CN111342477B - Four-order electric power system chaotic control method for bidirectionally optimizing BP neural network sliding mode variable structure - Google Patents

Four-order electric power system chaotic control method for bidirectionally optimizing BP neural network sliding mode variable structure Download PDF

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CN111342477B
CN111342477B CN202010080833.9A CN202010080833A CN111342477B CN 111342477 B CN111342477 B CN 111342477B CN 202010080833 A CN202010080833 A CN 202010080833A CN 111342477 B CN111342477 B CN 111342477B
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neural network
sliding mode
power system
variable structure
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CN111342477A (en
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吕艳玲
张雨辰
王硕
侯仕强
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Harbin University of Science and Technology
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    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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Abstract

The invention discloses a four-order power system chaotic control method for a bidirectional optimization BP neural network sliding mode variable structure. The invention controls the chaotic oscillation of the power system by using a control method combining bidirectional optimization BP neural network and sliding mode variable structure control on the basis of a fourth-order chaotic mathematical model of the power system. In the neural network, the excitation function used in the forward direction and the learning rate used in the reverse direction of the algorithm are respectively optimized, so that the buffeting phenomenon controlled by the sliding mode variable structure is effectively inhibited, and the chaotic oscillation control is more ideal; compared with the traditional sliding mode variable structure control, the method disclosed by the invention not only keeps the excellent characteristics of the BP neural network and the sliding mode variable structure control, but also more effectively weakens the buffeting phenomenon of the sliding mode variable structure control on the premise of overcoming the false saturation phenomenon of the neural network, improving the generalization capability and reasonably accelerating the learning process, so that the chaotic control of the power system obtains a better effect.

Description

Four-order electric power system chaotic control method for bidirectionally optimizing BP neural network sliding mode variable structure
Technical Field
The invention relates to the technical field of four-order electric power system chaotic control, in particular to a four-order electric power system chaotic control method for bidirectionally optimizing a BP neural network sliding mode variable structure.
Background
With the development trend that large power grids are interconnected and long-distance power transmission becomes a contemporary power grid, the structure of a power system is increasingly complex. As a typical nonlinear system, the nonlinearity of the power system itself will generate chaotic oscillation under specific conditions, which is represented as aperiodic and irregular low-frequency oscillation, and meanwhile, the chaotic oscillation phenomenon may occur in the system during operation due to an emergency and uncertain factors. At present, the phenomenon of low-frequency oscillation is observed for many times at home and abroad, wherein the harm caused by chaotic oscillation is not ignored. When the electric power system generates chaotic oscillation, if the chaotic oscillation cannot be timely inhibited, the stability among interconnected systems is reduced, even serious chain accidents are easily caused, so that large-scale power failure is caused, the safety and the stability of the normal operation of the electric power system are influenced, and economic loss and even personal safety are threatened.
At present, research aiming at the control of a nonlinear system has become a hot problem of domestic and foreign research. In the continuous exploration of chaotic control, people accumulate a great deal of valuable experience. Among a plurality of control methods, the sliding mode variable structure control method can overcome the uncertainty of the system, has strong robustness to interference and unmodeled dynamics, and particularly has good control effect on the control of a nonlinear system. In addition, the characteristics of simple algorithm, high response speed and strong robustness to external noise interference and parameter perturbation of the variable structure control system are also the reasons for making the sliding mode variable structure control method one of the nonlinear system control methods which are widely applied at present. Meanwhile, according to the existing research conclusion, the control method has a relatively ideal control effect on the chaotic oscillation of the power system.
The sliding mode variable structure control enables the state of the control system to reach the switching plane within a limited time by selecting the switching plane and reach a control target along the switching plane. In the control method, the variable structure control system movement comprises two parts, namely approach movement outside the switching surface and sliding movement on the switching surface, and the system is not influenced by external interference and parameter change after entering sliding mode movement, so that the control method has complete robustness.
However, in an actual sliding mode variable structure control system, due to the influence of factors such as time lag and inertia of the switching device, when the state of the system reaches the sliding mode surface, the system does not keep sliding movement on the sliding mode surface, but does traversing movement back and forth near the sliding mode surface, even generates limit ring oscillation, and the phenomenon is called buffeting. It may excite unmodeled high-frequency components in the system to cause high-frequency oscillation of the system. Therefore, suppressing or eliminating such buffeting is an important issue to be solved in sliding mode variable structure control.
Currently, many efforts have been made to solve the problem of buffeting in sliding mode variable structure control systems and some more effective solutions have been proposed, but in practice the results are not significant. With the continuous development of intelligent control, the application of the neural network becomes a hot research direction in the world at present under the assistance of a computer, and the control of the sliding mode variable structure of the neural network is generated at the beginning. At present, a plurality of research results show that after the neural network is combined with the sliding mode variable structure control, the buffeting phenomenon in the sliding mode variable structure is effectively weakened.
The main contribution of neural networks is to provide a non-linear static mapping that can approximate any given non-linear relationship with any degree of accuracy. As one of the neural networks with wide application, there are some problems, such as false saturation of the neural network, insufficient generalization capability, and unsatisfactory learning speed, which directly affect the application effect of the neural network, and even the jitter problem of the sliding mode variable structure cannot be solved after the sliding mode variable structure control is combined, so that the requirement of ideally controlling chaotic oscillation cannot be met.
Disclosure of Invention
The invention provides a four-order electric power system chaotic control method for bidirectionally optimizing a BP neural network sliding mode variable structure, aiming at realizing four-order electric power system chaotic control of the bidirectionally optimizing BP neural network sliding mode variable structure, and the invention provides the following technical scheme:
a four-order electric power system chaotic control method for a bidirectional optimization BP neural network sliding mode variable structure comprises the following steps:
step 1: establishing a four-order power system chaotic mathematical model, and establishing a controlled system after simplifying the four-order power system chaotic mathematical model;
step 2: determining a system initial state and a target balance point, and determining a relation function between a coefficient of an exponential approximation law and a sliding hyperplane according to the system initial state and the target balance point;
and step 3: carrying out BP neural bidirectional optimization on the basis of integrally selecting a Sigmoid excitation function;
and 4, step 4: selecting single-input and single-output data samples of the neural network according to the relation function in the step 2, and training the bidirectional optimized BP neural network;
and 5: and (3) approximating the relation function in the step (2) according to the application of the trained bidirectional optimization BP neural network in the sliding mode variable structure, and controlling chaotic oscillation in the fourth-order power system.
Preferably, the step 1 specifically comprises:
step 1.1: the four-order power system chaos mathematical model is represented by the following formula:
Figure BDA0002380254410000031
wherein, deltamIs the power angle, omega, of the generatorsIs the slip angular frequency, delta is the node voltage phase angle, U node voltage amplitude, Q1For loading reactive power, PmFor mechanical input of power, dmFor damping coefficient, M is an inertia constant, M is related to the generator, EmIs generator electromotive force, E'0Is network transient electromotive force, Y'0Is a network admittance parameter, θ'0Is the network impedance angle, YmFor generator admittance parameters, thetamIs the generator impedance angle, Q0For constant reactive power of the system, T is a simplified load parameter of a four-order power system, Kqω、Kqv2Simplifying the load reactive parameters, K, for a four-stage power systempvAnd KpωSimplifying the load active parameter, P, for a four-stage power system0For constant active power of the system, P1Active power for the load;
step 1.2: the method comprises the following steps of establishing a controlled system after simplifying a four-order power system chaos mathematical model, and representing the simplified controlled system through the following formula:
Figure BDA0002380254410000032
wherein, KiAnd HiTo simplify the parameters, uiFor the control amount, i is 1,2,3, 4.
Preferably, an initial state of the system is selected, and the selected initial state of the system is represented by the following formula:
[δm,ωs,δ,U]＝[0.3,0,0.2,0.97]
the system target balance point is represented by:
Figure BDA0002380254410000033
determining an exponential approximation law, wherein the exponential approximation law is represented by the following formula:
Figure BDA0002380254410000034
Figure BDA0002380254410000035
Figure BDA0002380254410000041
Figure BDA0002380254410000042
wherein eta isiIs an exponential approximation law coefficient, k is an exponential approximation law constant value,
Figure BDA0002380254410000043
the derivative of the system state, n ═ 1,2,3, 4.
Preferably, when(s)1-0.3366) < 0, where s10Setting the system for a finite time for the initial value of the system state
Figure BDA0002380254410000044
From the negative state to the zero state, s is in this time1Become η1Is represented by the following formula1Eta of1Function of (c):
Figure BDA0002380254410000045
when(s)1-0.3366) > 0, at
Figure BDA0002380254410000046
During this time s1Eta of1The function of (d) is:
Figure BDA0002380254410000047
wherein the content of the first and second substances,
Figure BDA0002380254410000048
in order to be of limited duration,
Figure BDA0002380254410000049
the initial value of the system state in the positive state for the first system variable,
Figure BDA00023802544100000410
the initial value of the system state in the negative state is the first system variable.
Preferably, the relation function between the coefficient of the exponential approximation law and the sliding hyperplane is determined according to the initial state of the system and the target balance point, and the relation function between the coefficient of the exponential approximation law and the sliding hyperplane is expressed by the following formula:
Figure BDA00023802544100000411
wherein the content of the first and second substances,
Figure BDA00023802544100000412
is a relation ηj-sjThe parameters are simplified, and the parameters are simplified,
Figure BDA00023802544100000413
is a relation ηj-sjReduction of the parameter, sjFor the jth system state of the system, ajAnd j is a preset value of the jth sliding mode surface, and j is 1,2,3 and 4.
Preferably, the step 3 specifically comprises:
step 3.1: and (3) performing forward optimization, selecting a Sigmoid excitation function by the forward optimization BP neural network, and expressing the Sigmoid excitation function by the following formula:
Figure BDA00023802544100000414
wherein f (x) is a Sigmoid excitation function;
replacing the excitation function hidden in the Sigmoid with an excitation function with a logistic mapping equation, and representing the replaced mechanism function by the following formula:
fc(x)＝μx(1-x)；
wherein mu is a variable parameter and x is an input variable;
step 3.2: performing reverse optimization, optimizing the learning rate lambda, and expressing the optimized learning rate lambda by the following formula:
Figure BDA0002380254410000051
where α ∈ (1.1,1.3) is an enhanced learning rate coefficient, e (i) is an objective function, λ (i) is a learning rate, and β ∈ (0.7,0.9) is a weakened learning rate coefficient.
The invention has the following beneficial effects:
the generalization ability of the neural network can be improved by adding noise in a learning sample, the excitation function in the form of the logistic mapping equation used in the invention has chaotic characteristics, and the chaos and the noise have many similarities in properties and forms, so that fc(x) The existence of (2) is equivalent to adding noise inside the network so as to improve generalization capability.
The invention uses the control to control the chaotic oscillation of the fourth-order power system, theoretically, the chaotic oscillation in the fourth-order power system can be effectively controlled while the buffeting in the variable structure is ideally weakened.
In the neural network, the excitation function used in the forward direction and the learning rate used in the reverse direction of the algorithm are respectively optimized, so that the buffeting phenomenon controlled by the sliding mode variable structure is effectively inhibited, and the chaotic oscillation control is more ideal; compared with the traditional sliding mode variable structure control, the method disclosed by the invention not only keeps the excellent characteristics of the BP neural network and the sliding mode variable structure control, but also more effectively weakens the buffeting phenomenon of the sliding mode variable structure control on the premise of overcoming the false saturation phenomenon of the neural network, improving the generalization capability and reasonably accelerating the learning process, so that the chaotic control of the power system obtains a better effect.
Drawings
FIG. 1 is a flow chart of bi-directional optimized BP neural network learning;
FIG. 2 is a flow chart of bi-directional optimized BP neural network offline training;
FIG. 3 is a structural diagram of a sliding mode control system of a bidirectional optimized BP neural network;
fig. 4 is an equivalent circuit of the power system.
Detailed Description
The present invention will be described in detail with reference to specific examples.
The first embodiment is as follows:
the invention provides a four-order electric power system chaotic control method for a bidirectional optimization BP neural network sliding mode variable structure, which comprises the following steps:
step 1: establishing a four-order power system chaotic mathematical model, and establishing a controlled system after simplifying the four-order power system chaotic mathematical model;
as shown in fig. 4, the fourth-order chaotic mathematical model of the power system in step 1 is:
Figure BDA0002380254410000061
wherein
Figure BDA0002380254410000062
Power angle delta of generatormAngular frequency of slip ωsNode voltage phase angle delta, node voltage amplitude U, load reactive power Q1And mechanical input power Pm，dmFor damping coefficient, M is an inertia constant, M is related to the generator, EmIs generator electromotive force, E'0Is network transient electromotive force, Y'0Is a network admittance parameter, θ'0Is the network impedance angle, YmFor generator admittance parameters, thetamIs the generator impedance angle, Q0For constant reactive power of the system, T is a simplified load parameter of a four-order power systemNumber, Kqω、Kqv2Simplifying the load reactive parameters, K, for a four-stage power systempvAnd KpωSimplifying the load active parameter, P, for a four-stage power system0For constant active power of the system, P1Is the load active power.
Further, carrying out parametric degeneration on the mathematical model in the step 1 to establish a controlled system:
Figure BDA0002380254410000063
wherein
Figure BDA0002380254410000064
Figure BDA0002380254410000065
Figure BDA0002380254410000066
Figure BDA0002380254410000067
Figure BDA0002380254410000071
uiFor the control amount, i is 1,2,3, 4.
Step 2: determining a system initial state and a target balance point, and determining a relation function between a coefficient of an exponential approximation law and a sliding hyperplane according to the system initial state and the target balance point;
determining the initial state of the system in the step 2 as [ delta ]m,ωs,δ,U]＝[0.3,0,0.2,0.97]The target balance point is
Figure BDA0002380254410000072
Further, an exponential approximation law is obtained according to step 2:
Figure BDA0002380254410000073
Figure BDA0002380254410000074
Figure BDA0002380254410000075
Figure BDA0002380254410000076
Figure BDA0002380254410000077
the derivative of the system state, also used to express the exponential approach law, is 1,2,3, 4.
When(s)1-0.3366) < 0, solved according to high-order knowledge:
Figure BDA0002380254410000078
wherein s is10Setting the system at a given finite time for the initial value of the system state
Figure BDA0002380254410000079
From the negative state to the zero state, and the value of k is properly selected, s is obtained in the period of time1Become η1Function of (c):
Figure BDA00023802544100000710
in the same way, when(s)1-0.3366) > 0, at
Figure BDA00023802544100000711
During this time s1About η1The function of (d) is:
Figure BDA00023802544100000712
wherein the content of the first and second substances,
Figure BDA00023802544100000713
the initial value of the system state in the positive state for the first system variable,
Figure BDA00023802544100000714
the initial value of the system state in the negative state is the first system variable.
Similarly, the function of η with respect to s when in other cases is:
Figure BDA0002380254410000081
Figure BDA0002380254410000082
Figure BDA0002380254410000083
order to
Figure BDA0002380254410000084
When j is 1,2,3,4, the above equation is:
Figure BDA0002380254410000085
order to
Figure BDA0002380254410000086
The function of the conversion η with respect to s is then:
Figure BDA0002380254410000087
the above equation is a relation function to be approximated by the bi-directional optimized BP neural network,
Figure BDA0002380254410000088
is a relation ηj-sjThe parameters are simplified, and the parameters are simplified,
Figure BDA0002380254410000089
is a relation ηj-sjReduction of the parameter, sjFor the jth system state of the system, ajAnd j is a preset value of the jth sliding mode surface, and j is 1,2,3 and 4.
And step 3: carrying out BP neural bidirectional optimization on the basis of integrally selecting a Sigmoid excitation function;
for variable structure control, the control quantity is composed of two parts, one part is an approaching control quantity u in the process of approaching the sliding mode surfacesvThe other part is an equivalent control quantity u of the system moving on the sliding mode surfaceeqAnd the reason for generating buffeting is to approach the control quantity, so a bidirectional optimization BP neural network is selected to carry out the approximation of the relation function, and the learning flow chart is shown in FIG. 1. In the forward direction, a stimulus function is selected as a Sigmoid function on the traditional BP neural network, and the form of the stimulus function is as follows:
Figure BDA00023802544100000810
further, a few Sigmoid excitation functions in the hidden layer are replaced by excitation functions in the form of a logistic mapping equation, the logistic mapping equation is a typical nonlinear dynamics discrete chaotic mapping system, the parameter x belongs to (0,1), and when 3.5699. < mu ≦ 4, the system is in a chaotic state. The substituted excitation function can be expressed as:
fc(x)＝μx(1-x)
wherein mu is a variable parameter, and the value of mu is 3.5699. mu.less than or equal to 4, and x is an input variable.
Since the neural network has self-adaptability and fault tolerance, changing a few excitation functions in the hidden layer does not have great influence on the neural network. By using the Sigmoid function as the excitation function, a problem of "false saturation phenomenon" may exist in the neural network, that is, the weight cannot be adjusted smoothly, so that the convergence of the learning process is slow or even cannot be converged (the weight variation Δ ω ≈ 0). Due to the addition of f having chaotic characteristicsc(x) Therefore, even if the excitation functions of other neurons in the network enter the saturation region, the whole network is in fc(x) Also has strong weight adjustment capability (individual weight variation Δ ω [. omega. ])cLarger) to take the entire network out of false saturation. Currently, there are efforts to show that adding noise to learning samples can improve the generalization ability of neural networks. The excitation function in the form of the logistic mapping equation used in the present invention has chaotic characteristics, and chaos and noise have many similarities in nature and form, so fc(x) The existence of (2) is equivalent to adding noise inside the network so as to improve generalization capability. In addition, though fc(x) Different from the form of Sigmoid excitation function, but the input quantity has the same value range as the Sigmoid excitation function, and is between 0 and 1, which is also expressed by fc(x) The important reason for optimization.
When the traditional BP algorithm is adopted, the learning rate lambda is a fixed value, and if the learning rate lambda is too large, the learning speed is accelerated and vibration may be generated in the learning process; if the value is too small, stability is ensured but learning speed is ignored. In the reverse direction, therefore, the principle that the learning rate λ adaptively adjusts its gradient according to the objective function is optimized, and the algorithm is described as follows:
Figure BDA0002380254410000091
where α ∈ (1.1,1.3) is the reinforcement learning rate coefficient, β ∈ (0.7,0.9) is the attenuation learning rate coefficient, E (i) is the objective function, and λ (i) is the learning rate.
And 4, step 4: selecting single-input and single-output data samples of the neural network according to the relation function in the step 2, and training the bidirectional optimized BP neural network;
and 5: and (3) approximating the relation function in the step (2) according to the application of the trained bidirectional optimization BP neural network in the sliding mode variable structure, and controlling chaotic oscillation in the fourth-order power system.
Further, as shown in fig. 2, a sufficient number of data samples of single input and single output of the neural networks are selected in a reasonable range through a relation function of the approximation law coefficient η in the step 2 with respect to the sliding mode surface s, and the bi-directional optimization BP neural network is trained offline. The obtained trained neural network is applied to sliding mode variable structure control, as shown in fig. 3, the control is used for controlling the chaotic oscillation of the fourth-order power system, and theoretically, the chaotic oscillation of the fourth-order power system can be effectively controlled while the buffeting in the variable structure is ideally weakened.
The above description is only a preferred embodiment of the four-order power system chaotic control method for bidirectionally optimizing the sliding mode variable structure of the BP neural network, and the protection range of the four-order power system chaotic control method for bidirectionally optimizing the sliding mode variable structure of the BP neural network is not limited to the above embodiments, and all technical schemes belonging to the idea belong to the protection range of the invention. It should be noted that modifications and variations which do not depart from the gist of the invention will be those skilled in the art to which the invention pertains and which are intended to be within the scope of the invention.

Claims (5)

1. A four-order electric power system chaotic control method for bidirectionally optimizing a BP neural network sliding mode variable structure is characterized by comprising the following steps of: the method comprises the following steps:
step 1: establishing a four-order power system chaotic mathematical model, and establishing a controlled system after simplifying the four-order power system chaotic mathematical model;
step 2: determining a system initial state and a target balance point, and determining a relation function between a coefficient of an exponential approximation law and a sliding hyperplane according to the system initial state and the target balance point;
and step 3: carrying out BP neural bidirectional optimization on the basis of integrally selecting a Sigmoid excitation function;
and 4, step 4: selecting single-input and single-output data samples of the neural network according to the relation function in the step 2, and training the bidirectional optimized BP neural network;
and 5: according to the fact that the trained bidirectional optimization BP neural network is applied to the sliding mode variable structure to approximate the relation function in the step 2, chaotic oscillation in the fourth-order power system is controlled;
the step 1 specifically comprises the following steps:
step 1.1: the four-order power system chaos mathematical model is represented by the following formula:
Figure FDA0003313957700000011
wherein, deltamIs the power angle, omega, of the generatorsIs the slip angular frequency, delta is the node voltage phase angle, U node voltage amplitude, Q1For loading reactive power, PmFor mechanical input of power, dmFor damping coefficient, M is an inertia constant, M is related to the generator, EmIs generator electromotive force, E'0Is network transient electromotive force, Y'0Is a network admittance parameter, θ'0Is the network impedance angle, YmFor generator admittance parameters, thetamIs the generator impedance angle, Q0For constant reactive power of the system, T is a simplified load parameter of a four-order power system, Kqω、Kqv2Simplifying the load reactive parameters, K, for a four-stage power systempvAnd KpωSimplifying the load active parameter, P, for a four-stage power system0For constant active power of the system, P1Active power for the load;
step 1.2: the method comprises the following steps of establishing a controlled system after simplifying a four-order power system chaos mathematical model, and representing the simplified controlled system through the following formula:
Figure FDA0003313957700000021
wherein, KdAnd HdTo simplify the parameters, uiFor the control amount, i is 1,2,3, 4.
2. The four-order electric power system chaotic control method for the bidirectional optimization BP neural network sliding mode variable structure according to claim 1, characterized in that: selecting an initial state of the system, wherein the selected initial state of the system is represented by the following formula:
[δm,ωs,δ,U]＝[0.3,0,0.2,0.97]
the system target balance point is represented by:
Figure FDA0003313957700000022
determining an exponential approximation law, wherein the exponential approximation law is represented by the following formula:
Figure FDA0003313957700000023
Figure FDA0003313957700000024
Figure FDA0003313957700000025
Figure FDA0003313957700000026
wherein eta isiIs an exponential approximation law coefficient, k is an exponential approximation law constant value,
Figure FDA0003313957700000027
the derivative of the state of the system is,n＝1,2,3,4。
3. the four-order electric power system chaotic control method for the bidirectional optimization BP neural network sliding mode variable structure according to claim 1, characterized in that: when(s)1-0.3366) < 0, wherein s10Setting the system for a finite time for the initial value of the system state
Figure FDA00033139577000000214
From the negative state to the zero state, s is in this time1Become η1Is represented by the following formula1Eta of1Function of (c):
Figure FDA0003313957700000028
when(s)1-0.3366) > 0, at
Figure FDA0003313957700000029
During this time s1Eta of1The function of (d) is:
Figure FDA00033139577000000210
wherein the content of the first and second substances,
Figure FDA00033139577000000211
in order to be of limited duration,
Figure FDA00033139577000000212
the initial value of the system state in the positive state for the first system variable,
Figure FDA00033139577000000213
the initial value of the system state in the negative state is the first system variable.
4. The four-order electric power system chaotic control method for the bidirectional optimization BP neural network sliding mode variable structure according to claim 1, characterized in that: determining a relation function of the coefficient of the exponential approximation law and the sliding hyperplane according to the initial state of the system and the target balance point, and expressing the relation function of the coefficient of the exponential approximation law and the sliding hyperplane by the following formula:
Figure FDA0003313957700000031
wherein the content of the first and second substances,
Figure FDA0003313957700000032
is a relation ηj-sjThe parameters are simplified, and the parameters are simplified,
Figure FDA0003313957700000033
is a relation ηj-sjReduction of the parameter, sjFor the jth system state of the system, ajAnd j is a preset value of the jth sliding mode surface, and j is 1,2,3 and 4.
5. The four-order electric power system chaotic control method for the bidirectional optimization BP neural network sliding mode variable structure according to claim 1, characterized in that: the step 3 specifically comprises the following steps:
step 3.1: and (3) performing forward optimization, selecting a Sigmoid excitation function by the forward optimization BP neural network, and expressing the Sigmoid excitation function by the following formula:
Figure FDA0003313957700000034
wherein f (x) is a Sigmoid excitation function;
replacing the excitation function hidden in the Sigmoid with an excitation function with a logistic mapping equation, and representing the replaced mechanism function by the following formula:
fc(x)＝μx(1-x)；
wherein mu is a variable parameter and x is an input variable;
step 3.2: performing reverse optimization, optimizing the learning rate lambda, and expressing the optimized learning rate lambda by the following formula:
Figure FDA0003313957700000035
where α ∈ (1.1,1.3) is an enhanced learning rate coefficient, e (i) is an objective function, λ (i) is a learning rate, and β ∈ (0.7,0.9) is a weakened learning rate coefficient.
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