Fault diagnosis for cooling dehumidifier based on fuzzy classifier optimized by adaptive genetic algorithm

Abstract

The running of cooling dehumidifier is characterized by strong coupling, large delay and nonlinearity, so it is not easy to establish a precise quantitative model for fault diagnosis. Aiming at this problem, a fuzzy classifier optimized by adaptive genetic algorithm (AGA) is proposed for the dehumidifier fault diagnosis. Firstly, the data acquisition and experiment system is built and the dehumidifier work statuses are simulated. Secondly, the fuzzy classifier for fault diagnosis is built. The classifier fuzzy rules and membership functions are step-wisely optimized by AGA to improve the model output precision, and a novel nearby mutation operator is proposed in order to extract the rules more accurately. Finally, the fuzzy classifier is validated and also compared with the conventional fuzzy classifier. The results demonstrate that this proposed model optimized by AGA is not only effective for the dehumidifier fault diagnosis, but also has advantages over the conventional model.

Cooling dehumidifier; Fault diagnosis; Qualitative model; Fuzzy classifier; Adaptive genetic algorithm.

1. Introduction

The cooling dehumidifier is a kind of heating, ventilating, air conditioning and refrigeration (HVAC&R) equipment, which is widely used in many environments where the temperature and humidity need to be controlled. However, the equipment degradation and improper operation may cause some faults, which may lead to equipment performance degradation, energy consumption increase, complete failure and even harm the environment. These faults are generally classified into two types: one is the hard fault, and the other is the soft fault. The soft fault not only occurs frequently, but also is not easy to be found, it can lead to increased energy consumption of equipment running, so its harm is more serious than the hard fault.

Therefore, fault detection and diagnosis (FDD) for dehumidifier is significant. It can not only guarantee the equipment work in normal station, but also significantly reduce energy consumption and prolong the equipment work life (Lee and Yik, 2010). The related literature shows that the equipment operation can save 20–30% energy consumption if the FDD and optimal management technology are adopted (Bruton et al., 2014), so it can be seen FDD in HVAC&R field is of great significance for energy conservation, emission reduction and coping with energy crisis.

In the HVAC&R research field, many scholars have made contributions to FDD for different types of equipment. Among the related research literatures, Katipamula and Brambley (2005a, 2005b) classified the HVAC&R equipment FDD methods into two types: one is the model based, and the other is the process history dada based. The model based methods can be divided into quantitative model methods and qualitative model methods. The quantitative model methods have complex modeling, large amount of calculation and high accuracy requirements, and the interference and error will have a great impact on the output results, so the application of these method are limited to a certain extent. The qualitative model methods are generally easy to model, and some of them can also employ the equipment process history data, so they are widely used, but these methods have a certain dependence on expert knowledge. The methods based on process history data don’t need to build the accurate mathematical or physical model and depend on expert knowledge, they also can employ many available theories, but they have poor physical interpretability of fault. In general, the qualitative model is suitable for use on the nonlinear system such as HVAC&R system which is difficult for accurately modeling. The method based on rule belongs to qualitative model that doesn’t need to build accurate model for application, and it also can employ system or process causal knowledge for fault diagnosis. The rule based method still can reason even under uncertainty so that it is widely applied to HVAC&R system FDD, e.g. Schein and Bushby (2006) proposed a method based on the rule for HVAC&R system FDD; Bruton et al. (2015) developed a new rule-based expert system for air handling unit FDD.

Although the methods based on rule have played an important role in FDD, the conventional rule extraction depends on expert experience or prior knowledge, and thus the precision and perfection of rule are seriously affected by human subjectivity. With the complexity of system modeling increasing and system status changing, the rule extraction and maintenance are becoming more tedious which leads to inconvenience for application. The fault diagnosis can be attributed to the problem of classification, but the common classifier can’t preferably dispose the fuzzy and uncertain problems. Fuzzy theory can imitate human characteristic fuzzy logic thought, so it acts as a strong tool for describing and disposing fuzzy and uncertain problems, e.g. Huo et al. (2020) proposed a mechanical equipment fault detection model based on the fuzzy pattern recognition method; Wang and Zhang (2021) proposed a linear approximation boolean fuzzifier model for detecting faults in the cyber systems of supply chain management. Moreover, the fuzzy theory can fuse expert knowledge so that it is widely applied to classification problems, e.g. Wu et al. (2007) developed an expert system for fault diagnosis in scooter engine platform using fuzzy-logic inference; Sarikh et al. (2021) presented a fuzzy diagnostic algorithm relying on the electrical parameters classification.

Fuzzy classification is the binding product of fuzzy theory and classification, and it not only acts as common classifier for classifying but also can dispose fuzzy and uncertain problems of engineering application so that it is quite suitable for fault diagnosis. For fuzzy classification system, rule extraction and membership function design are two important works, because they seriously affect classifier output precision. Although fuzzy classification can imitate human fuzzy logic thought, the rule extraction and membership function design critically depends on human expertise or prior knowledge, which implies it lacks of self-learning ability. The way of rule extraction and membership function design is the anamnestic language description according to human specialty or the dialog between expertise and careful organization survey table. According to this way, the special rule prototype is generated, and the final rule and membership function are generated after repeated test and cutting. From this it can be seen the conventional way is cumbersome. If the knowledge is lacked or the system is complicated, the difficulty of rule extraction and membership function design would be increased. So how to automatically generate optimized rule and design membership function parameters is becoming an important research work, e.g. White and Lakany (2008) developed a fault detection and isolation system based on adaptive fuzzy rules optimized by an evolutionary algorithm for a fluid system. With the development of machine learning theory and methods, many optimization algorithms have emerged and been successfully applied (e.g. Singh et al., 2020, 2021; Mittal et al., 2021). Among these optimization algorithms, genetic algorithm (GA) is very suitable for solving nonlinear problems according to the characteristics of population searching strategy, information interchange and searching independent on gradient information, and it has been applied to many fields such as machine learning, function optimization, pattern recognition and so on (e.g. Balaga et al., 2015; Prasanna and Ezhilmaran, 2016). In view of the advantages of GA, it can be employed for fuzzy system aided design and optimization which will improve the fuzzy system practicality and output precision, e.g. Pawar and Ganguli (2003) proposed a fuzzy system optimized by GA for damage detection in beams and helicopter rotor blades; Jammu et al. (2016) employed GA for optimizing field programmable gate arrays implementation of rule for stand-alone tunable fuzzy logic controller.

Considering the advantages of fuzzy inference system for FDD and the strong learning ability of GA, this paper employs GA for fuzzy classification system aided design. After the rule and membership function are optimized by GA using the system input and output data, the fuzzy classification system is applied to the cooling dehumidifier fault diagnosis.

2. Data acquisition and experiment system

The modeling and application of fault diagnosis method need adequate equipment process history data. However, it is difficult to obtain all faults data samples of the equipment during its normal life, so it is necessary to build the data acquisition and experiment system for acquiring data samples of the dehumidifier in different working status. The data acquisition and experiment system consists of the cooling dehumidifier, sensors, data acquisition equipment and upper computer. The sensor types are selected according to the status parameters of the dehumidifier to be monitored, mainly including temperature, pressure, relative humidity (RH), wind speed, flow and power sensors. In addition to acquiring and monitoring data, another important function of the data acquisition and experiment system is to simulate the working statuses of the dehumidifier to obtain data samples of the normal and fault statuses. The fault simulation is realized by introducing artificial faults.

The simulation of dehumidifier working statuses mainly includes three steps: firstly, establish a controllable temperature and humidity environment; secondly, simulate the different working statuses of dehumidifier in the controllable environment; thirdly, acquire the steady working state data of the dehumidifier. Whether the dehumidifier is in steady state can be judged by analyzing the changes of the working parameters and the steady state detector (Lee et al., 2004).

The data acquisition and experiment system diagrammatic sketch of the cooling dehumidifier in the study is shown as Figure 1. The acquired data are displayed and stored in the upper computer after they are converted to decimal format. In order to improve the quality of data samples, the moving average and normalization are employed to process the acquired data before they are applied to model building and FDD.

Figure 1.

The cooling dehumidifier data acquisition and experiment system.

The calculation of moving average is shown as Eq. (1):

$$x_{\mathrm{a}}^i=\sum _{j=-k}^l{w}_j{x}_{i+j}$$ (1)

Where, $x_{i+j}$ is the original data, w_j is the weight coefficient, and $\sum _{j=-k}^l{w}_j=1$; $k$, $l$ and $M$ are the set integer parameters, N is the number of data, and $k+l+1=M$, $i=k+1,k+2,\cdots ,N-l$. Here, $k$ takes 10, $l$ takes 9, and $w_j$ takes 0.05.

The calculation of normalization is shown as Eq. (2):

$$x_{\mathrm{n}}^i=s_1-\frac{s_1-s_2}{\max x_i-\min x_i}\left(\max x_i-x_i\right)$$ (2)

Where $x_i$ is the input data, $\max x_i$ and $\min x_i$ are, respectively, the maximum and minimum value of $x_i$; $s_1$ and $s_2$ are, respectively, the maximum and minimum value of the normalization span, here $s_1$ takes 1, $s_2$ takes -1.

3. Adaptive genetic algorithm

GA is a global probability search algorithm that imitates the nature biological evolution mechanism (Palmes et al., 2005). It provides a general framework for solving the optimization problem of complex system. In general, a standard GA flow is shown as Figure 2, where p_c is cross probability and p_m is mutation probability.

Figure 2.

Flow of standard GA.

The operations of GA mainly include selection, cross, mutation and fitness evaluation. The genetic operation schemes need to be designed for solving different problems. Cross probability p_c and mutation probability p_m are two important parameters that affect the performance of GA. In standard GA, the selection of these two parameters is depended on the expert experience, which may lead to premature convergence or local optimization. In order to overcome this problem, many scholars have explored and researched the adaptive selection methods of these two parameters. The most representative scheme is the adaptive genetic algorithm (AGA) proposed by Srinivas and Patnaik (1994). The calculation of parameters p_c and p_m in AGA are shown as Eqs. (3) and (4):

$$p_{\mathrm{c}}=\{\begin{array}{cc}{p}_1-\frac{\left(p_1-p_2\right)\left(f_{\mathrm{c}}-f_{\mathrm{a}}\right)}{f_{\mathrm{m}}-f_{\mathrm{a}}},& f_{\mathrm{c}}\ge f_{\mathrm{a}}\\ p_1,& f_{\mathrm{c}}<f_{\mathrm{a}}\end{array}$$ (3)

$$p_{\mathrm{m}}=\{\begin{array}{cc}{p}_3-\frac{\left(p_3-p_4\right)\left(f_{\mathrm{m}}-f\right)}{f_{\mathrm{m}}-f_{\mathrm{a}}},& f\ge f_{\mathrm{a}}\\ p_3,& f<f_{\mathrm{a}}\end{array}$$ (4)

Where f_m is the maximum value of population fitness, f_a is the average value of individual fitness, f_c is the larger fitness value of cross individuals, and f is the fitness value of mutation individual. Here, p₁, p₂, p₃ and p₄ are, respectively, set to 0.75, 0.55, 0.15 and 0.005.

4. Fuzzy classifier optimization

4.1. Fuzzy classifier

Fuzzy system is a system based on fuzzy logic which not only acts as the base of representing different system knowledge but also construct system variable relationship. Fuzzy system consists of IF-THEN rules according to that the system output is determined by input language variable. The essence of fuzzy system theory is to induce input space that has similar output, and describes input space by fuzzy set, thus the complex or uncertain system can be simplified by describing several input spaces, i.e. the complex or uncertain system can be described by several fuzzy rules. The conventional fuzzy system is mainly constructed by expert experience and knowledge. With the development of data driven technology, the fuzzy modeling method based on process history data are drawn more and more attention by the researchers. The fuzzy system commonly used in engineering is the fuzzy system has fuzzifier and defuzzifier, which is mainly composed of fuzzifier, knowledge base, fuzzy inference machine and defuzzifier. The structure of this fuzzy system is shown as Figure 3.

Figure 3.

The fuzzy system with fuzzifier and defuzzifier.

The model based on IF-THEN rule belongs to a classification method. Generally, the important work for model construction is to find a set of suitable rules according to specific classification problem. In general, there are two ways for rule selection, one is directly generated by expert experience and knowledge, the other is acquired from the system process history data by machine learning. It’s not hard to see that the first way has obvious subjectivity and empiricism, so it is easily affected by human subjective factors. In recent years, the research about fuzzy classification rule is mostly based on automatic extraction method. Furthermore, how to select and optimize the suitable membership function is another research content which needs to consider for constructing fuzzy classification model.

In fact, fault diagnosis based on rule also can be seen a pattern recognition problem which applies fuzzy system for classification. Supposing the input variable set is $\mathit{X}=\left\{X_1,X_2,\cdots ,X_N\right\}$, the corresponding language variable set is $\mathit{L}\left(X_k\right)=\left\{L_1^k,L_2^k,\cdots L_S^k\right\}$, the fault set is $\mathit{F}=\left\{F_1,F_2,\cdots F_p\right\}$, the rule set is $\mathit{R}=\left\{r_1,r_2,\cdots r_M\right\}$, in that way, the i-th fuzzy rule can be represented as Eq. (5):

r_i: IF (X₁ is L¹_j) AND (X_k is L^k_j) AND…(X_N is L^N_j) THEN (fault is F_a) (5)

Where N is the number of input variables, S is the number of language variables, M is the number of rules, p is the type of fault; 1 ≤ k ≤ N,1 ≤ i ≤ M,1 ≤ j ≤ S,1≤a≤p. The statement behind IF is the rule antecedent, and the statement behind THEN is the rule consequent.

It can be seen that the fuzzy rule directly affect classification result. In general, rule extraction and maintenance are depended on artificial expert experience and knowledge, so the labor workload is big, and the rule set hasn’t been optimized. Aiming at this problem, applying GA to fuzzy classification system design for optimizing rule and membership function based on the system input and output data.

Considering the cooling dehumidifier work has obvious nonlinear characteristics and there are many parameter variables that affect the equipment performance, the stepwise optimization strategy is proposed for fuzzy classification system design in order to reduce the algorithm complexity, improve the search efficiency and get the best solution more easily. According to this strategy, the rule is extracted and optimized based on the given membership function at first; then the membership function is optimized based on the extracted and optimized rules in order to improve the system output precision.

4.2. Fuzzy rules extraction and optimization

Based on the system input and output data, the fuzzy system rule can be extracted and optimized by GA. In general, the steps of GA application are as follows:

• (1)Defining the solution space of problem;
• (2)Building optimization model, defining fitness evaluation function and object function;
• (3)Defining encoding and decoding method for solution represented by chromosome;
• (4)Selecting selection, cross and mutation operator;
• (5)Selecting GA parameters such as population scale, cross probability, mutation probability and so on.

4.2.1. Rule table encoding

Supposing a fuzzy system has two inputs and one output, each input has three language variables, which are, respectively, represented as NB (Negative big), ZE (Zero) and PB (Positive big); the output has four language variables, which are, respectively, represented as 1, 2, 3 and 4. In that way the fuzzy rule can be encoded according to the mode shown as Figure 4.

Figure 4.

Schematic plan of rule encoding for two input and single output fuzzy system.

The chromosome encoding length is related to the number of language variables. If the number of input variables is n, the number of language variables is m, then the chromosome length will be mⁿ corresponding to complete rule space. From here it can see that too many inputs and language variables will sharply increase the chromosome encoding length, which will lead to the algorithm search space and difficulty increasing. Aiming at this problem, seven typical input variables are employed here, which are dehumidifier air intake temperature (T1), air intake RH (H1), compressor discharge temperature (T14), suction temperature (T13), power (P_w), discharge pressure (P2) and suction pressure (P1); the number of corresponding language variables is three, which are, respectively, NB, ZE and PB; the output variable is single, which are, respectively, fault type 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. In order to reduce the chromosome encoding length, the integer real encoding for rule table is employed here, so the chromosome encoding length is 3⁷ (i.e. 2187), and each chromosome gene spans [1, 10].

4.2.2. Fitness evaluation

The fitness evaluation function is designed as Eq. (6):

$$fi{t}_r=\frac{1}{{\omega }_1\sum _{i=1}^N{\left(d_i-f_i\right)}^2+{\omega }_2{N}_r+1}$$ (6)

Where d_i is the expected output of the fuzzy classification system, f_i is the real output, N is the number of learning samples, N_r is the number of rules for misclassification, ω₁ and ω₂ are weighted factor, ω₁ = 1/N, ω₂ = 1-1/N. f_i can be calculated by the centroid defuzzifier, which is calculated as Eq. (7):

$$f_i=\frac{\sum _{j=1}^k{F}_j\times {\mu }_j}{\sum _{j=1}^k{\mu }_j}$$ (7)

Where F_j is the j-th output language variable, i.e. the j-th fault type, which are defined as Table 1.

Table 1.

Definition of fault type.

Equipment work status	Fault type
Normal work	1
Water intake volume overfull	2
Air intake filter fouled	3
Evaporator fouled	4
Air cooling condenser fouled	5
Air intake volume decrease	6
Air intake temperature lower	7
Expansion valve open oversize	8
Expansion valve open undersize	9
Refrigerant insufficient	10

In order to improve the fuzzy classification robustness, the input data samples is smoothed and normalized to the span [−1, 1]. The output variable is represented to the span [1, 10]. Both the input and the output membership functions employ triangle function, each top vertex horizontal ordinate of triangle takes integer corresponding to the variable scope, which coincides with the adjacent triangle lower corner vertex horizontal ordinate. The input and output fuzzy membership functions are, respectively, represented as Figure 5(a-h).

Figure 5.

The input and output membership functions.

4.2.3. Genetic operation and enactment

The selection operation employs roulette operator and the best preserving strategy. The cross operation employs arithmetic cross operator.

The roulette operator is calculated as Eq. (8):

$$P_i=\frac{f_i}{\sum _{i=1}^M{f}_i}$$ (8)

Where P_i is the i-th individual selection probability, f_i is i-th individual fitness, and M is the number of individuals.

The arithmetic cross operator is calculated as Eq. (9):

$$\begin{array}{c}{X}_1^{\prime }=r{X}_1+\left(1-r\right)X_2\\ X_2^{\prime }=r{X}_2+\left(1-r\right)X_1\end{array}$$ (9)

Where $X_1^{\prime }$ and $X_2^{\prime }$ are the new individuals after the cross operation, X₁ and X₂ are the selected individuals for cross operation, and r is a random number spanned [0, 1].

In order to improve the algorithm search efficiency, here, a nearby mutation operator (i.e. an improved boundary mutation operator) is proposed, which is defined as follows:

Supposing X΄ is the mutation gene of X, it can be calculated as Eq. (10):

$$X^{\prime }=\{\begin{array}{c}X+1,round\left(\alpha \right)=1,X<10\\ X-1,round\left(\alpha \right)=0,X>1\end{array}$$ (10)

Where α is a random number spanned [0, 1], round(·) represents rounding function, and 1 ≤ X΄≤10. This proposed operator can urge the gene to mutate towards neighbor in order to reduce mutation blindness and search the optimal value fast. This is consistent with the reality, because the system commonly needs to trim in order to achieve the ideal output precision. Compared with other methods, this nearby mutation operator can make the algorithm converging fast and restrain the algorithm premature convergence that has been proved by experiment.

In the cross and mutation operation, the cross probability p_c and mutation probability p_m are adaptively calculated according to Eqs. (3) and (4).

The initial population generated at random, and the size is 60; the algorithm is terminated until the generations achieve 1000.

4.2.4. Rules optimization and compaction

For this designed fuzzy system, the rule set will contains 2187 rules in theory. But it’s not that the rules are more the effect is better, by contrary, too many rules will lead to mutual conflict and produce inconsistency, which will reduce the fuzzy classification system explanation. So the extracted rules need to be optimized and compacted. Here, the rule compaction employs setting threshold method according to effective and useful enough principle. If a rule activation degree H_i is higher than the threshold β, then this rule is preserved; if H_i is lower than the threshold β, then this rule is cut. Here, the threshold β is set to 0.45.

In the fuzzy rule set, the i-th rule activation degree can be represented as Eq. (11):

$$H_i=\stackrel{m}{\underset{j=1}{\cap }}{\mu }_{A_j^i}\left(x_j\right)$$ (11)

Where m is the number of fuzzy variables, ${\mu }_{A_j^i}\left(x_j\right)$ is the membership of the j-th fuzzy input variable x_j in the i-th rule. Here, the fuzzy set conjunction method is defined as Eq. (12):

$$H_i=\min \left[{\mu }_{A_1^i}\left(x_1\right),{\mu }_{A_2^i}\left(x_2\right),\cdots ,{\mu }_{A_m^i}\left(x_m\right)\right]$$ (12)

In fact, compared with the rule with high activation degree, the possibility of result reasoning from the rule with low activation degree is very low, which can be ignored. In that way, not only the rules can be optimized and compacted but also the algorithm complexity is reduced and computation speed is improved.

4.3. Membership functions optimization

In order to improve the fuzzy system output precision, both the input and output membership function parameters are optimized by AGA based on the rules extracted and optimized in subsection 4.2. Here, the membership function center (i.e. top vertex horizontal ordinate) doesn’t change, only the left and right triangle lower corner horizontal ordinate are trimmed by AGA.

The membership function optimization for triangle lower corner horizontal ordinate employs indirect mode. Supposing c_j is the j-th chromosome gene, and then the calculation method of triangle lower corner horizontal ordinate is defined as follows:

(1) For each input membership function:

(a) Triangle left lower corner horizontal ordinate is represented as Eq. (13):

$$t{l}_i^{in}=m_i-\delta c_j-\Delta ,i=\mathrm{2,3}$$ (13)

(b) Triangle right lower corner horizontal ordinate is represented as Eq. (14):

$$t{r}_i^{in}=m_i+\delta c_j+\Delta ,i=\mathrm{1,2}$$ (14)

(2) For each output membership function:

(a) Triangle left lower corner horizontal ordinate is represented as Eq. (15):

$$t{l}_i^{out}=m_i-\delta c_j-\Delta ,i=\mathrm{2,3},\cdots 10$$ (15)

(b) Triangle right lower corner horizontal ordinate is represented as Eq. (16):

$$t{r}_i^{out}=m_i+\delta c_j+\Delta ,i=\mathrm{1,2},\cdots 9$$ (16)

In Eqs. (13), (14), (15), and (16), m_i is the top vertex horizontal ordinate of the membership function, δ = 0.25, Δ is trimming variable, which is assigned according to Eq. (17):

$$\Delta =\{\begin{array}{cc}0.05,& round\left(c_j/6\right)=0\\ -0.05,& round\left(c_j/6\right)=1\end{array}$$ (17)

Where round(·) represents rounding function.

In order to improve the calculation precision, the real coding mode is employed. According to the triangle membership function defined method, the chromosome encoding length is 46, the gene spans [0, 6].

The fitness evaluation function is designed as Eq. (18):

$$fi{t}_{\mu }=\frac{1}{\frac{1}{N}\sum _{i=1}^N{\left(d_i-f_i\right)}^2+1}$$ (18)

Where d_i is the fuzzy system expected output, f_i is the real output, N is the number of training samples.

Here, the mutation operation employs non-uniform mutation operator, and other genetic operating and enactment are as same as subsection 4.2.3.

The non-uniform mutation operator is calculated as Eq. (19):

$$x_k^{\prime }=\{\begin{array}{cc}{x}_k+\Delta \left(t,U_{k,\max }-x_k\right)& round\left(\alpha \right)=0\\ x_k-\Delta \left(t,x_k-U_{k,\min }\right)& round\left(\alpha \right)=1\end{array}$$ (19)

Where $x_k^{\prime }$ is new the individual after mutation operating, α is a random number spanned [0, 1], round(·) represents rounding function, Δ(t,y) represents a random number spanned [0, y] which conforms to non-uniform distribution, and it will gradually increase in the degree of approaching to probability 0 with the evolutional generation t increasing, y represents U_k,max-x_k or x_k-U_k,min. Δ(t,y) is calculated as Eq. (20):

$$\Delta \left(t,y\right)=y·{\left(r·\left(1-\frac{t}{T}\right)\right)}^b$$ (20)

Where r is a random number spanned [0,1], T is the maximum number of generations, and b is the determined non-uniform parameter, which is set to 3.

5. Fault diagnosis application

Firstly, the dehumidifier work statuses are simulated by the data acquisition and experiment system and the data samples corresponding to the work statuses are acquired. Secondly, the fuzzy classification system is designed with the fuzzy rules and membership functions being optimized by AGA based on the system input and output data. Thirdly, the fuzzy model is validated, if the model satisfies the application demand, then it is applied to the dehumidifier fault diagnosis by the real time measurement data. The flow of the whole method for application is shown as Figure 6.

Figure 6.

Flow of the method for application.

The 100 groups of standard data samples are trained for rule extracting and optimizing by AGA according to subsection 4.2, each 10 groups of samples are corresponding to different dehumidifier work statuses defined in Table 1. The fitness evaluation function value change process of rules being extracted and optimized by AGA is shown as Figure 7. The solution result (i.e. fuzzy rules) is shown as Table 2. From Figure 7, it can be seen that the fitness value increases gradually before the 439 generation; the maximum fitness value reaches to the maximum value 0.6162 at the 440 generation; the maximum fitness value doesn’t change and near which the average fitness fluctuates after the 440 generation. This shows that the AGA has converged within the enactment generation, i.e. the optimal solution is found.

Figure 7.

Process of fitness value change for optimizing fuzzy rules.

Table 2.

The optimized fuzzy rules.

Rule antecedent							Rule consequent
2	2	2	2	2	2	2	1
2	1	1	2	2	1	2	2
3	3	2	3	3	3	2	3
2	2	2	1	2	2	2	4
3	1	3	3	2	3	2	5
2	3	2	1	3	3	2	6
1	2	1	2	2	1	2	7
2	2	1	2	2	2	2	8
3	1	2	2	3	2	3	9
3	1	2	2	3	3	3	9
2	2	3	3	1	1	1	10
3	2	3	3	1	1	1	10

The fitness evaluation function value change process of optimizing membership functions by AGA is shown as Figure 8. The optimized membership functions are, respectively, shown as Figure 9(a-h). From Figure 8, it can be seen that the fitness value increases significantly before the 378 generation and increases slowly from the generation 379 to 729; the maximum fitness value reaches to the maximum value 0.9896 at the 730 generation; the maximum fitness value doesn’t change after the generation 730, and it equals to the average fitness after the 767 generation. This shows that the AGA has converged within the enactment generation, i.e. the optimal solution is found. From Figure 9, it can be seen that the shape of membership functions optimized by AGA has changed compared with the original shape of membership functions shown in Figure 5. The main reason is that the parameters of membership function have been trimmed according to the fuzzy system input and output data, therefore, the membership function enactment are more in line with the system actual situation and not just depends on the expertise. It can be said that the method of membership function enactment depended on both the system process history data and expertise is more objective.

Figure 8.

Process of fitness value change for optimizing membership functions.

Figure 9.

The optimized input and output membership functions.

In order to test this fuzzy classifier application effect for fault diagnosis, 100 groups of new measured data samples in total corresponding to 10 groups of each work status are selected for inputting the fuzzy classifier to calculate, the output result for fault recognition according to maximum membership principle. Here, it is given randomly 1 group data samples recognition result shown in Table 3 corresponding to different work status in order to save space. From Table 3, it can be seen that the fuzzy classifier output result is consistent with the reality.

Table 3.

Result of dehumidifier fault diagnosis.

Sample No.	Input (fuzzy disposed)	Output	Diagnosis result
1	-0.0138,0.0138,-0.0046,0.0000,-0.0191,0.0013, 0.0278	1.0829	1
2	-0.1475,-0.9136,-0.7231,-0.2036,-0.3376,-0.6727,-0.0550	1.9661	2
3	0.9384,0.8173,0.4429,0.5725,1.0000,0.9037,-0.0053	3.0700	3
4	-0.1521,0.2272,0.0601,-0.9961,-0.2866,-0.0971,-0.2744	4.0075	4
5	0.9923, -0.9824,0.7505,1.0000,0.4247,0.5890,-0.2978	5.0071	5
6	0.0680, 1.0000,0.2751,-0.9974,0.7169,0.7495,-0.1691	6.0051	6
7	-1.0000, 0.0422,-0.9967,-0.3398,-0.4140,-0.8984,-0.0901	7.0059	7
8	0.2054, -0.3639,-0.6605,-0.1933,0.0959,0.1329,0.3519	8.0047	8
9	0.7664, -0.6631,0.1093,0.2649,0.5434,0.4894,1.0000	9.0273	9
10	0.4531, -0.2031,0.9498,0.8851,-0.9745,-0.6501,-0.9824	9.8715	10

In order to further demonstrate that the advantages of this proposed method, it is compared with the conventional method of designing fuzzy rules and membership functions based on artificial expertise. The 10 groups of data samples selected from the validation samples corresponding to each work status are, respectively, inputted to the fuzzy classifier optimized by AGA and the conventional fuzzy classifier for calculating. The classifier output errors are, respectively, shown as Figure 10(a, b), and the fault recognition results are, respectively, shown as Figure 11(a, b). Corresponding to the optimized fuzzy classifier, the mean absolute error (MAE) is 0.0251; the mean squared error (MSE) is 0.0027; the fault correct recognition rate is 100%. Corresponding to the conventional fuzzy classifier, the MAE is 0.4884; the MSE is 0.6229; the fault correct recognition rate is 69%.

Figure 10.

The output errors of two kinds of fuzzy classifiers.

Figure 11.

The fault recognition results of the two kinds of fuzzy classifiers.

The MAE is calculated as Eq. (21):

$$MAE=\frac{1}{n}\sum _{i=1}^n\left|y_i-{\hat{y}}_i\right|$$ (21)

The MSE is calculated as Eq. (22):

$$MSE=\frac{1}{n}\sum _{i=1}^n{\left(y_i-{\hat{y}}_i\right)}^2$$ (22)

In Eqs. (21) and (22), $y_i$ is the expected output, ${\hat{y}}_i$ is the classifier output, and n is the number of samples.

From the comparative analysis, it can be seen that this proposed fuzzy classifier optimized by AGA not only can be effectively applied to the cooling dehumidifier fault diagnosis, but also the model output precision and fault diagnosis accuracy are improved compared with the conventional fuzzy classifier.

Compared with the nonlinear ARX method proposed in the literature (Gao et al., 2016), which employed the system model for fault detection and local model for fault location, and further needed the help of inference for more complex fault diagnosis, this proposed method does not need to establish more complex system and local models, it automatically extract rules from the system process history data and has less dependence on expertise, the modeling is simple and the fault diagnosis is direct, both the interpretability of fault causes and fault diagnosis function are stronger. In order to further test this method reliability, 100 groups of real measured equipment samples in total corresponding to each work status besides the modeling and validation are selected for inputting the fuzzy classifier. The fault diagnosis accuracy rate is 97% and the fault false alarm rate is only 3%, which shows that the method has high robustness. By analysis, the main reason for the false alarm is that the measured data sample status has changed compared with the modeling sample database state. This problem can be solved by updating the dehumidifier work status sample database and remodeling.

6. Conclusions

The equipment fault diagnosis can be attributed to the problem of classification. Due to the fuzzy classifier has the ability to simulate human logical thinking, it is widely applied to fault diagnosis. But the conventional fuzzy classifier construction depends on expertise, which implies that it lacks of self-learning ability and limits it being applied to engineering. Aiming at this problem, a fuzzy classification system based on AGA aided design and optimization is proposed, and it is well applied to the dehumidifier fault diagnosis. Firstly, the cooling dehumidifier work statuses are simulated by artificial enactment. Secondly, AGA is aided to design the fuzzy classifier by the equipment steady work data samples, the fuzzy rules and membership functions are step-wisely extracted and optimized by AGA. Lastly, the optimized fuzzy classifier is applied to dehumidifier fault diagnosis, i.e. the dehumidifier real measurement data are inputted to the fuzzy classifier for calculating the output result which is employed for diagnosing the equipment fault corresponding to the input data.

The method combined fuzzy classifier and AGA not only depresses the degree of dependence on expertise for fuzzy classifier modeling but also improves the classifier output precision. The proposed method extends qualitative model method to data driven method, due to fusing the advantages of this two methods, it can not only make the physical explanation for fault diagnosis but also take full advantages of the equipment process history data, so the applicability and effect of model based method for fault diagnosis is strengthened. Take the 4-th rule in Table 2 for instance, it represents that if the air intake temperature doesn’t change (ZE), the air intake RH doesn’t change (ZE), the compressor discharge temperature doesn’t change (ZE), the compressor suction temperature descends (NB), the power doesn’t change (ZE), the discharge pressure doesn’t change (ZE), and the suction pressure doesn’t change (ZE), then the work status is fault type 4, i.e. the evaporator fouled. From this, it can be seen that the fault physical reason can be properly explained according to the rules of fuzzy classifier.

7. Discussions

This paper employs fuzzy classifier optimized by AGA for cooling dehumidifier fault diagnosis, and the experiment result proves the proposed method is effective. In order to guarantee the reliability of the model fault diagnosis, the fault samples selected for modeling cover the data of equipment different work statuses, and the modeling data is disposed by the moving average method. The fuzzy rules and membership functions are optimized by AGA, which further improves the model output precision.

From the point of view of the method, considering the calculation complexity, this proposed method selects seven typical input variables closely related the dehumidifier performance, but how many variables are the optical variables for the system input need to research furthermore. From the point of view of the fault, subjecting to the experimental condition, the faults simulated are all based on steady state, the fault occurs in transient state need to research furthermore. Although the cooling dehumidifier has the same commonalities as the other HVAC&R equipments, the cooling dehumidifier work has its own characteristics, e.g. compared with the air conditioning, firstly there are differences in the work status, the cooling dehumidifier only has cooling mode, the air conditioning has both cooling and heating mode, and the cooling mode can be divided into multiple modes, the evaporator and condenser can be interchangeable according to the cooling or heating mode; secondly there are differences in heat exchange mode, the cooling dehumidifier has both water cooling and air cooling modes and even has a requirement for cooling water intake temperature, the air conditioning only has air cooling mode; thirdly there are differences in air exhaust temperature control mode, the cooling dehumidifier control the air exhaust temperature by condenser, the air conditioning control the air exhaust temperature by evaporator in cooling mode; and so on. These differences bring some slight varieties for the cooling dehumidifier fault diagnosis in contrast to other HVAC&R equipments. In the follow-up work, the peculiar fault symptoms, fault types and fault magnitude of the cooling dehumidifier need to be further studied.

Declarations

Author contribution statement

Yunguang Gao: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Method design and validation; Wrote the paper.

Changlin Ma: Conceived and designed the experiments.

Tao Wang: Contributed materials, analysis tools or data.

Funding statement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability statement

The authors do not have permission to share data.

Declaration of interest’s statement

The authors declare no conflict of interest.

Additional information

No additional information is available for this paper.