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CN112329324B - Construction method of aluminum electrolytic power consumption evolution model based on MCMC-UPFNN - Google Patents

Construction method of aluminum electrolytic power consumption evolution model based on MCMC-UPFNN Download PDF

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CN112329324B
CN112329324B CN202011184199.XA CN202011184199A CN112329324B CN 112329324 B CN112329324 B CN 112329324B CN 202011184199 A CN202011184199 A CN 202011184199A CN 112329324 B CN112329324 B CN 112329324B
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姚立忠
丁伟
聂玲
张玉泽
李太福
易军
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Chongqing University of Science and Technology
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Abstract

本发明提供一种基于MCMC‑UPFNN的铝电解工耗演化模型构建方法，所述铝电解工耗演化模型构建方法采用如下步骤：S1，建立基于神经网络的滤波方程；S2，从神经网络权值阈值所建立的先验分布中抽取N个粒子

Figure DDA0002750998490000011
i＝1，2，…，N；S3，在每一时刻用无迹卡尔曼滤波更新S2的粒子；S4，通过有效粒子数判断是否进一步更新粒子；S5，通过MCMC方法来产生新的粒子；S6，融合结果输出。本发明的有益效果是，在保持粒子多样性的同时，提高了模型的自适应能力，使得铝电解工耗演化模型的预测更准确。

Figure 202011184199

The present invention provides a method for constructing an evolution model of power consumption of aluminum electrolysis based on MCMC-UPFNN. The method for constructing a power consumption evolution model of aluminum electrolysis adopts the following steps: S1, establishing a filtering equation based on a neural network; S2, obtaining weights from a neural network N particles are drawn from the prior distribution established by the threshold

Figure DDA0002750998490000011
i=1, 2,..., N; S3, use the unscented Kalman filter to update the particles of S2 at each moment; S4, judge whether to update the particles further by the number of effective particles; S5, generate new particles through the MCMC method; S6, outputting the fusion result. The beneficial effect of the invention is that while maintaining the diversity of particles, the self-adaptive ability of the model is improved, so that the prediction of the evolution model of the aluminum electrolytic power consumption is more accurate.

Figure 202011184199

Description

基于MCMC-UPFNN的铝电解工耗演化模型构建方法Construction method of aluminum electrolytic power consumption evolution model based on MCMC-UPFNN

技术领域technical field

本发明涉及构建铝电解工耗演化模型技术领域，具体的说，涉及一种基于MCMC-UPFNN的铝电解工耗演化模型构建方法。The invention relates to the technical field of building an aluminum electrolysis power consumption evolution model, in particular to a method for building an aluminum electrolysis power consumption evolution model based on MCMC-UPFNN.

背景技术Background technique

如今，电解铝产品已广泛应用于航天、交通、建筑、机械制造等重要领域，在世界工业发展过程中占有举足轻重的战略地位。然而，我国铝电解工业已进入到技术瓶颈期，其主要原因是铝电解工耗过高。因此，研究高精度铝电解工耗建模技术对工业生产提质增效具有重要意义。Today, electrolytic aluminum products have been widely used in important fields such as aerospace, transportation, construction, and machinery manufacturing, and occupy a pivotal strategic position in the process of world industrial development. However, my country's aluminum electrolysis industry has entered a technical bottleneck period, the main reason being the high labor consumption of aluminum electrolysis. Therefore, it is of great significance to study the high-precision aluminum electrolytic power consumption modeling technology to improve the quality and efficiency of industrial production.

铝电解工艺制造系统存在一系列的物理化学反应，机理复杂不易量化。因神经网络可处理系统机理未知的建模问题而备受关注。然而，当传统神经网络建模完成时，其权值和阈值将保持不变。当铝电解系统工艺参数因实时工况变化而发生改变时，基于先前数据所建立的静态神经网络模型将无法满足铝电解工艺条件动态优化的需求。此时，为保证工耗模型对铝电解制造系统运行规律具有一定的渐进学习能力，可引进滤波技术来实时更新系统模型参数。There are a series of physical and chemical reactions in the aluminum electrolysis process manufacturing system, and the mechanism is complex and difficult to quantify. It has attracted much attention because neural networks can deal with modeling problems where the mechanism of the system is unknown. However, when a traditional neural network is modeled, its weights and thresholds remain the same. When the process parameters of the aluminum electrolysis system change due to real-time working conditions, the static neural network model established based on the previous data will not be able to meet the needs of dynamic optimization of the aluminum electrolysis process conditions. At this time, in order to ensure that the labor consumption model has a certain gradual learning ability for the operation rules of the aluminum electrolysis manufacturing system, filtering technology can be introduced to update the system model parameters in real time.

滤波神经网络本质是通过引入扩展卡尔曼滤波和无迹卡尔曼滤波技术对神经网络的权值阈值进行动态调整。相比于静态神经网络模型，EKFNN与UKFNN所建立的模型能够随工艺条件的改变而实时变化，具有良好的渐进学习能力，有效拓展了铝电解工耗建模技术。但已有技术往往限定在高斯环境的假设条件下，缺乏对非线性非高斯系统工耗建模技术的探讨，而实际上铝电解系统具有噪声密集且分布类型未知等特征。The essence of filtering neural network is to dynamically adjust the weight threshold of neural network by introducing extended Kalman filter and unscented Kalman filter technology. Compared with the static neural network model, the models established by EKFNN and UKFNN can change in real time with the change of process conditions, have good gradual learning ability, and effectively expand the modeling technology of aluminum electrolysis power consumption. However, existing technologies are often limited to Gaussian environment assumptions, and lack of discussion on nonlinear non-Gaussian system power consumption modeling technology. In fact, aluminum electrolysis systems are characterized by dense noise and unknown distribution types.

发明内容Contents of the invention

本发明的目的是提供一种能够适用于噪声密集且分布类型未知环境的基于MCMC-UPFNN的铝电解工耗演化模型构建方法，将神经网络与无迹粒子滤波结合来更新权值阈值，并用MCMC理论解决粒子多样性损失问题，提高模型的自适应能力和预测能力。The purpose of the present invention is to provide a method for building an evolution model of aluminum electrolysis power consumption based on MCMC-UPFNN, which can be applied to environments with dense noise and unknown distribution types. The neural network and unscented particle filter are combined to update the weight threshold, and use MCMC Theoretically solve the problem of particle diversity loss and improve the adaptive ability and predictive ability of the model.

为达到上述目的，本发明采用的具体技术方案如下：In order to achieve the above object, the concrete technical scheme that the present invention adopts is as follows:

本发明提供一种基于MCMC-UPFNN的铝电解工耗演化模型构建方法，其特征在于，所述铝电解工耗演化模型构建方法采用如下步骤：The present invention provides a MCMC-UPFNN-based method for building an evolution model of aluminum electrolysis power consumption, which is characterized in that the method for building an aluminum electrolysis power consumption evolution model adopts the following steps:

S1，建立基于神经网络的滤波方程；S1, establishing a filtering equation based on a neural network;

S2，从神经网络权值阈值所建立的先验分布中抽取N个粒子

Figure BDA0002750998470000021
Figure BDA0002750998470000022
S2, extract N particles from the prior distribution established by the neural network weight threshold
Figure BDA0002750998470000021
Figure BDA0002750998470000022

S3，在每一时刻用无迹卡尔曼滤波更新S2的粒子；S3, update the particles of S2 with unscented Kalman filter at each moment;

S4，通过有效粒子数判断是否进一步更新粒子；S4, judging whether to further update particles according to the number of effective particles;

S5，使用MCMC理论来产生新的粒子；S5, using MCMC theory to generate new particles;

S6，融合结果输出。S6, outputting the fusion result.

进一步的，步骤S3的具体步骤如下：Further, the specific steps of step S3 are as follows:

S3.1，采用以下公式计算每个粒子的西格玛点，S3.1, calculate the sigma point of each particle using the following formula,

Figure BDA0002750998470000023
Figure BDA0002750998470000023

式中，λ为比例系数，nα为无迹卡尔曼滤波中设定参数，i(a)表示Sigma点集序号，

Figure BDA0002750998470000024
表示原采样点；In the formula, λ is the proportional coefficient, n α is the parameter set in the unscented Kalman filter, i(a) represents the number of the Sigma point set,
Figure BDA0002750998470000024
Indicates the original sampling point;

S3.2，时间更新；S3.2, time update;

Figure BDA0002750998470000031
Figure BDA0002750998470000031

Figure BDA0002750998470000032
Figure BDA0002750998470000032

Figure BDA0002750998470000033
Figure BDA0002750998470000033

Figure BDA0002750998470000034
Figure BDA0002750998470000034

其中，χ为通过UT变换得到的采样点；

Figure BDA0002750998470000035
表示原采样点，
Figure BDA0002750998470000036
表示通过对称分布采样所得到的采样点；
Figure BDA00027509984700000312
为第j个采样点均值所对应的权值；
Figure BDA00027509984700000313
为第j个采样点方差所对应的权值，
Figure BDA00027509984700000314
表示采样点的协方差矩阵，k表示时刻序号，j表示采样点的序号，i表示粒子的序号，h(·)表示非线性测量函数，上标表示粒子序列，下标表示时间序列，i(x)表示对称采样后点集序号；Among them, χ is the sampling point obtained by UT transformation;
Figure BDA0002750998470000035
represents the original sampling point,
Figure BDA0002750998470000036
Indicates the sampling points obtained by sampling from a symmetrical distribution;
Figure BDA00027509984700000312
is the weight corresponding to the mean value of the jth sampling point;
Figure BDA00027509984700000313
is the weight corresponding to the variance of the jth sampling point,
Figure BDA00027509984700000314
Represents the covariance matrix of sampling points, k represents the time sequence number, j represents the sequence number of sampling points, i represents the particle sequence number, h(·) represents the nonlinear measurement function, the superscript represents the particle sequence, the subscript represents the time sequence, i( x) represents the serial number of the point set after symmetrical sampling;

S3.3，量测更新；S3.3, measurement update;

采用以下公式计算统计量y的均值

Figure BDA00027509984700000315
和方差
Figure BDA00027509984700000316
Calculate the mean of the statistic y using the following formula
Figure BDA00027509984700000315
and variance
Figure BDA00027509984700000316

Figure BDA0002750998470000037
Figure BDA0002750998470000037

Figure BDA0002750998470000038
Figure BDA0002750998470000038

Figure BDA0002750998470000039
Figure BDA0002750998470000039

Figure BDA00027509984700000310
Figure BDA00027509984700000310

Figure BDA00027509984700000311
Figure BDA00027509984700000311

Figure BDA0002750998470000041
Figure BDA0002750998470000041

其中，

Figure BDA0002750998470000042
为第j个采样点k时刻所对应的统计量，
Figure BDA0002750998470000043
为第k个采样点均值和统计量所对应的方差阵。in,
Figure BDA0002750998470000042
is the statistic corresponding to the jth sampling point k time,
Figure BDA0002750998470000043
is the variance matrix corresponding to the mean and statistics of the kth sampling point.

S3.4，采用密度分布函数N(·)来替代后验概率密度，再从

Figure BDA0002750998470000044
中抽取粒子，其中，q(·)为重要性函数，N(·)为高斯函数。S3.4, use the density distribution function N( ) to replace the posterior probability density, and then from
Figure BDA0002750998470000044
Particles are extracted in , where q(·) is the importance function, and N(·) is the Gaussian function.

进一步的，步骤S4包括，Further, step S4 includes,

计算权重并归一化：Compute weights and normalize:

Figure BDA0002750998470000045
Figure BDA0002750998470000045

Figure BDA0002750998470000046
Figure BDA0002750998470000046

其中，

Figure BDA0002750998470000047
为第i个采样点k-1时刻权值所对应的权重，
Figure BDA0002750998470000048
为第i个采样点k-1时刻所对应的权值，
Figure BDA0002750998470000049
为第i个采样点从零时刻到k-1时刻所对应的权值，y1：k为从零时刻到k时刻所对应的统计量。in,
Figure BDA0002750998470000047
is the weight corresponding to the weight of the i-th sampling point k-1 time,
Figure BDA0002750998470000048
is the weight corresponding to the i-th sampling point k-1 time,
Figure BDA0002750998470000049
is the weight corresponding to the i-th sampling point from time zero to time k-1, and y 1: k is the corresponding statistic from time zero to time k.

进一步的，步骤S5的具体步骤如下：Further, the specific steps of step S5 are as follows:

S5.1，计算粒子的接收概率：S5.1, calculate the acceptance probability of the particle:

Figure BDA00027509984700000410
Figure BDA00027509984700000410

S5.2，接受移动：S5.2, Accept the move:

Figure BDA00027509984700000411
Figure BDA00027509984700000411

S5.3，否则拒绝移动。S5.3, otherwise reject the move.

Figure BDA0002750998470000051
Figure BDA0002750998470000051

其中，yk为第k个采样点均值所对应的统计量，

Figure BDA0002750998470000052
为在MCMC采样阶段第i个采样点k时刻所对应的原权值，
Figure BDA0002750998470000053
为在MCMC采样阶段第i个采样点k时刻所对应的新权值。Among them, y k is the statistic corresponding to the mean value of the kth sampling point,
Figure BDA0002750998470000052
is the original weight corresponding to the i-th sampling point k in the MCMC sampling stage,
Figure BDA0002750998470000053
is the new weight corresponding to the i-th sampling point k in the MCMC sampling phase.

进一步的，步骤S6的具体步骤如下：Further, the specific steps of step S6 are as follows:

融合结果输出：Fusion result output:

Figure BDA0002750998470000054
Figure BDA0002750998470000054

MCMC表示马尔科夫链蒙特卡洛方法(Markov Chain Monte Carlo)。MCMC stands for Markov Chain Monte Carlo.

UPFNN表示无迹粒子滤波神经网络(Unscented Particle FilterNeuralNetwork)。UPFNN stands for Unscented Particle Filter Neural Network.

本发明的有益效果是，以建立的滤波方程为研究对象，将神经网络权值阈值作为UPF的状态变量；并引入MCMC理论来解决UPFNN中粒子多样性损失问题。所提出的算法建模与UKFNN模型相比，在保持粒子多样性的同时，提高了模型的自适应能力，使得铝电解工耗演化模型的预测更准确。The invention has the beneficial effects of taking the established filtering equation as the research object, using the weight threshold of the neural network as the state variable of the UPF; and introducing MCMC theory to solve the problem of particle diversity loss in the UPFNN. Compared with the UKFNN model, the proposed algorithm modeling improves the adaptive ability of the model while maintaining the particle diversity, making the prediction of the aluminum electrolytic power consumption evolution model more accurate.

附图说明Description of drawings

图1是本发明的流程图Fig. 1 is a flowchart of the present invention

图2是步骤S3的具体流程图Fig. 2 is the concrete flowchart of step S3

图3是步骤S5的具体流程图Fig. 3 is the concrete flowchart of step S5

图4是实施例检验样本预测效果图Fig. 4 is the forecasting effect figure of embodiment inspection sample

图5是UKFNN模型检验样本预测效果图Figure 5 is the prediction effect diagram of the UKFNN model test sample

图6是PFNN模型检验样本预测效果图Figure 6 is the prediction effect diagram of the PFNN model test sample

图7是UPFNN模型检验样本预测效果图Figure 7 is the prediction effect diagram of the UPFNN model test sample

图8是四种模型预测误差百分比对比图Figure 8 is a comparison chart of the prediction error percentages of the four models

具体实施方式Detailed ways

下面结合附图及具体实施例对本发明作进一步详细说明：Below in conjunction with accompanying drawing and specific embodiment the present invention is described in further detail:

如图1所示，一种基于MCMC-UPFNN的铝电解工耗演化模型构建方法，其特征在于：所述铝电解工耗演化模型构建方法采用如下步骤：As shown in Figure 1, a method for building an evolution model of aluminum electrolysis power consumption based on MCMC-UPFNN is characterized in that: the construction method for the evolution model of aluminum electrolysis power consumption adopts the following steps:

S1，建立基于神经网络的滤波方程：S1, establish the filtering equation based on the neural network:

Figure BDA0002750998470000061
Figure BDA0002750998470000061

其中，ωt表示t时刻状态变量(即神经网络的权值阈值)；ut表示t时刻铝电解制造系统的输入变量，yt表示t时刻量测变量(即评价工业制造系统优劣的输出变量)；θt和νt分别表示铝电解制造系统中过程噪声和量测噪声；非线性测量函数f(·)表示一个多层感知器。Among them, ω t represents the state variable at time t (that is, the weight threshold of the neural network); u t represents the input variable of the aluminum electrolysis manufacturing system at time t, and y t represents the measured variable at time t (that is, the output for evaluating the quality of the industrial manufacturing system variables); θ t and ν t represent the process noise and measurement noise in the aluminum electrolysis manufacturing system respectively; the nonlinear measurement function f( ) represents a multilayer perceptron.

S2，从神经网络权值阈值所建立的先验分布中抽取N个粒子

Figure BDA0002750998470000062
Figure BDA0002750998470000063
(注：这里把神经网络的权值阈值作为粒子滤波中的粒子)S2, extract N particles from the prior distribution established by the neural network weight threshold
Figure BDA0002750998470000062
Figure BDA0002750998470000063
(Note: Here, the weight threshold of the neural network is used as the particle in the particle filter)

Figure BDA0002750998470000064
Figure BDA0002750998470000064

Figure BDA0002750998470000065
Figure BDA0002750998470000065

由于模型构建时假设系统测量噪声vk和过程噪声θk为0均值高斯噪声，方差分别为R和Q，故：Since the system measurement noise v k and process noise θ k are assumed to be 0-mean Gaussian noise when the model is constructed, the variances are R and Q respectively, so:

Figure BDA0002750998470000066
Figure BDA0002750998470000066

Figure BDA0002750998470000071
Figure BDA0002750998470000071

其中，

Figure BDA0002750998470000072
表示粒子的数学期望(均值)；
Figure BDA0002750998470000076
为粒子的方差阵；上标数字代表粒子序列，下标数字代表时刻序列；
Figure BDA0002750998470000077
表示状态变量、测量噪声、过程噪声的均值矩阵集合；
Figure BDA0002750998470000078
表示状态变量、测量噪声、过程噪声的方差阵集合。in,
Figure BDA0002750998470000072
Represents the mathematical expectation (mean) of the particle;
Figure BDA0002750998470000076
is the variance matrix of particles; the superscript number represents the particle sequence, and the subscript number represents the time sequence;
Figure BDA0002750998470000077
Represents a set of mean matrices of state variables, measurement noise, and process noise;
Figure BDA0002750998470000078
A collection of variance matrices representing state variables, measurement noise, and process noise.

S3，在每一时刻用无迹Kalman滤波更新S2的粒子；S3, update the particles of S2 with unscented Kalman filter at each moment;

S4，通过有效粒子数判断是否采用SIR来进一步更新粒子；S4, judging whether to use SIR to further update particles according to the number of effective particles;

计算权重并归一化：Compute weights and normalize:

Figure BDA0002750998470000073
Figure BDA0002750998470000073

Figure BDA0002750998470000074
Figure BDA0002750998470000074

若

Figure BDA0002750998470000075
(Neff为有效粒子数，Nth为设定的阈值，一般取为N/3)则说明粒子的权值已经退化严重，需要进行二次重采样，从而采样出新的粒子。like
Figure BDA0002750998470000075
(N eff is the number of effective particles, N th is the set threshold, generally taken as N/3), which means that the weight of the particles has degraded seriously, and a second resampling is required to sample new particles.

S5，采用MCMC理论中贝叶斯推断Metropolis-Hastings(MH)算法产生新的粒子；S5, using Bayesian inference Metropolis-Hastings (MH) algorithm in MCMC theory to generate new particles;

S6，融合结果输出：S6, fusion result output:

Figure BDA0002750998470000081
Figure BDA0002750998470000081

如图2所示，步骤S3的具体步骤如下：As shown in Figure 2, the specific steps of step S3 are as follows:

S3.1，计算每个粒子的Sigma点：S3.1, calculate the Sigma point of each particle:

Figure BDA0002750998470000082
Figure BDA0002750998470000082

式中：k＝1，2，…；λ＝α2(nx+κ)-nx为比例系数，α的大小决定了选取的样本点围绕均值

Figure BDA0002750998470000088
的分布情况，它越小则可以更大程度的降低高阶效应；κ与nx、na为无迹Kalman滤波中设定参数。In the formula: k=1, 2,...; λ=α 2 (n x +κ)-n x is the proportional coefficient, and the size of α determines the selected sample points around the mean value
Figure BDA0002750998470000088
The distribution of , the smaller it is, the higher order effect can be reduced to a greater extent; κ and n x , na are the setting parameters in the unscented Kalman filter.

S3.2，时间更新(粒子递推)；S3.2, time update (particle recursion);

Figure BDA0002750998470000083
Figure BDA0002750998470000083

Figure BDA0002750998470000084
Figure BDA0002750998470000084

Figure BDA0002750998470000085
Figure BDA0002750998470000085

Figure BDA0002750998470000086
Figure BDA0002750998470000086

其中，χ为通过UT变换得到的采样点；

Figure BDA0002750998470000089
表示原采样点，
Figure BDA00027509984700000810
表示通过对称分布采样所得到的采样点；
Figure BDA00027509984700000811
为第j个采样点均值所对应的权值；
Figure BDA0002750998470000087
为第j个采样点方差所对应的权值。Among them, χ is the sampling point obtained by UT transformation;
Figure BDA0002750998470000089
represents the original sampling point,
Figure BDA00027509984700000810
Indicates the sampling points obtained by sampling from a symmetrical distribution;
Figure BDA00027509984700000811
is the weight corresponding to the mean value of the jth sampling point;
Figure BDA0002750998470000087
is the weight corresponding to the variance of the jth sampling point.

S3.3，量测更新(结合新的测量值)；S3.3, measurement update (combined with new measurement value);

统计量y的均值

Figure BDA00027509984700000911
和方差
Figure BDA00027509984700000912
计算过程如下：the mean of the statistic y
Figure BDA00027509984700000911
and variance
Figure BDA00027509984700000912
The calculation process is as follows:

Figure BDA0002750998470000091
Figure BDA0002750998470000091

Figure BDA0002750998470000092
Figure BDA0002750998470000092

Figure BDA0002750998470000093
Figure BDA0002750998470000093

Figure BDA0002750998470000094
Figure BDA0002750998470000094

Figure BDA0002750998470000095
Figure BDA0002750998470000095

Figure BDA0002750998470000096
Figure BDA0002750998470000096

S3.4，采用密度分布函数N(·)来替代后验概率密度，再从

Figure BDA0002750998470000097
中抽取粒子。S3.4, use the density distribution function N( ) to replace the posterior probability density, and then from
Figure BDA0002750998470000097
extract particles.

如图3所示，步骤S5的具体步骤如下：As shown in Figure 3, the specific steps of step S5 are as follows:

S5.1，计算粒子的接收概率：S5.1, calculate the acceptance probability of the particle:

Figure BDA0002750998470000098
Figure BDA0002750998470000098

S5.2，接受移动：S5.2, Accept the move:

Figure BDA0002750998470000099
Figure BDA0002750998470000099

S5.3，否则拒绝移动：S5.3, otherwise reject the move:

Figure BDA00027509984700000910
Figure BDA00027509984700000910

本实施例采用9种与铝电解工艺相关的决策变量，分别是：铝水平(cm)、电解质水平(cm)、系列电流(A)、工作电压(mV)、出铝量(kg)、NB次数、分子比、槽温(℃)和氟化盐日用量(kg)；同时，将测量值取吨铝直流电耗(kW.h/t-Al)作为输出参数；In this embodiment, 9 decision variables related to the aluminum electrolysis process are used, namely: aluminum level (cm), electrolyte level (cm), series current (A), working voltage (mV), aluminum output (kg), NB Number of times, molecular ratio, bath temperature (°C) and daily fluoride salt consumption (kg); at the same time, take the measured value as the output parameter of DC power consumption per ton of aluminum (kW.h/t-Al);

其中，电解槽数据样本共计873组，将800组作为训练样本，73组作为检验样本。Among them, there are a total of 873 groups of electrolyzer data samples, 800 groups are used as training samples, and 73 groups are used as test samples.

根据神经网络隐含层经验公式，模型选择9个输入层、10个隐含层、1个输出层。According to the empirical formula of the hidden layer of the neural network, the model selects 9 input layers, 10 hidden layers, and 1 output layer.

则采用本发明的MCMC-UPFNN算法建模的预测性能如图4，另同样采用UKFNN、PFNN、UPFNN算法进行建模对比，三种算法的预测性能如图5、图6、图7所示。Then adopt the prediction performance of MCMC-UPFNN algorithm modeling of the present invention as shown in Figure 4, and use UKFNN, PFNN, UPFNN algorithm to carry out modeling comparison in addition, the prediction performance of three kinds of algorithms is shown in Figure 5, Figure 6, Figure 7.

从图中可以看出，UKFNN、PFNN、UPFNN算法的预测效果弱于MCMC-UPFNN，这是由于MCMC-UPFNN算法可应用于噪声密集且分布类型未知系统；并且MCMC理论能保持PFNN中粒子的多样性，并降低粒子运算量，提高建模精度。It can be seen from the figure that the prediction effect of the UKFNN, PFNN, and UPFNN algorithms is weaker than that of the MCMC-UPFNN algorithm, because the MCMC-UPFNN algorithm can be applied to systems with dense noise and unknown distribution types; and MCMC theory can maintain the diversity of particles in PFNN performance, reduce the amount of particle calculations, and improve modeling accuracy.

四种算法建模预测误差百分比由图8展示出，具体性能指标对比如下表：The percentages of modeling prediction errors of the four algorithms are shown in Figure 8, and the specific performance indicators are compared in the following table:

Figure BDA0002750998470000101
Figure BDA0002750998470000101

可以看出，MCMC-UPFNN的预测精度误差比UKFNN降低了5％左右，同时也降低了粒子运算量，因此在噪声密集且分布类型未知系统中更加有效地提高了铝电解工耗演化模型的预测性能。It can be seen that the prediction accuracy error of MCMC-UPFNN is about 5% lower than that of UKFNN, and at the same time, the amount of particle calculation is also reduced. Therefore, in the system with dense noise and unknown distribution type, the prediction of the evolution model of aluminum electrolytic power consumption is more effectively improved. performance.

以上所述仅为本发明的优选实施例而已，并不用于限制本发明，对于本领域的技术人员来说，本发明可以有各种更改和变化。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (2)

1.一种基于MCMC-UPFNN的铝电解工耗演化模型构建方法，其特征在于，所述铝电解工耗演化模型构建方法采用如下步骤：1. A method for building an evolution model of aluminum electrolysis power consumption based on MCMC-UPFNN, characterized in that, the method for building an evolution model of aluminum electrolysis power consumption adopts the following steps: S1，建立基于神经网络的滤波方程；S1, establishing a filtering equation based on a neural network; S2，从神经网络权值阈值所建立的先验分布中抽取N个粒子
Figure FDA0003939671490000011
Figure FDA0003939671490000012
S2, extract N particles from the prior distribution established by the neural network weight threshold
Figure FDA0003939671490000011
Figure FDA0003939671490000012
 S3，在每一时刻用无迹卡尔曼滤波更新S2的粒子；S3, update the particles of S2 with unscented Kalman filter at each moment; S4，通过有效粒子数判断是否进一步更新粒子；S4, judging whether to further update particles according to the number of effective particles; S5，使用MCMC理论来产生新的粒子；S5, using MCMC theory to generate new particles; S6，融合结果输出，根据神经网络隐含层经验公式，模型选择9个输入层、10个隐含层、1个输出层，并使用电解槽数据样本对所述模型进行训练和检验；S6, the fusion result output, according to the neural network hidden layer empirical formula, the model selects 9 input layers, 10 hidden layers, and 1 output layer, and uses the electrolyzer data samples to train and test the model; 所述模型采用9种与铝电解工艺相关的决策变量，分别是：铝水平、电解质水平、系列电流、工作电压、出铝量、NB次数、分子比、槽温和氟化盐日用量；同时，将测量值取吨铝直流电耗作为所述模型的输出参数；The model uses 9 decision variables related to the aluminum electrolysis process, which are: aluminum level, electrolyte level, series current, working voltage, aluminum output, NB times, molecular ratio, bath temperature and daily fluoride salt consumption; at the same time, Taking the measured value as the output parameter of the model; 步骤S3的具体步骤如下：The specific steps of step S3 are as follows: S3.1，采用以下公式计算每个粒子的西格玛点，S3.1, calculate the sigma point of each particle using the following formula,
Figure FDA0003939671490000013
Figure FDA0003939671490000013
 式中，λ为比例系数，nα为无迹卡尔曼滤波中设定参数，i(a)表示Sigma点集序号，
Figure FDA0003939671490000014
表示原采样点；In the formula, λ is the proportional coefficient, n α is the parameter set in the unscented Kalman filter, i(a) represents the number of the Sigma point set,
Figure FDA0003939671490000014
Indicates the original sampling point; S3.2，时间更新；S3.2, time update;
Figure FDA0003939671490000015
Figure FDA0003939671490000015
Figure FDA0003939671490000021
Figure FDA0003939671490000021
Figure FDA0003939671490000022
Figure FDA0003939671490000022
Figure FDA0003939671490000023
Figure FDA0003939671490000023
 其中，x为通过UT变换得到的采样点；
Figure FDA0003939671490000024
表示原采样点，
Figure FDA0003939671490000025
表示通过对称分布采样所得到的采样点；
Figure FDA0003939671490000026
为第j个采样点均值所对应的权值；
Figure FDA0003939671490000027
为第j个采样点方差所对应的权值，
Figure FDA0003939671490000028
表示采样点的协方差矩阵，k表示时刻序号，j表示采样点的序号，i表示粒子的序号，h(·)表示非线性测量函数，上标表示粒子序列，下标表示时间序列，i(x)表示对称采样后点集序号；Among them, x is the sampling point obtained by UT transformation;
Figure FDA0003939671490000024
represents the original sampling point,
Figure FDA0003939671490000025
Indicates the sampling points obtained by sampling from a symmetrical distribution;
Figure FDA0003939671490000026
is the weight corresponding to the mean value of the jth sampling point;
Figure FDA0003939671490000027
is the weight corresponding to the variance of the jth sampling point,
Figure FDA0003939671490000028
Represents the covariance matrix of sampling points, k represents the time sequence number, j represents the sequence number of sampling points, i represents the particle sequence number, h(·) represents the nonlinear measurement function, the superscript represents the particle sequence, the subscript represents the time sequence, i( x) represents the serial number of the point set after symmetrical sampling; S3.3，量测更新；S3.3, measurement update; 采用以下公式计算统计量y的均值
Figure FDA0003939671490000029
和方差
Figure FDA00039396714900000210
Calculate the mean of the statistic y using the following formula
Figure FDA0003939671490000029
and variance
Figure FDA00039396714900000210
Figure FDA00039396714900000211
Figure FDA00039396714900000211
Figure FDA00039396714900000212
Figure FDA00039396714900000212
Figure FDA00039396714900000213
Figure FDA00039396714900000213
Figure FDA00039396714900000214
Figure FDA00039396714900000214
Figure FDA00039396714900000215
Figure FDA00039396714900000215
Figure FDA00039396714900000216
Figure FDA00039396714900000216
 其中，
Figure FDA0003939671490000031
为第j个采样点k时刻所对应的统计量，
Figure FDA0003939671490000032
为第k个采样点均值和统计量所对应的方差阵；in,
Figure FDA0003939671490000031
is the statistic corresponding to the jth sampling point k time,
Figure FDA0003939671490000032
is the variance matrix corresponding to the mean value and statistics of the kth sampling point; S3.4，采用密度分布函数N(·)来替代后验概率密度，再从
Figure FDA0003939671490000033
中抽取粒子，其中，q(·)为重要性函数，N(·)为高斯函数；S3.4, use the density distribution function N( ) to replace the posterior probability density, and then from
Figure FDA0003939671490000033
Particles are extracted from , where q(·) is the importance function, and N(·) is the Gaussian function; 步骤S4包括，Step S4 includes, 计算权重并归一化：Compute weights and normalize:
Figure FDA0003939671490000034
Figure FDA0003939671490000034
Figure FDA0003939671490000035
Figure FDA0003939671490000035
 其中,
Figure FDA0003939671490000036
为第i个采样点k-1时刻权值所对应的权重，
Figure FDA0003939671490000037
为第i个采样点k-1时刻所对应的权值，
Figure FDA0003939671490000038
为第i个采样点从零时刻到k-1时刻所对应的权值，y1:k为从零时刻到k时刻所对应的统计量；in,
Figure FDA0003939671490000036
is the weight corresponding to the weight of the i-th sampling point k-1 time,
Figure FDA0003939671490000037
is the weight corresponding to the i-th sampling point k-1 time,
Figure FDA0003939671490000038
is the weight corresponding to the i-th sampling point from time zero to time k-1, and y 1:k is the corresponding statistic from time zero to time k; 步骤S5的具体步骤如下：The specific steps of step S5 are as follows: S5.1，计算粒子的接收概率：S5.1, calculate the acceptance probability of the particle:
Figure FDA0003939671490000039
Figure FDA0003939671490000039
 S5.2，接受移动：S5.2, Accept the move:
Figure FDA00039396714900000310
Figure FDA00039396714900000310
 S5.3，否则拒绝移动；S5.3, otherwise reject the move;
Figure FDA0003939671490000041
Figure FDA0003939671490000041
 其中，yk为第k个采样点均值所对应的统计量，
Figure FDA0003939671490000042
为在MCMC采样阶段第i个采样点k时刻所对应的原权值，
Figure FDA0003939671490000043
为在MCMC采样阶段第i个采样点k时刻所对应的新权值。Among them, y k is the statistic corresponding to the mean value of the kth sampling point,
Figure FDA0003939671490000042
is the original weight corresponding to the i-th sampling point k in the MCMC sampling stage,
Figure FDA0003939671490000043
is the new weight corresponding to the i-th sampling point k in the MCMC sampling phase. 2.根据权利要求1所述的基于MCMC-UPFNN的铝电解工耗演化模型构建方法，其特征在于：步骤S6的具体步骤如下：2. The MCMC-UPFNN-based aluminum electrolysis power consumption evolution model building method according to claim 1 is characterized in that: the concrete steps of step S6 are as follows: 融合结果输出：Fusion result output:
Figure FDA0003939671490000044
Figure FDA0003939671490000044
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