Sugarcane squeezing process index interval prediction method and device based on multi-objective optimization

Abstract

The invention discloses a sugarcane squeezing process index interval prediction method based on multi-objective optimization, which belongs to the technical field of sugarcane squeezing process optimization, and comprises the following steps: taking a minimum prediction interval width (PINAW) and a maximum prediction interval coverage rate (PICP) as optimization objectives; the method comprises the following steps: taking a process of searching optimal parameters of a kernel extreme learning machine (KELM) model meeting requirements as a multi-objective optimization problem, and solving the multi-objective optimization problem by using a multi-objective particle swarm optimization (MOPSO) algorithm to obtain a Pareto solution set; selecting an optimal compromise solution from the corresponding Pareto frontier by adopting an entropy weight-based approximate ideal solution sorting method (TOPSIS-EW), and allocating the determined optimal parameter to the kernel extreme learning machine model to obtain an optimized kernel extreme learning machine model; and applying the obtained optimized kernel extreme learning machine model to sugarcane squeezing process index interval prediction. According to the method, the uncertainty of the interval prediction of the sugarcane squeezing process indexes can be reduced, and the coverage of the prediction interval is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of sugarcane squeezing process optimization, and more specifically, to a method and device for predicting sugarcane squeezing process index intervals based on multi-objective optimization. Background Art

[0002] Process industries generally contain many important production process indicators or variables. Some key indicators of particular concern need to be monitored to regulate the entire production process and ultimately achieve the goal of stable production. Taking the sugarcane pressing section in the sugar production process as an example, its pressing extraction rate and production energy consumption are two important indicators of this section. Whether these indicators meet the standards will affect the smooth operation and economic benefits of the entire sugar production. Due to the complex nonlinear relationship between these indicators and other process variables, as well as the lag of the industrial production process, the measurement of these indicators is often very difficult or time-consuming, or even impossible to measure. Therefore, it is particularly important to establish an effective mathematical model for real-time prediction.

[0003] After searching, Chinese patents with publication number CN113743652A and announcement date 2021.12.03 disclose a sugarcane crushing process prediction method based on deep feature recognition. According to the idea of ​​data-driven modeling, combined with mutual information theory, mixed chicken swarm algorithm and principal component analysis, the characteristic variables under the optimal performance of different data-driven models are effectively identified, and a multi-model combination model integrating several models is proposed to establish a prediction model for the energy consumption and extraction rate of the sugarcane crushing process, thereby improving the prediction accuracy. It discloses that the production data is pre-processed and input into the kernel extreme learning machine (KELM) model to obtain the first-layer prediction results, and then the first-layer prediction results are integrated and predicted to finally obtain the prediction target. Different from this method, the present invention proposes a method for optimizing the prediction interval to reduce the uncertainty in the prediction of sugarcane crushing process indicators. Summary of the invention

[0004] The purpose of the present invention is to provide a method for predicting the interval of sugarcane pressing process indicators based on multi-objective optimization, which optimizes the prediction interval by optimizing model parameters, increasing the coverage probability of the prediction interval and reducing the width of the prediction interval, thereby obtaining the optimal prediction interval, reducing the uncertainty of the interval prediction of the sugarcane pressing process indicators, and improving the coverage of the prediction interval.

[0005] In order to achieve these objectives of the present invention, the present invention provides a method for predicting intervals of sugarcane squeezing process indicators based on multi-objective optimization, comprising:

[0006] Step 1: The process of finding the optimal parameters of the sugarcane pressing process index prediction model that meets the requirements is regarded as a multi-objective optimization problem, with minimizing the prediction interval width (PINAW) and maximizing the prediction interval coverage (PICP) as the optimization goals, and the multi-objective particle swarm (MOPSO) algorithm is used to solve the multi-objective optimization problem to obtain a Pareto solution set; the prediction interval coverage of the present invention refers to the probability that the true value falls within the prediction interval, and is an indicator for evaluating the degree of coverage of the prediction interval to the true value; the prediction interval width refers to the upper and lower limit width range of the prediction interval, and is an indicator for evaluating the width of the prediction interval.

[0007] Step 2: Using the TOPSIS-EW method, the optimal compromise solution is selected from the Pareto frontier corresponding to the Pareto solution set, and the optimal parameters are assigned to the sugarcane pressing process index prediction model to obtain the optimized sugarcane pressing process index prediction model;

[0008] Step 3: Use the obtained optimized sugarcane pressing process index prediction model for sugarcane pressing process index interval prediction to achieve the purpose of optimizing the prediction interval PI.

[0009] Furthermore, the sugarcane pressing process index prediction model includes but is not limited to the kernel extreme learning machine (KELM) model, the least squares support vector machine LSSVM model, the multi-layer induction machine MLP model, and the radial basis RBF model. For example, the twin support vector machine, the kernel extreme learning machine, and the deep kernel extreme learning machine model disclosed in the Chinese patent publication number CN113743652A. Preferably, the present invention is directed to the prediction interval optimization of the kernel extreme learning machine (KELM) model.

[0010] Furthermore, the kernel extreme learning machine (KELM) model for predicting sugarcane pressing process indicators has an input layer data of production data of the sugarcane pressing process; the production data includes press speed, two double-roller speeds, primary and secondary belt speeds, infiltration water flow, mixed juice flow, bagasse moisture, fiber content and sucrose content, etc.; the production data is obtained from several groups of historical production data and corresponding detection data of the monitoring system; the output layer is the prediction interval (PI) of the sugarcane pressing process indicators.

[0011] Specifically, in the kernel extreme learning machine (KELM) model of the present invention:

[0012] The output formula of the extreme learning machine ELM is as follows:

[0013]

[0014] Among them, x is the input variable, N is the number of data samples, I is the sparse matrix, T is the actual output matrix, C is the penalty coefficient, L is the number of hidden layer nodes, H is the L-dimensional hidden layer feature space, β = [β1,…,β L ] T is the output weight between the hidden layer node and the output node, h(x)=[h1(x),…,h L (x)] represents the output vector of the hidden layer relative to the d-dimensional input x.

[0015] h(x) is a feature map that maps data from the input space to H. Without knowing h(x), Mercer's condition is applied to ELM to define a kernel matrix Ω for ELM. ELM :

[0016] Ω ELM =HH T : Ω ELMi,j =h(x i )·h(x j )=K(x i , x j ) (1-5)

[0017] The output formula of the kernel extreme learning machine KELM is as follows

[0018]

[0019] KELM directly obtains the output through kernel point multiplication, which greatly reduces the amount of calculation compared with ELM. In one embodiment, the present invention uses Gaussian kernel function for calculation, and its expression is as follows

[0020] K(x i ,x j ) = exp(-γ||x i -x j || 2 ) (1-7)

[0021] Where γ is the kernel parameter.

[0022] In one embodiment, the present invention mainly optimizes the penalty coefficient C and the kernel parameter γ.

[0023] Furthermore, the pressing process indicators include at least power consumption and extraction rate.

[0024] Furthermore, the production data is divided into training set data and test set data.

[0025] Furthermore, in step 1, given a set of data sets where x i is the input variable, t iObserve the output variable (true value). Specifically, the input variable x i is the production data, and the observed output variable t i It is the true value of the sugarcane pressing process indicator results obtained by observation, such as the true value of power consumption and extraction rate.

[0026] The true value is used as the expected data of the model. Among them, the target t i The (1-α)% confidence (probability) prediction interval PI can be expressed as:

[0027]

[0028] and are the upper and lower boundaries of the prediction interval PI, (1-α)% is the confidence level, α is the error probability, and the expected probability that its value is within the PI range can be expressed as follows:

[0029]

[0030] Furthermore, in the step 1, the prediction interval width (PINAW) is used to characterize the uncertainty of the prediction interval (PI), and the prediction interval coverage ratio (PICP) is used to characterize the reliability of the prediction interval (PI);

[0031] (1) Regarding reliability:

[0032] The expected target is in the constructed prediction interval (PI) with a nominal probability of (1-α)%, which is called the prediction interval (PI) nominal confidence level (PINC), then PINC = (1-α)%, α is the error probability; the prediction interval coverage (PICP) is a key measure of the reliability of the constructed prediction interval (PI), defined as:

[0033]

[0034] Where N is the number of samples (the number of samples in the training set), L i and U i are the upper and lower limits of the prediction interval respectively; t i Observed output variable (true value); c i is a Boolean quantity. If t i If the observed output variable (true value) is included in the upper and lower limits of the prediction interval, then c i =1, otherwise c i =0; To obtain a valid prediction interval PI, the value of the prediction interval coverage ratio PICP should be greater than or equal to the nominal confidence level PINC; otherwise, they are invalid and should be discarded.

[0035] (2) Regarding uncertainty:

[0036] Due to different observed output variables t i (True value) has different prediction intervals (PI), and the prediction interval width (PINAW) can be calculated by the following formula:

[0037]

[0038] Where, t max and t min are the maximum and minimum observed values, i.e., the limits of the range of true values; by normalizing the prediction interval (PI) width by the target range, the PI can be compared objectively without considering its construction method and the size of the true target.

[0039] Furthermore, in step 1, the multi-objective optimization model established for the multi-objective optimization problem is expressed as:

[0040]

[0041] max Obj1 represents maximization objective 1, min Obj2 represents minimization objective 2, stPINC≤PICP<100% and PINAW>0 are constraints; the above problem shows that in order to meet the corresponding constraints, a solution must be found at PICP≥PINC.

[0042] In the step 1, in order to find the optimal parameters of the kernel extreme learning machine (KELM) model, the method flow of using the multi-objective particle swarm optimization (MOPSO) algorithm to optimize the KELM model to construct the prediction interval PI is as follows: Figure 2 As shown, the specific steps are as follows:

[0043] (1) Divide the production data into training set and test set data, input the training set data, calculate the training set data according to formula (2-4), and obtain the initial output interval of the training set;

[0044] Y i =[y i (1-a), y i (1+a)] (2-4)

[0045] Among them, y i is the original output of the training set data, Y i is the output interval after processing, α is the error probability;

[0046] (2) Generate an initial population, initialize parameters, and apply the kernel extreme learning machine (KELM) model with the initialized parameters to the training set;

[0047] (3) The true value (t i) is compared with the prediction interval (PI) obtained from the training set, and evaluation indicators such as PICP and PINAW are calculated to form the objective function according to formula (2-3);

[0048] (4) In each iteration, the MOPSO algorithm is used to optimize the parameters of the kernel extreme learning machine (KELM) model (in one embodiment, the present invention mainly optimizes the penalty coefficient C and the kernel parameter γ), the expected interval PI obtained from the training set is used to calculate the objective function, and the Pareto solution set is updated;

[0049] (5) The TOPSIS-EW method is used to select the optimal compromise solution from the Pareto frontier; the determined optimal parameters are assigned to the kernel extreme learning machine (KELM) model and applied to the test set, and finally the predicted PI results of the sugarcane pressing process indicators are output.

[0050] Furthermore, the interval prediction performance is quantitatively evaluated using evaluation indicators, PICP is used to characterize the reliability of PI, and PINAW is used to characterize the uncertainty of PI. In addition to the above two main evaluation indicators, the average error coverage (ACE), mean prediction width (MPI), Winkler score or interval score (W S ) and coverage width criterion (CWC) four indicators.

[0051] Furthermore, the evaluation indicators are as follows:

[0052] (1) It is expected that the PICP of PI should be close to the PINC, so the ACE indicator can be expressed as:

[0053] ACE=PICP-PINC (2-5)

[0054] (2) The MPI calculation formula is as follows:

[0055]

[0056] N is the number of samples (the number of samples in the training set), L i and U i are the upper and lower limits of the prediction interval respectively;

[0057] (3) The quality of the prediction interval PI can also be calculated using W S To evaluate, the interval score can be used to evaluate the overall performance of PI, and the width of the i-th prediction interval PI is expressed as follows:

[0058] θ i =U i -L i (2-7)

[0059] For the i-th prediction interval, the PI score can be defined by the following formula

[0060]

[0061] L i and U i are the upper and lower limits of the prediction interval respectively; t i Observed output variable (true value); α is the error probability;

[0062] Then the total score calculation formula is as follows:

[0063]

[0064] At a given nominal confidence level (PINC), lower absolute values ​​of the scores indicate higher quality of the PI.

[0065] (4) Coverage Width Criterion CWC

[0066] In order to comprehensively evaluate PINC and PINAW at the same time, the CWC composed of these two indicators is calculated as follows:

[0067]

[0068] Where η and μ are two hyperparameters that control the size of the CWC index, and μ represents the PINC that the constructed PI must satisfy.

[0069] η amplifies the difference between μ and PICP and is usually set to a large value to highly penalize μ when it is lower than PICP. CWC provides a way to strike a balance between informativeness (PINAW) and effectiveness (PICP).

[0070] Furthermore, TOPSIS represents the approximate ideal solution ranking method, EW represents the entropy method, also known as the entropy weight method, and TOPSIS-EW represents the approximate ideal solution ranking method based on the entropy method (i.e., a comprehensive evaluation method combining the two). The present invention uses the approximate ideal solution ranking method based on entropy weight to make decisions on the Pareto frontier corresponding to the Pareto solution set and select the optimal compromise solution.

[0071] The present invention provides a device including a processor and a memory, wherein the memory stores executable code, and when the processor executes the executable code, any one of the methods described above is implemented.

[0072] The present invention has at least the following beneficial effects:

[0073] 1. The sugarcane pressing process index interval prediction method based on multi-objective optimization of the present invention regards the process of finding the optimal parameters of the kernel extreme learning machine (KELM) model that meets the requirements as a multi-objective optimization problem, takes minimizing the prediction interval width (PINAW) and maximizing the prediction interval coverage (PICP) as the optimization objectives, and uses the multi-objective particle swarm (MOPSO) algorithm to solve the multi-objective optimization problem to obtain a Pareto solution set; uses the TOPSIS-EW method to select the optimal compromise solution from the Pareto frontier corresponding to the Pareto solution set, and assigns the determined optimal parameters to the kernel extreme learning machine (KELM) model to obtain an optimized kernel extreme learning machine (KELM) model; and uses the obtained optimized kernel extreme learning machine (KELM) model for sugarcane pressing process interval prediction to achieve the purpose of optimizing the expected interval, reduce the uncertainty of the interval prediction of the sugarcane pressing process index, and improve the coverage of the prediction interval.

[0074] 2. Compared with interval prediction models such as NSGA-II-KELM (fast elite multi-objective genetic algorithm optimized KELM model), MOPSO-LSSVM (improved particle swarm algorithm optimized LSSVM model), MOPSO-MLP (improved particle swarm algorithm optimized MLP model) and MOPSO-RBF (improved particle swarm algorithm optimized RBF model), the method of the present invention has better coverage and smaller prediction interval PI width for power consumption and extraction rate, indicating that the prediction interval PI quality of the MOPSO-KELM model of the method of the present invention is better than all the compared models, that is, while reducing prediction uncertainty, it can cover the target value well.

[0075] Other advantages, objectives and features of the present invention will be embodied in part through the following description, and in part will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is a multi-objective optimization framework diagram of the prediction interval of the sugarcane pressing process index of the present invention;

[0077] Figure 2 It is a flow chart of the method for optimizing KELM to construct PI using multi-objective particle swarm (MOPSO) algorithm of the present invention;

[0078] Figure 3 is a Pareto frontier of an operation result of the present invention;

[0079] Figure 4 is the interval prediction result of the MOPSO-KELM model of the present invention;

[0080] Figure 5is the interval prediction result of the NSGA-II-KELM model of the present invention;

[0081] Figure 6 It is the power consumption prediction interval result of each model of the present invention; among them (1) MOPSO-KELM; (2) MOPSO-LSSVM; (3) MOPSO-MLP; (4) MOPSO-RBF;

[0082] Figure 7 It is the extraction rate prediction interval result of each model of the present invention; among them: (1) MOPSO-KELM; (2) MOPSO-LSSVM; (3) MOPSO-MLP; (4) MOPSO-RBF. DETAILED DESCRIPTION

[0083] The present invention is further described in detail below with reference to examples so that those skilled in the art can implement the invention with reference to the description.

[0084] It should be understood that the terms such as “having”, “including” and “comprising” used herein do not exclude the existence or addition of one or more other elements or combinations thereof.

[0085] like Figure 1 As shown, it is a multi-objective optimization framework diagram of the prediction interval (PI) of the sugarcane pressing process index provided by the present invention, which includes three parts: multi-objective optimization, multi-objective decision-making, and prediction interval performance evaluation;

[0086] In multi-objective optimization: minimizing the prediction interval width (PINAW) and maximizing the prediction interval coverage (PICP) are taken as optimization objectives, the process of finding the optimal parameters of the KELM model that meets the requirements is regarded as a multi-objective optimization problem, and the MOPSO algorithm is used to solve the multi-objective optimization problem to obtain the Pareto solution set and its Pareto frontier.

[0087] In multi-objective decision-making: the TOPSIS-EW method and the minimum CWC method were used respectively to make multi-objective decisions. The results showed that the solution selected by the TOPSIS-EW method had better performance. Therefore, the TOPSIS-EW method is the best method for selecting the optimal Pareto frontier.

[0088] In the prediction interval performance evaluation, six evaluation indicators including PINAW and PICP were used to evaluate the prediction interval quality of the optimization model.

[0089] Specifically, a method for predicting intervals of sugarcane pressing process indicators based on multi-objective optimization of the present invention comprises:

[0090] Step 1: For the prediction model of sugarcane pressing process indicators, the process indicators take extraction rate and power consumption as examples, and the model takes the kernel extreme learning machine (KELM) model as an example. The process of finding the optimal parameters of the kernel extreme learning machine (KELM) model that meets the requirements is regarded as a multi-objective optimization problem and modeled. The minimization of prediction interval width (PINAW) and maximization of prediction interval coverage (PICP) are taken as optimization objectives. The multi-objective particle swarm (MOPSO) algorithm is used to solve the multi-objective optimization problem and obtain the Pareto solution set.

[0091] Step 2: Use the TOPSIS-EW method to select the optimal compromise solution from the Pareto frontier corresponding to the Pareto solution set, assign the determined optimal parameters to the KELM model, and obtain the optimized KELM model;

[0092] Step 3: Use the obtained optimized kernel extreme learning machine (KELM) model to predict the interval of sugarcane pressing process indicators to achieve multi-objective optimization of the prediction interval PI.

[0093] Specifically, the kernel extreme learning machine (KELM) model for predicting sugarcane pressing process indicators has an input layer data that is a production data variable of the sugarcane pressing process; the production data includes the press speed, the speed of two double rollers, the primary and secondary belt speeds, the infiltration water flow, the mixed juice flow, the bagasse moisture, the fiber content and the sucrose content, etc.; the production data is obtained from several groups of historical production data and corresponding detection data of the monitoring system; the output layer is the prediction interval of the sugarcane pressing process indicators.

[0094] Specifically, the kernel extreme learning machine (KELM) model of the present invention is:

[0095] The output formula of ELM is as follows:

[0096]

[0097] Among them, x is the input variable, N is the number of data samples, I is the sparse matrix, T is the actual output matrix, C is the penalty coefficient, L is the number of hidden layer nodes, H is the L-dimensional hidden layer feature space, β = [β1,…,β L ] T is the output weight between the hidden layer node and the output node, h(x)=[h1(x),…,h L (x)] represents the output vector of the hidden layer relative to the d-dimensional input x.

[0098] h(x) is a feature map that maps data from the input space to H. Without knowing h(x), Mercer's condition is applied to ELM to define a kernel matrix Ω for ELM. ELM:

[0099] Ω ELM =HH T :Ω ELMi,j =h(x i )·h(x j )=K(x i ,x j ) (1-5)

[0100] The output formula of KELM is as follows

[0101]

[0102] KELM directly obtains the output through kernel point multiplication, which greatly reduces the amount of calculation compared with ELM. In one embodiment, the present invention uses Gaussian kernel function for calculation, and its expression is as follows

[0103] K(x i ,x j ) = exp(-γ||x i -x j || 2 ) (1-7)

[0104] Where γ is the kernel parameter.

[0105] Collect production data variable x i , and the true value t of the observed change in sugarcane pressing process indicators i , forming a data set For example, the data of the speed of the press is collected, and the extraction rate and power consumption of the sugarcane pressing process indicators are observed accordingly.

[0106] In order to train the KELM model of the present invention, the production data is divided into training set data and test set data.

[0107] Furthermore, the modeling process of the multi-objective optimization problem in step 1 is as follows:

[0108] Given a set of data where x i is the input variable, t i Observe the output variable (true value). Specifically, the input variable x i is the variable of production data, and the observed output variable t i It is the true value of the change results of sugarcane pressing process indicators observed subsequently, such as the true value of power consumption and extraction rate changes.

[0109] Among them, the target t i The (1-α)% confidence (probability) prediction interval PI is expressed as:

[0110]

[0111] and are the upper and lower boundaries of the prediction interval PI, (1-α)% is the confidence level, α is the error probability, and the expected probability that its value is within the PI range can be expressed as follows:

[0112]

[0113] Furthermore, the prediction interval width (PINAW) is used to characterize the uncertainty of the prediction interval (PI), and the prediction interval coverage (PICP) is used to characterize the reliability of the prediction interval (PI);

[0114] (1) Regarding reliability:

[0115] The expected target is in the constructed prediction interval (PI) with a nominal probability of (1-α)%, which is called the prediction interval (PI) nominal confidence level (PINC), then PINC = (1-α)%, α is the error probability; the prediction interval coverage (PICP) is a key measure of the reliability of the constructed prediction interval (PI), defined as:

[0116]

[0117] Where N is the number of samples, L is i and U i are the upper and lower limits of the prediction interval respectively; t i is the observed output variable (true value); c i is a Boolean quantity. If t i If the observed output variable (true value) is included in the upper and lower limits of the prediction interval, then c i =1, otherwise c i =0; To obtain a valid prediction interval PI, the value of the prediction interval coverage ratio PICP should be greater than or equal to the nominal confidence level PINC; otherwise, they are invalid and should be discarded.

[0118] (2) Regarding uncertainty:

[0119] Since the observed output variable t i (True value) has different prediction intervals (PI), and the prediction interval width (PINAW) can be calculated by the following formula:

[0120]

[0121] Where, t max and t minare the maximum and minimum observed values, i.e., the limits of the range of true values; by normalizing the prediction interval (PI) width by the target range, the PI can be compared objectively without considering its construction method and the size of the true target.

[0122] Furthermore, the multi-objective optimization model established for the multi-objective optimization problem is expressed as:

[0123]

[0124] Among them, max Obj1 represents maximization objective 1, min Obj2 represents minimization objective 2, stPINC≤PICP<100% and PINAW>0 are constraints; the above problem shows that in order to meet the corresponding constraints, a solution must be found at PICP≥PINC.

[0125] Furthermore, in order to find the optimal parameters of the kernel extreme learning machine (KELM) model, the multi-objective particle swarm optimization (MOPSO) algorithm is used to optimize the KELM to construct the prediction interval PI. Figure 2 As shown, the specific steps are as follows:

[0126] (1) Input the training set data and calculate the training set data according to formula (2-4) to obtain the initial output interval of the training set

[0127] Y i =[y i (1-a), y i (1+a)] (2-4)

[0128] Among them, y i is the original output of the training set data, Y i is the output interval after processing, α is the error probability;

[0129] (2) Generate an initial population, initialize parameters, and apply the kernel extreme learning machine (KELM) model with the initialized parameters to the training set;

[0130] (3) The true value (t i ) is compared with the prediction interval (PI) obtained from the training set, and PICP, PINAW, average error coverage (ACE), mean prediction width (MPI), Winkler score or interval score (W) are calculated according to formulas (2-1) to (2-10). S ), coverage width criterion (CWC) and other evaluation indicators, and form the objective function according to formula (2-3);

[0131] (4) In each iteration, the MOPSO algorithm is used to optimize the parameters of the kernel extreme learning machine (KELM) model, the prediction interval PI obtained from the training set is used to calculate the objective function, and the Pareto solution set is updated;

[0132] (5) TOPSIS-EW is used to select the optimal compromise solution from the Pareto frontier; the determined optimal parameters are assigned to the kernel extreme learning machine (KELM) model and applied to the test set, and finally the prediction interval PI results of the pressing process indicators are output.

[0133] Furthermore, the interval prediction performance is quantitatively evaluated using evaluation indicators, PICP is used to characterize the reliability of PI, and PINAW is used to characterize the uncertainty of PI. In addition to the above two main evaluation indicators, the average error coverage (ACE), mean prediction width (MPI), Winkler score or interval score (W S ) and coverage width criterion (CWC) four indicators.

[0134] Furthermore, the calculation formulas of each evaluation index are as follows:

[0135] (1) It is expected that the PICP of PI should be close to PINC, so the ACE index can be expressed as

[0136] ACE=PICP-PINC (2-5)

[0137] (2) The MPI calculation formula is as follows

[0138]

[0139] N is the number of samples (the number of samples in the training set), L i and U i are the upper and lower limits of the prediction interval respectively;

[0140] (3) PI quality can also be expressed as W S To evaluate, the interval score can be used to evaluate the overall performance of PI, and the width of the i-th PI is expressed as follows

[0141] θ i =U i -L i (2-7)

[0142] For the i-th PI score, it can be defined by the following formula:

[0143]

[0144] L i and U i are the upper and lower limits of the prediction interval respectively; t i Observed output variable (true value); α is the error probability;

[0145] Then the total score calculation formula is as follows:

[0146]

[0147] At a given nominal confidence level (PINC), lower absolute values ​​of the scores indicate higher quality of the PI.

[0148] (4) Coverage Width Criterion CWC

[0149] In order to comprehensively evaluate PINC and PINAW at the same time, the CWC composed of these two indicators is calculated as follows:

[0150]

[0151] Where η and μ are two hyperparameters that control the size of the CWC index, and μ represents the PINC that the constructed PI must satisfy.

[0152] η amplifies the difference between μ and PICP and is usually set to a large value to highly penalize μ when it is lower than PICP. CWC provides a way to strike a balance between informativeness (PINAW) and effectiveness (PICP).

[0153] Furthermore, TOPSIS represents the approximate ideal solution ranking method, EW represents the entropy method, also known as the entropy weight method, and TOPSIS-EW represents the approximate ideal solution ranking method based on the entropy method (i.e., a comprehensive evaluation method combining the two). The present invention uses the approximate ideal solution ranking method based on entropy weight to make decisions on the Pareto frontier corresponding to the Pareto solution set and select the optimal compromise solution.

[0154] A specific implementation process of TOPSIS-EW of the present invention is given below:

[0155] If there are Q evaluation objects and m evaluation indicators in the Pareto solution set, X is the matrix composed of the evaluation indicator values ​​of each evaluation object, x ij Represents the jth indicator value of the i-th evaluation object. The specific steps include:

[0156] (1) Data normalization

[0157] In order to avoid the influence of the dimensions of each indicator, the indicator value should be normalized to obtain the standard value y ij ;

[0158]

[0159] (2) Determination of index entropy weight

[0160] According to the standard value y ijThe information entropy H(y i ), information entropy is defined by the following formula:

[0161]

[0162] In the formula, 0ln0 is always equal to 0;

[0163] According to the information entropy H(y i ) Calculate the output entropy E j , the formula is as follows:

[0164] E j =H(y i ) / lnQ

[0165] According to the output entropy E j Calculate the difference G of the index j , the formula is as follows:

[0166] G j =1-E j (1≤j≤m)

[0167] According to the difference G j Calculate the entropy weight a j , the formula is as follows:

[0168]

[0169] Where, j = 1, 2, ..., m;

[0170] (3) Construct the weighted normalization matrix V

[0171]

[0172] (4) Determine the negative ideal solution V of the matrix V - and the ideal solution V +

[0173]

[0174] In the formula, J1 is a benefit-based indicator, and J2 is a cost-based indicator;

[0175] (5) Calculate distance

[0176] The distance between each evaluation object and the negative ideal solution The distance between each evaluation object and the ideal solution They are as follows:

[0177]

[0178] Where, i = 1, 2, ..., Q;

[0179] (6) Calculate the relative closeness C i

[0180]

[0181] Where, i = 1, 2, ..., Q;

[0182] According to C i Sort by value, C i The larger the value, the closer the evaluation object is to the optimal value. In one embodiment of the present invention, the Pareto frontier in the Pareto solution set is selected. i The point with the highest value is taken as the optimal compromise solution.

[0183] A device of the present invention comprises a processor and a memory, wherein the memory stores executable codes, and when the processor executes the executable codes, a multi-objective optimization method for the prediction interval of the pressing process index is implemented.

[0184] Figure 3 The Pareto front of a running result is shown. Each point on the Pareto front represents a different optimal solution. The TOPSIS-EW and minimum CWC methods are used to select an optimal compromise solution from these Pareto solutions. Decision makers can also choose a solution that reflects the trade-off between the two objectives of PICP and PINAW according to their own preferences and actual conditions. Figure 3 As shown, the optimal compromise solutions determined by the minimum CWC selection method and the TOPSIS-EW method are marked in the Pareto front. For power consumption, the optimal solutions selected by CWC and TOPSIS-EW are consistent. However, for the extraction rate, the minimum CWC method selects a solution located on the edge of the Pareto front, while the TOPSIS-EW method selects a solution located in the middle of the Pareto front. Since the solution selected by TOPSIS-EW is located in the center of the Pareto front, this shows that the compromise performance of the solution selected by TOPSIS-EW is better. Therefore, in the present invention, the TOPSIS-EW method is the best method for selecting the optimal Pareto front.

[0185] In order to evaluate the performance of the MOPSO-KELM model of the method of the present invention, the present invention compares the MOPSO-KELM model with the interval prediction models of NSGA-II-KELM, MOPSO-LSSVM, MOPSO-MLP and MOPSO-RBF respectively. The six model evaluation indicators such as PICP and PINAW mentioned above are used to comprehensively evaluate the performance of the proposed multi-objective prediction interval model.

[0186] like Figure 4Shown are the interval prediction results of the MOPSO-KELM model, including (1) power consumption PI, (2) extraction rate PI; Figure 5 is the interval prediction result of the NSGA-II-KELM model, where (1) power consumption PI, (2) extraction rate PI. Target is the target value (i.e., the true value), and Fitting Number refers to the number of test data sets, which is given by Figure 4 and Figure 5 It can be clearly seen that for the MOPSO-KELM model, the target value Target (i.e., the true value) is basically within the prediction interval PI. However, for the NSGA-II-KLEM model, some target values ​​are scattered outside the interval, and the width of PI is large, indicating that the uncertainty of PI is large. Therefore, the PI quality of the MOPSO-KELM model is better than that of the NSGA-II-KLEM model.

[0187] like Figure 6 The figure shows the power consumption prediction interval results of each model, including (1) MOPSO-KELM; (2) MOPSO-LSSVM; (3) MOPSO-MLP; (4) MOPSO-RBF. The PI of the MOPSO-KELM model for power consumption can effectively cover the target value. While the coverage is good, the interval uncertainty is also the smallest. For the comparison model, although the PI uncertainty of the MOPSO-LSSVM model is also small, the coverage of the PI is slightly worse, and some target values ​​are scattered outside the PI. Similarly, some target points of MOPSO-MLP are not surrounded by the PI. Although all target values ​​of MOPSO-RBF are surrounded by the PI, the uncertainty of the PI of this model is the largest.

[0188] like Figure 7 The figure shows the prediction interval results of the extraction rate of each model, including (1) MOPSO-KELM; (2) MOPSO-LSSVM; (3) MOPSO-MLP; (4) MOPSO-RBF. Figure 7 It can be seen that the PI of the MOPSO-KELM model with extraction rate can effectively cover the target value, and the interval uncertainty is also the smallest while the coverage is good. For the comparison model, although the PI uncertainty of the MOPSO-LSSVM model is also small, the coverage of the PI is slightly worse, and some target values ​​are scattered outside the PI. Similarly, some points of the MOPSO-RBF are not surrounded by the PI range. Although all the target values ​​of the MOPSO-MLP are surrounded by the PI, the PI uncertainty of this model is the largest.

[0189] From the above analysis, it can be seen that for power consumption and extraction rate, the MOPSO-KELM model of the present invention has better coverage and smaller PI width at the same time, indicating that the PI quality of the MOPSO-KELM model is better than that of all the comparison models, that is, it can cover the target value well while reducing the prediction uncertainty.

[0190] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and the embodiments. They can be applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily realized.

Claims

1. A method for predicting intervals of sugarcane pressing process indicators based on multi-objective optimization, characterized in that: include: Step 1: Taking minimizing the prediction interval width and maximizing the prediction interval coverage as the optimization goals, the process of finding the optimal parameters of the prediction model that meets the requirements is regarded as a multi-objective optimization problem, and the multi-objective particle swarm algorithm is used to solve the multi-objective optimization problem to obtain the Pareto solution set; Step 2: Use the entropy-based approach to ideal solution sorting method to select the optimal compromise solution from the corresponding Pareto frontier, assign the determined optimal parameters to the prediction model, and obtain the optimized prediction model; Step 3: Use the obtained prediction model to predict the interval of sugarcane pressing process indicators.

2. The sugarcane squeezing process index interval prediction method based on multi-objective optimization according to claim 1, characterized in that: The prediction model is a kernel extreme learning machine model.

3. The sugarcane squeezing process index interval prediction method based on multi-objective optimization according to claim 2, characterized in that: The sugarcane squeezing process indicators at least include power consumption and extraction rate.

4. The method for predicting the interval of sugarcane pressing process indexes based on multi-objective optimization according to claim 3, characterized in that: The modeling process for multi-objective optimization problems is as follows: The production data and the true values ​​of the sugarcane pressing process index results obtained from the subsequent observations are obtained, and the true values ​​are used as the expected data of the model. The prediction interval width PINAW is used to characterize the uncertainty of the model prediction interval PI, and the prediction interval coverage PICP is used to characterize the reliability of the model prediction interval. The multi-objective optimization problem is modeled as follows: In the established multi-objective optimization model, max Obj1 represents maximization of objective 1, min Obj2 represents minimization of objective 2, stPINC≤PICP<100% and PINAW>0 are constraints; to meet the corresponding constraints, a solution must be found at PICP≥PINC.

5. The sugarcane squeezing process index interval prediction method based on multi-objective optimization according to claim 4, characterized in that: The specific steps of the method of using multi-objective particle swarm optimization to optimize the kernel extreme learning machine model to construct the prediction interval are as follows: 1) Divide the production data into training set and test set; 2) Generate an initial population, initialize parameters, and apply the kernel extreme learning machine model with the initialized parameters to the training set; 3) Compare the true value with the prediction interval obtained from the training set, calculate the evaluation index, and form the objective function according to the formula for modeling the multi-objective optimization problem; 4) In each iteration, the multi-objective particle swarm algorithm is used to optimize the parameters of the kernel extreme learning machine model, the prediction interval obtained from the training set is used to calculate the objective function, and the Pareto solution set is updated; 5) The optimal compromise solution is selected from the corresponding Pareto front using the approximate ideal solution sorting method based on entropy weight; the optimal parameters are assigned to the kernel extreme learning machine model and applied to the test set, and finally the prediction interval results of the sugarcane pressing process indicators are output.

6. The method for predicting the interval of sugarcane pressing process indexes based on multi-objective optimization according to claim 5, characterized in that: In the data input in step 1), the training set data is calculated according to the following formula to obtain the initial output interval of the training set; AND i =[and i (1-a),and i (1+a)] Among them, y i is the original output, Y i is the output interval after processing, and α is the error probability.

7. The method for predicting the interval of sugarcane pressing process indexes based on multi-objective optimization according to claim 6, characterized in that: The evaluation index of step 3) includes at least the prediction interval coverage ratio PICP and the prediction interval width PINAW.

8. The method for predicting the interval of sugarcane pressing process indexes based on multi-objective optimization according to claim 7, characterized in that: The evaluation indicators also include: average error coverage rate ACE, average prediction width MPI, Winkler score or interval score W S , any one of the coverage width criterion CWC.

9. The method for predicting intervals of sugarcane pressing process indicators based on multi-objective optimization according to claim 8, characterized in that: The evaluation index is further used to evaluate the quality of the prediction interval.

10. A device comprising a processor and a memory, characterized in that: The memory stores executable codes, and when the processor executes the executable codes, the method according to any one of claims 1 to 8 is implemented.

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