Robust optimization-based hydrogen fuel cell hybrid electric vehicle energy management method

Abstract

The invention discloses a hydrogen fuel cell hybrid electric vehicle energy management method based on robust optimization, and the method comprises the following steps: building a vehicle model: building a longitudinal dynamic model of a hydrogen fuel cell hybrid electric vehicle, determining a vehicle demand power model, and building an evaluation function of instantaneous hydrogen consumption, constructing an output power model of the hydrogen fuel cell and the capacitor; performing uncertainty analysis on the hydrogen fuel cell hybrid electric vehicle, determining uncertain parameters in the vehicle model, and constructing an uncertainty set of the uncertain parameters; the method comprises the following steps: constructing an sLSTM vehicle speed prediction model through vehicle historical speed data, predicting a future driving speed, analyzing the uncertainty of the prediction model, and outputting a prediction speed error in a current prediction time domain; and according to the optimization target, constructing a target function for minimizing the hydrogen consumption, solving the target function by applying a robust optimization algorithm, and outputting a first control result of the optimal control sequence.

Description

Technical Field

[0001] The present invention relates to the field of energy management of hybrid vehicles, and particularly to an energy management method for a hydrogen fuel cell hybrid vehicle based on robust optimization. Background Art

[0002] Due to gasoline shortages and environmental factors such as pollution and global warming, electric vehicles have increasingly attracted the interest of researchers and the industry. Currently, the international automotive industry is attempting to adopt cleaner and safer alternative technologies. Hydrogen fuel cell hybrid electric vehicles are one of the most effective technologies and are receiving continuous attention and development. Optimal energy management is one of the many key aspects of the technological progress of hybrid vehicles.

[0003] Currently, the energy management strategies of hybrid vehicles are mainly divided into rule-based and optimization-based energy management strategies. The rule-based energy management strategy mainly designs the system working mode and the energy distribution method of different power sources according to engineering experience and considering the characteristics of each component of the power system. This control strategy does not have a specific optimization problem, and the formulated rules mainly come from engineering experience, with strong practicability and good real-time effect, but the energy-saving effect is poor.

[0004] The existing energy management strategies of hybrid vehicles optimize the hybrid for the entire working condition according to the state equation and objective function of the vehicle system, using the optimal control theory to obtain the global optimal solution of the feasible region. In theory, it can achieve the optimal fuel economy, but it requires the global driving condition of the vehicle, and the large amount of calculation is prone to cause delay, making it difficult to achieve real-time application.

[0005] In order to further improve the energy-saving performance, advanced energy management research combines speed prediction, enabling the energy management strategy to have prior knowledge of the future driving cycle, so that when making the optimal decision, it not only pays attention to the current state but also considers the future situation.

[0006] In addition to requiring the economy of the vehicle to reach optimality, the robustness of the solution is also considered a key performance criterion. Since previous research has focused on the expected optimal performance under a deterministic framework and ignored data ambiguity, changing operating conditions, modeling, and estimation will bring multiple error sources. In practice, ignoring these uncertainties will lead to high operating costs, low overall system efficiency, performance failures, and even the inability to solve problems due to constraint violations.

[0007] Some advanced research on energy management strategies has begun to focus on the uncertainties introduced by real-world random factors. However, if the uncertainties are not properly quantified, the optimization results output by traditional model predictive or stochastic model predictive may deviate from the optimal control strategy or fail to achieve stable control. In dynamic traffic scenarios, when facing strong random factors, the following three aspects of problems still need to be solved:

[0008] 1) Previous studies have focused on the expected optimal performance under a deterministic framework, while ignoring data ambiguity, and changing operating conditions, modeling, and estimation can introduce multiple error sources.

[0009] 2) These uncertainties can lead to high operating costs, low overall system efficiency, performance failures, and even inability to solve problems due to constraint violations.

[0010] 3) If the uncertainties are not properly quantified, the optimization results output by traditional model predictive or stochastic model predictive may deviate from the optimal control strategy or fail to achieve stable control.

[0011] The Chinese patent fuel cell vehicle model - interference dual predictive control energy management method and system with patent number CN1 12925209B uses a Markov correction model to predict the future speed of the vehicle. The present invention uses a scalar long short-term memory neural network (sLSTM) to construct a speed prediction model, making the speed prediction more accurate and efficient.

[0012] The Chinese patent plug-in hybrid electric vehicle energy management method based on multi-source information fusion with patent number CN1 15534929A obtains the vehicle speed prediction sequence within a future finite time domain, and performs rolling optimization within the finite time domain based on the Pontryagin minimum principle to ensure fuel economy, only considering a single optimization goal. The present invention quantifies the uncertainty factors and uses a robust optimization algorithm to solve the control variables, enhancing the robustness of the system while ensuring economy.

[0013] The present invention intends to propose a hydrogen fuel cell vehicle energy management method based on robust optimization. Taking the hydrogen fuel cell hybrid vehicle as the research object, abandoning the optimization of the economy of the vehicle under the traditional deterministic framework, and considering both the economy and robustness of the hybrid vehicle, a dynamic uncertainty analysis method based on a scalar long short-term memory network is proposed. This method can predict the future speed of the vehicle according to the vehicle's historical speed data, analyze the dynamic uncertainty of the speed based on the predicted speed, and improve the uncertainty source to solve the technical problems of low system efficiency, output results deviating from the optimal control strategy, and inability to achieve stable control in the face of random factors in the energy management strategy under the deterministic framework. Summary of the Invention

[0014] The technical solution of the present invention is as follows:

[0015] An energy management method for a hydrogen fuel cell hybrid vehicle based on robust optimization, characterized by comprising the following steps:

[0016] Step 1: Construct a vehicle model, including: establishing a longitudinal dynamics model of a hydrogen fuel cell hybrid vehicle, determining a vehicle demand power model, constructing an evaluation function for instantaneous hydrogen consumption, and constructing an output power model of a hydrogen fuel cell and a capacitor;

[0017] Step 2: Conduct a static uncertainty analysis on the hydrogen fuel cell hybrid vehicle, determine the uncertain parameters in the vehicle model, and construct an uncertainty set of the uncertain parameters;

[0018] Step 3: Based on the sLSTM algorithm, construct an sLSTM vehicle speed prediction model through vehicle historical speed data, predict the future driving speed, perform feedback correction according to the difference between the predicted speed and the actual speed, and output the predicted speed error within the current prediction time domain;

[0019] Step 4: According to the optimization objective, construct an objective function for minimizing hydrogen consumption, which is jointly constrained by the uncertainty set and the predicted speed error. Use the speed prediction model to predict the driving speed of the vehicle within the future time domain n of the vehicle, and apply the robust optimization algorithm to perform uncertain optimization on the objective function within [k, k + n] to obtain the optimal control sequence within [k, k + n], and output the first control result of the optimal control sequence.

[0020] The optimization objective of the present invention is to achieve optimal energy management by comprehensively considering multiple performance indicators through a robust model predictive control framework, specifically including: minimizing hydrogen consumption, paying attention to maintaining the health state of the battery, balancing the durability of the fuel cell and the battery, ensuring the robustness and stability of the system, and improving the dynamic performance of the system. By introducing the uncertainty set of uncertain parameters, the optimization algorithm can still maintain good performance under uncertain conditions, ensuring the robustness and stability of the system. The optimization algorithm can also dynamically adjust the output power of the hydrogen fuel cell according to the predicted speed value and load demand, ensuring that the vehicle can operate smoothly under different working conditions and avoiding energy waste or system failures caused by power mismatch.

[0021] Before establishing the longitudinal dynamics model of the hydrogen fuel cell hybrid vehicle, vehicle parameters are obtained, and the vehicle parameters include vehicle parameters and power source parameters;

[0022] The vehicle parameters include: mass, frontal area, air resistance coefficient, air density, rolling resistance coefficient;

[0023] The power source parameters include: battery energy, battery capacity, maximum output power of the fuel cell.

[0024] In the first step:

[0025] The vehicle demand power model is specifically:

[0026] P veh =(F r +F w +F i +F j )u a ,

[0027] where P veh is the demand power, F r is the rolling resistance, F w is the air resistance, F i is the gradient resistance, F j is the acceleration resistance, and u a is the driving speed;

[0028] The resistance model of the vehicle is specifically:

[0029]

[0030] where m is the vehicle mass, g is the acceleration due to gravity, C r is the rolling resistance coefficient, α is the road gradient, C d is the air resistance coefficient, A is the frontal area, ρ is the air density, u a is the driving speed, is the driving acceleration.

[0031] In the first step, the output power model of the hydrogen fuel cell is specifically:

[0032] P fc =P H η fc ,

[0033] where P fc is the fuel cell output power, P H is the hydrogen input power, and η fc is the fuel cell efficiency;

[0034] Estimate the instantaneously consumed hydrogen C H2 according to the fuel cell output power and the overall efficiency, specifically:

[0035]

[0036] where LHV = 120 mJ / kg is the calorific value of hydrogen;

[0037] The capacitor module includes individual capacitor units, which are modeled by an equivalent series circuit. The total resistive loss power is established by the following formula, specifically:

[0038]

[0039] Where, P ohm is the resistive loss power, R UC is the series resistance of the capacitor module, and I UC is the current of the capacitor module;

[0040] The provided power P UC is determined by the original power P UC，r The resistive loss power P ohm is determined according to the charge / discharge mode. The capacitor output power model is specifically:

[0041]

[0042] The state of charge SOC is the most important state variable of the capacitor module, which is expressed by an energy ratio, specifically:

[0043]

[0044] Where, E UC is the available energy in the capacitor module, and E max is the maximum energy of the capacitor module.

[0045] In the second step, the uncertain parameters determined in the vehicle model include:

[0046] To estimate the required power P veh of the vehicle, the air resistance F d is approximately calculated by considering the vehicle as having a frontal area A and a constant air resistance coefficient C w ; During the optimization process, the uncertainty interval is considered, and the uncertain values and

[0047] are introduced. According to the battery operating conditions, is defined to represent the uncertain efficiency of the fuel cell system.

[0048] In the second step, the uncertainty set of the uncertain parameters constructed includes:

[0049] Under the robust optimization framework, the uncertain parameters are represented by their nominal values and uncertainty values:

[0050]

[0051] is the vector of parameter uncertainty values, P unis the vector of nominal parameter values, and α represents the vector containing the uncertainties associated with each parameter, specifically:

[0052]

[0053] P un =[C d ,C r ,η fc ,

[0054]

[0055] where α sup (i) is the maximum possible value that the uncertainty α(i) can take, and the uncertain parameter takes values according to a symmetric distribution with a mean equal to the nominal value P un (i), and the uncertainty set is:

[0056]

[0057] The specific steps of step three include:

[0058] Based on the sLSTM algorithm, construct an sLSTM vehicle speed prediction model through vehicle historical speed data;

[0059] Based on the predicted speed D n output by the sLSTM speed prediction model at time k, in the future time domain of length n, specifically:

[0060] D n =[v p (k + 1),..., v p (k + n)],

[0061] Regard the actual speed value y and the predicted speed value as continuous random variables Y and where there exists a unique Copula function C(.) that satisfies the following equation:

[0062]

[0063] where, F Y (y) and are the marginal cumulative distribution functions of the random variables Y and , is the joint cumulative distribution function of the random variable ;

[0064] The present invention uses the non-parametric kernel density estimation method to fit the appropriate marginal distribution, and the specific expression is:

[0065]

[0066] Among them, h is the bandwidth, which is used to control the smoothness of the estimation; KER is the kernel function, and Xj is the data value of the observed sample.

[0067] Express the joint probability density function of Y and as:

[0068]

[0069] where θ y and are the unknown parameters involved in the marginal density functions of the random variables Y and respectively,

[0070] is the corresponding Copula density function, and β is the unknown parameter;

[0071] According to the actually observed discrete data sequence the empirical cumulative distribution function of the j-th sample data can be obtained as and On this basis, the estimated value of the unknown parameter in the Copula density function is:

[0072]

[0073] After estimating the unknown parameters, establish a Copula function to obtain the conditional probability distribution of Y as:

[0074]

[0075] where is the conditional probability distribution function of the random variable Y under the condition of is the corresponding conditional probability density function, is the probability density function corresponding to the distribution function and is the probability density function corresponding to the distribution function ;

[0076] Define the prediction speed uncertainty interval as Then the uncertainty interval can be determined by the following formula:

[0077]

[0078] In the fourth step described above, before applying the model predictive control method based on robust optimization, construct a nonlinear system of a hydrogen fuel cell hybrid vehicle:

[0079] x k+1= f(x k , u k ),

[0080] where x k+1 is the state variable at the (k + 1)-th stage; x k and u k are the state variable and control variable at the k-th stage, respectively;

[0081]

[0082] where x and u are the state variable and control variable of the non-linear system of a hydrogen fuel cell hybrid vehicle, respectively, and SOC is the state of charge of the capacitor;

[0083] The cost function of the non-linear system of a hydrogen fuel cell hybrid vehicle is:

[0084]

[0085] The said step four includes:

[0086] Establish a robust optimization model for the non-linear system of a hydrogen fuel cell hybrid vehicle, considering the uncertainty vector α related to uncertain parameters and the prediction speed uncertainty interval

[0087] Establish an objective function for minimizing hydrogen consumption as:

[0088]

[0089] Establish equality constraint conditions:

[0090]

[0091] Establish inequality constraint conditions:

[0092] h1(k) = P fc (k) - P fc，min ≥ 0,

[0093] h2(k) = P fc，max - P fc (k) ≥ 0,

[0094] h3(k) = P fc (k) - P fc (k - 1) - ΔP fc，fall ΔT ≥ 0,

[0095] h4(k) = ΔP fc，rise ΔT - P fc (k) - P fc (k - 1) ≥ 0,

[0096] h5(k) = SOC(k) - SOC min ≥ 0,

[0097] h6(k) = SOC max - SOC(k) ≥ 0,

[0098] where ΔT is the sampling time, P fc，min is the minimum output power of the hydrogen fuel cell, P fc，max is the maximum output power of the hydrogen fuel cell, ΔP fc，fall is the power decline rate limit of the hydrogen fuel cell, ΔP fc，rise is the power rise rate limit of the hydrogen fuel cell, SOC min is the minimum state of charge of the capacitor, SOC max is the maximum state of charge of the capacitor;

[0099] Solve the objective function to obtain the optimal control sequence, and output the first control result of the optimal control sequence.

[0100] Apply the first control result to the hydrogen fuel cell hybrid vehicle to control the output power of the fuel cell, and achieve vehicle energy management and optimization.

[0101] The beneficial effects of the present invention are:

[0102] Since previous studies focused on the expected optimal performance under a deterministic framework and ignored data ambiguity, changing operating conditions, modeling, and estimation would introduce multiple error sources. In practice, ignoring these uncertainties would lead to high operating costs, low overall system efficiency, performance failures, and even inability to solve problems due to constraint violations. Moreover, if the uncertainties are not properly quantified, the optimization results output by traditional model prediction or stochastic model prediction may deviate from the optimal control strategy or fail to achieve stable control.

[0103] A novel energy management method for hydrogen fuel cell hybrid vehicles based on robust optimization proposed by the present invention has the remarkable effects that:

[0104] 1. Most traditional energy management strategies are based on a deterministic framework and ignore the influence of uncertainty factors. By introducing a robust optimization framework, the present invention considers various uncertain factors (such as vehicle speed prediction errors, environmental condition changes, etc.), and significantly improves the robustness and adaptability of the system. Compared with the prior art, the present invention can still maintain efficient and stable energy management under uncertain conditions, avoiding performance fluctuations and low efficiency caused by uncertain factors.

[0105] 2. Dynamic Uncertainty Analysis: Most existing vehicle speed prediction methods use a single prediction model and cannot effectively capture the dynamic changes in speed. By combining the sLSTM algorithm, the present invention can update the prediction error in real time, accurately predict the future vehicle speed, and evaluate the dynamic uncertainty of speed. This dynamic uncertainty analysis not only improves the accuracy of prediction but also provides important input data for subsequent robust optimization, ensuring the real-time performance and stability of the system.

[0106] 3. Comprehensive Energy Management Strategy: The present invention combines vehicle longitudinal dynamics modeling, uncertainty analysis, and robust model predictive control to form a complete set of energy management strategies. Compared with the prior art, the present invention not only optimizes energy distribution but also considers the robustness of the system, significantly improving the overall performance of the vehicle. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 It is a schematic diagram of uncertainty integration;

[0108] Figure 2 It is a schematic diagram of robust predictive control;

[0109] Figure 3 It is a schematic diagram of a robust optimization algorithm;

[0110] Figure 4 It is the acquisition route of the training set;

[0111] Figure 5 It is the acquisition route of the test set;

[0112] Figure 6 It is the training set data collected in the embodiment;

[0113] Figure 7 It is the test set data collected in the embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0114] A method for energy management of a hydrogen fuel cell hybrid vehicle based on robust optimization according to the present invention mainly includes the following steps:

[0115] Step 1, Vehicle Longitudinal Dynamics Modeling

[0116] Construct a vehicle model, including: establishing a longitudinal dynamics model of a hydrogen fuel cell hybrid vehicle, determining a vehicle demand power model, constructing an evaluation function for instantaneous hydrogen consumption, and constructing an output power model of a hydrogen fuel cell and a capacitor.

[0117] First, obtain vehicle parameters, including vehicle parameters and power source parameters:

[0118] Vehicle parameters include: mass, frontal area, air resistance coefficient, air density, rolling resistance coefficient;

[0119] The power source parameters include: battery energy, battery capacity, and maximum output power of the fuel cell.

[0120] By performing longitudinal dynamics analysis on a hydrogen fuel cell hybrid vehicle, a model of the vehicle's components is built. The demand power model of the vehicle is specifically:

[0121] P veh =(F r +F w +F i +F j )u a (1)

[0122] Wherein, P veh is the demand power, Fr is the rolling resistance, F w is the air resistance, F i is the gradient resistance, F j is the acceleration resistance, and u a is the driving speed.

[0123] The resistance model of the vehicle is specifically:

[0124]

[0125] Wherein, m is the total vehicle mass, g is the acceleration due to gravity, C r is the rolling resistance coefficient, α is the road gradient, C d is the air resistance coefficient, A is the frontal area, ρ is the air density, u a is the driving speed, is the driving acceleration.

[0126] The power of the fuel cell hybrid vehicle comes from the hydrogen fuel cell, and the output power model is specifically:

[0127] P fc =P H η fc (3)

[0128] Wherein, P fc is the fuel cell output power, P H is the hydrogen input power, and η fc is the fuel cell efficiency.

[0129] To evaluate the energy consumption of the fuel cell system, the hydrogen C H2 instantaneously consumed is estimated based on the fuel cell output power and the overall efficiency, specifically:

[0130]

[0131] Wherein, LHV = 120 mJ / kg is the calorific value of hydrogen.

[0132] The capacitor module includes individual capacitor units and can be modeled by an equivalent series circuit. The total resistive loss power is established by the following formula, specifically:

[0133]

[0134] where P ohm is the resistive loss power, R UC is the series resistance of the capacitor module, and I UC is the current of the capacitor module.

[0135] The supplied power P UC is determined by the original power P UC，r , and the resistive loss power P ohm is determined according to the charge / discharge mode, specifically:

[0136]

[0137] The state of charge SOC is the most important state variable of the capacitor module and can be expressed by the available energy ratio, specifically:

[0138]

[0139] where E UC is the available energy in the capacitor module, and E max is the maximum energy of the capacitor module.

[0140] Step 2, Static uncertainty analysis

[0141] Perform a static uncertainty analysis on the hydrogen fuel cell hybrid vehicle to determine the uncertain parameters in the vehicle model and construct the uncertainty set of the uncertain parameters.

[0142] (1) Vehicle model uncertainty

[0143] To estimate the required power P veh of the vehicle, the vehicle is approximated as having a frontal area A and a constant air resistance coefficient C d to calculate the air resistance F w . In addition, when calculating the rolling resistance F r , the rolling resistance coefficient C r is considered nominal, but C r depends on many variables such as vehicle speed, tire pressure, and road surface conditions, and it may deviate from its nominal value when the operating conditions change. Therefore, the uncertainty interval is considered in the optimization process, and the uncertain values and

[0144] (2) Uncertainty in power production level

[0145] Battery operating conditions, namely stress factors, temperature variations, gas pressure, extreme driving conditions, oxygen starvation effect, degradation problems, and aging phenomena, can all affect fuel cell system parameters, mainly leading to a decrease in the fc fuel cell efficiency value. The resulting uncertainty must be considered because it can affect the decision-making process and may lead to a non-optimal selection of the outcome non-design variables, denoted by the uncertain efficiency of the fuel cell system.

[0146] Unlike other methods that require probability assignments, in the robust optimization framework, uncertainty is modeled based on a bounded interval called the uncertainty set, where the uncertainty can take any random value. The uncertain parameters are represented by their nominal values and uncertainty values:

[0147]

[0148] is the vector of parameter uncertainty values, and un is the vector of parameter nominal values. The vector α represents the uncertainty associated with each parameter, specifically:

[0149]

[0150] and un P d = [C r , C fc , η

[0151]

[0152] where α sup (i) is the maximum possible value that the uncertainty α(i) can take, and the uncertain parameter takes values according to a symmetric distribution with a mean equal to the nominal value P un (i). The uncertainty set is:

[0153]

[0154] Step 3: Dynamic uncertainty analysis

[0155] Based on the sLSTM algorithm, a sLSTM vehicle speed prediction model is constructed using historical vehicle speed data to predict future driving speeds. Feedback correction is performed according to the difference between the predicted speed and the actual speed, and the predicted speed error within the current prediction time domain is output.

[0156] During the driving process of a vehicle, there are different working conditions such as acceleration, deceleration, idling, and constant speed, that is, the driving speed of the vehicle changes at each moment. Due to different working conditions, the uncertainty corresponding to its speed also changes at any time. Therefore, the uncertainty of the vehicle speed cannot be approximately estimated by a static probability distribution. Due to the error between the predicted speed and the actual speed, it is easy to cause the output optimization result to deviate from the optimal control strategy, or stable control cannot be achieved. The present invention is based on a Scalar Long Short-Term Memory (sLSTM) network for predicting the future vehicle speed and estimating the uncertainty of the predicted speed. This algorithm is a time-recurrent neural network. sLSTM is an extension of the traditional Long Short-Term Memory (LSTM) network. sLSTM uses exponential gating and normalization techniques to improve the stability and accuracy of the model in processing long-sequence data, making it more suitable for processing sequence data with subtle time changes. In this way, sLSTM can provide performance comparable to that of complex models while maintaining a low computational complexity, and is particularly suitable for resource-constrained environments or applications that require quick responses. Using this algorithm can solve the problem of dynamic uncertainty estimation of speed, and can update the dynamic uncertainty of speed in real time while outputting the uncertainty set of the predicted speed.

[0157] The dynamic uncertainty analysis method consists of two parts. The first part is the prediction strategy, and the second part is the feedback correction. The first part mainly trains the sLSTM vehicle speed prediction model based on the historical driving speed of the vehicle, and outputs the predicted vehicle speed based on the vehicle speed prediction model. The second part performs feedback correction according to the difference between the predicted speed and the actual speed at the previous moment. The algorithm principle is as follows:

[0158] The sLSTM architecture has a basic unit called a memory block in its hidden layer. The memory block of sLSTM has one or more memory units, and there are also 3 gates (input gate, output gate, and forget gate).

[0159] First, construct the forget gate, input gate, and output gate, and add the forget gate, input gate, and output gate to the recurrent neural network, so as to construct a speed prediction model based on the long short-term memory network algorithm. Then, according to the historical speed data of the vehicle, calculate the predicted speed of the vehicle through the speed prediction model.

[0160] Based on the predicted speed D output by the sLSTM speed prediction model at time k n On the future time domain with a length of n, specifically:

[0161] D n =[v p (k + 1),..., v p (k + n)] (14)

[0162] Regarding the actual speed value y and the predicted speed value as continuous random variables Y and where there exists a unique Copula function C(.) that satisfies the following equation:

[0163]

[0164] In Equation (15): F Y (y) and are the marginal cumulative distribution functions of the random variables Y and , and is the joint cumulative distribution function of the random variable .

[0165] In the actual prediction process, the distribution types of random variables are unknown, and the assumed marginal distribution types may affect the final joint distribution. To solve this problem, this paper adopts the non-parametric kernel density estimation method to fit the appropriate marginal distribution, and the specific expression is:

[0166]

[0167] In Equation (16): h is the bandwidth, which is used to control the smoothness of the estimation; KER is the kernel function, and X j is the data value of the observed sample.

[0168] Since the estimation error involves two random variables Y and this paper selects the bivariate Copula function to fit the joint distribution of Y and , and the parameters of the bivariate Copula function are obtained by the maximum likelihood estimation method. The joint probability density function of Y and is expressed as:

[0169]

[0170] In Equation (17): θ y and are the unknown parameters involved in the marginal density functions of the random variables Y and ,

[0171] is the corresponding Copula density function, and β is the unknown parameter.

[0172] Through non-parametric and density estimation, based on the actually observed discrete data sequence the empirical cumulative distribution function of the jth sample data can be obtained as and On this basis, the estimated values of the unknown parameters in the Copula density function are:

[0173]

[0174] After estimating the unknown parameters, a Copula function is established, and the conditional probability distribution of Y is obtained as follows:

[0175]

[0176] In Equation (19): is the conditional probability distribution function of the random variable Y under the condition of is the corresponding conditional probability density function, is the probability density function corresponding to the distribution function and is the probability density function corresponding to the distribution function and

[0177] Assume that the prediction speed uncertainty interval is defined as Then the uncertainty interval can be determined by the following formula:

[0178]

[0179] Step 4, Robust Model Predictive Control

[0180] Model predictive control based on robust optimization. The optimization objective of the present invention is to achieve optimal energy management by comprehensively considering multiple performance indicators through a robust model predictive control framework, specifically including: minimizing hydrogen consumption, paying attention to maintaining the health state of the battery, balancing the durability of the fuel cell and the battery, ensuring the robustness and stability of the system, and improving the dynamic performance of the system. By introducing the uncertainty set of uncertain parameters, the optimization algorithm can still maintain good performance under uncertain conditions, ensuring the robustness and stability of the system. The optimization algorithm can also dynamically adjust the output power of the fuel cell according to the predicted speed value and load demand, ensuring that the vehicle can run smoothly under different working conditions and avoiding energy waste or system failures caused by power mismatch.

[0181] The hydrogen fuel cell hybrid vehicle is a nonlinear system. Using the method of model predictive control, according to the optimization objective, an objective function of the control variable is constructed. The objective function is jointly constrained by the uncertainty set and the prediction speed error, and the control variable during driving is solved. First, the speed prediction model is used to predict the driving speed of the vehicle within the future time domain n, and the uncertainty set of uncertain parameters is integrated. As Figure 2 shown, within [k, k + n], the robust optimization algorithm is used to perform uncertain optimization on the objective function to obtain the optimal control sequence within [k, k + n], and the first control result of the optimal control sequence is output.

[0182] The robust model predictive control process proposed by the present invention is as follows Figure 3 shown. The nonlinear system of a hydrogen fuel cell hybrid vehicle can be described as:

[0183] x k+1 = f(x k , u k ) (21)

[0184] where, x k+1 is the state variable at the (k + 1)-th stage; xk and u k are the state variable and control variable at the k-th stage respectively.

[0185]

[0186] where, x and u are the state variable and control variable of the nonlinear system of the hydrogen fuel cell hybrid vehicle respectively, and SOC is the state of charge of the capacitor.

[0187] The cost function of the nonlinear system of the hydrogen fuel cell hybrid vehicle is:

[0188]

[0189] A robust optimization model of the nonlinear system of the hydrogen fuel cell hybrid vehicle is established, and the uncertainty vector α related to the uncertain parameters and the prediction speed uncertainty interval are considered The schematic diagram of its algorithm is as shown in Figure 4 and the algorithm principle is as follows:

[0190] The objective function of the control variable is established as:

[0191]

[0192] The equality constraint conditions are established:

[0193]

[0194] The inequality constraint conditions are established:

[0195] h1(k) = P fc (k) - P fc,min ≥ 0 (29)

[0196] h2(k) = P fc，max - P fc (k) ≥ 0 (30)

[0197] h3(k) = P fc (k) - P fc (k - 1) - AP fc,fall ΔT ≥ 0 (31)

[0198] h4(k) = ΔP fc,rise ΔT - P fc (k) - P fc (k - 1) ≥ 0 (32)

[0199] h5(k) = SOC(k) - SOC min ≥ 0 (33)

[0200] h6(k) = SOC max -SOC(k) ≥ 0 (34)

[0201] where ΔT is the sampling time, P fc,min is the minimum output power of the hydrogen fuel cell, P fc,max is the maximum output power of the hydrogen fuel cell, ΔP fc,fall is the power decline rate limit of the hydrogen fuel cell, ΔP fc,rise is the power rise rate limit of the hydrogen fuel cell, SOC mi n is the minimum state of charge of the capacitor, SOC max is the maximum state of charge of the capacitor.

[0202] Solve the objective function to obtain the optimal control sequence, and output the first control result of the optimal control sequence.

[0203] Apply the first control result to the hydrogen fuel cell hybrid vehicle to control the output power of the fuel cell and achieve vehicle energy management and optimization.

[0204] The training set and test set of the xLSTM speed prediction model are both obtained by collecting road conditions from actual vehicles, covering congested road section conditions, ordinary urban area conditions and highway conditions. The route maps of the training set and test set are as Figure 4 and Figure 5 shown, and the training set and test set are respectively as Figure 6 and Figure 7 shown.

[0205] To verify the effectiveness of the sLSTM - based speed prediction model, a traditional LSTM speed prediction model is selected for a comparative experiment with this model. The root mean square error (RMSE) of the trained models is used to compare the accuracy of the speed prediction results in different historical time domains and different prediction time domains. The smaller the root mean square error of the trained model, the better the corresponding speed prediction result accuracy. Table 1 shows the root mean square error values of the two speed prediction models in different historical time domains and different prediction time domains.

[0206] Table 1 Comparison of Root Mean Square Errors of Speed Prediction Models

[0207]

[0208]

[0209] As can be seen from Table 1, the root mean square error of the sLSTM speed prediction model is lower than that of the traditional LSTM speed prediction model during the entire driving condition, so the corresponding speed prediction result has better accuracy.

Claims

1. An energy management method for a hydrogen fuel cell hybrid vehicle based on robust optimization, characterized in that, It includes the following steps: Step 1: Build a vehicle model, including: establishing a longitudinal dynamics model of a hydrogen fuel cell hybrid vehicle, determining a vehicle demand power model, constructing an evaluation function for instantaneous hydrogen consumption, and constructing an output power model of a hydrogen fuel cell and a capacitor; Step 2: Conduct uncertainty analysis on the hydrogen fuel cell hybrid vehicle, determine the uncertain parameters in the vehicle model, and construct an uncertainty set of the uncertain parameters; Step 3: Based on the sLSTM algorithm, construct an sLSTM vehicle speed prediction model through historical vehicle speed data, predict the future driving speed, analyze the uncertainty of the prediction model, perform feedback correction according to the difference between the predicted speed and the actual speed, and output the prediction speed error within the current prediction time domain; Step 4: According to the optimization objective, construct an objective function for minimizing hydrogen consumption, which is jointly constrained by the uncertainty set and the prediction speed error. Use the speed prediction model to predict the driving speed of the vehicle within the future time domain n, and apply the robust optimization algorithm to perform uncertain optimization and solution on the objective function within [k, k + n] to obtain the optimal control sequence within [k, k + n], and output the first control result of the optimal control sequence.

2. The method according to claim 1, wherein Before establishing the longitudinal dynamics model of the hydrogen fuel cell hybrid vehicle, obtain vehicle parameters, where the vehicle parameters include vehicle parameters and power source parameters; The vehicle parameters include: mass, frontal area, air resistance coefficient, air density, rolling resistance coefficient; The power source parameters include: battery energy, battery capacity, maximum output power of the fuel cell.

3. The method according to claim 1, wherein In Step 1: The vehicle demand power model is specifically: P veh =(F r +F w +F i +F j )u a , Among them, P veh is the required power, F r is the rolling resistance, F w is the air resistance, F i is the gradient resistance, F j is the acceleration resistance, u a is the driving speed; The resistance model of the vehicle is specifically: where m is the vehicle mass, g is the acceleration due to gravity, C r is the rolling resistance coefficient, α is the road slope, C d is the air resistance coefficient, A is the frontal area, ρ is the air density, u a is the driving speed, and is the driving acceleration.

4. The method according to claim 1, wherein In Step 1, the output power model of the hydrogen fuel cell is specifically: P fc = P H η fc , Among them, P fc is the output power of the fuel cell, P H is the hydrogen input power, and η fc is the fuel cell efficiency; Estimate the instantaneously consumed hydrogen C based on the output power and overall efficiency of the fuel cell H2 , specifically as follows: where LHV = 120 mJ / kg is the calorific value of hydrogen; The capacitor module includes individual capacitor units, which are modeled through an equivalent series circuit. The total resistance loss power is established by the following formula, specifically: Among them, P ohm is the resistive loss power, R UC is the series resistance of the capacitor module, I UC is the current of the capacitor module; The provided power P UC Via the original power P UC，r Determined, the resistive loss power P ohm Determined according to the charge / discharge mode, the capacitor output power model is specifically: The state of charge SOC is the most important state variable of the capacitor module, which is expressed by an energy ratio, specifically: Among them, E UC is the available energy in the capacitor module, and E max is the maximum energy of the capacitor module.

5. The method according to claim 1, wherein In Step 2, the determination of the uncertain parameters in the vehicle model includes: To estimate the required power P of the vehicle veh , the vehicle is considered to have a frontal area A and a constant air resistance coefficient C d to approximately calculate the air resistance F w ; during the optimization process, uncertainty intervals are considered, and uncertainty values and Define according to the battery operating conditions representing the uncertain efficiency of the fuel cell system 6. The method according to claim 1, wherein In Step 2, the construction of the uncertainty set of the uncertain parameters includes: Under the robust optimization framework, the uncertain parameters are represented by their nominal values and uncertainty values: is the vector of uncertain parameter values, P un is the vector of nominal parameter values, and α represents a vector containing the uncertainties associated with each parameter, specifically: P un = [C d , C r , η fc , where α sup (i) is the maximum possible value that the uncertainty α(i) can take, and the uncertain parameter takes values according to a symmetric distribution with a mean equal to the nominal value P un (i), and the uncertainty set is:

7. The method according to claim 1, wherein Step 3 specifically includes: Based on the xLSTM algorithm, construct an xLSTM vehicle speed prediction model through historical vehicle speed data; The predicted speed D output by the xLSTM speed prediction model at time k n Over a future time domain of length n, specifically: D n = [v p (k + 1),..., v p (k + n)], The actual speed value y and the predicted speed value are regarded as continuous random variables Y and where there exists a unique Copula function C(.) that satisfies the following equation: Among them, F Y (y) and are the marginal cumulative distribution functions of the random variable Y and , and is the joint cumulative distribution function of the random variable ; Define the prediction speed uncertainty interval as Then the uncertainty interval Can be determined by the following formula:

8. The method according to claim 1, characterized in that In Step 4, before applying the model predictive control method based on robust optimization, construct a hydrogen fuel cell hybrid vehicle nonlinear system: x k+1 = f(x k , u k ), where, x k+1 is the state variable at the (k + 1)-th stage; x k and u k are the state variable and control variable at the k-th stage, respectively; where x and u are the state variables and control variables of the hydrogen fuel cell hybrid vehicle nonlinear system respectively, and SOC is the state of charge of the capacitor; The cost function of the hydrogen fuel cell hybrid vehicle nonlinear system is:

9. The method according to claim 1, characterized in that Step 4 includes: A nonlinear system robust optimization model for a hydrogen fuel cell hybrid vehicle is established, considering the uncertainty vector α related to uncertain parameters and the prediction speed uncertainty interval : Establish an objective function for minimizing hydrogen consumption as: Establish equality constraint conditions: Establish inequality constraint conditions: h1(k) = P fc (k) - P fc,min ≥ 0, h2(k) = P fc，max -P fc (k) ≥ 0, h3(k) = P fc (k) - P fc (k - 1) - ΔP fc，fall ΔT ≥ 0, h4(k) = ΔP fc，rise ΔT - P fc (k) - P fc (k - 1) ≥ 0, h5(k) = SOC(k) - SOC min ≥ 0, h6(k) = SOC max -SOC(k) ≥ 0, where ΔT is the sampling time, P fc，min is the minimum output power of the hydrogen fuel cell, P fc，max is the maximum output power of the hydrogen fuel cell, ΔP fc，fall is the power decline rate limit of the hydrogen fuel cell, ΔP fc，rise is the power rise rate limit of the hydrogen fuel cell, SOC min is the minimum state of charge of the capacitor, SOC max is the maximum state of charge of the capacitor; Solve the objective function to obtain the optimal control sequence, and output the first control result of the optimal control sequence.

10. The method according to claim 1, wherein Apply the first control result to the hydrogen fuel cell hybrid vehicle to control the output power of the fuel cell and achieve vehicle energy management and optimization.

Images