WO2023123184A1 - 一种离心泵效率预测方法 - Google Patents

一种离心泵效率预测方法 Download PDF

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WO2023123184A1
WO2023123184A1 PCT/CN2021/142973 CN2021142973W WO2023123184A1 WO 2023123184 A1 WO2023123184 A1 WO 2023123184A1 CN 2021142973 W CN2021142973 W CN 2021142973W WO 2023123184 A1 WO2023123184 A1 WO 2023123184A1
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model
centrifugal pump
efficiency
lssvr
small flow
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PCT/CN2021/142973
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郑水华
刘建飞
柴敏
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浙江工业大学台州研究院
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model

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  • the invention relates to the technical field of centrifugal pumps, in particular to a centrifugal pump efficiency prediction method based on flow interval segmentation.
  • the prediction of the efficiency of centrifugal pumps at different speeds is mainly based on the similarity theory of pumps, which assumes that the efficiency of pumps is approximately constant at different speeds. But in practice, when the speed changes, the volumetric efficiency ( ⁇ v ), hydraulic efficiency ( ⁇ h ) and mechanical efficiency ( ⁇ w ) of the centrifugal pump will change, especially the mechanical efficiency ( ⁇ w ) will change greatly. In addition, some studies have used the introduction of the Reynolds number combined with the similar laws of fluid mechanics to correlate the speed of the centrifugal pump with the efficiency change and summarize the mechanism model to predict the efficiency of the centrifugal pump at different speeds.
  • the above mechanism model introduces some assumptions and empirical coefficients for the convenience of use, especially ignores the friction loss of the pipeline system, so there is a large empirical error in the prediction of the mechanism model.
  • the change of flow at the same speed is mainly regulated by the outlet throttle valve of the system, so the friction loss of the pipeline system is constantly changing, which makes it difficult for the mechanism model to accurately predict the full flow of the centrifugal pump operating efficiency.
  • the purpose of the present invention is to provide a method for predicting the efficiency of centrifugal pumps, which combines the similarity law of centrifugal pumps and data-driven technology to perform hybrid modeling, and proposes a hybrid model suitable for the prediction of centrifugal pump efficiency at different speeds. Improving the accuracy of centrifugal pump efficiency predictions.
  • the present invention adopts the following technical solutions:
  • a centrifugal pump efficiency prediction method comprising the steps of:
  • a centrifugal pump efficiency prediction model at different speeds is established based on the flow interval, the prediction model includes a large flow interval model constructed based on the similarity law, and a small flow interval model constructed based on a local LSSVR model;
  • the large flow interval model based on the similarity law includes:
  • ⁇ e represents the efficiency at the rated speed ne
  • ⁇ x represents the desired efficiency at the speed n x
  • 0.1 is an empirical coefficient
  • the small flow interval model based on the local LSSVR model includes:
  • f represents the LSSVR model
  • w represents the model parameter vector
  • ei represents the approximation error of the sample
  • c represents the bias term of the model
  • ⁇ represents the feature map of the model
  • N is the number of training samples.
  • sample set of centrifugal pump efficiency in the small flow range at different speeds obtained through preset experiments includes:
  • a self-priming centrifugal pump driven by a variable frequency motor is adopted, the operating speed of the centrifugal pump is adjusted through the variable frequency drive, and the outlet flow of the centrifugal pump is adjusted through the opening of the outlet valve in the pipeline system.
  • V valve openings
  • flow meters The inlet and outlet pressure sensors and torque sensors respectively record outlet flow Q, inlet and outlet pressures (P s , P d ) and shaft power N, and then obtain the efficiency values of each flow point at different speeds as a sample subset;
  • H st is the static head
  • using the small flow interval sample set to train the small flow interval model includes:
  • H p is the head of the piping system
  • H p ⁇ H H is the head of the centrifugal pump
  • H st is the static head of the piping system
  • Q is the outlet flow
  • K is the friction loss coefficient, which represents the opening of the valve
  • the preset The threshold is 0.01.
  • the centrifugal pump efficiency prediction method of the present invention effectively integrates the mechanism knowledge of the centrifugal pump and the LSSVR model into the hybrid model, and is used to predict the efficiency of the centrifugal pump at different speeds.
  • the hybrid model can pass limited samples to improve the predictive reliability of the model.
  • processes with different characteristics can be better handled, while the dependence on experimental data is reduced, and the prediction accuracy is improved. From an engineering point of view, it can be implemented simply and directly. The actual experimental results also reflect the feasibility and simplicity of the model.
  • Fig. 1 is a schematic diagram of an experimental system for obtaining a sample set by the centrifugal pump efficiency prediction method of the present invention.
  • Fig. 2 is a graph showing the variation of efficiency with flow rate at different rotational speeds in an illustrative example of the present invention.
  • Fig. 3 is a schematic diagram of the variation of the K value with the opening of the valve at different rotational speeds in an illustrative example of the present invention.
  • Figure 4 is a schematic diagram of a hybrid model in an illustrative example of the invention.
  • Fig. 5 is the relative error of the local LSSVR model and the global LSSVR model predicting the S 5 small flow segment in an illustrative example of the present invention.
  • Fig. 6 is an effect diagram of the local LSSVR model and the global LSSVR model predicting the S 5 small flow section in an illustrative example of the present invention.
  • Fig. 7 is an effect diagram of the local LSSVR model and the global LSSVR model predicting the S 6 small flow section in an illustrative example of the present invention.
  • Fig. 8 is the relative error of the LSSVR model and the LSSVR model predicting the S 6 small flow section in the illustrative example of the present invention.
  • Fig. 9 is an effect diagram of prediction S 5 of the hybrid model, the LSSVR model and the mechanism model in an illustrative example of the present invention.
  • Figure 10 is a graph of the relative error in predicting S5 for the hybrid model, the LSSVR model, and the mechanistic model in an illustrative example of the invention.
  • Fig. 11 is an effect diagram of prediction S 6 of the hybrid model, the LSSVR model and the mechanism model in an illustrative example of the present invention.
  • FIG. 12 is a graph of the relative errors of hybrid model, LSSVR model, and mechanistic model prediction S 6 in an illustrative example of the invention.
  • the mechanism model is used to predict the large flow range, and the local data-driven model is used to predict the small flow range, combining the advantages of the two models will improve prediction accuracy.
  • an embodiment of the present invention provides a method for predicting the efficiency of a centrifugal pump, combining similarity laws of centrifugal pumps and data-driven technology for hybrid modeling, and proposes a hybrid model suitable for predicting the efficiency of centrifugal pumps at different speeds.
  • the efficiency curve of the centrifugal pump at different speeds is divided into two stages, and the similarity law of the centrifugal pump and the least squares support vector regression (LSSVR ) to build a model, and finally use the hybrid model to dynamically predict the efficiency of the two stages at different speeds. Specifically include the following steps:
  • centrifugal pump efficiency prediction models at different speeds are established based on the flow interval, including the large flow interval model based on the similarity law and the small flow interval model based on the local LSSVR model.
  • the mechanism model for the large flow range is mainly based on the function relationship between the speed and efficiency based on the similarity law of the pump, and the efficiency at the desired speed is obtained through the rated speed and rated efficiency of the centrifugal pump, and its expression is as follows:
  • ⁇ e represents the efficiency at the rotational speed ne (rated rotational speed);
  • ⁇ x represents the efficiency at the rotational speed n x (required efficiency);
  • 0.1 is an empirical coefficient.
  • the mechanism model method is used to construct the model in the large flow interval.
  • the prediction results of the mechanism model in the small flow range are not ideal.
  • the size is sensitive to changes in flow, so more sample data can be easily obtained in small flow intervals. Therefore, the method of local LSSVR model is used to construct the model in the small flow interval.
  • the sample sets of small flow ranges at different rotational speeds are divided into training set X 1 and test set X t , then construct an LSSVR model, and use X 1 to train a local LSSVR model, and finally use training A good local LSSVR model makes predictions on the test set X t to obtain efficiencies in small flow intervals.
  • f represents the LSSVR model
  • w represents the model parameter vector
  • e i represents the approximation error of the sample
  • c represents the bias term of the model
  • ⁇ represents the feature map of the model.
  • a test system for acquiring a sample set is shown.
  • 1 is the cavitation tank
  • 2 is the electric butterfly valve
  • 3 is the manual valve
  • 4 is the console
  • 5 is the electric valve
  • 6 is the pump outlet pressure sensor
  • 7 is the pump inlet pressure sensor
  • 8 is the electric parameter measuring instrument
  • 9 10 is a flow meter
  • 10 is a manual valve
  • 11 is a test centrifugal pump
  • 12 is a torque sensor
  • 13 is a motor
  • 14 is a manual valve
  • 15 is a surge tank
  • 16 is an electric butterfly valve.
  • the test centrifugal pump 11 is a self-priming centrifugal pump driven by a variable frequency motor, and liquid (clear water) flows into the system through the centrifugal pump.
  • the operating speed of the centrifugal pump is changed by the variable frequency drive.
  • the outlet flow of the centrifugal pump is adjusted through the opening of the outlet valve in the pipeline system.
  • V valve openings
  • flowmeters, inlet and outlet pressure sensors are used.
  • the outlet flow rate (Q), the inlet and outlet pressure (P s , P d ) and the shaft power (N) are recorded respectively by the torque sensor.
  • the efficiency formula for different flow points is:
  • H st is the static head.
  • the efficiency curves at eight different speeds including the rated speed are obtained from the experimental system, as shown in Figure 2.
  • the small flow interval model is trained using the small flow interval sample set.
  • the prediction accuracy of the LSSVR model depends on the selection of appropriate kernel parameters ⁇ and regularization parameters ⁇ .
  • This illustrative example uses the leave-one-out cross-validation criterion (FLOO) to select appropriate ⁇ and ⁇ .
  • the FLOO criterion can avoid small sample regression In the problem, LSSVR has an overfitting problem.
  • the FLOO criterion is that ⁇ and ⁇ can be selected when the FLOO prediction error is the smallest, and the FLOO prediction error for N samples is as follows:
  • G ii represents the element of row i and column i of G
  • v i represents the element of v
  • the friction loss of the pipeline system changes continuously with the valve opening, and the friction loss of the pipeline system can be obtained through the head curve of the system.
  • the head curve of the system can be obtained from the information of the pipeline and the static head through the laws of hydraulics.
  • the head curve of the pipeline system can be expressed as:
  • H p is the head of the piping system (H p ⁇ H)
  • H st is the static head of the piping system
  • K is the coefficient of dynamic head (that is, the coefficient of friction loss).
  • the K value curves at different speeds have a common feature, that is, with the continuous increase of the valve opening, the K value decreases sharply, and when the valve opening increases to 50%, the K value is close to zero. , so define the interval of the valve opening greater than 50% as the high flow interval, and the interval of the valve opening less than 50% as the small flow interval.
  • RMSE root mean square error
  • MARE maximum absolute relative error
  • the local LSSVR model is used to predict the efficiency of the small flow intervals of the two test sample sets S5 and S6 , and the prediction results are shown in Figures 5 to 8, and compared with the global LSSVR model The prediction results verified the superiority of the local LSSVR model for the first time.
  • the training sample set is divided into intervals by the valve opening, and the local LSSVR model trained by using the training sample set in the small flow interval through formula (5-7), because the local LSSVR model does not include the large flow interval features, so the needle flow interval has good predictive performance.
  • the efficiency at different speeds is divided into two stages by using the valve opening, the efficiency in the small flow range is predicted by the local LSSVR model, and the efficiency in the large flow range is predicted by the mechanism model.
  • the hybrid model is used to predict the efficiency and the detailed prediction results are shown in Figures 8-11. The prediction results show that the hybrid model has relatively good prediction performance.
  • Table 2 (LSSVR model, mechanism model and hybrid model predicting the RMSE (%) of S 5 and S 6 ) lists the performance comparison results of these three models, where the hybrid The prediction effect of the model is the best, the experimental data required by the mechanism model is the least, the experimental data required by the global LSSVR model is the most, and the number of samples required by the mixed model is in between, as shown in Table 3 (LSSVR model, mechanism model and mixed model prediction The number of samples required for S 5 and S 6 ) is shown.
  • the hybrid model makes full use of the process knowledge of the centrifugal pump and avoids the empirical error of the mechanism model, so it has better predictive performance.
  • the hybrid model requires fewer samples and reduces The excessive dependence on experimental data reduces the burden of experiments.

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Abstract

一种离心泵效率预测方法，结合离心泵的相似定律和数据驱动技术进行混合建模，提出了一种适用于不同转速下离心泵效率预测的混合模型。根据离心泵外特性的过程知识制定标准将不同转速下的离心泵的效率曲线分为两个阶段，并针对两者的特点分别利用离心泵的相似定律和最小二乘支持向量回归LSSVR构建模型，采用混合模型动态预测不同转速下两个阶段的效率。实验结果表明所构建的混合模型提高了预测准确性，相比现有单一模型具备优越性。

Description

一种离心泵效率预测方法 技术领域
本发明涉及离心泵技术领域，具体涉及一种基于流量区间分段的离心泵效率预测方法。
背景技术
目前，预测离心泵在不同转速下的效率主要基于泵的相似理论，该理论假设泵的效率在不同转速下效率近似不变。但是实际情况下，当转速变化后离心泵的容积效率(η v)、水力效率(η h)和机械效率(η w)会发生变化，尤其是机械效率(η w)会发生较大变化。另外有一些研究利用引入雷诺数结合流体力学的相似定律将离心泵的转速与效率变化相关联而总结的机理模型来预测不同转速下离心泵的效率。但是上述机理模型为了使用方便引入了一些假设条件和经验系数，特别是忽略了管路系统的摩擦损失，所以机理模型的预测存在较大经验误差。同时离心泵运行时，相同转速下流量的变化主要是依靠系统的出口节流阀调节，因而管路系统的摩擦损失是不断变化的，这也就导致机理模型很难准确预测离心泵的全流量运行效率。
发明内容
基于上述背景，本发明的目的在于提供一种离心泵效率预测方法，结合离心泵的相似定律和数据驱动技术进行混合建模，提出一种适用于不同转速下离心泵效率预测的混合模型，以提高离心泵效率预测的准确性。
为实现上述目的，本发明采用了如下技术方案：
一种离心泵效率预测方法，包括如下步骤：
基于流量区间建立不同转速下的离心泵效率预测模型，所述预测模型包括基于相似定律构建的大流量区间模型，以及基于局部LSSVR模型构建的小流量区间模型；
通过预设试验获取不同转速下的小流量区间离心泵效率样本集，并使用所述小流量区间样本集训练所述小流量区间模型；
使用训练完成的预测模型预测不同转速下的离心泵效率；其中，当K值小于预设阈值时，采用大流量区间模型，大于等于预设阈值时，采用小流量区间模型，所述K值用于表征阀门开度。
进一步的，基于相似定律构建的大流量区间模型包括：
基于离心泵的相似定律，通过离心泵的额定转速和额定效率获取所求转速下的效率，其表达形式如下:
Figure PCTCN2021142973-appb-000001
其中η e表示在额定转速n e下的效率，η x表示在转速n x下的所求效率，0.1为经验系数。
进一步的，基于局部LSSVR模型构建的小流量区间模型包括：
基于局部LSSVR模型构建表达式：
Figure PCTCN2021142973-appb-000002
其中f表示LSSVR模型，w表示模型参数向量，e i表示样本的近似误差，c表示模型的偏置项，φ表示模型的特征映射，N为训练样本数。
进一步的，通过预设试验获取不同转速下的小流量区间离心泵效率样本集包括：
采用由变频电机驱动的自吸式离心泵，通过变频驱动器调节离心泵的运行转速，通过管路系统中出口阀门开度调节离心泵的出口流量，在不同阀门开度V下，采用流量计、进出口压力传感器和扭矩传感器分别记录出口流量Q、进出口压力(P s,P d)和轴功率N，进而获取不同转速下各流量点的效率值作为样本子集；
其中，不同流量点的效率公式为：
Figure PCTCN2021142973-appb-000003
其中ρ为传输液体的密度，H为离心泵扬程：
Figure PCTCN2021142973-appb-000004
其中H st为静扬程。
进一步的，使用所述小流量区间样本集训练所述小流量区间模型包括：
针对基于局部LSSVR模型构建的表达式设置如下优化目标：
Figure PCTCN2021142973-appb-000005
其中e＝[e 1,…,e N] T表示近似误差，…>0，表征模型复杂程度与近似精度之间的权衡系数；
基于上述优化目标对构建的表达式进行优化，获得如下式所示的小流量区间模型：
Figure PCTCN2021142973-appb-000006
其中
Figure PCTCN2021142973-appb-000007
为预测值，
Figure PCTCN2021142973-appb-000008
是一个估算测试集X t的和向量，采用高斯核函数K(x,x *)＝exp(-‖x-x *‖/2σ 2)，其中σ>0为核参数。
进一步的，所述K值基于如下公式获得：
H p＝H st+KQ 2
其中为H p管路系统扬程，H p≈H，，H为离心泵扬程；H st为管路系统静扬程，Q为出口流量，K为摩擦损失系数，表征阀门开度；所述预设阈值为0.01。
本发明的有益效果是：
本发明的离心泵效率预测方法，将离心泵的机理知识与LSSVR模型有效的集成到混合模型中，用于预测离心泵在不同转速下的效率，相比于单一的模型，混合模型可以通过有限的样本提高模型的预测可靠性。通过不同流量区间的单独建模，可以更好的处理具有不同特征的过程，同时减少了对实验数据的依赖，并且提高了预测精度。从工程学的角度来看，可以简单直接的实现。实际实验结果也体现了该模型的可行性和简洁性。
附图说明
图1是本发明的离心泵效率预测方法获取样本集的实验系统示意图。
图2是本发明的示出性实例中不同转速下效率随流量的变化图。
图3是本发明的示出性实例中不同转速下K值随阀门开度的变化示意图。
图4本发明的示出性实例中混合模型示意图。
图5是本发明的示出性实例中局部LSSVR模型和全局LSSVR模型预测S 5小流量段的相对误差。
图6是本发明的示出性实例中局部LSSVR模型和全局LSSVR模型预测S 5小流量段的效果图。
图7是本发明的示出性实例中局部LSSVR模型和全局LSSVR模型预测S 6小流量段的效果图。
图8是本发明的示出性实例中LSSVR模型和LSSVR模型预测S 6小流量段的相对误差。
图9是本发明的示出性实例中混合模型、LSSVR模型和机理模型预测S 5的效果图。
图10是本发明的示出性实例中混合模型、LSSVR模型和机理模型预测S 5的相对误差。
图11是本发明的示出性实例中混合模型、LSSVR模型和机理模型预测S 6的效果图。
图12是本发明的示出性实例中混合模型、LSSVR模型和机理模型预测S 6的相对误差。
具体实施方式
为了进一步理解本发明，下面结合实施例对本发明优选实施方案进行描述，但是应当理解，这些描述只是为进一步说明本发明的特征和优点，而不是对本发明权利要求的限制。
目前，在流体机械领域中使用数据驱动模型已成为一种新的方法。与机理模型相比，数据驱动模型能在对机理缺乏全面了解的情况下，仅通过数据本身 内部存在的规律建立模型。所以数据驱动模型的预测效果取决于建模数据的可靠性，但是由于某些实验数据并不能容易获取，因此在数据驱动模型的方法中，必须开发有效的策略来增强有限数据的预测性能。
通过将机理模型和数据驱动模型集成在一起发展混合模型是一个可行的思路，它既能规避机理模型的经验误差也能减少数据驱动模型对实验数据的过度依赖，从而减少数据驱动模型的预测压力。所以在没有足够样本的情况下，混合模型也拥有不错的预测效果。在离心泵的效率预测过程中，离心泵运行的大流量区间由于供水系统的阀门开度大，所以管路系统的摩擦损失较小，机理模型的预测结果是可以接受的，而在小流量区间由于管路系统的摩擦损失较大，利用机理模型的预测结果不理想。如果将不同转速下离心泵的效率曲线分为大流量区间和小流量区间，使用机理模型对大流量区间进行预测，使用局部数据驱动模型对小流量区间进行预测，结合两种模型的优势将提高预测精度。
基于上述理论，本发明实施例提供了一种离心泵效率预测方法，结合离心泵的相似定律和数据驱动技术进行混合建模，提出了一种适用于不同转速下离心泵效率预测的混合模型。首先，根据离心泵外特性的过程知识制定标准将不同转速下的离心泵的效率曲线分为两个阶段，并针对两者的特点分别利用离心泵的相似定律和最小二乘支持向量回归(LSSVR)构建模型，最后采用混合模型动态预测不同转速下两个阶段的效率。具体包括如下步骤：
首先，基于流量区间建立不同转速下的离心泵效率预测模型，包括基于相似定律构建的大流量区间模型，以及基于局部LSSVR模型构建的小流量区间模型。
针对大流量区间的机理模型主要是通过基于泵的相似定律总结得到的转速与效率的函数关系，通过离心泵的额定转速和额定效率获取所求转速下的效率，其表达形式如下:
Figure PCTCN2021142973-appb-000009
其中η e表示在转速n e(额定转速)下的效率；η x表示在转速n x下的效率(所求效率)；0.1为经验系数。
在大流量区间，机理模型的预测结果精度是可以接受的，所以在大流量区间采用机理模型的方法来构建模型。在小流量区间，由于系统摩擦损失的影响，导致机理模型在小流量区间的预测结果并不理想，同时小流量区间的出口阀门开度较小，阀门内外的压差较大，阀门开度的大小对流量的变化比较敏感，所以在小流量区间可以轻松的获得更多的样本数据。所以在小流量区间采用局部LSSVR模型的方法来构建模型。
在一示出性实施例中，将不同转速下小流量区间的样本集划分为训练集X l和测试集X t,然后构建一个LSSVR模型，并利用X l训练一个局部LSSVR模型，最后利用训练好的局部LSSVR模型对测试集X t进行预测，从而获得小流量区间的效率。
其中基于LSSVR的预测模型的表达式如：
Figure PCTCN2021142973-appb-000010
其中f表示LSSVR模型；w表示模型参数向量；e i表示样本的近似误差；c表示模型的偏置项；φ表示模型的特征映射。
另一方面，通过预设试验获取不同转速下的小流量区间离心泵效率样本集。
参见附图1，示出了获取样本集的试验系统。其中，1是汽蚀罐，2是电动蝶阀，3是手动阀，4是控制台，5是电动阀，6是泵出口压力传感器，7是泵进口压力传感器，8是电参数测量仪，9是流量计，10是手动阀，11是测试离心泵，12是扭矩传感器，13是电动机，14是手动阀，15是稳压罐，16是电动蝶阀。测试离心泵11为自吸式离心泵，由变频电机驱动，液体(清水)通过离心泵流入系统。通过变频驱动器改变离心泵的运行转速，在同一转速下，通过管路系统中出口阀门开度调节离心泵的出口流量，并在不同阀门开度(V)下，采用流量计、进出口压力传感器和扭矩传感器分别记录出口流量(Q)、进出口压力(P s,P d)和轴功率(N)。不同流量点的效率公式为：
Figure PCTCN2021142973-appb-000011
其中ρ为传输液体的密度，H为离心泵扬程：
Figure PCTCN2021142973-appb-000012
其中H st为静扬程。从实验系统中共获取包括额定转速在内的八种不同转速下的效率曲线，如图2所示。
之后，使用所述小流量区间样本集训练所述小流量区间模型。
同时针对前述基于LSSVR的预测模型表达式的优化提出如下问题:
Figure PCTCN2021142973-appb-000013
其中e＝[e 1,…,e N] T表示近似误差；‖w‖ 2/2可以视为一种避免模型过于复杂的形式，γ>0决定着模型复杂程度与近似精度之间的权衡，选择合适的γ可以避免模型出现过拟合的问题。
为了更好求解上述优化问题，构建如下参数：
Figure PCTCN2021142973-appb-000014
其中α＝[α 1，…，α N] T表示Lagrange乘子；1＝[1,1,…1] T表示一个单位列向量；G被定义为G＝(K+I/γ) -1其中I表示为一个单位向量；K是一个包含
Figure PCTCN2021142973-appb-000015
元素的核矩阵。
所述LSSVR模型的预测精度取决于选择合适的核参数σ和正则化参数γ，本示出性实例采用留一交叉验证准则(FLOO)来选择合适的σ和γ，FLOO准则可以避免小样本回归问题中LSSVR出现过拟合问题。FLOO准则是，当FLOO预测误差最小时可以选择σ和γ，FLOO关于N个样本的预测误差如下所示：
Figure PCTCN2021142973-appb-000016
其中G ii表示G的第i行第i列的元素；v i表示为v的元素，其中v表示为：v＝G1＝[v 1,…,v N] T；o表示为o＝-1 TG1。
最后获得模型的预测值
Figure PCTCN2021142973-appb-000017
如下式所示：
Figure PCTCN2021142973-appb-000018
其中
Figure PCTCN2021142973-appb-000019
是一个估算测试集X t的和向量。本发明采用的是高斯核函数K(x,x *)＝exp(-‖x-x *‖/2σ 2)，其中σ>0为核参数。
最后，使用训练完成的预测模型预测不同转速下的离心泵效率；其中，当K值小于预设阈值时，采用大流量区间模型，大于等于预设阈值时，采用小流量区间模型，所述K值用于表征阀门开度。
由于在同一转速下流量主要是靠系统的出口节流阀门调节，所以管路系统的摩擦损失随阀门开度不断变化，其中管路系统的摩擦损失可以通过系统的扬程曲线获得。系统的扬程曲线可以通过水力学定律从管道和静水头的信息中获得，一般供管路系统扬程曲线可以表示为：
H p＝H st+KQ 2
其中为H p管路系统扬程(H p≈H)，H st为管路系统静扬程，K为动扬程系数(即摩擦损失系数)。通过上式可求得八种不同转速下的K值。
如图3所示，不同转速下的K值曲线存在一个共同特点，即随着阀门开度的不断增大，K值急剧减小，当阀门开度增大到50％时K值接近于零，所以定义阀门开度大于50％的区间为大流量区间，阀门开度小于50％的区间为小流量区间。
下面对本发明的方法结合不同模型试验结果进行进一步说明。
从图1的试验系统中总共收集到八种转速下的134个样本，表示为S＝(S 1,…,S 8)，其中六组做训练样本集(S 1,S 2,S 3,S 4,S 7,S 8),两组做测试样本集(S 5,S 6)。
为了比较不同模型的预测性能，采用两个通用的指标，即均方根误差(RMSE)，最大绝对相对误差(MARE)，两者定义如下：
Figure PCTCN2021142973-appb-000020
Figure PCTCN2021142973-appb-000021
其中
Figure PCTCN2021142973-appb-000022
表示y t,i的预测值。
如图5～图8所示，针对两个测试样本集S 5和S 6的小流量区间使用局部LSSVR模型进行预测其效率，其预测效果如图5～8所示，同时对比于全局LSSVR模型的预测结果，次验证了局部LSSVR模型的优越性。与全局LSSVR模型相比，通过阀门开度对训练样本集进行划分区间，使用小流量区间的训练样本集通过式(5～7)训练的局部LSSVR模型，由于局部LSSVR模型中不包含大流量区间的特征，所以针流量区间具有很好的预测性能。如表1(全局LSSVR模型和局部LSSVR模型预测S 5和S 6的MARE(％))所示在小流量区间使用全局LSSVR模型的MARE(根据式(11))是48.9226％和29.5488％而使用局部LSSVR模型的MARE是9.6654％和2.2734％，所以使用局部LSSVR模型在小流量区间具有较好的预测性能。
表1
Figure PCTCN2021142973-appb-000023
如图4所示，利用阀门开度将不同转速下的效率划分为两个阶段，使用局部LSSVR模型预测小流量区间的效率，使用机理模型预测大流量区间的效率。针对两种不同的转速下的测试集即S 5和S 6，使用混合模型预测其效率其详细预测结果如图8～11所示，其预测结果表明混合模型拥有比较好的预测性能。
同时对比全局LSSVR模型和基于相似定律的机理模型，表2(LSSVR模型、机理模型和混合模型预测S 5和S 6的RMSE(％))列出了这三种模型的性能比较结果，其中混合模型的预测效果最佳，机理模型需要的实验数据最少，全局LSSVR 模型需要的实验数据最多，混合模型需要的样本数介于两者之间，如表3(LSSVR模型、机理模型和混合模型预测S 5和S 6需要的样本数)所示。
可以看出，混合模型充分发挥了离心泵的过程知识，同时规避了机理模型的经验误差，所以具有更好的预测性能，相比于全局LSSVR模型,混合模型需要的样本数较少，减少了实验数据的多度依赖，降低了实验的负担。
表2
Figure PCTCN2021142973-appb-000024
表3
Figure PCTCN2021142973-appb-000025
实验结果表明本方法发明所构建的混合模型提高了预测准确性，证明了该混合模型的优越性。
以上实施例的说明只是用于帮助理解本发明的方法及其核心思想。应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以对本发明进行若干改进和修饰，这些改进和修饰也落入本发明权利要求的保护范围内。

Claims (6)

  1. 一种离心泵效率预测方法，其特征在于，包括如下步骤：
    基于流量区间建立不同转速下的离心泵效率预测模型，所述预测模型包括基于相似定律构建的大流量区间模型，以及基于局部LSSVR模型构建的小流量区间模型；
    通过预设试验获取不同转速下的小流量区间离心泵效率样本集，并使用所述小流量区间样本集训练所述小流量区间模型；
    使用训练完成的预测模型预测不同转速下的离心泵效率；其中，当K值小于预设阈值时，采用大流量区间模型，大于等于预设阈值时，采用小流量区间模型，所述K值用于表征阀门开度。
  2. 如权利要求1所述的离心泵效率预测方法，其特征在于，基于相似定律构建的大流量区间模型包括：
    基于离心泵的相似定律，通过离心泵的额定转速和额定效率获取所求转速下的效率，其表达形式如下:
    Figure PCTCN2021142973-appb-100001
    其中η e表示在额定转速n e下的效率，η x表示在转速n x下的所求效率，0.1为经验系数。
  3. 如权利要求1所述的离心泵效率预测方法，其特征在于，基于局部LSSVR模型构建的小流量区间模型包括：
    基于局部LSSVR模型构建效率预测表达式：
    Figure PCTCN2021142973-appb-100002
    其中f表示LSSVR模型，w表示模型参数向量，e i表示样本的近似误差，c表示模型的偏置项，φ表示模型的特征映射，N为训练样本数。
  4. 如权利要求3所述的离心泵效率预测方法，其特征在于，通过预设试验获取不同转速下的小流量区间离心泵效率样本集包括：
    采用由变频电机驱动的自吸式离心泵，通过变频驱动器调节离心泵的运行 转速，通过管路系统中出口阀门开度调节离心泵的出口流量，在不同阀门开度V下，采用流量计、进出口压力传感器和扭矩传感器分别记录出口流量Q、进出口压力(P s,P d)和轴功率N，进而获取不同转速下各流量点的效率值作为样本子集；
    其中，不同流量点的效率公式为：
    Figure PCTCN2021142973-appb-100003
    其中ρ为传输液体的密度，H为离心泵扬程：
    Figure PCTCN2021142973-appb-100004
    其中H st为静扬程。
  5. 如权利要求4所述的离心泵效率预测方法，其特征在于，使用所述小流量区间样本集训练所述小流量区间模型包括：
    针对基于局部LSSVR模型构建的表达式设置如下优化目标：
    Figure PCTCN2021142973-appb-100005
    其中e＝[e 1,…,e N] T表示近似误差，γ>0，表征模型复杂程度与近似精度之间的权衡系数；
    基于上述优化目标对构建的表达式进行优化，获得如下式所示的小流量区间模型：
    Figure PCTCN2021142973-appb-100006
    其中
    Figure PCTCN2021142973-appb-100007
    为预测值，
    Figure PCTCN2021142973-appb-100008
    是一个估算测试集X t的和向量，采用高斯核函数K(x,x *)＝exp(-‖x-x *‖/2σ 2)，其中σ>0为核参数。
  6. 如权利要求1-5任一项所述的离心泵效率预测方法，其特征在于：
    所述K值基于如下公式获得：
    H p＝H st+KQ 2
    其中为H p管路系统扬程，H p≈H，，H为离心泵扬程；H st为管路系统静扬程，Q为出口流量，K为摩擦损失系数，表征阀门开度；所述预设阈值为0.01。
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