基于主成分分析与支持向量机的热泵系统制冷剂泄漏识别研究

doi:10.11949/0438-1157.20191139

摘要/Abstract

摘要：

为了研究热泵系统制冷剂泄漏识别的数据挖掘理论方法和实验验证，首先建立空气源热泵系统制冷剂泄漏实验台，进行热泵系统正常工况、干扰工况、泄漏工况的实验参数测试；其次，采用主成分分析法对测试数据进行特征提取处理，采用支持向量机对数据进行分类识别，建立了用于热泵系统的制冷剂泄漏识别的主成分分析-支持向量机模型，在二分类和多分类模式下验证了模型的性能，并研究了泄漏速率和不同故障工况对模型的影响。采用RefliefF特征选择算法对原始特征参数进行筛选，简化了识别模型的特征参数。研究结果表明：对于空气源热泵热水系统，PCA-SVM泄漏识别模型在多种验证集中对泄漏工况的识别准确度达100%，缓慢泄漏的诊断识别性能弱于快速泄漏，同一模型在不同故障诊断识别中性能不同，对系统运行影响轻微的故障诊断识别性能弱于其他故障。RefliefF特征选择方法将原始41个系统特征参数精简至10个特征参数，参数筛选优化后的泄漏识别模型识别精度也维持在较高水平，优化的泄漏识别模型更利于实际应用。

关键词: 泄漏识别, 支持向量机, 主成分分析, 特征选择, 热泵系统, 算法, 数学模型

Abstract:

To study the data mining theory method and experimental verification of the refrigerant leakage identification of the heat pump system, firstly establish an air source heat pump system refrigerant leakage test bench to test the experimental parameters of the heat pump system in normal working conditions, interference working conditions, and leakage working conditions. Then, principal component analysis (PCA) was used to process the experimental data, and support vector machine (SVM) was used to classify and identify the data. A leakage identification model based on PCA-SVM was established which verified in both two classification and multi classification model. The leakage rate and the influence of different fault conditions of the model was studied. RefliefF feature selection algorithm is used to screen the original feature parameters which simplify the feature parameters of the identification model. The results show that, for the air source heat pump water heater, the leakage identification model has a high identification of 100% in the leakage mode, and the slow leak diagnosis recognition performance of the weak in rapid leak, the same model in different fault diagnosis recognition performance is different, slight influence on the system s running fault diagnosis recognition performance is weaker than other malfunction. RefliefF feature selection method reduces the original 41 system characteristic parameters to 10 characteristic parameters. The identification accuracy of the leakage identification model after parameter screening and optimization is also maintained at a high level, the optimized leakage identification model is more conducive to practical application.

Key words: leakage identification, SVM, PCA, feature selection, heat pump, algorithm, mathematical modeling

中图分类号:

TP 312

于仙毅, 巫江虹, 高云辉. 基于主成分分析与支持向量机的热泵系统制冷剂泄漏识别研究[J]. 化工学报, 2020, 71(7): 3151-3164.

Xianyi YU, Jianghong WU, Yunhui GAO. Research on refrigerant leakage identification for heat pump system based on PCA-SVM models[J]. CIESC Journal, 2020, 71(7): 3151-3164.

图/表 22

表1 制冷剂泄漏实验系统部件信息

Table 1 Refrigerant leak test system component information

系统	部件	规格型号
制冷循环系统	压缩机	BSA645CV-R1EN型 R134a制冷剂
	冷凝器	U型套管式
	节流阀	丹佛斯TN2型热力膨胀阀
	蒸发器（含小型风扇组）	单流层微通道换热器
水路循环系统	保温水箱	30 L、?20 mm进出水口
	水泵	1个自吸式磁力循环泵
	水流量计	1个 LWGY型涡轮流量计
制冷剂泄漏控制及收集部件	手阀	4个
	开度阀	4个
	气体收集袋	1个 20 L超高密封袋
测试部件	热电偶	若干 J型热电偶
	压力变送器	8个 0~0.6 MPa、0~4 MPa
	电子秤	100 g/0.02 g 15 kg/0.2 g
	功率仪	1个 HOPI型
	安捷伦	1台 34972型
	计算机	1台

图1 泄漏实验系统及测点布置示意图温度测点；压力测点；1—压缩机；2—防爆气囊；3—可调开度阀；4—开度阀；5—水流量计；6—水箱；7—水泵；8—套管冷凝器；9—热力膨胀阀；10—蒸发器；11—风机；12—制冷剂气瓶；13—开度阀

Fig.1 Schematic diagram of leakage test system and arrangement of measurement points

图2 制冷剂泄漏实验实物图

Fig.2 Refrigerant leakage experimental

表2 恒定水温热泵系统测试工况

Table 2 Test conditions of the heat pump system with constant water temperature

工况类型	工况详情及引入方法
正常工况(normal)	系统开机后，恒定30℃水温，系统稳定运行
泄漏工况(Refleak)	以正常工况为基准，在其开机平稳运行一小段时间后，系统趋于稳定的一个时间点作为泄漏工况的开始点，开始控制泄漏口阀门开度
冷凝器脏污工况(ReduCF)	调节冷凝器水泵，降低冷凝器水流量
蒸发器脏污工况(ReduEF)	通过遮挡蒸发器，降低蒸发器换热面积
热力膨胀阀预紧力过小工况(loosTV)	人为调松热力膨胀阀预紧弹簧
热力膨胀阀预紧力过大工况(ClosTV)	人为调紧热力膨胀阀预紧弹簧
冷凝温度变化工况(IncrTW)(DecrTW)	分别恒定6号大水箱内的水温为25℃和35℃

表3 特征变量名称符号及对应的系统表征含义

Table 3 Name symbols of characteristic variables and their corresponding system representation meanings

序号	变量符号	变量名称	意义
1	Tci1	冷凝器进口温度1	测点温度
2	Tci2	冷凝器进口温度2	测点温度
3	Tci3	冷凝器进口温度3	测点温度
4	Tci4	冷凝器进口温度4	测点温度
5	Tci5	冷凝器进口温度5	测点温度
6	Tco1	冷凝器出口温度1	测点温度
7	Tco2	冷凝器出口温度2	测点温度
8	Tco3	冷凝器出口温度3	测点温度
9	Tco4	冷凝器出口温度4	测点温度
10	Tco5	冷凝器出口温度5	测点温度
11	Tei1	蒸发器进口温度1	测点温度
12	Tei2	蒸发器进口温度2	测点温度
13	Tei3	蒸发器进口温度3	测点温度
14	Tei4	蒸发器进口温度4	测点温度
15	Tei5	蒸发器进口温度5	测点温度
16	Teo1	蒸发器出口温度1	测点温度
17	Teo2	蒸发器出口温度2	测点温度
18	Teo3	蒸发器出口温度3	测点温度
19	Teo4	蒸发器出口温度4	测点温度
20	Teo5	蒸发器出口温度5	测点温度
21	Tesu	蒸发器风冷出口环温	蒸发端环境温度
22	Twat	水箱水温	冷凝端环境温度
23	POcom	压缩机耗功	系统输入耗功
24	Tesub	过热度	Teo1-Tgsat
25	Tcsub	过冷度	Tlsat-Tco1
26	P01	压缩机出口压力	压力测点
27	P02	冷凝器进口压力	压力测点
28	P03	冷凝器出口压力	压力测点
29	P04	节流阀入口压力	压力测点
30	P05	节流阀出口压力	压力测点
31	P06	蒸发器进口压力	压力测点
32	P07	蒸发器出口压力	压力测点
33	P08	压缩机进口压力	压力测点
34	ΔTcom	压缩机进出口温差	Tci1-Teo5
35	ΔTcon	冷凝器进出口温差	Tci5-Tco1
36	ΔTvel	节流阀温差	Tco5-Tei1
37	ΔPcom	压缩机进出口压差	P01-P08
38	ΔPcon	冷凝器进出口压差	P02-P03
39	ΔPvel	节流阀压差	P04-P05
40	ΔPeva	蒸发器进出口压差	P06-P07
41	ΔHcon	冷凝器进出口焓差	Hci-Hco

图3 泄漏工况实验制冷剂泄漏速率

Fig.3 Refrigerant leakage rate of experimental in leakage condition

表4 不同核函数类型的SVM模型表达式及其参数

Table 4 SVM model expressions and parameters of different kernel function types

名称	表达式	参数
线性核	$k x i, x j = x i T x j$
多项式核	$k x i, x j = x i T x j d$	$d ≥ 1$ 为多项式次数
高斯核	$k x i, x j = e x p - x i - x j 2 2 δ 2$	$δ > 0$ 为高斯核的带宽
拉普拉斯核	$k x i, x j = e x p - x i - x j δ$	$δ > 0$
Sigmoid核	$k x i, x j = t a n h ? β x i T x j + θ$	$t a n h$ 为双曲正切函数， $β > 0, θ < 0$

表4 不同核函数类型的SVM模型表达式及其参数

Table 4 SVM model expressions and parameters of different kernel function types

名称	表达式	参数
线性核	$k x i, x j = x i T x j$
多项式核	$k x i, x j = x i T x j d$	$d ≥ 1$ 为多项式次数
高斯核	$k x i, x j = e x p - x i - x j 2 2 δ 2$	$δ > 0$ 为高斯核的带宽
拉普拉斯核	$k x i, x j = e x p - x i - x j δ$	$δ > 0$
Sigmoid核	$k x i, x j = t a n h ? β x i T x j + θ$	$t a n h$ 为双曲正切函数， $β > 0, θ < 0$

图4 基于PCA-SVM的制冷剂泄漏识别模型

Fig.4 Refrigerant leak identification model based on PCA-SVM

表5 二分类结果的混淆矩阵

Table 5 Confusion matrix of binary classification results

真实结果	识别结果
真实结果	泄漏	非泄漏
泄漏	TP	FN
非泄露	FP	TN

表6 泄漏识别模型评级评价指标及其定义

Table 6 Leak identification model rating evaluation index and its definition

评价指标		定义	计算公式
按类性能	命中率TPR	对于给定类，发生且正确预测的样本占总发生样本的比率	$T P R = T P T P + F N$
按类性能	虚警率FPR	对于给定类，没发生但被预测为发生的样本占没发生样本总数的比率	$F P R = F P F P + T N$
总体性能	准确率Acc	正确分类数占总样本数的比率	$A c c = T P + F N T P + F P + F N + T N$
总体性能	错误分类率Mcr	错误分类样本数占总样本数的比率	$M c r = 1 - A c c$

表6 泄漏识别模型评级评价指标及其定义

Table 6 Leak identification model rating evaluation index and its definition

评价指标		定义	计算公式
按类性能	命中率TPR	对于给定类，发生且正确预测的样本占总发生样本的比率	$T P R = T P T P + F N$
按类性能	虚警率FPR	对于给定类，没发生但被预测为发生的样本占没发生样本总数的比率	$F P R = F P F P + T N$
总体性能	准确率Acc	正确分类数占总样本数的比率	$A c c = T P + F N T P + F P + F N + T N$
总体性能	错误分类率Mcr	错误分类样本数占总样本数的比率	$M c r = 1 - A c c$

表7 泄漏特征的主成分分析结果

Table 7 Principal component analysis results of leakage characteristics

主元编号	特征值	主元方差贡献率/%	累计方差贡献率/%	Tci1		Tci3	Tci4	…	ΔPvel	ΔPeva	ΔHcon
1	15.80	38.55	38.55	0.052	0.220	0.246	-0.135	…	-0.289	0.249	0.112
2	9.64	23.51	62.06	0.048	0.213	0.253	-0.143	…	-0.000	0.000	-0.000
3	7.12	17.36	79.42	0.048	0.216	0.250	-0.142	…	-0.000	0.000	-0.000
4	3.12	7.61	87.03	0.045	0.213	0.254	-0.145	…	0.000	0.000	0.000
5	2.37	5.78	92.81	0.034	0.216	0.254	-0.148	…	-0.121	0.312	0.446
6	0.82	2.01	94.82	-0.173	0.214	-0.072	0.036	…	0.054	-0.140	-0.200
7	0.71	1.74	96.56	-0.208	0.157	-0.052	0.036	…	-0.000	-0.000	-0.000
…	…	…	…	…	…	…	…	…	…	…	…

表8 不同核函数类型的SVM模型信息

Table 8 SVM model information of different kernel function types

SVM模型编号	名称	意义
1	Linear SVM	线性核函数
2	Quadratic SVM	二次多项式核函数 d=2
3	Cubic SVM	三次多项式核函数 d=3
4	Fine Gaussian SVM	精细高斯核函数 $δ 2 ∝ 0$
5	Medium Gaussian SVM	中位高斯核函数 $0 < δ 2 < ∞$
6	Coarse Gaussisn SVM	粗糙高斯核函数 $δ 2 ∝ ∞$

表8 不同核函数类型的SVM模型信息

Table 8 SVM model information of different kernel function types

SVM模型编号	名称	意义
1	Linear SVM	线性核函数
2	Quadratic SVM	二次多项式核函数 d=2
3	Cubic SVM	三次多项式核函数 d=3
4	Fine Gaussian SVM	精细高斯核函数 $δ 2 ∝ 0$
5	Medium Gaussian SVM	中位高斯核函数 $0 < δ 2 < ∞$
6	Coarse Gaussisn SVM	粗糙高斯核函数 $δ 2 ∝ ∞$

图5 泄漏识别模型训练过程识别准确率变化

Fig.5 Change of recognition accuracy in the training process of leak recognition model

图6 泄漏识别模型训练过程识别命中率和虚警率变化

Fig.6 Changes in the TPR and FPR during the training process of the leak recognition model

表9 泄漏/非泄漏模式下PCA-SVM识别模型及性能

Table 9 PCA-SVM leak identification model and performance

CPVa	主元组合	SVM核函数	Acc/%	Mcr/%	TPR/%	FPR/%	测试集混淆矩阵
87.02%	[1,2,3,4]	Fine Gaussian SVM	100	0	99.5	0	$20510436$

表9 泄漏/非泄漏模式下PCA-SVM识别模型及性能

Table 9 PCA-SVM leak identification model and performance

CPVa	主元组合	SVM核函数	Acc/%	Mcr/%	TPR/%	FPR/%	测试集混淆矩阵
87.02%	[1,2,3,4]	Fine Gaussian SVM	100	0	99.5	0	$20510436$

图7 不同模型在各个故障的诊断识别准确率

Fig.7 Diagnosis and recognition accuracy of different models in each fault

表10 不同模型在各个故障的诊断识别的混淆矩阵

Table 10 Confusion matrix of different models in each fault diagnosis identification

工况	Model-o	Model-pca4
Refleak normal ReduCF ReduEF loosTV ClosTV IncrTW DecrTW	$258000000042250000004023000007302500001500076000810005200300000420300000054$	$25440000001228000000002600000060281000030088000510015400000000460000000057$
工况	Model-pca5	Model-pca6
Refleak normal ReduCF ReduEF loosTV ClosTV IncrTW DecrTW	$25710000003224020000002600000130281000110089000010015900000000460000000057$	$256200000042230200001223000004130171000510085000410005600110000440100000056$
工况	Model-pca7
Refleak normal ReduCF ReduEF loosTV ClosTV IncrTW DecrTW	$256200000010216030000412100000814013000014100760001300004800600000460200000055$

表10 不同模型在各个故障的诊断识别的混淆矩阵

Table 10 Confusion matrix of different models in each fault diagnosis identification

工况	Model-o	Model-pca4
Refleak normal ReduCF ReduEF loosTV ClosTV IncrTW DecrTW	$258000000042250000004023000007302500001500076000810005200300000420300000054$	$25440000001228000000002600000060281000030088000510015400000000460000000057$
工况	Model-pca5	Model-pca6
Refleak normal ReduCF ReduEF loosTV ClosTV IncrTW DecrTW	$25710000003224020000002600000130281000110089000010015900000000460000000057$	$256200000042230200001223000004130171000510085000410005600110000440100000056$
工况	Model-pca7
Refleak normal ReduCF ReduEF loosTV ClosTV IncrTW DecrTW	$256200000010216030000412100000814013000014100760001300004800600000460200000055$

图8 四种模型各泄漏故障的诊断识别准确率对比

Fig.8 Comparison of the diagnostic and identification accuracy of each leakage fault of the four models

图9 四种模型在相同数据集中的各泄漏诊断识别准确率对比

Fig.9 Comparison of leakage diagnosis and identification accuracy of four models in the same data set

表11 四种模型在相同数据集的各泄漏诊断识别结果混淆矩阵

Table 11 Confusion matrix of leakage diagnosis and identification results of four models in the same data set

Refleak_slow

Refleak_fast

normal

911402150304539

96902152100543

911225145501542

80121331391300543

表11 四种模型在相同数据集的各泄漏诊断识别结果混淆矩阵

Table 11 Confusion matrix of leakage diagnosis and identification results of four models in the same data set

工况

Model-pca4

Model-pca5

Model-pca6

Model-pca7

Refleak_slow

Refleak_fast

normal

911402150304539

96902152100543

911225145501542

80121331391300543

图10 RefliefF特征选择权重结果

Fig.10 RefliefF feature selection weight result

表12 RefliefF特征选择前后的PCA-SVM泄漏识别模型及性能结果对比

Table 12 Comparison of PCA-SVM leak identification model and performance results before and after RefliefF FS

方式	序号	主元组合	SVM核函数	Acc/%	Mcr/%	TPR/%	FPR/%	测试集混淆矩阵
PCA-SVM	1	[1,2,3,4]	Fine Gaussian SVM	100	0	99.5	0	$20510436$
	2	[12,3,4,5]		100	0	99.5	0	$20510436$
	3	[1,2,3,4,5,6]		99.1	0.9	97.6	0.2	$20151435$
RefliefF PCA-SVM	4	[1^r,2^r,3^r,4^r]	Fine Gaussian SVM	97.8	2.2	97.1	1.8	$20068428$
	5	[1^r,2^r,3^r,4^r,5^r]		97.4	2.6	95.6	1.8	$19798428$
	6	[1^r,2^r,3^r,4^r,5^r,6^r]		97.4	2.6	93.7	0.9	$193134432$

表12 RefliefF特征选择前后的PCA-SVM泄漏识别模型及性能结果对比

Table 12 Comparison of PCA-SVM leak identification model and performance results before and after RefliefF FS

方式	序号	主元组合	SVM核函数	Acc/%	Mcr/%	TPR/%	FPR/%	测试集混淆矩阵
PCA-SVM	1	[1,2,3,4]	Fine Gaussian SVM	100	0	99.5	0	$20510436$
	2	[12,3,4,5]		100	0	99.5	0	$20510436$
	3	[1,2,3,4,5,6]		99.1	0.9	97.6	0.2	$20151435$
RefliefF PCA-SVM	4	[1^r,2^r,3^r,4^r]	Fine Gaussian SVM	97.8	2.2	97.1	1.8	$20068428$
	5	[1^r,2^r,3^r,4^r,5^r]		97.4	2.6	95.6	1.8	$19798428$
	6	[1^r,2^r,3^r,4^r,5^r,6^r]		97.4	2.6	93.7	0.9	$193134432$

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