CN114235111B - Ultrasonic water meter flow calibration method based on model optimization - Google Patents

Ultrasonic water meter flow calibration method based on model optimization Download PDF

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CN114235111B
CN114235111B CN202210168812.1A CN202210168812A CN114235111B CN 114235111 B CN114235111 B CN 114235111B CN 202210168812 A CN202210168812 A CN 202210168812A CN 114235111 B CN114235111 B CN 114235111B
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杨金合
宋冠锋
毕晨家
沈华刚
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Qingdao Zhidian New Energy Technology Co.,Ltd.
Qingdao Topscomm Communication Co Ltd
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Abstract

The invention relates to the technical field of intelligent water affairs and discloses an ultrasonic water meter flow calibration method based on model optimization, which comprises the following steps: s1, controlling the flow rate to obtain a standard group and a test group; s2, performing nonlinear fitting on the flow characteristic curve based on the standard group data, and calculating an initial mathematical model; s3, evaluating the mathematical model based on the test panel data; s4, optimizing model parameters based on the test set data; s5, obtaining the optimal sectional calibration coefficient of a single water meter through a differential evolution algorithm based on a mathematical model; and s6, repeating the steps from s3 to s5, and completing the flow calibration of all the water meters. The method directly uses the original data to solve the calibration coefficient, is simple and efficient, avoids accuracy errors caused by unreasonable manual selection of segmentation points, corrects the calibration coefficient from the source, optimizes an independent model for each water meter, eliminates the influence caused by processing or installation errors, controls the accuracy within a required range, and realizes the high consistency of water meters in the same batch or model.

Description

一种基于模型优化的超声波水表流量校准方法A flow calibration method for ultrasonic water meters based on model optimization

技术领域technical field

本发明涉及智慧水务技术领域，尤其涉及一种基于模型优化的超声波水表流量校准方法。The invention relates to the technical field of smart water affairs, in particular to an ultrasonic water meter flow calibration method based on model optimization.

背景技术Background technique

超声波水表因计量精度高、量程比宽、压损小等优势，在民用、工业等领域得以广泛应用，其通过计算上下游超声波信号的传播时间差计算流速，基于校准系数，获得管道内平均流速。当前，在流量校准过程中，一般参考流体力学的理论公式，依据人工经验，进行流量分段校准，过程反复迭代，且很难保证最优解。此外，考虑时间成本和经济成本，在对同型号多支水表的校准系数进行二次修正时，利用的测量数据往往较少，通过传统二次修正方法很难保证水表在全流量区间内的精度。Ultrasonic water meters are widely used in civil, industrial and other fields due to the advantages of high measurement accuracy, wide range ratio, and small pressure loss. At present, in the process of flow calibration, the theoretical formula of fluid mechanics is generally referred to, and the flow is calibrated in segments based on manual experience. The process is repeated and iterative, and it is difficult to guarantee the optimal solution. In addition, considering the time cost and economic cost, when the calibration coefficient of multiple water meters of the same model is corrected twice, less measurement data is often used, and it is difficult to ensure the accuracy of the water meter in the full flow range through the traditional second correction method. .

发明内容SUMMARY OF THE INVENTION

本发明针对现有技术存在的不足和缺陷，提供了一种基于模型优化的超声波水表流量校准方法。该方法直接使用原始测量数据求解校准系数，避免了因人工选择分段点不合理而引起的精度误差。此外，从源头修正校准系数，在初始数学模型基础上，为每支水表优化独立的数学模型参数，消除因加工或安装误差带来的影响，将精度控制在要求范围内。Aiming at the deficiencies and defects existing in the prior art, the present invention provides a flow calibration method for ultrasonic water meters based on model optimization. This method directly uses the original measurement data to solve the calibration coefficient, which avoids the precision error caused by the unreasonable manual selection of segmentation points. In addition, the calibration coefficient is corrected from the source, and on the basis of the initial mathematical model, the independent mathematical model parameters are optimized for each water meter to eliminate the influence caused by processing or installation errors, and control the accuracy within the required range.

本发明的目的可以通过以下技术方案来实现：The object of the present invention can be realized through the following technical solutions:

一种基于模型优化的超声波水表流量校准方法，其特征在于，包括以下步骤：A method for calibrating ultrasonic water meter flow based on model optimization is characterized in that, comprising the following steps:

s1：使用一只已校准的超声波水表在全流量区间内测量到的流量数据作为标准组，以所有待校准的超声波水表在全流量区间内测量到的流量数据作为测试组； s1: Use the flow data measured by a calibrated ultrasonic water meter in the full flow range as the standard group, and use the flow data measured by all ultrasonic water meters to be calibrated in the full flow range as the test group;

s2：基于标准组数据，绘制流量特征曲线，对流量特征曲线进行非线性拟合，获得初始数学模型；s2: Based on the standard group data, draw the flow characteristic curve, perform nonlinear fitting on the flow characteristic curve, and obtain the initial mathematical model;

s3：基于测试组数据计算相对误差RD，根据相对误差RD评价数学模型，以评价结果决定是否跳过步骤s4；s3: Calculate the relative error RD based on the test group data, evaluate the mathematical model according to the relative error RD , and decide whether to skip step s4 according to the evaluation result;

s4：基于测试组数据，通过差分进化算法，对数学模型参数进行优化；s4: Based on the test group data, the parameters of the mathematical model are optimized through the differential evolution algorithm;

s5：基于数学模型，通过差分进化算法，获得单只待校准超声波水表最优的分段校准系数；s5: Based on the mathematical model, through the differential evolution algorithm, the optimal segmentation calibration coefficient of the single ultrasonic water meter to be calibrated is obtained;

s6：重复步骤s3至步骤s5，完成所有待校准超声波水表的流量校准。s6: Repeat steps s3 to s5 to complete the flow calibration of all ultrasonic water meters to be calibrated.

进一步地，所述步骤s1中数据集包括每支超声波水表测得的平均流速及上下游接收信号传播时间差的平均值

Figure 875268DEST_PATH_IMAGE001
，其中平均流速
Figure 147111DEST_PATH_IMAGE002
的计算公式如下：Further, in the step s1, the data set includes the average flow rate measured by each ultrasonic water meter and the average value of the difference in the propagation time of the upstream and downstream received signals.
Figure 875268DEST_PATH_IMAGE001
, where the average velocity
Figure 147111DEST_PATH_IMAGE002
The calculation formula is as follows:

Figure 334510DEST_PATH_IMAGE003
Figure 334510DEST_PATH_IMAGE003

式中，T j 为第j次测量时长，m j 为第j次测量时长T j 内流入水箱内的水的质量，

Figure 506735DEST_PATH_IMAGE004
为第j次测量时的水密度，S为测量段管道截面积。In the formula, T j is the jth measurement duration, m j is the quality of the water flowing into the water tank during the jth measurement duration T j ,
Figure 506735DEST_PATH_IMAGE004
is the water density at the jth measurement, and S is the cross-sectional area of the pipeline in the measurement section.

进一步地，所述上下游接收信号传播时间差是以上下游接收信号作为输入，通过时差法计算得到的。Further, the propagation time difference of the upstream and downstream received signals is obtained by taking the upstream and downstream received signals as input and calculated by the time difference method.

进一步地，所述步骤s2中流量特征曲线为校准系数随上下游接收信号传播时间差的平均值变化的曲线，其中校准系数K计算公式如下：Further, in the step s2, the flow characteristic curve is a curve in which the calibration coefficient changes with the average value of the propagation time difference of the upstream and downstream received signals, and the calculation formula of the calibration coefficient K is as follows:

Figure 754176DEST_PATH_IMAGE005
Figure 754176DEST_PATH_IMAGE005

Figure 513316DEST_PATH_IMAGE006
Figure 513316DEST_PATH_IMAGE006

式中，

Figure 301143DEST_PATH_IMAGE007
为在第j次测量时第i组的上下游接收信号传播时间差，Nj为第j次测量时的上下游接收信号传播时间差总数，
Figure 327874DEST_PATH_IMAGE008
为第j次测量的已校准的超声波水表获得的标准组的平均流速，
Figure 746217DEST_PATH_IMAGE009
为第j次测量的上下游接收信号传播时间差的平均值。In the formula,
Figure 301143DEST_PATH_IMAGE007
is the propagation time difference of the upstream and downstream received signals of the i -th group at the jth measurement, N j is the total number of upstream and downstream received signal propagation time differences at the jth measurement,
Figure 327874DEST_PATH_IMAGE008
the mean flow rate of the standard set obtained for the jth measurement of the calibrated ultrasonic water meter,
Figure 746217DEST_PATH_IMAGE009
is the average value of the propagation time difference between the upstream and downstream received signals measured for the jth time.

进一步地，所述步骤s2中的非线性拟合为最小二乘拟合，获得初始数学模型

Figure 727074DEST_PATH_IMAGE010
，其中
Figure 521854DEST_PATH_IMAGE011
为模型参数。Further, the nonlinear fitting in the step s2 is the least square fitting to obtain an initial mathematical model
Figure 727074DEST_PATH_IMAGE010
,in
Figure 521854DEST_PATH_IMAGE011
are model parameters.

进一步地，所述步骤s3中相对误差RD的计算公式如下：Further, the calculation formula of the relative error RD in the step s3 is as follows:

Figure 403092DEST_PATH_IMAGE012
Figure 403092DEST_PATH_IMAGE012

式中，

Figure 992336DEST_PATH_IMAGE013
为测试组第l组的平均流速，K为通过数学模型计算的校准系数，
Figure 460489DEST_PATH_IMAGE014
为测试组中第l组的上下游接收信号传播时间差的平均值；In the formula,
Figure 992336DEST_PATH_IMAGE013
is the average flow velocity of the lth group of the test group, K is the calibration coefficient calculated by the mathematical model,
Figure 460489DEST_PATH_IMAGE014
is the average value of the propagation time difference of the upstream and downstream received signals of the lth group in the test group;

数学模型评价原则如下：The evaluation principles of the mathematical model are as follows:

若RD l 均小于或等于最大允许误差的二分之一，则认为数学模型与测试组数据吻合，跳过步骤s4；If RD l is less than or equal to half of the maximum allowable error, it is considered that the mathematical model is consistent with the test group data, and step s4 is skipped;

若存在RD l 大于最大允许误差的二分之一，且小于或等于最大允许误差，则认为数学模型与测试组数据不吻合，需进入步骤s4进行数学模型参数的优化；If there is RD1 greater than half of the maximum allowable error, and less than or equal to the maximum allowable error, it is considered that the mathematical model does not match the test group data, and it is necessary to enter step s4 to optimize the parameters of the mathematical model;

若存在RD l 大于最大允许误差，则认为数学模型不满足要求，需脱离本流程，对该超声波水表单独分析。If there is RD l greater than the maximum allowable error, it is considered that the mathematical model does not meet the requirements, and the ultrasonic water meter needs to be analyzed separately from this process.

进一步地，所述步骤s4具体步骤如下： Further, the specific steps of the step s4 are as follows:

s4.1：基于测试组数据的平均流速值

Figure 714752DEST_PATH_IMAGE013
与（
Figure 732387DEST_PATH_IMAGE015
）之间的欧氏距离定义目标函数，以数学模型
Figure 243265DEST_PATH_IMAGE016
中参数
Figure 447981DEST_PATH_IMAGE017
的预设允许范围为约束条件，基于数学模型参数θ设计变量；s4.1: Average flow velocity value based on test group data
Figure 714752DEST_PATH_IMAGE013
and(
Figure 732387DEST_PATH_IMAGE015
) between the Euclidean distances to define the objective function to the mathematical model
Figure 243265DEST_PATH_IMAGE016
Medium parameter
Figure 447981DEST_PATH_IMAGE017
The preset allowable range of is the constraint condition, and the design variable is based on the mathematical model parameter θ;

s4.2：设定差分进化算法对数学模型的搜索范围，初始化种群个体数目、最大迭代次数、交叉因子和变异因子；s4.2: Set the search range of the differential evolution algorithm for the mathematical model, initialize the number of individuals in the population, the maximum number of iterations, the crossover factor and the mutation factor;

s4.3：在数学模型参数θ的搜索范围内随机生成种群作为父代种群，迭代次数加1，根据目标函数和约束条件，计算父代种群中个体的适应度；s4.3: Randomly generate a population within the search range of the mathematical model parameter θ as the parent population, add 1 to the number of iterations, and calculate the fitness of individuals in the parent population according to the objective function and constraints;

s4.4：基于交叉因子与变异因子，在父代种群中随机选择个体进行交叉和变异，生成试验种群；s4.4: Based on the crossover factor and variation factor, randomly select individuals in the parent population for crossover and mutation to generate a test population;

s4.5：计算试验种群中个体的适应度，将父代种群与试验种群中个体的适应度进行比较，根据比较结果生成子代种群；s4.5: Calculate the fitness of individuals in the test population, compare the fitness of the parent population with that of the individuals in the test population, and generate the offspring population according to the comparison results;

s4.6：进行子代种群中个体的非支配排序；s4.6: Perform non-dominated sorting of individuals in the offspring population;

s4.7：计算子代种群中个体的拥挤距离，剔除拥挤距离相对较小的个体以保持子代种群个体数目与初始种群个体数目一致；s4.7: Calculate the crowding distance of individuals in the offspring population, and remove the individuals with relatively small crowding distances to keep the number of individuals in the offspring population consistent with the number of individuals in the initial population;

s4.8：判断现有迭代次数是否到达最大迭代次数要求，若满足，则完成数学模型参数优化，结束流程；否则跳转至步骤s4.3。s4.8: Determine whether the current number of iterations reaches the maximum number of iterations. If so, complete the mathematical model parameter optimization and end the process; otherwise, jump to step s4.3.

进一步地，所述步骤s5具体步骤如下： Further, the specific steps of the step s5 are as follows:

s5.1：基于测试组数据的平均流速值

Figure 833832DEST_PATH_IMAGE013
与（
Figure 174815DEST_PATH_IMAGE015
）之间的欧氏距离定义目标函数，随机生成分段点位置β和分段校准系数α，以分段点位置β和分段校准系数α的允许范围作为约束条件，以参数
Figure 387753DEST_PATH_IMAGE018
设计变量；s5.1: Average flow velocity value based on test group data
Figure 833832DEST_PATH_IMAGE013
and(
Figure 174815DEST_PATH_IMAGE015
) defines the objective function, randomly generates the segment point position β and the segment calibration coefficient α, and takes the allowable range of the segment point position β and the segment calibration coefficient α as the constraint condition, and uses the parameter
Figure 387753DEST_PATH_IMAGE018
design variable;

s5.2：设定差分进化算法对参数γ的搜索范围，初始化种群个体数目、最大迭代次数、交叉因子和变异因子；s5.2: Set the search range of the parameter γ by the differential evolution algorithm, initialize the number of individuals in the population, the maximum number of iterations, the crossover factor and the mutation factor;

s5.3：在参数γ的搜索范围内随机生成种群作为父代种群，迭代次数加1，根据目标函数和约束条件，计算父代种群中个体的适应度；s5.3: Randomly generate a population as the parent population within the search range of the parameter γ, add 1 to the number of iterations, and calculate the fitness of the individuals in the parent population according to the objective function and constraints;

s5.4：基于交叉因子与变异因子，在父代种群中随机选择个体进行交叉和变异，生成试验种群；s5.4: Based on the crossover factor and variation factor, randomly select individuals in the parent population for crossover and mutation to generate a test population;

s5.5：计算试验种群中个体的适应度，将父代种群与试验种群中个体的适应度进行比较，根据比较结果生成子代种群；s5.5: Calculate the fitness of individuals in the test population, compare the fitness of the parent population with that of the individuals in the test population, and generate offspring populations according to the comparison results;

s5.6：进行子代种群中个体的非支配排序； s5.6: Perform non-dominated sorting of individuals in the offspring population;

s5.7：计算子代种群中个体的拥挤距离，剔除拥挤距离相对较小的个体以保持子代种群个体数目与初始种群个体数目一致； s5.7: Calculate the crowding distance of individuals in the offspring population, and remove individuals with relatively small crowding distances to keep the number of individuals in the offspring population consistent with the number of individuals in the initial population;

s5.8：判断现有迭代次数是否到达最大迭代次数要求，若满足，则完成参数优化，结束流程；否则跳转至步骤s5.3。s5.8: Determine whether the existing number of iterations reaches the maximum number of iterations. If so, complete the parameter optimization and end the process; otherwise, jump to step s5.3.

本发明的有益技术效果：直接使用原始测量数据求解校准系数，简单高效，避免了因人工选择分段点不合理而引起的精度误差。此外，从源头修正校准系数，在初始数学模型基础上，为每支水表优化独立的数学模型参数，消除因加工或安装误差带来的影响，将精度控制在要求范围内，从而实现同批次或型号水表的高度一致性。 Beneficial technical effects of the present invention: directly use the original measurement data to solve the calibration coefficient, which is simple and efficient, and avoids precision errors caused by unreasonable manual selection of segment points. In addition, the calibration coefficient is corrected from the source. On the basis of the initial mathematical model, the independent mathematical model parameters are optimized for each water meter to eliminate the influence caused by processing or installation errors, and control the accuracy within the required range, so as to achieve the same batch of water. or high consistency of model water meters.

附图说明Description of drawings

图1为本发明的总体流程图。FIG. 1 is an overall flow chart of the present invention.

图2为本发明实施例中超声波水表的流量特征曲线。Fig. 2 is the flow characteristic curve of the ultrasonic water meter in the embodiment of the present invention.

具体实施方式Detailed ways

为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅用以解释本发明，并不限定本发明。In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to illustrate the present invention, but not to limit the present invention.

实施例： Example:

如图1所示，一种基于模型优化的超声波水表流量校准方法，包括以下步骤：As shown in Figure 1, a model-based optimization method for ultrasonic water meter flow calibration includes the following steps:

s1：调节流量控制装置，待流量稳定后，使用一只已校准的超声波水表在全流量区间内测量到的流量数据作为标准组，以所有待校准的超声波水表在全流量区间内测量到的流量数据作为测试组。数据集包括每支超声波水表测得的平均流速及上下游接收信号传播时间差的平均值

Figure 79765DEST_PATH_IMAGE019
，其中平均流速
Figure 738148DEST_PATH_IMAGE020
的计算公式如下：s1: Adjust the flow control device. After the flow is stable, use the flow data measured by a calibrated ultrasonic water meter in the full flow range as the standard group, and use the flow measured by all ultrasonic water meters to be calibrated in the full flow range. data as a test group. The data set includes the average flow velocity measured by each ultrasonic water meter and the average value of the propagation time difference of the upstream and downstream received signals
Figure 79765DEST_PATH_IMAGE019
, where the average velocity
Figure 738148DEST_PATH_IMAGE020
The calculation formula is as follows:

Figure 622053DEST_PATH_IMAGE003
Figure 622053DEST_PATH_IMAGE003

式中，T j 为第j次测量时长，m j 为第j次测量时长T j 内流入水箱内的水的质量，

Figure 989581DEST_PATH_IMAGE004
为第j次测量时的水密度，S为测量段管道截面积。In the formula, T j is the jth measurement duration, m j is the quality of the water flowing into the water tank during the jth measurement duration T j ,
Figure 989581DEST_PATH_IMAGE004
is the water density at the jth measurement, and S is the cross-sectional area of the pipeline in the measurement section.

所述上下游接收信号传播时间差是以上下游接收信号作为输入，通过时差法计算得到的。 The propagation time difference of the upstream and downstream received signals is obtained by taking the upstream and downstream received signals as input and calculated by the time difference method.

s2：基于标准组数据，绘制流量特征曲线，对流量特征曲线进行非线性拟合，获得初始数学模型。流量特征曲线为校准系数随上下游接收信号传播时间差的平均值的变化曲线，其中校准系数K计算公式如下：s2: Based on the standard group data, draw the flow characteristic curve, perform nonlinear fitting on the flow characteristic curve, and obtain the initial mathematical model. The flow characteristic curve is the change curve of the calibration coefficient with the average value of the propagation time difference of the upstream and downstream received signals, and the calculation formula of the calibration coefficient K is as follows:

Figure 886998DEST_PATH_IMAGE005
Figure 886998DEST_PATH_IMAGE005

Figure 365384DEST_PATH_IMAGE006
Figure 365384DEST_PATH_IMAGE006

式中，

Figure 708989DEST_PATH_IMAGE021
为在第j次测量时第i组的上下游接收信号传播时间差，Nj为第j次测量时的上下游接收信号传播时间差总数，
Figure 981839DEST_PATH_IMAGE008
为第j次测量的已校准的超声波水表获得的标准组的平均流速，
Figure 897711DEST_PATH_IMAGE009
为第j次测量的上下游接收信号传播时间差的平均值。In the formula,
Figure 708989DEST_PATH_IMAGE021
is the propagation time difference of the upstream and downstream received signals of the i -th group at the jth measurement, N j is the total number of upstream and downstream received signal propagation time differences at the jth measurement,
Figure 981839DEST_PATH_IMAGE008
the mean flow rate of the standard set obtained for the jth measurement of the calibrated ultrasonic water meter,
Figure 897711DEST_PATH_IMAGE009
is the average value of the propagation time difference between the upstream and downstream received signals measured for the jth time.

所述非线性拟合为最小二乘拟合，获得初始数学模型

Figure 914209DEST_PATH_IMAGE022
。数学模型表达式与超声波水表型号相关，数学模型中参数与水表管道结构和声路设计参数相关。The nonlinear fitting is a least squares fitting to obtain an initial mathematical model
Figure 914209DEST_PATH_IMAGE022
. The mathematical model expression is related to the ultrasonic water meter model, and the parameters in the mathematical model are related to the water meter pipeline structure and sound path design parameters.

如图2所示为某型号DN15超声波水表的流量特征曲线，校准系数随上下游接收信号传播时间差的平均值的变化而改变。基于图2数据进行最小二乘拟合后，获得初始数学模型的表达式如下： Figure 2 shows the flow characteristic curve of a certain type of DN15 ultrasonic water meter. The calibration coefficient changes with the average value of the propagation time difference of the upstream and downstream received signals. After performing least squares fitting based on the data in Figure 2, the expression of the initial mathematical model is obtained as follows:

Figure 100602DEST_PATH_IMAGE023
Figure 100602DEST_PATH_IMAGE023

式中，a、b、c、d均为数学模型中的可调参数，取值与超声波水表型号相关。参数 a的取值范围为[0.02016, 0.02107]，参数b的取值范围为[-0.0001136, 0.0003671]，参数c的取值范围为[-0.009227, -0.008075]，参数d的取值范围为[-0.2465, -0.1726]。In the formula, a, b, c, and d are all adjustable parameters in the mathematical model, and the values are related to the model of the ultrasonic water meter. The value range of parameter a is [0.02016, 0.02107], the value range of parameter b is [-0.0001136, 0.0003671], the value range of parameter c is [-0.009227, -0.008075], and the value range of parameter d is [ -0.2465, -0.1726].

s3：基于测试组数据计算相对误差RD，根据相对误差RD评价数学模型，以评价结果决定是否跳过步骤s4。相对误差RD的计算公式如下：s3: Calculate the relative error RD based on the test group data, evaluate the mathematical model according to the relative error RD , and decide whether to skip step s4 according to the evaluation result. The formula for calculating the relative error RD is as follows:

Figure 996882DEST_PATH_IMAGE012
Figure 996882DEST_PATH_IMAGE012

式中，

Figure 150783DEST_PATH_IMAGE013
为测试组第l组的平均流速，K为通过数学模型计算的校准系数，
Figure 298868DEST_PATH_IMAGE014
为测试组中第l组的上下游接收信号传播时间差的平均值。In the formula,
Figure 150783DEST_PATH_IMAGE013
is the average flow velocity of the lth group of the test group, K is the calibration coefficient calculated by the mathematical model,
Figure 298868DEST_PATH_IMAGE014
is the average value of the propagation time difference of the upstream and downstream received signals of the lth group in the test group.

数学模型评价原则如下： The evaluation principles of the mathematical model are as follows:

若RD l 均小于或等于最大允许误差的二分之一，则认为数学模型与测试组数据吻合，跳过步骤s4；If RD l is less than or equal to half of the maximum allowable error, it is considered that the mathematical model is consistent with the test group data, and step s4 is skipped;

若存在RD l 大于最大允许误差的二分之一，且小于或等于最大允许误差，则认为数学模型与测试组数据不吻合，需进入步骤s4进行数学模型参数的优化；If there is RD1 greater than half of the maximum allowable error, and less than or equal to the maximum allowable error, it is considered that the mathematical model does not match the test group data, and it is necessary to enter step s4 to optimize the parameters of the mathematical model;

若存在RD l 大于最大允许误差，则认为数学模型不满足要求，需脱离本流程，对该超声波水表单独分析。If there is RD l greater than the maximum allowable error, it is considered that the mathematical model does not meet the requirements, and the ultrasonic water meter needs to be analyzed separately from this process.

实施例中，某型号DN15超声波水表为2级表，设定最大允许误差即为国标要求的2级精度。 In the embodiment, a certain type of DN15 ultrasonic water meter is a 2-level meter, and the maximum allowable error is set to be the 2-level accuracy required by the national standard.

s4：基于测试组数据，通过差分进化算法，对数学模型参数进行优化。具体步骤如下： s4: Based on the test group data, the parameters of the mathematical model are optimized through the differential evolution algorithm. Specific steps are as follows:

s4.1：基于测试组数据的平均流速值

Figure 11871DEST_PATH_IMAGE013
与（
Figure 626523DEST_PATH_IMAGE015
）之间的欧氏距离定义目标函数，以数学模型
Figure 487294DEST_PATH_IMAGE016
中参数
Figure 845594DEST_PATH_IMAGE017
的预设允许范围为约束条件，基于数学模型参数θ设计变量；s4.1: Average flow velocity value based on test group data
Figure 11871DEST_PATH_IMAGE013
and(
Figure 626523DEST_PATH_IMAGE015
) between the Euclidean distances to define the objective function to the mathematical model
Figure 487294DEST_PATH_IMAGE016
Medium parameter
Figure 845594DEST_PATH_IMAGE017
The preset allowable range of is the constraint condition, and the design variable is based on the mathematical model parameter θ;

s4.2：设定差分进化算法对数学模型的搜索范围，初始化种群个体数目、最大迭代次数、交叉因子和变异因子；s4.2: Set the search range of the differential evolution algorithm for the mathematical model, initialize the number of individuals in the population, the maximum number of iterations, the crossover factor and the mutation factor;

s4.3：在数学模型参数θ的搜索范围内随机生成种群作为父代种群，迭代次数加1，根据目标函数和约束条件，计算父代种群中个体的适应度；s4.3: Randomly generate a population within the search range of the mathematical model parameter θ as the parent population, add 1 to the number of iterations, and calculate the fitness of individuals in the parent population according to the objective function and constraints;

s4.4：基于交叉因子与变异因子，在父代种群中随机选择个体进行交叉和变异，生成试验种群；s4.4: Based on the crossover factor and variation factor, randomly select individuals in the parent population for crossover and mutation to generate a test population;

s4.5：计算试验种群中个体的适应度，将父代种群与试验种群中个体的适应度进行比较，根据比较结果生成子代种群；s4.5: Calculate the fitness of individuals in the test population, compare the fitness of the parent population with that of the individuals in the test population, and generate the offspring population according to the comparison results;

s4.6：进行子代种群中个体的非支配排序；s4.6: Perform non-dominated sorting of individuals in the offspring population;

s4.7：计算子代种群中个体的拥挤距离，剔除拥挤距离相对较小的个体以保持子代种群个体数目与初始种群个体数目一致；s4.7: Calculate the crowding distance of individuals in the offspring population, and remove the individuals with relatively small crowding distances to keep the number of individuals in the offspring population consistent with the number of individuals in the initial population;

s4.8：判断现有迭代次数是否到达最大迭代次数要求，若满足，则完成数学模型参数优化，结束流程；否则跳转至步骤s4.3。s4.8: Determine whether the current number of iterations reaches the maximum number of iterations. If so, complete the mathematical model parameter optimization and end the process; otherwise, jump to step s4.3.

s5：基于数学模型，通过差分进化算法，获得单只待校准超声波水表最优的分段校准系数。分段校准系数是对数学模型

Figure 505114DEST_PATH_IMAGE024
的分段线性表征，s5的具体步骤如下：s5: Based on the mathematical model, through the differential evolution algorithm, the optimal segmentation calibration coefficient of the single ultrasonic water meter to be calibrated is obtained. The piecewise calibration coefficients are for the mathematical model
Figure 505114DEST_PATH_IMAGE024
The piecewise linear representation of , the specific steps of s5 are as follows:

s5.1：基于测试组数据的平均流速值

Figure 385608DEST_PATH_IMAGE013
与（
Figure 497789DEST_PATH_IMAGE015
）之间的欧氏距离定义目标函数，随机生成分段点位置β和分段校准系数α，以分段点位置β和分段校准系数α的允许范围作为约束条件，以参数
Figure 659781DEST_PATH_IMAGE018
设计变量；s5.1: Average flow velocity value based on test group data
Figure 385608DEST_PATH_IMAGE013
and(
Figure 497789DEST_PATH_IMAGE015
) defines the objective function, randomly generates the segment point position β and the segment calibration coefficient α, and takes the allowable range of the segment point position β and the segment calibration coefficient α as the constraint condition, and uses the parameter
Figure 659781DEST_PATH_IMAGE018
design variable;

s5.2：设定差分进化算法对参数γ的搜索范围，初始化种群个体数目、最大迭代次数、交叉因子和变异因子；s5.2: Set the search range of the parameter γ by the differential evolution algorithm, initialize the number of individuals in the population, the maximum number of iterations, the crossover factor and the mutation factor;

s5.3：在参数γ的搜索范围内随机生成种群作为父代种群，迭代次数加1，根据目标函数和约束条件，计算父代种群中个体的适应度；s5.3: Randomly generate a population as the parent population within the search range of the parameter γ, add 1 to the number of iterations, and calculate the fitness of the individuals in the parent population according to the objective function and constraints;

s5.4：基于交叉因子与变异因子，在父代种群中随机选择个体进行交叉和变异，生成试验种群；s5.4: Based on the crossover factor and variation factor, randomly select individuals in the parent population for crossover and mutation to generate a test population;

s5.5：计算试验种群中个体的适应度，将父代种群与试验种群中个体的适应度进行比较，根据比较结果生成子代种群；s5.5: Calculate the fitness of individuals in the test population, compare the fitness of the parent population with that of the individuals in the test population, and generate offspring populations according to the comparison results;

s5.6：进行子代种群中个体的非支配排序；s5.6: Perform non-dominated sorting of individuals in the offspring population;

s5.7：计算子代种群中个体的拥挤距离，剔除拥挤距离相对较小的个体以保持子代种群个体数目与初始种群个体数目一致；s5.7: Calculate the crowding distance of individuals in the offspring population, and remove individuals with relatively small crowding distances to keep the number of individuals in the offspring population consistent with the number of individuals in the initial population;

s5.8：判断现有迭代次数是否到达最大迭代次数要求，若满足，则完成参数优化，结束流程；否则跳转至步骤s5.3。s5.8: Determine whether the existing number of iterations reaches the maximum number of iterations. If so, complete the parameter optimization and end the process; otherwise, jump to step s5.3.

s6：重复步骤s3至步骤s5，完成所有待校准超声波水表的流量校准。s6: Repeat steps s3 to s5 to complete the flow calibration of all ultrasonic water meters to be calibrated.

上述实施例是对本发明的具体实施方式的说明，而非对本发明的限制，有关技术领域的技术人员在不脱离本发明的精神和范围的情况下，还可做出各种变换和变化以得到相对应的等同的技术方案，因此所有等同的技术方案均应归入本发明的专利保护范围。The above-mentioned embodiments are descriptions of specific embodiments of the present invention, rather than limitations of the present invention. Those skilled in the art can also make various transformations and changes without departing from the spirit and scope of the present invention to obtain Corresponding and equivalent technical solutions, therefore all equivalent technical solutions should be included in the patent protection scope of the present invention.

Claims (3)

1. A model optimization-based ultrasonic water meter flow calibration method is characterized by comprising the following steps:
s 1: the method comprises the steps that flow data measured by one calibrated ultrasonic water meter in a full-flow interval are used as a standard group, and flow data measured by all to-be-calibrated ultrasonic water meters in the full-flow interval are used as a test group; the finally obtained data set comprises the average flow speed measured by each ultrasonic water meter and the average value of the propagation time difference of the upstream and downstream received signals
Figure 432597DEST_PATH_IMAGE001
Wherein the average flow velocity
Figure 511411DEST_PATH_IMAGE002
The calculation formula of (a) is as follows:
Figure 947071DEST_PATH_IMAGE003
in the formula (I), the compound is shown in the specification,T j is a firstjThe duration of the secondary measurement is long,m j is a firstjDuration of time of secondary measurementT j The mass of water flowing into the tank,
Figure 892287DEST_PATH_IMAGE004
is a firstjSecond measurementThe density of water at the time of measurement,Smeasuring the sectional area of the pipeline at the section;
s 2: drawing a flow characteristic curve based on the standard group data, and carrying out nonlinear fitting on the flow characteristic curve to obtain an initial mathematical model; wherein the flow characteristic curve is a curve in which a calibration coefficient varies with an average value of propagation time differences of upstream and downstream received signals, wherein the calibration coefficientKThe calculation formula is as follows:
Figure 46188DEST_PATH_IMAGE005
Figure 866376DEST_PATH_IMAGE006
in the formula (I), the compound is shown in the specification,
Figure 156543DEST_PATH_IMAGE007
is at the firstjAt the time of secondary measurementiUpstream and downstream of the group, the difference in propagation time of the received signals, NjIs as followsjThe total number of differences in propagation time between the upstream and downstream received signals at the time of the secondary measurement,
Figure 472993DEST_PATH_IMAGE008
the average flow rate for the standard set obtained for the calibrated ultrasonic water meter for the jth measurement,
Figure 848611DEST_PATH_IMAGE009
is as followsjAn average value of the upstream and downstream received signal propagation time differences of the secondary measurements;
s 3: calculating relative error based on test set dataRDAccording to relative errorRDEvaluating the mathematical model to determine whether to skip step s 4; wherein the relative errorRDThe calculation formula of (c) is as follows:
Figure 472490DEST_PATH_IMAGE010
in the formula (I), the compound is shown in the specification,
Figure 882743DEST_PATH_IMAGE011
to test grouplThe average flow rate of the group is,Kfor the calibration coefficients calculated by the mathematical model,
Figure 169761DEST_PATH_IMAGE012
is the first in the test grouplAn average of the upstream and downstream received signal propagation time differences of the group;
the mathematical model evaluation principle is as follows:
if it isRD l If the error values are less than or equal to one half of the maximum allowable error, the mathematical model is considered to be consistent with the test group data, and the step s4 is skipped;
if present, isRD l If the maximum allowable error is greater than one half of the maximum allowable error and less than or equal to the maximum allowable error, the mathematical model is considered not to be consistent with the test group data, and the step s4 is required to optimize the parameters of the mathematical model;
if present, isRD l If the error is larger than the maximum allowable error, the mathematical model is considered not to meet the requirement, the process needs to be separated, and the ultrasonic water meter is analyzed independently;
s 4: optimizing mathematical model parameters by a differential evolution algorithm based on test group data; the method comprises the following specific steps:
s 4.1: average flow rate value based on test group data
Figure 298254DEST_PATH_IMAGE013
And (a) and
Figure 460245DEST_PATH_IMAGE014
) Define an objective function by the Euclidean distance between the two, and use a mathematical model
Figure 725004DEST_PATH_IMAGE015
Middle parameter
Figure 274934DEST_PATH_IMAGE016
The preset allowable range is a constraint condition, and variables are designed based on a mathematical model parameter theta;
s 4.2: setting a search range of a differential evolution algorithm on a mathematical model, and initializing the number of population individuals, the maximum iteration times, cross factors and variation factors;
s 4.3: randomly generating a population as a parent population in the search range of the mathematical model parameter theta, adding 1 to the iteration number, and calculating the fitness of individuals in the parent population according to the target function and the constraint condition;
s 4.4: randomly selecting individuals from the parent population to perform crossing and mutation based on the crossing factors and the mutation factors to generate a test population;
s 4.5: calculating the fitness of individuals in the test population, comparing the fitness of individuals in the parent population with the fitness of individuals in the test population, and generating a child population according to a comparison result;
s 4.6: performing non-dominated sorting of individuals in the progeny population;
s 4.7: calculating crowding distances of individuals in the offspring population, and eliminating individuals with relatively small crowding distances to keep the number of the individuals in the offspring population consistent with the number of the individuals in the initial population;
s 4.8: judging whether the existing iteration times reach the requirement of the maximum iteration times, if so, finishing the parameter optimization of the mathematical model, and ending the process; otherwise, jumping to the step s 4.3;
s 5: based on a mathematical model, obtaining an optimal sectional calibration coefficient of a single ultrasonic water meter to be calibrated through a differential evolution algorithm; the method comprises the following specific steps:
s 5.1: average flow rate value based on test group data
Figure 123679DEST_PATH_IMAGE013
And (a)
Figure 823782DEST_PATH_IMAGE014
) Defining an objective function by the Euclidean distance between the two points, randomly generating a segmentation point position beta and a segmentation calibration coefficient alpha, and using the segmentation point position beta and the segmentation calibration coefficientThe allowable range of alpha is used as a constraint condition, and the parameter is used as
Figure 208627DEST_PATH_IMAGE017
Designing variables;
s 5.2: setting a search range of a differential evolution algorithm for the parameter gamma, and initializing the number of population individuals, the maximum iteration times, cross factors and variation factors;
s 5.3: randomly generating a population as a parent population in the search range of the parameter gamma, adding 1 to the iteration times, and calculating the fitness of individuals in the parent population according to the target function and the constraint condition;
s 5.4: randomly selecting individuals from the parent population to perform crossing and mutation based on the crossing factors and the mutation factors to generate a test population;
s 5.5: calculating the fitness of individuals in the test population, comparing the fitness of individuals in the parent population with the fitness of individuals in the test population, and generating a child population according to a comparison result;
s 5.6: performing non-dominant sorting of individuals in the offspring population;
s 5.7: calculating crowding distances of individuals in the offspring population, and eliminating individuals with relatively small crowding distances to keep the number of the individuals in the offspring population consistent with the number of the individuals in the initial population;
s 5.8: judging whether the existing iteration times reach the maximum iteration time requirement, if so, completing parameter optimization, and ending the process; otherwise, jumping to the step s 5.3;
s 6: and (5) repeating the steps s3 to s5 to finish the flow calibration of all the ultrasonic water meters to be calibrated.
2. The method of claim 1, wherein the difference in propagation time between the upstream and downstream received signals is calculated by a time difference method using the upstream and downstream received signals as inputs.
3. The method for calibrating flow rate of an ultrasonic water meter based on model optimization of claim 1, wherein the step s is performed in a manner of2, obtaining an initial mathematical model by using least square fitting as the nonlinear fitting
Figure DEST_PATH_IMAGE019
Wherein
Figure DEST_PATH_IMAGE021
Are model parameters.
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