CN111487549B - Lithium battery state estimation method for small-sized rotary wing pure electric unmanned aerial vehicle - Google Patents

Lithium battery state estimation method for small-sized rotary wing pure electric unmanned aerial vehicle Download PDF

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CN111487549B
CN111487549B CN202010249028.4A CN202010249028A CN111487549B CN 111487549 B CN111487549 B CN 111487549B CN 202010249028 A CN202010249028 A CN 202010249028A CN 111487549 B CN111487549 B CN 111487549B
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CN111487549A (en
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汪秋婷
戚伟
沃奇中
肖铎
刘泓
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Zhejiang University City College ZUCC
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/385—Arrangements for measuring battery or accumulator variables
    • G01R31/387—Determining ampere-hour charge capacity or SoC
    • G01R31/388—Determining ampere-hour charge capacity or SoC involving voltage measurements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/378—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC] specially adapted for the type of battery or accumulator

Abstract

The invention relates to a lithium battery state estimation method for a small-sized rotary wing pure electric unmanned aerial vehicle, which comprises the following steps: step 1, predicting the structural design of a system; step 2, calculating the SOC value of the lithium battery in real time based on the internal resistance value of the battery; step 3, establishing an approximate power consumption model of the pure electric unmanned aerial vehicle with the rotary wings and predicting the power consumption; and 4, predicting the end life EOD of the lithium battery. The invention has the beneficial effects that: the method can accurately track the voltage variation trend of the battery, accurately predict the EOD expected value and has high calculation efficiency; the prediction frame structure designed by the invention realizes low hardware cost and stable overall performance; the method is based on a battery equivalent model, and the correlation among the battery load, the temperature and the SOC value is obtained by utilizing an artificial evolution theory; the invention utilizes an external feedback correction loop, introduces a Bayesian estimation method, adjusts the variance value of process noise, reduces the estimation deviation value and compensates the problem that the initial value of a dynamic system is incorrect; the overall function of the lithium battery state estimation method is achieved.

Description

Lithium battery state estimation method for small-sized rotary wing pure electric unmanned aerial vehicle
Technical Field
The invention relates to a lithium battery state estimation method of a small-sized rotary wing pure electric unmanned aerial vehicle, in particular to a lithium battery model building, state of charge estimation and end life estimation method of an unmanned aerial vehicle and a power consumption prediction method based on a model.
Background
The ideal drone is suitable for long-time flight applications, the flight duration of which is directly related to the total weight of the aircraft, and the lithium polymer battery (Li-Po) has high energy density and is generally used as the main power source of a pure electric drone. However, small rotary-wing, electric-only drones face problems and risks associated with battery use, such as temperature, load or aging, and battery endurance. The lithium battery state estimation system mainly achieves reasonable distribution and utilization of storage battery energy and provides real-time diagnosis information of batteries for operators. Therefore, the state estimation system must obtain effective information such as battery state of charge (SOC), Remaining Useful Life (RUL), and power consumption, which are known to be the prerequisite for verifying whether the target task is feasible and are also the key conditions for online work decision.
At present, researchers provide a plurality of battery state models with different granularities and abstraction levels, but the model complexity is high, and parameters which are difficult to calculate need to be identified in actual working conditions. Performance experiments show that high granularity and low abstraction levels can lead to more accurate prediction results, but this method requires a large number of parameter sets to be included in the state vector, reducing convergence performance. The end of life (EOD) of the lithium battery is estimated by using a novel electrochemical model, and the result is accurate and has small uncertainty. However, this method requires off-line estimation of 27 battery parameters, and has high computational complexity and long computation time. Scholars introduce an empirical model based on a Bayesian filtering method, the filtering method can effectively estimate the SOC value of a single battery in real time, and only 7 parameters need to be estimated off line. However, the number of parameter values of this method is insufficient for the Open Circuit Voltage (OCV) curves of a plurality of cells. The load characteristic trend is derived from the drone flight path, i.e., the length and speed of each flight phase (e.g., climb, hover, forward fly, etc.) are used to calculate the likely future load size. However, this method is affected by air density, wind speed, pressure, and temperature, reducing the estimation performance, affecting power efficiency.
Disclosure of Invention
The invention designs a lithium battery state estimation method suitable for a small-sized rotary wing pure electric unmanned aerial vehicle, establishes a lithium battery circuit equivalent model, and realizes state estimation such as lithium battery SOC real-time calculation, end life estimation, power consumption prediction and the like.
The lithium battery state estimation method for the small-sized rotating wing pure electric unmanned aerial vehicle comprises the following steps:
step 1, forecasting the structural design of a system: adopting a model-based prediction architecture, designing a new model to describe the time response of the system to an input vector, wherein the system model is defined as:
x(k+1)＝f(k,x(k),θ(k),u(k),m(k)) (1)
y(k)＝h(k,x(k),θ(k),u(k),n(k)) (2)
in the above formulas (1) to (2),
Figure GDA0003520461230000021
is a state vector, k is a discrete time variable,
Figure GDA0003520461230000022
for the unknown parameter vector to be the vector of parameters,
Figure GDA0003520461230000023
in order to input the vector, the vector is input,
Figure GDA0003520461230000024
in order to be a vector of the process noise,
Figure GDA0003520461230000025
in order to output the vector, the vector is,
Figure GDA0003520461230000026
measuring a noise vector, wherein f is a state equation and h is an output equation;
step 2, calculating the SOC value of the lithium battery in real time based on the internal resistance value of the battery: designing the absolute value calculation and SOC estimation of the internal resistance of the battery based on an artificial evolution algorithm by combining the correlation characteristics of the load, the temperature and the SOC value at the current moment;
step 3, establishing an approximate power consumption model of the pure electric unmanned aerial vehicle with the rotary wings and predicting the power consumption; an ideal model of the power consumption of the unmanned aerial vehicle can be established by utilizing an original aerodynamic model, and the ideal model is used for representing the power consumption under different flight actions, such as climbing, hovering, horizontal flight, descending and the like; establishing an approximate power consumption model based on a momentum theory, wherein the power consumption calculated by the approximate power consumption model is a function of weight, disk drive area, air density, translation speed and maneuvering type; meanwhile, the temperature factor is indirectly contained in the air density;
and 4, predicting the end life EOD of the lithium battery: based on the simplified model and SOC calculated value information of the lithium battery, the predicted value of the EOD of the lithium battery is defined as the operation period that the expected value of the voltage of the lithium battery reaches a threshold value EOD and the failure probability reaches a threshold value gamma (JITP gamma%).
Preferably, the step 1 specifically comprises the following steps:
step 1-1, defining the application basis of a prediction system: the observation history of k sampling times determines joint state parameters, and estimates a state p (x (k), theta (k) | y (k0: k)), wherein k0 is an initial sampling time point; determining a predicted output value at a sampling time point kp and using a probability distribution of p (x (k), θ (k) | y (k0: k));
step 1-2, designing a lithium battery state estimation method framework: in k discrete sampling time periods, the system input is u (k), u (k) is used as the input of the measured system, and the measurement output of the measured system is y (k); y (k) and u (k) as input to an estimation module, which calculates an estimated value p (x (k), θ (k) | y (k0: k)) using u (k), y (k) and a system model; taking p (x (k), θ (k) | y (k0: k)) as input to a prediction module, which calculates a probability distribution p (kp | y (k0: kp)) for time kp using the joint state parameter distribution, the system model, and assumed future input values;
step 1-3, designing an algorithm flow of a lithium battery management system, wherein the algorithm flow comprises an estimation stage and a prognosis stage; the input of the lithium battery management system is u (k), and the output is EOD (end of life) of the lithium battery; the estimation stage and the prognosis stage are both based on a lithium battery simplified model;
the estimation stage utilizes a Bayesian estimator to calculate estimated state values
Figure GDA0003520461230000031
And estimating an error value
Figure GDA0003520461230000032
An external feedback correction loop is introduced in the estimation stage and is used for detecting an error value between an output measurement value and an estimation value; the input of the external feedback correction loop is an observation error value e of a Bayes estimatorobs(k) The output is a stable correction value std (v (k)); the external feedback correction loop reduces the error value by increasing the process noise, reduces the process noise and increases the convergence;
calculating estimated end-life using a Monte Carlo predictor at the prognostic stage
Figure GDA0003520461230000033
Prognostic phase at sampling time point kEDetermining an aerodynamically based power consumption prediction and using the prediction as an auxiliary input value
Figure GDA0003520461230000034
And inputting a lithium battery simplified model and calculating the EOD of the end service life of the lithium battery.
Preferably, the step 2 specifically comprises the following steps:
step 2-1, establishing a state transition equation: assuming discrete characteristics of the dynamic characteristics of the battery, the model structure combines nonlinear characteristics in the OCV curve to realize correction of an observation equation and realize an offline parameter estimation process. Establishing a state equation:
R(k+1)＝R(k)+w1(k) (3)
SOC(k+1)＝SOC(k)-P(k)·Δt·Ecrit(k)-1+w2(k) (4)
Ecrit(k+1)＝Ecrit(k)+w3(k) (5)
in the above formulas (3) to (5), R (k) is internal resistance, SOC (k) is state of charge, P (k) is power, Δ t is time interval, Ecrit(k) For the expected total energy delivered, the SOC (k) is a unique state vector; SOC is the normalized remaining battery energy, normalized to Ecrit；w1(k) And w2(k) Being process noise, w3(k) To measure noise; w is a1(k) And w2(k) Normalized to the process noise vector m (k), w3(k) Normalizing the measured noise vector n (k), and setting the process noise vector m (k) and the measured noise vector n (k) to be Gaussian white noise;
step 2-2, establishing a measurement equation:
U(k)＝ucrit(k)-i(k)·R(k)+n(k) (6)
Figure GDA0003520461230000035
Figure GDA0003520461230000036
in the above formulas (6) to (8), u (k) is a terminal voltage in volts; u. ofcritThe terminal voltage of the equivalent model of the circuit is represented by i (k), and the unit is ampere; r (k) is internal resistance, n (k) is measurement noise vector, uocIs an open circuit voltage uLFor offline terminal voltages, λ, γ, β and μ are model parameters for offline estimation; SOC (k) is state of charge, P (k) is power, in watts; t is sampling time in seconds; taking P (k) and t as input vectors u (k), taking terminal voltage U (k) as output variables y (k), and solving a quadratic equation to obtain:
Figure GDA0003520461230000041
0＝R(k)·(i(k))2-uoc(k)·i(k)+P(k) (10)
in the above formulas (9) to (10), i (k) is a discharge current in ampere; p (k) is power in watts; u. ofocR (k) is an internal resistance value; the time variation of the state of charge soc (k) depends on the voltage measurement, the process noise is correlated to the measurement noise;
step 2-3, calculating initial values of the parameters: before the actual discharge cycle, by measuring the open-circuit voltage uocCalculating the initial value SOC (k) of SOC by combining equation (7)0) (ii) a Meanwhile, under the condition of off-line estimation, an initial internal resistance value R (k) is set0) And initial total energy Ecrit(k0) Is a constant; in the charge-discharge cycle estimation process, establishing a new value for the parameters at each time step by an artificial evolution algorithm;
step 2-4, iteratively calculating a real-time SOC value; and (3) substituting the results obtained by the expressions (9) and (10) into the expression (4), circularly calculating SOC (k), and finishing the calculation when the error value is less than the threshold value epsilon, wherein the formula is determined as delta SOC (k) ═ SOC (k +1) -SOC (k) ≦ epsilon.
Preferably, the step 3 specifically comprises the following steps:
step 3-1: giving the ideal power required by the pure electric unmanned aerial vehicle with the rotary wing when hovering:
Figure GDA0003520461230000042
in the above formula, W is the total weight of the pure electric unmanned aerial vehicle with rotary wings, and W is the no-load operation weight W0With payload weight WPSumming; a is the total area of the disk drive, and A ═ π R2R is the rotor radius; ρ is the air density;
step 3-2, the rotary wing pure electric unmanned aerial vehicle in the step 3-1 is expanded into n rotor rotors, the total weight of the multi-rotor pure electric unmanned aerial vehicle is uniformly distributed on the n rotors, and a power consumption calculation formula suitable for the multi-rotor pure electric unmanned aerial vehicle is established:
Figure GDA0003520461230000043
Figure GDA0003520461230000044
Figure GDA0003520461230000045
in the above formulae (12) to (14), PhTo hover power, PcFor climbing power, PdIn order to reduce power, W is the total weight of the multi-rotor pure electric unmanned aerial vehicle; alpha is the efficiency factor of the propulsion system, and corresponding three equations are respectively alphah，αcAnd alphad(ii) a ρ is the air density, AtIs the sum of the areas of n disc drives, VcFor vertical climbing speed, VdIs the vertical descent speed;
3-3, establishing a calculation formula of the climbing speed and the descending speed: definition of alphacFor climbing the efficiency factor, αdIs as followsThe efficiency reduction factor, the curve formula affecting the efficiency factor is:
αc(Vc)＝a0+a1·cos(Vc·a2)+a3·sin(Vc·a2) (15)
αd(Vd)＝b1·exp(Vd·b1)+b2·exp(Vd·b3) (16)
in the above formulae (15) to (16), a0、a1、a2、a3、b1、b2、b3Are all fitted curve parameters, VcFor vertical climbing speed, VdIs the vertical descent speed;
step 3-4, establishing horizontal flight power PhorThe calculation formula of (2):
Figure GDA0003520461230000051
in the above formula, VhorFor the flight speed of the multi-rotor pure electric unmanned aerial vehicle in the gravity coordinate system, W is the total weight of the multi-rotor pure electric unmanned aerial vehicle, avFor angle of attack for horizontal flight, the initial value is a0，μhorIs an efficiency factor; the calculation formula of the horizontal flying speed is as follows:
Figure GDA0003520461230000052
in the above formula, VhorFor the flight speed of the multi-rotor pure electric unmanned aerial vehicle in a gravity coordinate system, W is the total weight of the multi-rotor pure electric unmanned aerial vehicle, rho is the air density, AtIs the sum of the areas of the n disc drives; angle of attack a for horizontal flightvAnd an efficiency factor muhorAs horizontal flying speed VhorSatisfies the following conditions:
Figure GDA0003520461230000053
μhor(Vhor)＝d0+d1·cos(Vhor·d2)+d3·sin(Vhor·d2) (20)
in the above formulae (19) to (20), avAngle of attack for horizontal flight, VhorFor the flight speed of a multi-rotor pure electric unmanned plane in a gravity coordinate system, c0、c1、c2、c3、d0、d1、d2、d3Are all fitted curve parameters, muhorIs an efficiency factor;
step 3-5, calculating fitting curve parameters: calculating fitting curve parameters by curve fitting by using power consumption required by climbing and descending of the four-rotor pure electric unmanned aerial vehicle without the payload at different speeds;
preferably, the prediction formula for predicting the end life EOD of the lithium battery in step 4 is as follows:
Figure GDA0003520461230000054
Figure GDA0003520461230000061
Figure GDA0003520461230000062
in the above formulas (21) to (23): σ is a probability distribution parameter, r (k) is the probability distribution of RUL at time k, and φ is a non-parametric probability distribution; pi is the range [ sigma ]-，σ+]Total probability mass within, satisfying sigma-＝RUL*(1- σ) and σ+＝RUL*(1+ σ), wherein RUL*Is the true value; EOD is the threshold value of the lithium battery end life EOD, Pr is the abbreviation of a probability calculation formula p (x (k), theta (k) | y (k0: k)), and k0 is the initial sampling time point.
The invention has the beneficial effects that: the invention designs a lithium battery state estimation method of a rotary wing pure electric unmanned aerial vehicle, which utilizes a model-based prediction system structure to establish a circuit equivalent model and an electrochemical equivalent model of a lithium polymer battery and establish SOC estimation and EOD prediction methods based on battery internal resistance; meanwhile, a power consumption prediction method is designed based on aerodynamic characteristics and an unmanned aerial vehicle running track, the voltage variation trend of the battery can be accurately tracked, the EOD expected value can be accurately predicted, and the calculation efficiency is high; the prediction frame structure designed by the invention realizes low hardware cost and stable overall performance; the method is based on a battery equivalent model, and the correlation among the battery load, the temperature and the SOC value is obtained by utilizing an artificial evolution theory; the invention utilizes an external feedback correction loop, introduces a Bayesian estimation method, adjusts the variance value of process noise, reduces the estimation deviation value and compensates the problem that the initial value of a dynamic system is incorrect; the overall function of the lithium battery state estimation method is achieved.
Drawings
FIG. 1 is a block diagram of a model-based prediction system;
FIG. 2 is a flow chart of an algorithm for a lithium battery management system;
FIG. 3(a) is a Bayesian estimation SOC experiment result graph, and FIG. 3(b) is an MC prediction EOD experiment result graph;
fig. 4(a) is a diagram showing an experimental result of a bayesian and OFCL combined estimation SOC value, and fig. 4(b) is a diagram showing an experimental result of an MC prediction EOD.
Detailed Description
The present invention will be further described with reference to the following examples. The following examples are set forth merely to aid in the understanding of the invention. It should be noted that, for a person skilled in the art, several modifications can be made to the invention without departing from the principle of the invention, and these modifications and modifications also fall within the protection scope of the claims of the present invention.
The lithium battery state estimation method for the small-sized rotating wing pure electric unmanned aerial vehicle comprises the following steps:
step 1, forecasting the structural design of a system: adopting a model-based prediction architecture, designing a new model to describe the time response of the system to an input vector, wherein the system model is defined as:
x(k+1)＝f(k,x(k),θ(k),u(k),m(k)) (1)
y(k)＝h(k,x(k),θ(k),u(k),n(k)) (2)
in the above formulas (1) to (2),
Figure GDA0003520461230000071
is a state vector, k is a discrete time variable,
Figure GDA0003520461230000072
for the unknown parameter vector to be the vector of parameters,
Figure GDA0003520461230000073
in order to input the vector, the vector is input,
Figure GDA0003520461230000074
in order to be a vector of the process noise,
Figure GDA0003520461230000075
in order to output the vector, the vector is,
Figure GDA0003520461230000076
measuring a noise vector, wherein f is a state equation and h is an output equation;
FIG. 1 is a model-based framework of a predictive system, and in particular, a framework of a predictive system for designing lithium battery management strategies based on battery models; the framework is divided into a measured system and a prediction system; the measured system is a lithium battery application system of the pure electric unmanned aerial vehicle, and the prediction system is a battery mathematical model, a model parameter estimation module and an SOC/EOD prediction module.
Step 2, calculating the SOC value of the lithium battery in real time based on the internal resistance value of the battery: designing the absolute value calculation and SOC estimation of the internal resistance of the battery based on an artificial evolution algorithm by combining the correlation characteristics of the load, the temperature and the SOC value at the current moment;
step 3, establishing an approximate power consumption model of the pure electric unmanned aerial vehicle with the rotary wings and predicting the power consumption; an ideal model of the power consumption of the unmanned aerial vehicle can be established by utilizing an original aerodynamic model, and the ideal model is used for representing the power consumption under different flight actions, such as climbing, hovering, horizontal flight, descending and the like; establishing an approximate power consumption model based on a momentum theory, wherein the power consumption calculated by the approximate power consumption model is a function of weight, disk drive area, air density, translation speed and maneuvering type; meanwhile, the temperature factor is indirectly contained in the air density;
and 4, predicting the end life EOD of the lithium battery: based on the simplified model and SOC calculated value information of the lithium battery, the predicted value of the EOD of the lithium battery is defined as the operation period that the expected value of the voltage of the lithium battery reaches a threshold value EOD and the failure probability reaches a threshold value gamma (JITP gamma%).
The step 1 specifically comprises the following steps:
step 1-1, defining the application basis of a prediction system: the observation history of k sampling times determines joint state parameters, and estimates a state p (x (k), theta (k) | y (k0: k)), wherein k0 is an initial sampling time point; determining a predicted output value at a sampling time point kp and using a probability distribution of p (x (k), θ (k) | y (k0: k));
step 1-2, designing a lithium battery state estimation method framework: in k discrete sampling time periods, the system input is u (k), u (k) is used as the input of the measured system, and the measurement output of the measured system is y (k); y (k) and u (k) as input to an estimation module, which calculates an estimated value p (x (k), θ (k) | y (k0: k)) using u (k), y (k) and a system model; taking p (x (k), θ (k) | y (k0: k)) as input to a prediction module, which calculates a probability distribution p (kp | y (k0: kp)) for time kp using the joint state parameter distribution, the system model, and assumed future input values;
step 1-3, designing an algorithm flow of a lithium battery management system, wherein the algorithm flow comprises an estimation stage and a prognosis stage; the input of the lithium battery management system is u (k), and the output is EOD (end of life) of the lithium battery; the estimation stage and the prognosis stage are both based on a lithium battery simplified model;
the estimation stage utilizes a Bayesian estimator to calculate estimated state values
Figure GDA0003520461230000081
And estimating an error value
Figure GDA0003520461230000082
An external feedback correction loop is introduced in the estimation stage and is used for detecting an error value between an output measurement value and an estimation value; the input of the external feedback correction loop is an observation error value e of a Bayes estimatorobs(k) The output is a stable correction value std (v (k)); the external feedback correction loop reduces the error value by increasing the process noise, reduces the process noise and increases the convergence;
calculating estimated end-life using a Monte Carlo predictor at the prognostic stage
Figure GDA0003520461230000083
Prognostic phase at sampling time point kEDetermining an aerodynamically based power consumption prediction and using the prediction as an auxiliary input value
Figure GDA0003520461230000084
And inputting a lithium battery simplified model and calculating the EOD of the end service life of the lithium battery.
The step 2 specifically comprises the following steps:
step 2-1, establishing a state transition equation: assuming discrete characteristics of the dynamic characteristics of the battery, the model structure combines nonlinear characteristics in the OCV curve to realize correction of an observation equation and realize an offline parameter estimation process. Establishing a state equation:
R(k+1)＝R(k)+w1(k) (3)
SOC(k+1)＝SOC(k)-P(k)·Δt·Ecrit(k)-1+w2(k) (4)
Ecrit(k+1)＝Ecrit(k)+w3(k) (5)
in the above formulas (3) to (5), R (k) is internal resistance, SOC (k) is state of charge, P (k) is power, Δ t is time interval, Ecrit(k) For the expected total energy delivered, the SOC (k) is a unique state vector; the SOC is the normalized remaining battery energy,normalized to Ecrit；w1(k) And w2(k) Being process noise, w3(k) To measure noise; w is a1(k) And w2(k) Normalized to the process noise vector m (k), w3(k) Normalizing the measured noise vector n (k), and setting the process noise vector m (k) and the measured noise vector n (k) to be Gaussian white noise;
step 2-2, establishing a measurement equation:
U(k)＝ucrit(k)-i(k)·R(k)+n(k) (6)
Figure GDA0003520461230000085
Figure GDA0003520461230000086
in the above formulas (6) to (8), u (k) is a terminal voltage in volts; u. ofcritThe terminal voltage of the equivalent model of the circuit is represented by i (k), and the unit is ampere; r (k) is internal resistance, n (k) is measurement noise vector, uocIs an open circuit voltage uLFor offline terminal voltages, λ, γ, β and μ are model parameters for offline estimation; SOC (k) is state of charge, P (k) is power, in watts; t is sampling time in seconds; taking P (k) and t as input vectors u (k), taking terminal voltage U (k) as output variables y (k), and solving a quadratic equation to obtain:
Figure GDA0003520461230000091
0＝R(k)·(i(k))2-uoc(k)·i(k)+P(k) (10)
in the above formulas (9) to (10), i (k) is a discharge current in ampere; p (k) is power in watts; u. ofocR (k) is an internal resistance value; the time variation of the state of charge soc (k) depends on the voltage measurement, the process noise is correlated to the measurement noise;
step 2-3, calculating initial values of the parameters: fruit of Chinese wolfberryBy measuring the open-circuit voltage u before the cycle of the dischargeocCalculating the initial value SOC (k) of SOC by combining equation (7)0) (ii) a Meanwhile, under the condition of off-line estimation, an initial internal resistance value R (k) is set0) And initial total energy Ecrit(k0) Is a constant; in the charge-discharge cycle estimation process, establishing a new value for the parameters at each time step by an artificial evolution algorithm;
step 2-4, iteratively calculating a real-time SOC value; and (3) substituting the results obtained by the expressions (9) and (10) into the expression (4), circularly calculating SOC (k), and finishing the calculation when the error value is less than the threshold value epsilon, wherein the formula is determined as delta SOC (k) ═ SOC (k +1) -SOC (k) ≦ epsilon.
The step 3 specifically comprises the following steps:
step 3-1: giving the ideal power required by the pure electric unmanned aerial vehicle with the rotary wing when hovering:
Figure GDA0003520461230000092
in the above formula, W is the total weight of the pure electric unmanned aerial vehicle with rotary wings, and W is the no-load operation weight W0With payload weight WPSumming; a is the total area of the disk drive, and A ═ π R2R is the rotor radius; ρ is the air density;
step 3-2, the rotary wing pure electric unmanned aerial vehicle in the step 3-1 is expanded into n rotor rotors, the total weight of the multi-rotor pure electric unmanned aerial vehicle is uniformly distributed on the n rotors, and a power consumption calculation formula suitable for the multi-rotor pure electric unmanned aerial vehicle is established:
Figure GDA0003520461230000093
Figure GDA0003520461230000094
Figure GDA0003520461230000101
in the above formulae (12) to (14), PhTo hover power, PcFor climbing power, PdIn order to reduce power, W is the total weight of the multi-rotor pure electric unmanned aerial vehicle; alpha is the efficiency factor of the propulsion system, and corresponding three equations are respectively alphah，αcAnd alphad(ii) a ρ is the air density, AtIs the sum of the areas of n disc drives, VcFor vertical climbing speed, VdIs the vertical descent speed;
3-3, establishing a calculation formula of the climbing speed and the descending speed: definition of alphacFor climbing the efficiency factor, αdTo decrease the efficiency factor, the curve formula affecting the efficiency factor is:
αc(Vc)＝a0+a1·cos(Vc·a2)+a3·sin(Vc·a2) (15)
αd(Vd)＝b1·exp(Vd·b1)+b2·exp(Vd·b3) (16)
in the above formulae (15) to (16), a0、a1、a2、a3、b1、b2、b3Are all fitted curve parameters, VcFor vertical climbing speed, VdIs the vertical descent speed;
step 3-4, establishing horizontal flight power PhorThe calculation formula of (2):
Figure GDA0003520461230000102
in the above formula, VhorFor the flight speed of the multi-rotor pure electric unmanned aerial vehicle in the gravity coordinate system, W is the total weight of the multi-rotor pure electric unmanned aerial vehicle, avFor angle of attack for horizontal flight, the initial value is a0，μhorIs an efficiency factor; the calculation formula of the horizontal flying speed is as follows:
Figure GDA0003520461230000103
in the above formula, VhorFor the flight speed of the multi-rotor pure electric unmanned aerial vehicle in a gravity coordinate system, W is the total weight of the multi-rotor pure electric unmanned aerial vehicle, rho is the air density, AtIs the sum of the areas of the n disc drives; angle of attack a for horizontal flightvAnd an efficiency factor muhorAs horizontal flying speed VhorSatisfies the following conditions:
Figure GDA0003520461230000104
μhor(Vhor)＝d0+d1·cos(Vhor·d2)+d3·sin(Vhor·d2) (20)
in the above formulae (19) to (20), avAngle of attack for horizontal flight, VhorFor the flight speed of a multi-rotor pure electric unmanned plane in a gravity coordinate system, c0、c1、c2、c3、d0、d1、d2、d3Are all fitted curve parameters, muhorIs an efficiency factor;
step 3-5, calculating fitting curve parameters: the method comprises the steps of calculating fitting curve parameters through curve fitting by utilizing the power consumption required by climbing and descending of the four-rotor pure electric unmanned aerial vehicle without the payload at different speeds, wherein the values of the fitting curve parameters are shown in table 1, and i represents the number of the rotors.
TABLE 1 fitting Curve parameter values
i at bt ct dt
0 0.08842 0.5 0.4493 0.5691
1 1.289 0.03347 -0.02917 -0.0906
2 -0.07359 0.3904 1.037 -0.04085
3 0.006595 0.0236 -0.02318 2.488
And 4, the prediction formula for predicting the EOD of the lithium battery is as follows:
Figure GDA0003520461230000111
Figure GDA0003520461230000112
Figure GDA0003520461230000113
in the above formulas (21) to (23): σ is a probability distribution parameter, r (k) is the probability distribution of RUL at time k, and φ is a non-parametric probability distribution; pi is the range [ sigma ]-，σ+]Total probability mass within, satisfying sigma-＝RUL*(1- σ) and σ+＝RUL*(1+ σ), wherein RUL*Is the true value; EOD is the threshold value of the lithium battery end life EOD, Pr is the abbreviation of a probability calculation formula p (x (k), theta (k) | y (k0: k)), and k0 is the initial sampling time point.
Experimental result 1:
fig. 3 shows the experimental results of calculating the SOC value by the bayesian estimator and estimating the EOD by the monte carlo predictor (MC) based on the circuit equivalent model, and fig. 4 shows the experimental results of calculating the SOC value by the bayesian estimation/loop correction (bayes + OFCL) combination and estimating the EOD by the MC predictor based on the circuit equivalent model. As can be seen from fig. 3 and 4:
(1) the SOC value is estimated by the two methods, the time period is 500s-600s, and the error value is maximum;
(2) the Bayes + OFCL joint estimation method starts to converge to a true value at the 800s moment, but the Bayes estimation method has no good convergence effect;
(3) the two methods predict EOD, and the 95% confidence coefficient is between 1200 and 1300;
(4) the SOC value is obtained by Bayes + OFCL combined estimation, and the EOD prediction result is more accurate.
Experimental results 2:
table 2 shows the average of 50 predicted samples using different cell models, different estimation methods and prediction methods, with SOC values selected to be 75%, 50% and 25%.
Table 250 average of predicted sample values
Figure GDA0003520461230000121
As can be seen from Table 2:
(1) the time value of the EOD based on the circuit model prediction is smaller than that of the EOD based on the electrochemical model prediction, and the error probability is minimized;
(2) based on a circuit model and a Bayes + OFCL joint estimation method,
Figure GDA0003520461230000122
both reach 100%, in the other two cases, the value decays;
(3) three estimation and prediction methods, failure probability time JITP5％Equivalent parameter values, JITP of electrochemical model when SOC value is 25%5％The parameter values are significantly larger than the other two methods.

Claims (3)

1. A lithium battery state estimation method for a small-sized rotary wing pure electric unmanned aerial vehicle is characterized by comprising the following steps:
step 1, forecasting the structural design of a system: adopting a model-based prediction architecture, designing a new model to describe the time response of the system to an input vector, wherein the system model is defined as:
x(k+1)＝f(k,x(k),θ(k),u(k),m(k)) (1)
y(k)＝h(k,x(k),θ(k),u(k),n(k)) (2)
in the above formulas (1) to (2),
Figure FDA0003479726370000011
is a state vector, k is a discrete time variable,
Figure FDA0003479726370000012
for the unknown parameter vector to be the vector of parameters,
Figure FDA0003479726370000013
in order to input the vector, the vector is input,
Figure FDA0003479726370000014
in order to be a vector of the process noise,
Figure FDA0003479726370000015
in order to output the vector, the vector is,
Figure FDA0003479726370000016
measuring a noise vector, wherein f is a state equation and h is an output equation;
step 2, calculating the SOC value of the lithium battery in real time based on the internal resistance value of the battery: designing the absolute value calculation and SOC estimation of the internal resistance of the battery based on an artificial evolution algorithm by combining the correlation characteristics of the load, the temperature and the SOC value at the current moment;
step 2-1, establishing a state transition equation: assuming discrete characteristics of the battery dynamic characteristics, a state equation is established:
R(k+1)＝R(k)+w1(k) (3)
SOC(k+1)＝SOC(k)-P(k)ΔtEcrit(k)-1+w2(k) (4)
Ecrit(k+1)＝Ecrit(k)+w3(k) (5)
in the above formulas (3) to (5), R (k) is internal resistance, SOC (k) is state of charge, P (k) is power, Δ t is time interval, Ecrit(k) For the expected total energy delivered, the SOC (k) is a unique state vector; SOC is the normalized remaining battery energy, normalized to Ecrit；w1(k) And w2(k) Being process noise, w3(k) To measure noise; w is a1(k) And w2(k) Normalized to the process noise vector m (k), w3(k) Normalizing the measured noise vector n (k), and setting the process noise vector m (k) and the measured noise vector n (k) to be Gaussian white noise;
step 2-2, establishing a measurement equation:
U(k)＝ucrit(k)-i(k)R(k)+n(k) (6)
Figure FDA0003479726370000017
Figure FDA0003479726370000018
in the above formulas (6) to (8), u (k) is a terminal voltage in volts; u. ofcritThe terminal voltage of the equivalent model of the circuit is represented by i (k), and the unit is ampere; r (k) is internal resistance, n (k) is measurement noise vector, uocIs an open circuit voltage uLFor offline terminal voltages, λ, γ, β and μ are model parameters for offline estimation; SOC (k) is state of charge, P (k) is power, in watts; t is sampling time in seconds; taking P (k) and t as input vectors u (k), taking terminal voltage U (k) as output variables y (k), and solving a quadratic equation to obtain:
Figure FDA0003479726370000021
0＝R(k)(i(k))2-uoc(k)·i(k)+P(k) (10)
in the above formulas (9) to (10), i (k) is a discharge current in ampere; p (k) is power in watts; u. ofocR (k) is an internal resistance value; the time variation of the state of charge soc (k) depends on the voltage measurement, the process noise is correlated to the measurement noise;
step 2-3, calculating initial values of the parameters: before the actual discharge cycle, by measuring the open-circuit voltage uocCalculating the initial value SOC (k) of SOC by combining equation (7)0) (ii) a Meanwhile, under the condition of off-line estimation, an initial internal resistance value R (k) is set0) And initial total energy Ecrit(k0) Is a constant; in the charge-discharge cycle estimation process, establishing a new value for the parameters at each time step by an artificial evolution algorithm;
step 2-4, iteratively calculating a real-time SOC value; substituting the results obtained by the formulas (9) and (10) into the formula (4), circularly calculating SOC (k), and finishing the calculation when the error value is less than the threshold value epsilon, wherein the formula is that delta SOC (k) is SOC (k +1) -SOC (k) is less than or equal to epsilon;
step 3, establishing an approximate power consumption model of the pure electric unmanned aerial vehicle with the rotary wings and predicting the power consumption; establishing an approximate power consumption model based on a momentum theory, wherein the power consumption calculated by the approximate power consumption model is a function of weight, disk drive area, air density, translation speed and maneuvering type; meanwhile, the temperature factor is indirectly contained in the air density;
step 3-1: giving the ideal power required by the pure electric unmanned aerial vehicle with the rotary wing when hovering:
Figure FDA0003479726370000022
in the above formula, W is the total weight of the pure electric unmanned aerial vehicle with rotary wings, and W is the no-load operation weight W0With payload weight WPSumming; a is the total area of the disk drive, and A ═ π R2R is the rotor radius; ρ is the air density;
step 3-2, the rotary wing pure electric unmanned aerial vehicle in the step 3-1 is expanded into n rotor rotors, the total weight of the multi-rotor pure electric unmanned aerial vehicle is uniformly distributed on the n rotors, and a power consumption calculation formula suitable for the multi-rotor pure electric unmanned aerial vehicle is established:
Figure FDA0003479726370000031
Figure FDA0003479726370000032
Figure FDA0003479726370000033
in the above formulae (12) to (14), PhTo hover power, PcFor climbing power, PdIn order to reduce power, W is the total weight of the multi-rotor pure electric unmanned aerial vehicle; alpha is the efficiency factor of the propulsion system,corresponding to three equations respectively as alphah，αcAnd alphad(ii) a ρ is the air density, AtIs the sum of the areas of n disc drives, VcFor vertical climbing speed, VdIs the vertical descent speed;
3-3, establishing a calculation formula of the climbing speed and the descending speed: definition of alphacFor a climbing efficiency factor, α d is a descending efficiency factor, and the curve formula affecting the efficiency factor is:
αc(Vc)＝a0+a1·cos(Vc·a2)+a3·sin(Vc·a2) (15)
αd(Vd)＝b1·exp(Vd·b1)+b2·exp(Vd·b3) (16)
in the above formulae (15) to (16), a0、a1、a2、a3、b1、b2、b3Are all fitted curve parameters, VcFor vertical climbing speed, VdIs the vertical descent speed;
step 3-4, establishing horizontal flight power PhorThe calculation formula of (2):
Figure FDA0003479726370000034
in the above formula, VhorFor the flight speed of the multi-rotor pure electric unmanned aerial vehicle in the gravity coordinate system, W is the total weight of the multi-rotor pure electric unmanned aerial vehicle, avFor angle of attack for horizontal flight, the initial value is a0，μhorIs an efficiency factor; the calculation formula of the horizontal flying speed is as follows:
Figure FDA0003479726370000035
in the above formula, VhorFor the flight speed of the multi-rotor pure electric unmanned plane in a gravity coordinate system, W is the multi-rotor pure electric unmanned planeTotal weight of unmanned aerial vehicle, ρ is air density, AtIs the sum of the areas of the n disc drives; angle of attack a for horizontal flightvAnd an efficiency factor muhorAs horizontal flying speed VhorSatisfies the following conditions:
Figure FDA0003479726370000041
μhor(Vhor)＝d0+d1·cos(Vhor·d2)+d3·sin(Vhor·d2) (20)
in the above formulae (19) to (20), avAngle of attack for horizontal flight, VhorFor the flight speed of a multi-rotor pure electric unmanned plane in a gravity coordinate system, c0、c1、c2、c3、d0、d1、d2、d3Are all fitted curve parameters, muhorIs an efficiency factor;
step 3-5, calculating fitting curve parameters: calculating fitting curve parameters by curve fitting by using power consumption required by climbing and descending of the four-rotor pure electric unmanned aerial vehicle without the payload at different speeds;
and 4, predicting the end life EOD of the lithium battery: based on the simplified model and SOC calculated value information of the lithium battery, the predicted value of the EOD of the end service life of the lithium battery is defined as the expected value of the voltage of the lithium battery reaching a threshold value EOD, and meanwhile, the operation period that the fault probability reaches a threshold value gamma is specified.
2. The lithium battery state estimation method for the small-sized rotary wing pure electric unmanned aerial vehicle according to claim 1, wherein the step 1 specifically comprises the following steps:
step 1-1, defining the application basis of a prediction system: the observation history of k sampling times determines joint state parameters, and estimates a state p (x (k), theta (k) | y (k0: k)), wherein k0 is an initial sampling time point; determining a predicted output value at a sampling time point kp and using a probability distribution of p (x (k), θ (k) | y (k0: k));
step 1-2, designing a lithium battery state estimation method framework: in k discrete sampling time periods, the system input is u (k), u (k) is used as the input of the measured system, and the measurement output of the measured system is y (k); y (k) and u (k) as input to an estimation module, which calculates an estimated value p (x (k), θ (k) | y (k0: k)) using u (k), y (k) and a system model; taking p (x (k), θ (k) | y (k0: k)) as input to a prediction module, which calculates a probability distribution p (kp | y (k0: kp)) for time kp using the joint state parameter distribution, the system model, and assumed future input values;
step 1-3, designing an algorithm flow of a lithium battery management system, wherein the algorithm flow comprises an estimation stage and a prognosis stage; the input of the lithium battery management system is u (k), and the output is EOD (end of life) of the lithium battery; the estimation stage and the prognosis stage are both based on a lithium battery simplified model;
the estimation stage utilizes a Bayesian estimator to calculate estimated state values
Figure FDA0003479726370000042
And estimating an error value
Figure FDA0003479726370000043
An external feedback correction loop is introduced in the estimation stage and is used for detecting an error value between an output measurement value and an estimation value; the input of the external feedback correction loop is an observation error value e of a Bayes estimatorobs(k) The output is a stable correction value std (v (k)); the external feedback correction loop reduces the error value by increasing the process noise, reduces the process noise and increases the convergence;
calculating estimated end-life using a Monte Carlo predictor at the prognostic stage
Figure FDA0003479726370000051
Prognostic phase at sampling time point kEDetermining an aerodynamically based power consumption prediction and using the prediction as an auxiliary input value
Figure FDA0003479726370000052
Input lithium batterySimplifying the model and calculating the EOD of the lithium battery.
3. The lithium battery state estimation method for the small-sized rotary wing pure electric unmanned aerial vehicle according to claim 1, wherein the prediction formula for predicting the end life EOD of the lithium battery in the step 4 is as follows:
Figure FDA0003479726370000053
Figure FDA0003479726370000054
Figure FDA0003479726370000055
in the above formulas (21) to (23): σ is a probability distribution parameter, r (k) is the probability distribution of RUL at time k, and φ is a non-parametric probability distribution; pi is the range [ sigma ]-，σ+]Total probability mass within, satisfying sigma-＝RUL*(1- σ) and σ+＝RUL*(1+ σ), wherein RUL*Is the true value; EOD is the threshold value of the lithium battery end life EOD, Pr is the abbreviation of a probability calculation formula p (x (k), theta (k) | y (k0: k)), and k0 is the initial sampling time point.
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