WO2024016556A1 - 一种适用于流程工业预测控制的模型自主学习方法 - Google Patents

一种适用于流程工业预测控制的模型自主学习方法 Download PDF

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WO2024016556A1
WO2024016556A1 PCT/CN2022/136000 CN2022136000W WO2024016556A1 WO 2024016556 A1 WO2024016556 A1 WO 2024016556A1 CN 2022136000 W CN2022136000 W CN 2022136000W WO 2024016556 A1 WO2024016556 A1 WO 2024016556A1
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model
transfer function
function model
parameter
parameters
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褚健
刘磊
冯凯
王家栋
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中控技术股份有限公司
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02PCLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

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  • the invention relates to the field of process industry prediction technology, and specifically relates to a model autonomous learning method suitable for process industry prediction control.
  • model predictive control is not only suitable for controlled objects that are difficult to control such as multi-coupling and large time delays, but also can model constraints such as process conditions and economic indicators, and cooperate with optimization technology to complete control tasks. Therefore, model predictive control has broad application prospects in the process industry.
  • the dynamic characteristics of the process will change as production targets change, production raw material ratio changes, equipment aging, insufficient catalyst activity and other factors. This change can cause a mismatch between the predictive model of predictive control and the dynamic characteristics of the real process.
  • the controller can achieve more accurate process output prediction, which will in turn help improve the control effect.
  • the industry has some ideas or methods to deal with changing dynamic characteristics, such as nonlinear modeling, multi-condition modeling, online identification and other methods.
  • the existing methods have the following shortcomings in implementation.
  • the first point is for nonlinear modeling and multi-condition modeling.
  • the large number of three transmission and one reverse processes in the process industry increases the difficulty of mechanism modeling, and it is difficult for on-site operation data to cover all working conditions. Therefore, data-driven modeling methods can only establish partial models or partial working condition models. If it is put into operation Running under unknown working conditions still requires a method of model online learning.
  • the second point is about online identification methods.
  • existing methods mostly use linear regression to model dynamic characteristics.
  • the parameters lack actual physical meaning, and there is also a lack of reasonable constraints on the parameters during identification, resulting in excessive freedom in identifying parameters.
  • the dynamic characteristics of the process Often changing slowly, the currently running prediction model should be instructive for new dynamic characteristic parameters.
  • no technical method has been found that can effectively take into account these two aspects.
  • the present invention provides a model autonomous learning method suitable for process industry predictive control.
  • the characteristics of this method are: first, it can learn the dynamic characteristics of the process independently online. It can be applied to multi-input and multi-output systems by dividing multi-input and single-output subsystems. Of course, it is also suitable for systems that are simpler than multi-input and multi-output systems.
  • the type of parameters to be learned can be automatically selected according to the preset model parameters, so that the parameters to be learned have real physical meanings, and during the learning process, the preset model has a constraint effect on the results of model learning, so as to Improve the reliability of the model; third, test the learning results of the parameters and evaluate the prediction results of the model to further improve the reliability of the model; fourth, use the parameter dead zone to increase the stability of the model parameters and reduce Control effect fluctuations caused by frequent changes in model parameters.
  • the method of the present invention is an online learning method that integrates model knowledge and process data, and is suitable for model autonomous learning problems of predictive control in the process industry.
  • Natural angular frequency a physical quantity that describes how fast an object vibrates, and is related to the inherent properties of the vibration system.
  • Damping coefficient A parameter that characterizes the reduction of system energy during the motion of a second-order or higher-order system.
  • Prediction model refers to the quantitative relationship between things described in mathematical language or formulas used for prediction in predictive control.
  • Parameter dead zone When the parameter changes, if the change amplitude does not exceed this value, the parameter is considered not to have changed.
  • a model autonomous learning method suitable for predictive control in the process industry is implemented through a multi-input single-output system as a basic subsystem, including the following steps:
  • Step 1 Model setting and learning parameter self-selection: Set all transfer function models, calculate each transfer function model and automatically select the parameters to be learned.
  • setting the transfer function model specifically includes:
  • M ⁇ P transfer function models need to be set according to the template shown in Equation (1), and additional flags Int p,m are set to illustrate the transfer function model.
  • G p, m whether an additional first-order integration link is connected in series;
  • K p, m is the model gain
  • ⁇ p, m is the delay time
  • s is the pull operator
  • a p, m and b p, m are the quadratic term coefficients and linear terms of the transfer function characteristic polynomial respectively.
  • each transfer function model is calculated and the parameters to be learned are automatically selected.
  • * indicates the model parameter values set before model self-learning, specifically including:
  • Step 2 Parameter distribution modeling: For each transfer function model participating in learning, use the lognormal distribution to establish a lognormal distribution model for the learning parameters. Specifically include the following:
  • the lognormal distribution is used A lognormal distribution model is established for the distribution of model parameter values, that is, the transfer function model parameters obey a lognormal distribution, where ⁇ ⁇ and is a distribution parameter related to the lognormal distribution of parameter ⁇ ; according to the type of parameters to be learned described in step 1, the user sets the coefficient ⁇ ⁇
  • T 1 , T 2 , ⁇ n , ⁇ For the parameter values of the set transfer function model, the parameters of the lognormal distribution are solved according to Equation (3).
  • Step 3 Data collection and processing: Collect input variable and output variable data and the quality codes corresponding to the input variables and output variables online, and handle the situation where the quality code is a bad value. Specifically include the following:
  • Collect process variables and quality codes of sensors online specifically, collect input variable and output variable data and quality codes corresponding to input variables and output variables.
  • the quality code is used to indicate whether the collected input variables and output variables are valid, record
  • the input variable is u m (k)
  • the output variable is y p (k)
  • k is the sampling time;
  • the quality code of y p (k) is bad, continue to collect data until a good value appears in y p . If the number of consecutive bad values during the period is greater than or equal to the preset N bad , clear all collected variable historical data and restart Collect; otherwise, use the good value data points at both ends of the bad value data segment to linearly interpolate the bad value data segment to complete the historical data online and continue to collect data.
  • Step 4 Model parameter learning: Establish a mathematical optimization model for autonomous learning of the transfer function model based on Bayesian optimization theory, and use the differential evolution algorithm to optimize the transfer function model parameters. Specifically include the following:
  • the system impulse response sequence is calculated according to the transfer function model, and the prediction sequence of the system output variable is calculated by using the convolution of the impulse response sequence and the system input variable.
  • N popu is the population number set by the user; randomly select continuous data segments with a length of N DS , and randomly initialize the population parameters depending on the type of parameters to be learned.
  • the three steps in the standard differential evolution algorithm are repeatedly executed for multiple rounds: population evolution, individual mutation and individual selection, and are recorded and updated based on the principle of minimizing the objective function. and corresponding model parameters; finally, the parameter learning results corresponding to the optimal individual are recorded in or in, among, are the model gain, two linear term coefficients, natural angular frequency and damping ratio of the optimal individual for the rth model parameter learning respectively.
  • Step 5 Model parameter testing: Perform parameter testing on each parameter of each transfer function model, including normality testing, parameter dead zone judgment and mean testing. Specifically include the following:
  • the normality test method adopts the Shapiro-Wilk test method in GB/T 4882-2001, and calculates the characteristics according to Equation (6) according to the type of parameters being learned. For the sample data of x r , if the normality test fails, the parameter remains No change; otherwise, enter step two.
  • Step 6 Model prediction error comparison: Use the original transfer function model to calculate the prediction root mean square error, use the learned transfer function model to calculate the prediction root mean square error, and decide whether to update the transmission of the multi-input single-output system based on the relationship between the two. function model, and then return to step one to continue execution. Specifically include the following:
  • the present invention is an autonomous learning technology that supports online operation of model parameters, and can use online data to actively learn model parameters.
  • the transfer function template adopts the general form of a second-order transfer function, which can not only learn a stable second-order real characteristic root system model, but also learn a stable second-order conjugate complex characteristic root system model, so that the learning parameters Has clear physical meaning.
  • the reliability of the online learning results of the transfer function model is increased through two methods: the first one is to integrate the prior knowledge of the process into the learning process of the transfer function model.
  • the prior knowledge includes the process being put into operation.
  • the second type includes parameter testing and comparison of the prediction error results of the transfer function model.
  • the parameter dead zone method is used to increase the stability of the transfer function model parameters.
  • the transfer function model parameters will not change, thereby increasing The stationarity of the transfer function model parameters is conducive to the stability of the control effect.
  • the parameter distribution assumption of the transfer function model of the lognormal distribution is adopted.
  • the value range of the random variable of the lognormal distribution is the positive domain, and the effective
  • the value ranges of , ⁇ n and ⁇ are also positive ranges, that is, they match; on the other hand, for the gain of the transfer function model, a larger gain will make the control slower, but a smaller gain may make the system unstable. Therefore, we should be more cautious when reducing the gain; while the probability density function curve of the lognormal distribution has a steeper shape to the left of the maximum value, and the probability density decays faster as the gain decreases; therefore, this prior model is suitable for gain Model the risks associated with being too small.
  • Figure 1 shows a flow chart of the model autonomous learning method suitable for process industry predictive control according to the present invention.
  • Figure 2 shows the three-step flow chart of normality testing, parameter dead zone judgment and mean value testing in the model parameter testing step.
  • Figure 3 shows the learning results of the transfer function model at different eta 2 and the step response curve of the original transfer function model.
  • Figure 4 shows the partial learning results of the transfer function model and the step response curve of the original transfer function model when using the parameter-free dead zone method.
  • the model autonomous learning method suitable for process industry predictive control according to the present invention can be applied to multiple input multiple output systems. Specifically, it is based on the division of multiple input single output subsystems. Therefore, in the specific implementation, Multiple input single output subsystems are described in detail.
  • Step 1 Model setting and learning parameter self-selection: Set all transfer function models, calculate each transfer function model and automatically select the parameters to be learned.
  • the transfer function model G 1,1 For the transfer function model G 1,1 , its characteristic polynomial (excluding pure integrals) can be decomposed into the form of a product of first-order polynomials in the real number domain. Therefore, calculated according to equation (2), the parameters to be learned for G 1,1 are K 1,1 and T 11,1 , and and
  • G 1,2 its characteristic polynomial (excluding pure integrals) contains two conjugate complex roots, so the parameters to be learned for G 1,2 are K 1,2 , ⁇ n1,2 and ⁇ 1,2 , and after transforming the characteristic polynomial into zero-pole form, we can know and
  • Step 2 Parameter distribution modeling: For each transfer function model participating in learning, use the lognormal distribution to establish a lognormal distribution model for the learning parameters.
  • Step 3 Data collection and processing: Collect input variable and output variable data and the quality codes corresponding to the input variables and output variables online, and handle the situation where the quality code is a bad value.
  • the input variables are u 1 (k) and u 2 (k), and the output variable is y 1 ( k), k is the sampling time;
  • the quality code of y 1 (k) is bad, continue to collect data until a good value appears in y 1. If the number of consecutive bad values during the period is greater than or equal to the preset N bad , clear all collected variable historical data and restart Collection, if the number of consecutive bad values during the period is less than N bad , use the good value data points at both ends of the bad value data segment to perform linear interpolation on the bad value data segment and then complete the historical data online to continue collecting data.
  • Step 4 Model parameter learning: Establish a mathematical optimization model for autonomous learning of the transfer function model based on Bayesian optimization theory, and use the differential evolution algorithm to optimize the transfer function model parameters.
  • Bilinear transformation is used for discretization to obtain the transfer G 1, 1 and G 1
  • the recursive function model calculates the predicted values output by the transfer function model G 1,1 and G 1,2 according to Equation (8) and Among them, ⁇ is the difference operator.
  • the three steps in the standard differential evolution algorithm are repeatedly executed for multiple rounds: population evolution, individual mutation and individual selection, and are recorded and updated based on the principle of minimizing the objective function. and corresponding model parameters, and finally record the parameter learning results corresponding to the optimal individual in and middle.
  • Step 5 Model parameter testing: Perform parameter testing on each parameter of each transfer function model, including normality testing, parameter dead zone judgment and mean testing.
  • Step 1 Normality test: Calculate the sample data of feature x r according to formula (6) according to the parameter type being learned. For example, if the test results of parameters T 1p and m fail, then the parameters T 1p and m remain unchanged at 5; if other parameters pass, step 2 will be entered.
  • Step 6 Model prediction error comparison: Use the original transfer function model to calculate the prediction root mean square error, use the learned transfer function model to calculate the prediction root mean square error, and decide whether to update the transmission of the multi-input single-output system based on the relationship between the two. function model, and then return to step one to continue execution.
  • This specific embodiment is a multi-input single-output system shown in formula (12).
  • the input variable is the water temperature set value of the two branches, and the output variable is the main road water temperature.
  • the control scheme Two branch circuits are used to control the water temperature of the main circuit.
  • eta 2 takes the value 0.3, the step response curve of the learning result of G 1,1 (s) is closer to The step response curve of G 1,1 (s) has a small change in model parameters; when eta 2 takes a value of 0.8, the step response curve of the learning result of G 1,1 (s) is further away from The step response curve has a large degree of change in the model parameters.
  • ⁇ 2 will affect the learning results of the G 1,1 (s) transfer function model.
  • the user can set different ⁇ 2 to control the parameter change speed of the model's autonomous learning. Increase the reliability of the model in uncertain operating conditions and prevent the impact of large changes in the model on the stability of the process.
  • Figure 4 shows the step response curve and the learning result of G 1,2 (s) without the parameter dead zone method. step response curve.
  • the transfer function model parameters of these learning results are the same as The relative difference in transfer function model parameters is less than 10%.
  • the predictive controller since the predictive controller has a feedback correction link, the predictive controller has robustness within a certain range. Therefore, in order to reduce small fluctuations in the transfer function model of the predictive controller, a parameter dead zone can be set at this time.
  • the range ⁇ 1 0.1, then the model learning results will remain No changes occur.
  • users can set different ⁇ 1 to increase the stability of the transfer function model parameters by leveraging the robustness of the controller, which is beneficial to the stability of the control effect.

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Abstract

一种适用于流程工业预测控制的模型自主学习方法,通过多输入单输出系统作为基本子系统予以实现;适用于流程工业预测控制的模型自主学习方法包括:步骤一、模型设置及学习参数自选择;步骤二、参数分布建模;步骤三、数据采集和处理;步骤四、模型参数学习;步骤五、模型参数检验;步骤六、模型预测误差对比。适用于流程工业预测控制的模型自主学习方法,能在线自主学习过程的动态特性,能根据预设的模型参数自动选择待学习参数的类型,使待学习参数具有真实的物理意义,且在学习过程中,预设模型对模型学习的结果具有约束作用以提高模型的可靠性,对参数的学习结果进行检验、对预测结果进行评价,进一步提高模型的可靠性;采用参数死区的方式增加了模型参数的平稳性,减少因模型参数频繁变化而引起的控制效果波动。

Description

一种适用于流程工业预测控制的模型自主学习方法 技术领域
本发明涉及流程工业预测技术领域,具体涉及一种适用于流程工业预测控制的模型自主学习方法。
背景技术
自20世纪末期以来,流程工业得到了快速发展,其中也包括模型预测控制在流程工业中的成功应用。模型预测控制与传统的PID控制相比,不仅适用于多耦合、大时滞等难控的被控对象,而且可以对工艺条件和经济指标等约束建模,配合优化技术完成控制任务。故,模型预测控制在流程工业中具有广泛的应用前景。然而,在实际生产中,随着生产目标改变、生产原料配比改变、设备老化、催化剂活性不足等多种因素,过程的动态特性会发生变化。这种变化会引发预测控制的预测模型与真实过程动态特性的失配问题。因此,如果能增加预测模型与真实过程动态特性的匹配程度,则控制器可以实现更加准确的过程输出预测,进而有利于控制效果的提升。目前,行业已有一些思想或者方法来应对变化的动态特性问题,比如非线性建模、多工况建模、在线辨识等方法。但现有的方法在实施时存在以下不足。
第一点,对于非线性建模和多工况建模。流程工业大量的三传一反过程增加了机理建模的难度,且现场运行数据难以覆盖所有工况,因此数据驱动的建模方法也只能建立局部模型或者部分工况模型,如果投运时运行在未知工况,仍然需要一种模型在线学习的方法。
第二点,对于在线辨识的方法。一方面,现有方法多采用线性回归对动态特性建模,参数缺乏实际的物理意义,辨识时也缺少对参数的合理约束,导致辨识参数的自由度过高;另一方面,过程的动态特性往往是缓慢变化的,当前正在运行的预测模型应该对新的动态特性参数具有指导意义。然而,暂未发现能有效兼顾这两方面的技术方法。
发明内容
本发明为了克服以上技术的不足,提供了一种适用于流程工业预测控制的模型自主学习方法。
该方法的特点在于:第一,可在线自主学习过程的动态特性,以多输入单输出子系统划分的方式可适用于多输入多输出系统,当然也适用于比多输入多输出系统更简单的其他系统;第二,可根据预设的模型参数自动选择待学习参数的类型,使待学习参数具有真实的物理意义,且在学习过程中,预设模型对模型学习的结果具有约束作用,以提高模型的可靠性;第三,对参数的学习结果进行检验,对模型的预测结果进行评价,进一步提高模型的可靠性;第四,采用参数死区的方式增加了模型参数的平稳性,减少因模型参数频繁变化而引起的控制效果波动。本发明的方法是一种融合模型知识和过程数据的在线学习方法,适用于流程工业预测控制的模型自主学习问题。
术语解释:
1、增益:放大倍数。
2、自然角频率:描述物体振动快慢的物理量,与振动系统的固有属性有关。
3、阻尼系数:表征二阶以及二阶以上的系统在运动过程中系统能量减少这一特性的参数。
4、对数正态分布:一个随机变量的对数服从正态分布,则该随机变量服从对数正态分布。
5、预测模型:指预测控制中用于预测的,用数学语言或公式所描述的事物间的数量关系。
6、参数死区:指参数变化时,如果变化幅度未超过该值,则认为参数没有发生变化。
本发明克服其技术问题所采用的技术方案是:
一种适用于流程工业预测控制的模型自主学习方法,通过多输入单输出系统作为基本子系统予以实现,包括如下步骤:
步骤一、模型设置及学习参数自选择:设置所有传递函数模型,对每个传 递函数模型进行计算并自动选择待学习参数。
其中,设置传递函数模型具体包括:
在固定的二阶系统加一阶积分加纯滞后传递函数模型模板下,设置每个输入变量到每个输出变量之间的传递函数模型。
假设传递函数模型有M个输入变量和P个输出变量,则需要按照式(1)所示的模板设置M×P个传递函数模型,且额外设置标志位Int p,m以说明该传递函数模型G p,m是否额外串联一个一阶积分环节;
Figure PCTCN2022136000-appb-000001
上式中,K p,m为模型增益,τ p,m为延迟时间,s为拉式算子,a p,m和b p,m分别为传递函数特征多项式的二次项系数和一次项系数;
然后,对每个传递函数模型进行计算并自动选择待学习参数,*表示模型自学习前设定的模型参数值,具体包括:
先对每个传递函数模型计算,然后进行如下分析:
如果某个传递函数模型的增益
Figure PCTCN2022136000-appb-000002
则该传递函数模型G p,m不参与模型在线学习;
否则,判断二阶系统的极点位置:(1)如果存在实部为正的根或者纯虚数根,则该传递函数模型G p,m也不参与模型在线学习;(2)如果存在两个实部为负数的共轭复数根,则计算传递函数模型G p,m的自然角频率
Figure PCTCN2022136000-appb-000003
和阻尼系数
Figure PCTCN2022136000-appb-000004
并将模型增益K p,m、自然角频率ω np,m和阻尼系数ζ p,m作为待学习参数。
除了上述(1)和(2)两种情况外,如果传递函数模型的分母多项式
Figure PCTCN2022136000-appb-000005
可以实现式(2)的因式分解,则将非零的一次项系数T 1p,m、非零的一次项系数T 2p,m和模型增益K p,m作为传递函数模型G p,m的待学习参数。
Figure PCTCN2022136000-appb-000006
步骤二、参数分布建模:对于参与学习的每个传递函数模型,采用对数正 态分布对待学习参数建立对数正态分布模型。具体包括如下:
在传递函数模型G p,m参与学习的情况下,采用对数正态分布
Figure PCTCN2022136000-appb-000007
对模型参数值的分布建立对数正态分布模型,即使得传递函数模型参数服从对数正态分布,其中,μ θ
Figure PCTCN2022136000-appb-000008
是关于参数θ对数正态分布的分布参数;根据步骤一所述的待学习参数的种类,由用户设定与分布形状相关的系数{β θθ>1},θ∈{K,T 1,T 2,ω n,ζ},
Figure PCTCN2022136000-appb-000009
为设定的传递函数模型的参数值,根据式(3)解算对数正态分布的参数。
Figure PCTCN2022136000-appb-000010
步骤三、数据采集和处理:在线采集输入变量和输出变量数据及输入变量和输出变量对应的质量码,并对质量码为坏值的情况进行处理。具体包括如下:
在线采集传感器的过程变量和质量码,具体是,采集输入变量和输出变量数据及输入变量和输出变量对应的质量码,其中,质量码用于表示采集到的输入变量和输出变量是否有效,记输入变量为u m(k),输出变量为y p(k),k为采样时刻;
若u m(k)的质量码为坏,则清空采集的所有变量历史数据并重新采集;
若y p(k)的质量码为坏,则继续采集数据,直到y p出现好值,若期间连续坏值的个数大于等于预设的N bad,则清空采集的所有变量历史数据并重新采集;否则,利用坏值数据段两端的好值数据点对坏值数据段进行线性插值以在线补全历史数据,继续采集数据。
步骤四、模型参数学习:基于贝叶斯优化理论建立传递函数模型自主学习的数学优化模型,利用差分进化算法优化传递函数模型参数。具体包括如下:
当输入变量或输出变量的数据量(输出变量和输入变量的测量次数始终是一样)累积到预设个数N S时,针对每个多输入单输出子系统,基于贝叶斯优化理论建立传递函数模型自主学习的数学优化模型。
根据传递函数模型计算系统脉冲响应序列,利用脉冲响应序列和系统输入变量的卷积计算系统输出变量的预测序列。
重复执行L次基于差分进化算法的传递函数模型参数学习,10≤L≤30。记当前情况为第p个多输入单输出子系统的第r次模型参数学习,N popu为用户设置的种群数量;随机选取长度为N DS的连续数据片段,视待学习参数类型随机初始化种群参数,根据学习参数计算系数a p,m和b p,m并代入式(1),采用双线性变换离散化,获取传递函数模型G p,m的脉冲响应{g p,m,k,k=1,2,...,N mdl+d},N mdl为脉冲响应序列阶段长度,d为延迟点个数,并计算传递函数模型G p,m输出的预测值
Figure PCTCN2022136000-appb-000011
如果Int p,m=1,则额外利用一阶积分环节的标准离散化计算方法更新
Figure PCTCN2022136000-appb-000012
序列;按照式(4)计算多输入单输出子系统的输出预测值
Figure PCTCN2022136000-appb-000013
视待学习参数类型按式(5)计算目标函数值并记录在
Figure PCTCN2022136000-appb-000014
其中,σ 2>0为用户设置的噪声水平,(θ 1,θ 2)∈{(T 1,T 2),(ω n,ξ)}。
Figure PCTCN2022136000-appb-000015
Figure PCTCN2022136000-appb-000016
接下来,反复执行多轮标准差分进化算法中的三个步骤:种群进化、个体变异和个体选择,以极小化目标函数的原则记录并更新
Figure PCTCN2022136000-appb-000017
和对应的模型参数;最终将最优个体对应的参数学习结果记录到
Figure PCTCN2022136000-appb-000018
Figure PCTCN2022136000-appb-000019
中,其中,
Figure PCTCN2022136000-appb-000020
分别为第r次模型参数学习的最优个体的模型增益、两个一次项系数、自然角频率和阻尼比。
步骤五、模型参数检验:对每个传递函数模型的每个参数执行参数检验,包括正态性检验、参数死区判断和均值检验。具体包括如下:
对{G p,m|p=1,2,...,P,m=1,2,...,M}的每个参数的L次学习结果进行检验。
环节一、正态性检验:正态性检验方法采用GB/T 4882-2001中的夏皮洛-威尔克(Shapiro-Wilk)检验方法,根据被学习的参数类型按照式(6)计算特征x r的样本数据,若正态性检验不通过,则该参数保持
Figure PCTCN2022136000-appb-000021
不变;否则,进入环节二。
Figure PCTCN2022136000-appb-000022
环节二、参数死区判断:计算{x r|r=1,..,L}的平均值
Figure PCTCN2022136000-appb-000023
如果
Figure PCTCN2022136000-appb-000024
则该参数保持
Figure PCTCN2022136000-appb-000025
不变,其中,η 1≥0是用户设定的参数死区范围;否则,进入环节三。
环节三、均值检验:由用户设定均值检验系数η 2∈[0,1],如果
Figure PCTCN2022136000-appb-000026
则原假设为总体均值
Figure PCTCN2022136000-appb-000027
反之,如果
Figure PCTCN2022136000-appb-000028
则原假设为总体均值
Figure PCTCN2022136000-appb-000029
如果均值检验不通过,则该参数保持
Figure PCTCN2022136000-appb-000030
不变;否则,将
Figure PCTCN2022136000-appb-000031
代入式(6)反算出参数的学习结果。
步骤六、模型预测误差对比:用原传递函数模型计算预测均方根误差,用学习后的传递函数模型计算预测均方根误差,根据两者的大小关系决定是否更新多输入单输出系统的传递函数模型,然后返回步骤一继续执行。具体包括如下:
对每个多输入单输出子系统,用原传递函数模型参数为准,计算第p个多输入单输出系统的预测均方根误差并记为
Figure PCTCN2022136000-appb-000032
用学习后的传递函数模型参数为准,计算第p个多输入单输出系统的预测均方根误差并记为
Figure PCTCN2022136000-appb-000033
如果
Figure PCTCN2022136000-appb-000034
则更新该多输入单输出系统的传递函数模型;反之,则该多输入单输出系统的传递函数模型保持不变;
然后返回步骤一继续运行。
本发明的有益效果是:
1、本发明是一种支持在线运行的模型参数的自主学习技术,可利用在线数据主动地学习模型参数。
2、本发明中,传递函数模板采用了二阶传递函数的一般形式,不仅可以学习稳定的二阶实特征根系统模型,而且可以学习稳定的二阶共轭复特征根系统模型,使学习参数具有明确的物理意义。
3、本发明中,通过两种方法增加了传递函数模型在线学习结果的可靠性:第一种,将过程的先验知识融合进了传递函数模型的学习过程,先验知识包括正在投运的控制器传递函数模型的结构、参数值、增益的符号和由系数自动计算出的、具有物理意义的传递函数模型待学习参数类型;第二种,包含参数检验和传递函数模型预测误差结果对比两个步骤,只有参数通过了假设检验且传递函数模型通过了预测误差结果对比,传递函数模型参数才会被自动更新为学习后的结果。
4、本发明中,采用参数死区的方法增加了传递函数模型参数的平稳性,当传递函数模型参数的变化位于用户设定的死区内,则传递函数模型参数不发生改变,以此增加传递函数模型参数的平稳性,有利于控制效果的稳定性。
5、本发明中,采用了对数正态分布的传递函数模型参数分布假设,一方面,对数正态分布的随机变量取值范围是正数域,有效的|K|、T 1、T 2、ω n、ζ的值域也是正数域,即二者吻合;另一方面,对于传递函数模型的增益而言,增益偏大会使控制偏慢,但增益偏小可能会使系统不稳定,故减小增益应更谨慎;而对数正态分布的概率密度函数曲线在最大值左侧形状较为陡峭,概率密度随着增益减小衰减较快;故,这种先验模型适用于对增益偏小带来的风险进行建模。
附图说明
图1示出了本发明所述的适用于流程工业预测控制的模型自主学习方法的流程框图。
图2示出了模型参数检验步骤中的正态性检验、参数死区判断和均值检验三环节流程图。
图3示出了不同η 2时的传递函数模型学习结果与原传递函数模型的阶跃响应曲线。
图4示出了无参数死区方法时的传递函数模型部分学习结果与原传递函数模型的阶跃响应曲线。
具体实施方式
为了便于本领域人员更好的理解本发明,下面结合附图和具体实施例对本发明做进一步详细说明,下述仅是示例性的不限定本发明的保护范围。
本发明所述的一种适用于流程工业预测控制的模型自主学习方法,可适用于多输入多输出系统,具体是基于多输入单输出子系统划分的方式进行的,故具体实施方式中,采用多输入单输出子系统进行详细说明。
下面以两输入单输出子系统为例进行说明,但并不局限于本实施所述的两输入单输出子系统,其他多输入单输出子系统均适用。
假设两输入单输出系统的当前传递函数模型通过下式(7)表示。
Figure PCTCN2022136000-appb-000035
步骤一、模型设置及学习参数自选择:设置所有传递函数模型,对每个传递函数模型进行计算并自动选择待学习参数。
根据式(1)和式(7),本实施例中对两个传递函数模型设置参数如下:
Figure PCTCN2022136000-appb-000036
对于传递函数模型G 1,1,其特征多项式(不含纯积分)可以在实数域内被分解为一阶多项式乘积的形式,故按照式(2)计算,G 1,1的待学习参数为K 1,1和T 11,1,且
Figure PCTCN2022136000-appb-000037
Figure PCTCN2022136000-appb-000038
对于传递函数模型G 1,2,其特征多项式(不含纯积分)包含两个共轭复数根,故G 1,2的待学习参数为K 1,2、ω n1,2和ζ 1,2,且将特征多项式转化为零极点形式后,可知
Figure PCTCN2022136000-appb-000039
Figure PCTCN2022136000-appb-000040
步骤二、参数分布建模:对于参与学习的每个传递函数模型,采用对数正态分布对待学习参数建立对数正态分布模型。
由于两个传递函数模型的增益均不为零,且特征根实部非正且无纯虚数根,故两个传递函数模型均应被学习;
假设设定β θ=1.1,θ∈{K,T 1,T 2,ω n,ζ},则根据式(3)可以解算出
Figure PCTCN2022136000-appb-000041
Figure PCTCN2022136000-appb-000042
Figure PCTCN2022136000-appb-000043
其中,
Figure PCTCN2022136000-appb-000044
Figure PCTCN2022136000-appb-000045
分别为参数K 1,1、T 11,1、K 1,2、ω n1,2和ζ 1,2的对数正态分布的分布参数。
步骤三、数据采集和处理:在线采集输入变量和输出变量数据及输入变量和输出变量对应的质量码,并对质量码为坏值的情况进行处理。
在线输入变量和输出变量数据及输入变量和输出变量对应的质量码,并判断数据质量码好坏,其中,记输入变量为u 1(k)和u 2(k),输出变量为y 1(k),k为采样时刻;
若u 1(k)或u 2(k)的质量码为坏,则清空采集的所有变量历史数据并重新采集;
若y 1(k)的质量码为坏,则继续采集数据,直到y 1出现好值,若期间连续坏值的个数大于等于预设的N bad,则清空采集的所有变量历史数据并重新采集,若期间连续坏值的个数小于N bad,则利用坏值数据段两端的好值数据点对坏值数据段进行线性插值后在线补全历史数据,继续采集数据。比如N bad=3,y 1(5)=1,y 1(6)=1,y 1(7)=1,y 1(8)=4,第6个和第7个样本点的质量码为坏,第5个和第8个样本点的质量码为好,则在k=8时,利用k=5和k=8的数据点对k=6和k=7进行线性插值,即y 1(6)=2,y 1(7)=3。
步骤四、模型参数学习:基于贝叶斯优化理论建立传递函数模型自主学习的数学优化模型,利用差分进化算法优化传递函数模型参数。
当输入变量或输出变量的数据量累积到预设个数N S=3000个时,对该两输入单输出系统重复执行L=20次基于差分进化算法的模型参数学习。
记当前情况为该两输入单输出系统的第r次模型参数学习:
随机选取长度为N DS=1000的连续数据片段;设置种群数目N popu=10,随机 初始化种群参数
Figure PCTCN2022136000-appb-000046
Figure PCTCN2022136000-appb-000047
根据学习参数反算系数a 1,1,b 1,1,a 1,2和b 1,2并代入传递函数模型的模板,采用双线性变换离散化,获取传G 1,1和G 1,2的脉冲响应,分别记为{g 1,1,k,k=1,2,...,N mdl+1}和{g 1,2,k,k=1,2,...,N mdl+1},递函数模型按照式(8)计算传递函数模型G 1,1和G 1,2输出的预测值
Figure PCTCN2022136000-appb-000048
Figure PCTCN2022136000-appb-000049
其中,Δ为差分算子。
Figure PCTCN2022136000-appb-000050
因为Int 1,1=1,故利用一阶纯积分环节的标准离散化计算方法更新
Figure PCTCN2022136000-appb-000051
按照式(9)计算多输入单输出系统的输出预测值
Figure PCTCN2022136000-appb-000052
按照式(10)计算目标函数值并记录在
Figure PCTCN2022136000-appb-000053
其中,σ 2>0为用户设置的噪声水平,(θ 1,θ 2)∈{(T 1,T 2),(ω n,ξ)}。
Figure PCTCN2022136000-appb-000054
Figure PCTCN2022136000-appb-000055
接下来,反复执行多轮标准差分进化算法中的三个步骤:种群进化、个体变异和个体选择,以极小化目标函数的原则记录并更新
Figure PCTCN2022136000-appb-000056
和对应的模型参数,最终将最优个体对应的参数学习结果记录到
Figure PCTCN2022136000-appb-000057
Figure PCTCN2022136000-appb-000058
中。
步骤五、模型参数检验:对每个传递函数模型的每个参数执行参数检验,包括正态性检验、参数死区判断和均值检验。
如图2所示,对递函数模型G 1,1和G 1,2的每个参数的20次学习结果进行检验。
环节一、正态性检验:根据被学习的参数类型按照式(6)计算特征x r的样本数据。比如,参数T 1p,m检验结果不通过,则参数T 1p,m保持5不变;其它参数通过,进入环节二。
环节二、参数死区判断:计算{x r|r=1,..,20}的平均值
Figure PCTCN2022136000-appb-000059
如果
Figure PCTCN2022136000-appb-000060
则该参数保持
Figure PCTCN2022136000-appb-000061
不变;比如η 1<0.2,如果在执行K 1,2的参数死区判断时,
Figure PCTCN2022136000-appb-000062
则K 1,2保持3.5不变;其它参数通过,进入环节三。
环节三、均值检验:如果
Figure PCTCN2022136000-appb-000063
则原假设为总体均值
Figure PCTCN2022136000-appb-000064
反之,如果
Figure PCTCN2022136000-appb-000065
则原假设为总体均值
Figure PCTCN2022136000-appb-000066
如果检验结果不通过,则该参数保持
Figure PCTCN2022136000-appb-000067
不变;比如在执行参数ω n1,2的均值检验时,η 2=0.8,
Figure PCTCN2022136000-appb-000068
如果检验结果为无法拒绝μ≤0.16的假设,则ω n1,2维持0.5不变;否则,拒绝原假设,将
Figure PCTCN2022136000-appb-000069
代入式(6)反算出参数的学习结果。
步骤六、模型预测误差对比:用原传递函数模型计算预测均方根误差,用学习后的传递函数模型计算预测均方根误差,根据两者的大小关系决定是否更新多输入单输出系统的传递函数模型,然后返回步骤一继续执行。
具体是,用原传递函数模型参数为准,计算该两输入单输出系统的输出预测值并按照式(11)计算预测均方根误差,记为
Figure PCTCN2022136000-appb-000070
以学习后的传递函数模型为准,再次计算该两输入单输出系统的输出预测值并按照式(11)计算预测均方根误差,记为
Figure PCTCN2022136000-appb-000071
Figure PCTCN2022136000-appb-000072
如果
Figure PCTCN2022136000-appb-000073
则更新该两输入单输出系统的模型参数
Figure PCTCN2022136000-appb-000074
反之,该两输入单输出系统的所有模型保持不变。
然后返回步骤一继续重复运行。
现结合另一具体实施例继续说明,该具体实施例为式(12)所示的多输入单输出系统,输入变量为两个支路的水温设定值,输出变量为干路水温,控制方案是用两路支路控制干路的水温。作为多输入单输出系统,其具体实施方式与上文所述相同,故不赘述实施过程,而是重点说明本发明的效果。
Y(s)=G 1,1(s)U 1(s)+G 1,2(s)U 2(s)           (12)
假设正在投运的控制器传递函数模型为式(13):
Figure PCTCN2022136000-appb-000075
分别设置η 2=0.3、η 2=0.6和η 2=0.8,进行模型参数自学习,将G 1,1(s)的学习结果的阶跃响应曲线和
Figure PCTCN2022136000-appb-000076
的阶跃响应曲线绘制在图3中。当η 2取值0.3时,G 1,1(s)的学习结果的阶跃响应曲线更接近
Figure PCTCN2022136000-appb-000077
的阶跃响应曲线,模型参数的变化程度小;当η 2取值0.8时,G 1,1(s)的学习结果的阶跃响应曲线更远离
Figure PCTCN2022136000-appb-000078
的阶跃响应曲线,模型参数的变化程度大。归纳上述现象,即η 2会影响G 1,1(s)传递函数模型的学习结果,在模型自主学习的迭代过程中,用户设定不同的η 2,可以控制模型自主学习的参数变化速度,在不确定工况中增加模型的可靠性,防止模型的大幅度变化对过程平稳性的影响。
图4画出了不含参数死区方法时,G 1,2(s)的学习结果的阶跃响应曲线与
Figure PCTCN2022136000-appb-000079
的阶跃响应曲线。这些学习结果的传递函数模型参数与
Figure PCTCN2022136000-appb-000080
的传递函数模型参数相对差别小于10%。在这种情况下,由于预测控制器具有反馈校正环节,预测控制器便具有一定范围内的鲁棒性,故为了减小预测控制器的传递函数模型的小幅波动,此时可以设置参数死区范围η 1=0.1,则模型学习结果将保持
Figure PCTCN2022136000-appb-000081
不发生变化。归纳上述现象,用户设定不同的η 1,可以借助控制器的鲁棒性,增加传递函数模型参数的平稳性,有利于控制效果的稳定性。
以上仅描述了本发明的基本原理和优选实施方式,本领域人员可以根据上述描述做出许多变化和改进,这些变化和改进应该属于本发明的保护范围。

Claims (10)

  1. 一种适用于流程工业预测控制的模型自主学习方法,其特征在于,通过多输入单输出系统作为基本子系统予以实现,包括步骤:
    步骤一、设置所有传递函数模型,对每个传递函数模型进行计算并自动选择待学习参数;
    步骤二、对于参与学习的每个传递函数模型,采用对数正态分布对待学习参数建立对数正态分布模型;
    步骤三、在线采集输入变量和输出变量数据及输入变量和输出变量对应的质量码,并对质量码为坏值的情况进行处理;
    步骤四、基于贝叶斯优化理论建立传递函数模型自主学习的数学优化模型,利用差分进化算法优化传递函数模型参数;
    步骤五、对每个传递函数模型的每个参数执行参数检验,包括正态性检验、参数死区判断和均值检验;
    步骤六、对每个多输入单输出子系统,用原传递函数模型计算预测均方根误差,用学习后的传递函数模型计算预测均方根误差,根据两者的大小关系决定是否更新多输入单输出系统的传递函数模型,然后返回步骤一继续执行。
  2. 根据权利要求1所述的适用于流程工业预测控制的模型自主学习方法,其特征在于,步骤一中,设置传递函数模型具体包括:
    在固定的二阶系统加一阶积分加纯滞后传递函数模型模板下,设置每个输入变量到每个输出变量之间的传递函数模型。
  3. 根据权利要求2所述的适用于流程工业预测控制的模型自主学习方法,其特征在于,步骤一中,传递函数模型的数量根据输入变量和输出变量的数量而定,设输入变量为M个、输出变量为P个,则需设置M×P个传递函数模型。
  4. 根据权利要求1所述的适用于流程工业预测控制的模型自主学习方法,其特征在于,步骤一中,对每个传递函数模型进行计算并自动选择待学习参数具体包括:
    先对每个传递函数模型计算,然后进行如下分析:
    如果某个传递函数模型的增益为0,则该传递函数模型不参与模型在线学 习;
    否则,判断二阶系统的极点位置:(1)如果存在实部为正的根或者纯虚数根,则该传递函数模型不参与模型在线学习;(2)如果存在两个实部为负数的共轭复数根,则计算传递函数模型的自然角频率和阻尼系数,并将模型增益、自然角频率和阻尼系数作为待学习参数;除上述(1)和(2)两种情况外,则将传递函数模型的分母多项式在实数域中进行因式分解,取分解后的所有的非零的一次项系数和模型增益作为待学习参数。
  5. 根据权利要求1所述的适用于流程工业预测控制的模型自主学习方法,其特征在于,步骤二具体包括:
    对于参与学习的每个传递函数模型,根据用户设定的与分布形状相关的系数,计算对数正态分布参数,利用对数正态分布对待学习参数建模。
  6. 根据权利要求1所述的适用于流程工业预测控制的模型自主学习方法,其特征在于,步骤三具体包括:
    在线采集输入变量和输出变量数据及输入变量和输出变量对应的质量码,并进行如下判断和处理:
    对于输入变量,只要出现坏质量码数据,则清空采集的所有变量历史数据并重新采集;
    对于输出变量,当连续出现预设个数N bad或N bad以上个坏质量码数据时,则清空采集的所有变量历史数据并重新采集,当连续出现的坏质量码数据少于N bad时,则利用坏值数据段两端的好值数据点采用线性插值方法在线补全历史数据。
  7. 根据权利要求1所述的适用于流程工业预测控制的模型自主学习方法,其特征在于,步骤四具体包括:
    当输入变量或输出变量的数据量累积到预设个数时,针对每个多输入单输出子系统,基于贝叶斯优化理论建立传递函数模型自主学习的数学优化模型;
    根据传递函数模型计算系统脉冲响应序列,利用脉冲响应序列和系统输入变量的卷积计算系统输出变量的预测序列;
    利用差分进化算法优化传递函数模型参数。
  8. 根据权利要求7所述的适用于流程工业预测控制的模型自主学习方法,其特征在于,差分进化算法包括三个步骤:种群进化、个体变异和个体选择。
  9. 根据权利要求1所述的适用于流程工业预测控制的模型自主学习方法,其特征在于,步骤五具体包括:
    对每个传递函数模型的每个参数按顺序依次执行正态性检验、参数死区判断和均值检验三个环节,当三个环节全部通过时,参数学习结果有效,否则,参数学习结果无效,保持原参数不变。
  10. 根据权利要求1所述的适用于流程工业预测控制的模型自主学习方法,其特征在于,步骤六具体包括:
    对每个多输入单输出子系统,以原传递函数模型参数为准,计算多输入单输出系统的预测均方根误差并记为RMSE 1,以学习后的传递函数模型参数为准,计算多输入单输出系统的预测均方根误差并记为RMSE 2
    如果RMSE 2<RMSE 1,则更新该多输入单输出子系统的传递函数模型,反之,则该多输入单输出子系统的传递函数模型保持不变;
    然后,返回步骤一继续执行。
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