weight, and the third control weight, respectively; transitionvalue constraint is the value of v 转折 when t 转折 ransition slope constraint is the slope of v penalty , k penalty is the range constraint of o, b penalty is the range constraint of l, c penalty is the range constraint of h.

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