A lithium ion battery remaining useful life prediction method based on BO-LSTM

Abstract

The present application relates to a kind of BO-LSTM-based lithium ion battery remaining useful life prediction method, to solve the problem of inaccurate battery remaining cycle number prediction in underwater vehicle power system, provide reference for the remaining cycle number prediction of battery.The characteristics are:1.the battery is subjected to charge-discharge cycle test and is divided into training set and test set2.the connection between battery health and remaining useful life is established;3.BO-LSTM model is established;4.data is substituted into BO-LSTM algorithm model, and the remaining useful life of battery is predicted.The method of the present application combines the good fitting ability of LSTM neural network algorithm with the excellent optimization ability of bayesian optimization algorithm, providing a more accurate method for predicting the remaining useful life of lithium ion battery, so that the remaining useful life of lithium ion battery can be more accurately predicted.

Description

Technical Field

[0001] This invention belongs to the field of energy and power application research technology for underwater vehicles, and relates to a method for predicting the remaining service life of lithium-ion batteries based on BO-LSTM. Background Technology

[0002] Lithium-ion batteries are widely used in the power energy field. During use, the decline in various performance parameters can lead to irreversible losses such as battery failure and explosion. Therefore, predicting the remaining lifespan of lithium-ion batteries is necessary.

[0003] Current prediction methods generally rely on indirect feature parameters, which accumulate errors during the prediction of Remaining Useful Life (RUL). This paper, based on the relationship between Remaining Useful Life (RUL) and State of Health (SOH), constructs a Bayesian long and short-term memory (BO-LSTM) neural network algorithm to predict RUL in a single prediction process, thus improving prediction accuracy. Summary of the Invention

[0004] Technical problems to be solved

[0005] To avoid the shortcomings of existing technologies, this invention proposes a method for predicting the remaining lifespan of lithium-ion batteries based on BO-LSTM, which solves the problem of inaccurate prediction of the remaining cycle count of batteries in underwater vehicle power systems and provides a reference for predicting the remaining cycle count of batteries.

[0006] Technical solution

[0007] Step 1: Conduct charge-discharge cycle tests on the battery to obtain the total number of cycles after battery failure, and divide the total number of cycles into a training set and a test set;

[0008] The number of training sets is the top 80% or top 90% of the total number of iterations;

[0009] The number of test sets is the total number of iterations minus the number of training sets;

[0010] Step 2: Calculate battery health:

[0011]

[0012] in, This represents the initially measured discharge capacity. Let be the discharge capacity measured in real time for the i-th time;

[0013] Step 3: Input the battery health data into the BO-LSTM algorithm model to predict the remaining battery life:

[0014] Step 3.1: Use the battery health data from Step 2 as the initial input sample for the BO-LSTM neural network model, and randomly generate initialization samples;

[0015] Step 3.2: Perform Gaussian calculation on the initialized sample points to obtain the mean and variance of the objective function:

[0016] Step 3.3: Input the mean and variance of the objective function into the EI sampling function, and select the next set of sample points to be evaluated from the corrected Gaussian model output by the sampling function. ;

[0017] The sample evaluation points are input into the LSTM model for training to obtain new output values ​​of the objective function. , with output value Update the sample set, i.e., the set of battery health scores. And Gaussian model;

[0018] Step 3.4: Repeat the iteration, within the set number of iterations, outputting the value each time. Update sample set And Gaussian model;

[0019] When the iteration terminates, the sampling function outputs the optimal set of battery health parameters and the corresponding loss value of the objective function of the LSTM model. ;

[0020] A collection of battery health information Half of the number is the predicted cycle life of the battery.

[0021] The process of conducting a charge-discharge cycle test on the battery is as follows: set the battery failure threshold, conduct a charge-discharge cycle test on the battery at room temperature, and obtain the total number of cycles required to cause battery failure.

[0022] The failure threshold of the battery is 80% of its initial capacity.

[0023] The sample set in step 3 The accuracy of the model algorithm is verified by comparing the total number of battery cycles obtained in step 1 with the total number of charge-discharge cycle tests.

[0024] The BO-LSTM algorithm model: uses a multiplication gate, which is also the input gate. Forgotten Gate and output gate The storage units are connected together; the LSTM algorithm performs forward and backward propagation. Forward propagation uses an activation function, and backward propagation uses the backpropagation algorithm to calculate gradients. In the following calculation process... Represents neurons arrive The weights between them express Time neuron Activation function, express The LSTM algorithm inputs data to neurons at specific times. The value. Subscript , , and These represent the input gate, forget gate, output gate, and... A memory unit, Let represent the activation functions of the three multiplication gates. and Let these represent the input activation function and the output activation function of the neuron, respectively. express Time memory unit The state of memory modules, the interconnections between memory modules are determined by the output of the neurons themselves. This is achieved, and the activation functions of the three multiplication gates in the memory module only work internally. The LSTM neural network algorithm includes the following steps:

[0025] Step 1): The input sequence is The duration is The forward propagation of the LSTM algorithm is based on It begins to increase until, over time, the equations for forward calculation are also updated accordingly; while backward calculation starts with... Starting from this point, it continuously decreases until... According to the backward inference formula of the RNN algorithm, the final weights are... The derivative value is expressed as:

[0026]

[0027] Among them, when and At that time, all expressions and activation functions in the network are set to 0;

[0028] Step 2): The forward propagation equation of the LSTM algorithm is as follows:

[0029] Input gate exist Expression for time:

[0030]

[0031] Forgotten Gate exist Expression for time:

[0032]

[0033] Memory unit in Expression for time:

[0034]

[0035] Output gate exist Expression for time:

[0036]

[0037] Step 3): Backpropagation equations for the LSTM algorithm, let...

[0038] Memory unit in The output value at time t is:

[0039] Output gate exist Expression for time:

[0040] The state at any given moment:

[0041] The derivative value of the weight of the memory cell is:

[0042] Forgotten Gate The derivative of the weights is:

[0043] Input gate The derivative of the weights is: .

[0044] The Gaussian operation process in steps 3.2 to 3.4: Establishing the Bayesian global optimization algorithm:

[0045]

[0046] in, Represents an unknown objective function; Represents the set of observed parameters and observations. ; This represents the observed data; Represents the observed value; express The posterior probability; express The likelihood distribution; Indicated The prior probability; Indicated The marginal likelihood distribution;

[0047] The observed value is the battery capacity value measured during each charge-discharge cycle.

[0048] The Bayesian algorithm comprises two core processes: a probabilistic surrogate model and a sampling function. The probabilistic surrogate model is a probabilistic model used to represent the unknown objective function. By iteratively increasing the amount of information, the prior probability is continuously corrected, making the surrogate model more accurate. The sampling function, based on the posterior distribution, samples from the region most likely to contain the global optimum and the unsampled region, selecting the most "potential" sample point from the candidate set to minimize the loss function value. Specifically, it includes the following steps:

[0049] Step (1): The Gaussian process is composed of a mean function And a positive semidefinite covariance function The Gaussian distribution is represented in the following form:

[0050]

[0051] in, express The mathematical expectation of the mean function is usually set to 0. Indicates the mean absolute error; express The covariance function;

[0052] Step (2): The explored historical information is ,in The next value to be searched is covariance matrix It is written as follows:

[0053]

[0054] Step (3): and All of them follow a joint Gaussian distribution with a mean of 0, and their joint Gaussian distribution is expressed as follows:

[0055]

[0056] in, ;

[0057] Step (4): Calculate the edge density function to obtain... Posterior probability:

[0058]

[0059] Among them, the mean and variance The calculation formulas are as follows:

[0060]

[0061]

[0062] Estimate The sample point follows a normal distribution at any given value, and a sampling function is used to locate the next optimal sample point.

[0063] Step (5): For The mean and variance are used for sample calculation, and the EI collection function for sampling is:

[0064]

[0065] in, Let be the probability density function of the standard normal distribution. Let be the distribution function of the standard normal distribution, where Represented as:

[0066]

[0067] Step (6): Add a weighted scalar to the EI algorithm And satisfy The EI acquisition function with a value greater than 0 is as follows:

[0068]

[0069] .

[0070] Beneficial effects

[0071] This invention proposes a method for predicting the remaining lifespan of lithium-ion batteries based on BO-LSTM, aiming to solve the problem of inaccurate prediction of the remaining cycle count of batteries in underwater vehicle propulsion systems, and providing a reference for predicting the remaining cycle count of batteries. Its features include: 1. Conducting charge-discharge cycle tests on the battery and dividing it into training and test sets; 2. Establishing the relationship between battery health and remaining lifespan; 3. Establishing a BO-LSTM model; 4. Substituting the data into the BO-LSTM algorithm model to predict the remaining lifespan of the battery. This invention combines the good fitting ability of the LSTM neural network algorithm with the excellent optimization ability of the Bayesian optimization algorithm, providing a more accurate method for predicting the remaining lifespan of lithium-ion batteries, thus enabling more accurate predictions of their remaining lifespan. Attached Figure Description

[0072] Figure 1 This is a flowchart illustrating the implementation process of the present invention.

[0073] Figure 2 Flowchart for Step 4

[0074] Figure 3 The estimation results of the first group of batteries with different training set sample sizes are shown in the figure.

[0075] Figure 4 The estimation results of the second group of batteries with different training set sample numbers are shown in the figure. Detailed Implementation

[0076] The present invention will now be further described in conjunction with the embodiments and accompanying drawings:

[0077] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below through specific embodiments and in conjunction with the accompanying drawings. Figure 1 This is a flowchart illustrating the implementation process of the present invention.

[0078] Table 1. Charge-discharge cycle test conditions arrangement

[0079] Table 2 Comparison of prediction performance of the first group of batteries with different training set sample sizes

[0080] Table 3 Comparison of prediction performance for the second group of batteries with different training set sample sizes

[0081] This invention relates to a method for predicting the remaining lifespan of lithium-ion batteries based on BO-LSTM, comprising the following steps:

[0082] Step 1. Conduct charge-discharge cycle tests on the battery and divide it into training and test sets, including the following steps:

[0083] Step 1.1: Conduct a charge-discharge cycle test on the battery at room temperature;

[0084] Step 1.2: Set the battery failure threshold to 80% of the initial capacity. The charge-discharge cycle test conditions are arranged as shown in Table 1. After the battery fails during the charge-discharge cycle test, the total number of cycles will be counted.

[0085] Step 1.3: Set the first 80% and first 90% of the total number of iterations as the number of training sets, respectively;

[0086] Step 1.4: The total number of iterations minus the number of training sets equals the number of test sets.

[0087] Step 2. Battery health is an indicator of battery performance; generally, a health level of 0.8 indicates battery failure. Remaining lifespan is the remaining normal operating cycle from now until the battery capacity declines to the failure threshold. Establishing the relationship between battery health and remaining lifespan includes the following steps;

[0088] Step 2.1: Obtain the capacity data related to the remaining battery life, i.e., the battery capacity, from the charge-discharge cycle test in Step 1;

[0089] Step 2.2: Among the obtained battery-related parameters, select battery capacity as the input parameter and calculate battery health. The formula for calculating battery health is as follows:

[0090] (1)

[0091] in, This represents the initially measured discharge capacity. Let be the discharge capacity measured in real time for the i-th time.

[0092] Battery health is equal to the ratio of the capacity measured in the i-th time to the initial capacity; the calculated value is the battery health at time i. Battery health is an indicator of battery performance; a battery health of 0.8 is considered faulty and unusable. This section was unclear and has been explained in step 2.

[0093] Step 3. Establish the BO-LSTM model, including the following steps:

[0094] Step 3.1: LSTM Neural Network Algorithm Steps: The LSTM algorithm has corresponding memory modules, which are established through multiplication gates (input gates). Forgotten Gate and output gate The LSTM algorithm connects the memory cells. It can perform forward and backward propagation. Forward propagation uses an activation function, while backward propagation uses the backpropagation algorithm to calculate gradients. The following calculations... Represents neurons arrive The weights between them express Time neuron Activation function, express The LSTM algorithm inputs data to neurons at specific times. The value. Subscript , , and These represent the input gate, forget gate, output gate, and... A memory unit, Let represent the activation functions of the three multiplication gates. and Let these represent the input activation function and the output activation function of the neuron, respectively. express Time memory unit The state of memory modules, the interconnections between memory modules are determined by the output of the neurons themselves. This is achieved, and the activation functions of the three multiplication gates in the memory module only work internally. The LSTM neural network algorithm includes the following steps:

[0095] Step 3.1.1: Assume an input sequence is The duration is The forward propagation of the LSTM algorithm is based on It begins to increase until, over time, the forward calculation equations are also updated accordingly. The backward calculation, on the other hand, starts with... Starting from this point, it continuously decreases until... According to the backward inference formula of the RNN algorithm, the final weights... The derivative value can be expressed as:

[0096] (2)

[0097] Among them, when and At that time, all expressions and activation functions in the network are set to 0.

[0098] Step 3.2.2: The forward propagation equation of the LSTM algorithm is as follows:

[0099] Input gate exist Expression for time:

[0100] (3)

[0101] (4)

[0102] Forgotten Gate exist Expression for time:

[0103] (5)

[0104] (6)

[0105] Memory unit in Expression for time:

[0106] (7)

[0107] (8)

[0108] Output gate exist Expression for time:

[0109] (9)

[0110] (10)

[0111] Step 3.2.3: Backpropagation equations of the LSTM algorithm

[0112] Assumption

[0113] (11)

[0114] Memory unit in The output value at time t is:

[0115] (12)

[0116] Output gate exist Expression for time:

[0117] (13)

[0118] The state at any given moment:

[0119] (14)

[0120] The derivative of the weights of the memory cells is:

[0121] (15)

[0122] Forgotten Gate The derivative of the weights is:

[0123] (16)

[0124] Input gate The derivative of the weights is:

[0125] (17)

[0126] Step 3.2: Establish the Bayesian global optimization algorithm, which can be expressed as the following formula:

[0127] (18)

[0128] in, Represents an unknown objective function; Represents the set of observed parameters and observations. ; This represents the observed data, specifically the battery capacity value measured during each charge-discharge cycle. Represents the observed value; express The posterior probability; express The likelihood distribution; Indicated The prior probability; Indicated The marginal likelihood distribution. The Bayesian algorithm comprises two core processes: a probabilistic surrogate model and a sampling function. The probabilistic surrogate model is a probabilistic model used to represent the unknown objective function. Through iterative increases in information, the prior probability is continuously revised, making the surrogate model more accurate. The sampling function, based on the posterior distribution, samples from the region most likely to contain the global optimum and unsampled regions, selecting the most "potential" sample point from the candidate set to minimize the loss function value. It includes the following steps:

[0129] Step 3.2.1: Gaussian Processes (GPs) can solve the problem of flexibly establishing a distribution in the objective function before using Bayesian optimization. A Gaussian process is a commonly used nonparametric probabilistic surrogate model; the generated multidimensional Gaussian distribution can simulate the appearance of any objective function.

[0130] A Gaussian process is a set of random variables in which any linear combination of samples from the set has a joint Gaussian distribution. The core of a Gaussian process is a mean function. And a positive semidefinite covariance function Composition. The Gaussian distribution can be represented in the following form:

[0131] (19)

[0132] in, express The mathematical expectation of the mean function is usually set to 0. Indicates the mean absolute error; express The covariance function.

[0133] Step 3.2.2: Assume that historical information that has been explored has already been obtained. ,in The next value to be searched is covariance matrix It is written as follows:

[0134] (20)

[0135] Step 3.2.3: Based on the properties of Gaussian processes, and All of them follow a joint Gaussian distribution. Assuming their mean is 0, their joint Gaussian distribution can be expressed as follows:

[0136] ( twenty one )

[0137] in,

[0138] Step 3.2.4: By calculating its edge density function, we can obtain... Posterior probability:

[0139] ( twenty two )

[0140] Among them, the mean and variance The calculation formulas are as follows:

[0141] ( twenty three )

[0142] ( twenty four )

[0143] After the above series of calculations, we can estimate... The sample follows a normal distribution at any given value, so a sampling function can be used to locate the next optimal sample point.

[0144] Step 3.2.5: After establishing the model through the Gaussian processes in steps 3.2.1 to 3.2.4, we can obtain... The mean and variance are calculated, and then sampling is required for sample calculation. The design idea of ​​the Excepted Improvement (EI) sampling function is to find the next sample point that maximizes the expected improvement. The EI acquisition function is:

[0145] (25)

[0146] in, Let be the probability density function of the standard normal distribution. Let be the distribution function of the standard normal distribution, where It can be represented as:

[0147] (26)

[0148] Step 3.2.6: The EI algorithm can incorporate a weighted scalar. (satisfy The EI acquisition function for >0 is shown below:

[0149] (27)

[0150] (28)

[0151] Step 4. Substitute the data into the BO-LSTM algorithm model to predict the remaining battery life. Figure 2 To implement the flowchart, the following steps are included:

[0152] Step 4.1: Import data: Use the battery health data from Step 2 as the input sample for the initial BO-LSTM model;

[0153] Step 4.2: Sample Initialization: Substitute the input data from Step 4.1 into the LSTM neural network model from Step 3.1. Randomly generate initial samples according to the range of the LSTM model hyperparameters.

[0154] The hyperparameters involved in the LSTM algorithm's lithium-ion battery remaining life estimation model mainly include: learning rate, number of hidden layer neurons, number of iterations, etc. These hyperparameters are determined according to requirements.

[0155] Step 4.3: Gaussian process: Input the initialized sample points into the Gaussian process in step 3.2.1, and calculate the mean and variance of the objective function;

[0156] The LSTM model is trained, and the loss value output by the objective function of the LSTM model is used to correct the Gaussian model, making the Gaussian model closer to the true function distribution.

[0157] Step 4.4: Sampling Function Selection: Input the mean and variance of the objective function obtained from the Gaussian process into the sampling function in Step 3.2.5, and use the sampling function to select the next set of sample points to be evaluated from the modified Gaussian model. ;

[0158] Sample evaluation points The input is fed into the LSTM model for training to obtain a new output value for the objective function. This is used to update the sample set, i.e., the battery health. And the Gaussian model.

[0159] Step 4.5: LSTM Model Training: When the number of iterations reaches a sufficient number, the algorithm terminates and exits. The sampling function outputs the optimal parameter combination and the corresponding loss value of the LSTM model's objective function. .

[0160] Step 4.6: When the newly selected sample points If the corresponding objective function loss value does not meet the requirements, then... Update to sample set In the next step, skip to step 4.3 and continue to modify the Gaussian model until the requirements are met.

[0161] Battery health Half of that is the battery's cycle life;

[0162] Verification: Use the sample set obtained in step 4.6 The accuracy of the model algorithm is verified by comparing the total number of battery cycles obtained in step 1.2 with the total number of charge-discharge cycle tests.

[0163] The estimation results of the number of samples in different training sets for the two battery groups are shown in the figure below. Figures 3-4 As shown, the prediction performance comparisons for the two battery groups with different training set sample sizes are presented in Tables 2 and 3. The mean absolute error (MAE), root mean square error (RMSE), and prediction relative error (PER) are used to verify the algorithm's accuracy, and their formulas are shown below:

[0164] (29)

[0165] (30)

[0166] (31)

[0167] (32)

[0168] in, This represents the actual value of SOH; PRUL represents the estimated SOH value; RUL represents the predicted remaining cycle life; RUL represents the actual remaining cycle life.

Claims

1. A method for predicting the remaining lifespan of lithium-ion batteries based on BO-LSTM, characterized in that... The steps are as follows: Step 1: Conduct charge-discharge cycle tests on the battery to obtain the total number of cycles after battery failure, and divide the total number of cycles into a training set and a test set; The number of training sets is the top 80% or top 90% of the total number of iterations; The number of test sets is the total number of iterations minus the number of training sets; Step 2: Calculate battery health: in, This represents the initially measured discharge capacity. Let be the discharge capacity measured in real time for the i-th time; Step 3: Input the battery health data into the BO-LSTM algorithm model to predict the remaining battery life: Step 3.1: Use the battery health data from Step 2 as the initial input sample for the BO-LSTM neural network model, and randomly generate initialization samples; Step 3.2: Perform Gaussian calculation on the initialized sample points to obtain the mean and variance of the objective function: Step 3.3: Input the mean and variance of the objective function into the EI sampling function, and select the next set of sample points to be evaluated from the corrected Gaussian model output by the sampling function. ; The sample evaluation points are input into the LSTM model for training to obtain new output values ​​of the objective function. , with output value Update the sample set, i.e., the set of battery health scores. And Gaussian model; Step 3.4: Repeat the iteration, within the set number of iterations, outputting the value each time. Update sample set And Gaussian model; When the iteration terminates, the sampling function outputs the optimal set of battery health parameters and the corresponding loss value of the objective function of the LSTM model. ; A collection of battery health information Half of the number is the predicted cycle life of the battery.

2. The method for predicting the remaining lifespan of lithium-ion batteries based on BO-LSTM according to claim 1, characterized in that: The process of conducting a charge-discharge cycle test on the battery is as follows: set the battery failure threshold, conduct a charge-discharge cycle test on the battery at room temperature, and obtain the total number of cycles required to cause battery failure.

3. The method for predicting the remaining lifespan of lithium-ion batteries based on BO-LSTM according to claim 1, characterized in that: The failure threshold of the battery is 80% of its initial capacity.

4. The method for predicting the remaining lifespan of lithium-ion batteries based on BO-LSTM according to claim 1, characterized in that: The sample set in step 3 D The accuracy of the model algorithm is verified by comparing the total number of battery cycles obtained in step 1 with the total number of charge-discharge cycle tests.

5. The method for predicting the remaining lifespan of lithium-ion batteries based on BO-LSTM according to claim 1, characterized in that: The BO-LSTM algorithm model: uses a multiplication gate, which is also the input gate. Forgotten Gate and output gate The storage units are connected together; the LSTM algorithm performs forward and backward propagation. Forward propagation uses an activation function, and backward propagation uses the backpropagation algorithm to calculate gradients. In the following calculation process... Represents neurons arrive The weights between them express Time neuron Activation function, express The LSTM algorithm inputs data to neurons at specific times. value, index , , and These represent the input gate, forget gate, output gate, and... A memory unit, Let represent the activation functions of the three multiplication gates. and Let these represent the input activation function and the output activation function of the neuron, respectively. express Time memory unit The state of memory modules, the interconnections between memory modules are determined by the output of the neurons themselves. This is achieved, and the activation functions of the three multiplication gates in the memory module only work internally. The LSTM neural network algorithm includes the following steps: Step 1): The input sequence is The duration is The forward propagation of the LSTM algorithm is based on Start increasing, until As time goes on, the forward calculation equations are updated accordingly; while the backward calculation is based on... Starting from this point, it continuously decreases until... According to the backward calculation formula of the RNN algorithm, the final weights are... The derivative value is expressed as: Among them, when and At that time, all expressions and activation functions in the network are set to 0; Step 2): The forward propagation equation of the LSTM algorithm is as follows: Input gate exist Expression for time: Forgotten Gate exist Expression for time: Memory unit in Expression for time: Output gate exist Expression for time: Step 3): Backpropagation equations for the LSTM algorithm, let... Memory unit in The output value at time t is: Output gate exist Expression for time: The state at any given moment: The derivative of the weights of the memory cells is: Forgotten Gate The derivative of the weights is: Input gate The derivative of the weights is: .

6. The method for predicting the remaining lifespan of lithium-ion batteries based on BO-LSTM according to claim 1, characterized in that: The Gaussian operation process in steps 3.2 to 3.4: Establishing the Bayesian global optimization algorithm: in, Represents an unknown objective function; A set representing battery health ; This represents the observed data; Represents the observed value; express The posterior probability; express The likelihood distribution; express The prior probability; express The marginal likelihood distribution; The Bayesian global optimization algorithm comprises two core processes: a probabilistic surrogate model and a sampling function. The probabilistic surrogate model is a probabilistic model used to represent the unknown objective function. By iteratively increasing the amount of information, the prior probability is continuously corrected, making the surrogate model more accurate. The sampling function, based on the posterior distribution, samples from the region where the global optimum is most likely to occur and from the unsampled region, selecting the most "potential" sample point from the candidate set to minimize the loss function value. Specifically, it includes the following steps: Step (1): The Gaussian process is composed of a mean function And a positive semidefinite covariance function The Gaussian distribution is represented in the following form: in, express The mathematical expectation of the mean function is usually set to 0. Indicates the mean absolute error; express The covariance function; Step (2): The explored historical information is ,in The next value to be searched is covariance matrix It is written as follows: Step (3): and All of them follow a joint Gaussian distribution with a mean of 0, and their joint Gaussian distribution is expressed as follows: in, ; Step (4): Calculate the edge density function to obtain... Posterior probability: Among them, the mean and variance The calculation formulas are as follows: Estimate The sample point follows a normal distribution at any given value, and a sampling function is used to locate the next optimal sample point. Step (5): For The mean and variance are used for sample calculation, and the EI collection function for sampling is: in, Let be the probability density function of the standard normal distribution. Let be the distribution function of the standard normal distribution, where Represented as: Step (6): Add a weighted scalar to the EI algorithm And satisfy The EI acquisition function with a value greater than 0 is as follows: 。

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