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Simplified Soft Sensing Model Applied in the Centralized Regenerator of a Distributed Operating Liquid Desiccant Dehumidification System Qiong Wu,†,‡ WenJian Cai,*,§ Xinli Wang,§ and Suping Shen§ †

Interdisciplinary Graduate School and §EXQUISITUS, Centre for E-City, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore ‡ Energy Research Institute at Nanyang Technological University, Singapore 639798, Singapore S Supporting Information *

ABSTRACT: A distributed operating Liquid Desiccant Dehumidification System (LDDS) designed for commercial building applications allows one regenerator to handle multiple dehumidifier units, which provides the potential to apply low-grade energy in a centralized form for desiccant solution regeneration. An online soft sensing model with the Adaptive Network-based Fuzzy Inference Systems (ANFIS) structure is developed to satisfy the operating scheme. The number of input variables is reduced by the regeneration mass transfer model, and the fuzzy interference is optimized by Genetic Algorithm (GA) with a constrained objective function. The accuracy of the soft sensing models with different simplicity levels are validated and compared in case studies. Results show that the proposed soft sensing model is accurate, and the simplification approaches can reduce the size of the model significantly without affecting the predictive accuracy.

temperature is employed to overcome this resistance,19 but this high regeneration temperature requires high-grade energy which may reduce the efficiency of heat generation equipment. In a distributed LDDS, multiple dehumidifiers are usually located on different floors with different concentration requirements, while the centralized regenerator is installed either with chiller plants in the plant room or solar energy apparatuses on the rooftop. To facilitate this distributed operation, each dehumidifier is integrated with a strong solution buffer and a regulating valve. The strong solution in the strong solution buffer is continuously charged into the working solution tank to maintain the working solution concentration in the dehumidifier. The regenerator regenerates the strong solution with a significantly higher concentration than that of working solution. Since the span between working and strong solution concentration is large, the online monitoring of concentration is necessary not only in determining regenerator stopping point but also in optimizing regeneration temperature at different concentration levels to reduce the energy consumption of this large centralized

1. INTRODUCTION A liquid desiccant dehumidification system (LDDS) is an energy effective alternative to a traditional cooling-based dehumidification system to handle the latent load due to certain advantages, such as utilizing the low-grade heat and renewable energy, dry operation to avoid water condensation in the duct and terminal units, and independent control of the air temperature and humidity ratio, which makes it more attractive in building applications. Extensive research has been conducted on topics related to the LDDS, including the system structure improvements,1−4 energy conservation,5,6 heat and mass transfer modeling,7−10 physical properties of conventional and new desiccant chemicals,11−13 performance analysis with respect to desiccant type14,15 and desiccant concentrations,16,17 etc. In the LDDS, the regenerator consumes a majority of the energy to regenerate the concentration of desiccant solution.18 Intensive studies have been conducted to investigate the energy consumption of regenerators in terms of thermal efficiency analysis19,20 and low-grade heat applications.21,22 One of the crucial parameters in evaluating the regeneration process is desiccant concentration. A high desiccant concentration reduces the surface water vapor pressure of liquid desiccant solution and increases the difficulty of the moisture migrating from solution to regenerator air.4 Mostly, a higher regeneration © 2016 American Chemical Society

Received: Revised: Accepted: Published: 9256

May 23, 2016 August 5, 2016 August 6, 2016 August 6, 2016 DOI: 10.1021/acs.iecr.6b01988 Ind. Eng. Chem. Res. 2016, 55, 9256−9266

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Industrial & Engineering Chemistry Research

Figure 1. Diagram of the LDDS in a distributed operating scheme.

approaches.35 As a method mimics the process of natural selection, GA is extensively applied in global optimization.36 Among several applications, Dahal et al.35 presented a learning approach based on GA for ANFIS structure improvement, and Tahmasebi et al.37 derived the most appropriate parameters for ANFIS with the assistance of GA. This current research suggests that GA optimized ANFIS is an appropriated choice for the development of soft sensing models. This study proposes a soft sensing technique to measure the concentration of liquid desiccant solution in a centralized regenerator of the distributed operating LDDS. A model with ANFIS framework is developed, and the number of input variables is reduced by utilizing the physical relationships from a regeneration mass transfer model. The fuzzy inference structure is further optimized by GA with a constrained objective function. To show the effectiveness of this proposed soft sensing model and the simplification methods, the performances of original data driven ANFIS, model-based ANFIS, and model-based ANFIS with a GA optimized structure have been compared experimentally. The results show that the model-based ANFIS with a GA optimized structure, with the advantage of simplicity and satisfied accuracy, is suitable for monitoring the real time solution concentration in the regenerator.

regeneration plant. Thus, the online solution concentration information is indispensable. Generally, there are two potential choices to monitor the solution concentration in real-time, i.e., installing an online concentration sensor or developing a soft sensing model. However, the corrosiveness of the desiccant solution reduces the long-term reliability of online sensors and requires frequent calibration and maintenance. The high cost also decreases the practicability of applying an online concentration sensor for monitoring, which is a driving force of some concentration soft sensor developments.23,24 On the other hand, the properties of liquid desiccant solution used in the LDDS have complicated mathematical expressions, which increase the difficulty in deriving a solution from physical relations.25 Therefore, a more intelligent method is needed to solve this problem. Various approaches have been discussed to build up soft sensing models such as principal component analysis,26 partial least-squares methods,27 multimodel prediction,28 fuzzy model,29 and ANFIS.30,31 As one of these approaches, ANFIS has been widely studied for soft measurements of concentration in various applications. This hybrid structure generates the mapping relationships between input−output pairs and also combines the advantage of learning mechanism in artificial neural networks and fuzzy decision making.32 Ghiasi et al.33 used ANFIS soft computing to detect the CO2 concentration in a CO2 capture process. Chong et al.34 developed a ANFIS framework model to predict the dye concentration. Compared with the predicted results of other models, ANFIS exhibited higher prediction accuracy in their research work. The fuzzy rule identification is an important topic in ANFIS development.35,36 The usage of genetic algorithm (GA) in fuzzy system development attracts greater research effort than other

2. WORKING PRINCIPLES OF A DISTRIBUTED LDDS The distributed LDDS under study is described in Figure 1, including the air treatment, regeneration, and solution storage sections. The air treatment section consists of several dehumidifiers located in different areas to provide the required treated air to the corresponding supply rooms. The centralized regenerator concentrates the diluted solution from the weak 9257

DOI: 10.1021/acs.iecr.6b01988 Ind. Eng. Chem. Res. 2016, 55, 9256−9266

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Figure 2. Schematic diagrams of two main components in a distributed LDDS.

2. The weak desiccant solution preheated by the heat exchanger is sprayed from the top of the regenerator tower by the distributor; 3. Inside the regenerator, the descending liquid desiccant contact with the process air, the heat, and mass transfer occurs due to the temperature and water vapor differences between these two working fluids; 4. The ascending air passes through the evaporator section of the heat pipe heat exchangers and transfers its heat to the condenser section to recover the waste energy to improve the regeneration rate; 5. The temperature of the inlet solution is manipulated according to the desiccant concentration inside the regeneration tank for a most energy efficiency working point; 6. The regeneration process stops when the preset concentration is reached, and the strong solution will be evacuated to the strong solution storage tank and then distributed to the strong solution buffer of each dehumidifier with respect to the dehumidification requirements. In the distributed operation scheme, the regenerator provides the strong solution at the preset concentration to ensure the controllability of the mixing process inside the dehumidifier. Moreover, to utilize the heating source wisely, the desiccant concentration in the regeneration tanks needs continuous monitoring to keep the regenerator works at an appropriated temperature with high energy efficiency. The development process of this soft sensing model is explicated in the following sections, which includes a mass transfer model for input variable simplification, a data-driven ANFIS model, and a GA optimization strategy for fuzzy rules.

solution tank to a higher concentration than that of the highest requirement among all the dehumidifiers. The solution storage section contains a strong solution tank and a weak solution tank arranged at different locations, to buffer the strong and weak solutions among different working components. The distributed LDDS is operated as follows: 1. The dehumidifiers working at different locations provide the cool and dry air to different air-conditioned spaces. In the dehumidifier, the moisture transfers from the air to the low temperature desiccant solution, and the solution becomes diluted; 2. Both the solution concentration and liquid volume in the dehumidifier are monitored during the whole operating process. The diluted solution will be discharged into the weak solution tank when the concentration or solution amount is outside the proper range; 3. The regenerator receives the weak solution from the weak solution tank and concentrates the desiccant solution to the required concentration value; 4. The strong solution in the regenerator will be transferred to the strong solution storage tank when the concentration reaches the standard and waits to be distributed to the dehumidifiers. In the distributed LDDS, each dehumidifier is integrated with a strong solution buffer as illustrated in Figure 2 (a). A regulating valve has been installed between the strong solution buffer and the working solution tank to regulate the mixing process between the strong and weak solution. The centralized regenerator, as described in Figure 2 (b), is equipped with the heat pipe heat exchangers to recover the wasted energy in the exhausted regenerating air38,39 to preheat the incoming ambient air, increase absorptive capability of desiccant solution, and ultimately increase the mass transfer efficiency in the regenerator. This centralized regeneration system is operated as follows: 1. The ambient air is drawn by a fan and flows through the condenser section of the heat pipe heat exchanger, where it is preheated by the heat pipes, and this preheated regenerating air enters the regenerator column from the bottom;

3. MODEL OF REGENERATION PROCESS The regeneration process removes the moisture absorbed in the dehumidification process, and the diluted desiccant solution becomes concentrated. The mass transfer rate from the desiccant solution to the regeneration air can be evaluated by a mass transfer model as40 ṁ re = KG(ps*, in − pa , in ) 9258

(1) DOI: 10.1021/acs.iecr.6b01988 Ind. Eng. Chem. Res. 2016, 55, 9256−9266

Article

Industrial & Engineering Chemistry Research of which ṁ re, KG, p*s,in, and pa,in are the mass transfer rate from solution to the regeneration air, the mass transfer coefficient, the equilibrium surface water vapor pressure of desiccant solution, and the water vapor pressure of inlet air, respectively. The mass transfer coefficient can be expressed as40 KG =

c1(ṁ s)c3 1 + c 2Ta , in(ṁ s)c3 (mȧ )c4

4. MODEL BASED INPUT DIMENSION REDUCTION Excessive input variables result in heavier computational loads in data clustering, parameter training, and more calculations during applications, and the mass transfer model developed in Section 3 can be used to reduce the input variables. Combining the two methods of calculating the mass transfer rate, by substituting eq 2 and eq 5 into eq 1, we have

(2)

ps*, in (conre , Ts , in) = pa , in −

where ṁ s, ṁ a, and Ta,in signify the mass flow rate of the solution, mass flow rate of regeneration inlet air, and temperature of the inlet air, respectively. The Levenberg−Marquardt method41 is utilized to identify the parameters c1−c4 in eq 2 using experimental data. The water vapor pressure of inlet air pa,in can be calculated from the definition of relative humidity as

pa , in = φa , inpsat , in

+

a

HRa , out(Ta , out ·φa , out )mȧ c (ṁ )c3

2 a , in

s

(6)

a

where p*s,in (conre, Ts,in) is defined in eq 4, and the values of pa,in, HRa, in, and HRa,out can be calculated from eq 3 and eq 5. Define the second and third terms on the right-hand side of eq 7 as G1 = −

(3b)

where φa,in and psat are the relative humidity and the saturated water vapor pressure of the inlet air, and a0−a2 are the fitting parameters, respectively. The surface water vapor pressure of the desiccant solution ps,in * , which is a function of regeneration solution concentration and solution inlet temperature, is given as25 2

s

V · 1 + c T 1 (ms ̇ )c3(ṁ )c4

with

ps*, in (conre , Ts , in) = pH O (Ts , in)f (conre , Ts , in)

c (ṁ )c3

V · 1 + c T 1 (ms ̇ )c3(ṁ )c4 2 a , in

(3a)

psat , in = a0Ta2, in + a1Ta , in + a 2

HRa , in(Ta , in·φa , in)mȧ

mȧ HRa , in(1 + c 2Ta , in(ṁ s)c3 (mȧ )c4 ) V ·c1(ṁ s)c3

(7a) c3

G2 =

c4

mȧ HRa , out(1 + c 2Ta , in(ṁ s) (mȧ ) ) V ·c1(ṁ s)c3

(7b)

The inlet and outlet air temperatures and relative humidity values, mass flow rates of air and desiccant solution, and solution inlet and outlet temperature can be measured by the sensors installed in the system. As illustrated in Figure 3, pa,in,

(4)

where conre and Ts,in are the desiccant concentration and the inlet solution temperature of the regenerator. The two functions pH2O(Ts,in) and f(conre, Ts,in) are the water vapor pressure and corresponding correction function derived from the properties of desiccant solution, as explained in eqs S1 and S2, respectively. The mass transfer rate in the regenerator can also be calculated with eq 5, based on the principle of mass conservation ṁ re =

with

HRa , out − HRa , in α·V

mȧ

(5a)

42

HRa , out =

HRa , in =

0.622psat , out ·φa , out 101.325 − φa , out ·psat , out

Figure 3. Reduction of input variables. (5b)

G1, G2, and Ts,in are the new group of ANFIS input variables, and the input dimension decreases from 8 to 4, which reduces half of the computational load of the model development and application process.

0.622psat , in ·φa , in 101.325 − φa , in ·psat , in

(5c)

of which HRa,in, HRa,out, V, and α are the humidity ratio of regenerating air, the humidity ratio of outlet air, and the volume and specific surface area of the regenerator tower, respectively. The outlet and inlet air humidity ratios HRa,out and HRa,in can be calculated with eqs 5b and 5c, and the value of psat,in and psat,out can be calculated with eq 3b with Ta,in and Ta,out, respectively. The equivalent contact area inside the regenerator is represented as α · V owing to structure packing. Thus, the regeneration rate can be calculated by eq 1 and eq 5 with different available input variable groups.

5. STRUCTURES FOR SOFT SENSING MODEL 5.1. Data Driven Takagi−Sugeno ANFIS Structure. A basic Takagi−Sugeno ANFIS framework has a total of five layers with a linear output membership function, as described in Figure 4, and each layer represents a specific function in this system: • Layer 1: Transmitting the crisp values to the next layer; • Layer 2: Clustering the crispy variables into several clusters; 9259


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Figure 4. ANFIS architecture.

• Layer 3: Mapping the rules to form a fuzzy interference system; • Layer 4: Evaluating of the weights of each fuzzy rule; • Layer 5: Aggregating the outputs of Layer 4 for the concentration values. To establish this ANFIS model, input samples clustering, weight tuning, and validating are carried out in sequence. Supposed that this model has M inputs, the jth input is denoted as inputj. The fuzzy linguistic rules conducted from the clustering algorithm43 with respect to inputj are noted as μ(c) (inputj), while the cluster number of the jth input is ncln (j). In this study, the data clustering are conducted in a vector mode, and the cluster number of j inputs is the same as the fuzzy rule number, Nfrn.43 With a generalized Gaussian membership function, each cluster has two nonlinear parameters: a center and an effective range, and the ANFIS has 2 × M × Nf rn nonlinear parameters collectively. The outlet membership functions are linear in a Takagi−Sugeno ANFIS structure,44 and, in this study, the number of linear parameters is (M + 1) × Nfrn. The weights ω are trained during the training process, and the adjustment of the weight ωk,k−1 is calculated as follows45 Δωk , k − 1 = −η

δk = −

∂error = ηδkinputk ∂wk , k − 1

∂error = −ekφk′[vk] ∂vk

Error =

1 S

S

∑ (coni − cone ,i)2

(9)

i=1

where S is the number of samples in the training database, coni is the model predictive result, and cone,i is the offline measurement result.25 The relationships between input variables and concentration values measured by this soft sensing model are expressed mathematically by46 N

Conre = f (input j) =

M (c) ∑l =frn1 [(ΠM j = 1μ (input j))(Π j = 0ωl , j(input j))] N

∑l =frn1 (ΠlM= 1μ(c)(input j)) (10)

where j and l are the mark numbers of the input variables and fuzzy rules. After the validation, a data-driven ANFIS is yielded to collect the real-time desiccant concentrations of a centralized regenerator. 5.2. GA-Optimized ANFIS Structure. GA is introduced to optimize the clustering parameters to develop an accurate soft sensing model with a simplified ANFIS structure. This optimization method encodes the effective ranges of the cluster centers into a chromosome, then finds out the individual with the smallest objective function through evolutions, and finally decodes this optimal solution into the target ANFIS structure. Encoding. A chromosome is a binary string of variables composed of several ranged genes. These genes signify the effective ranges of the centers during the data clustering processes and lead to different clustering results. Each cluster can be translated into a fuzzy rule, and all these fuzzy rules aggregated to form the fuzzy interference part of an ANFIS structure.43,47,48 For a soft sensing model with m inputs and 1 output, the potential optimized solution is an individual chromosome with m+1 genes. An example chromosome with 4 inputs and 1 output is depicted in Figure 5, which is the

(8a)

(8b)

where η, δk, φk, and vk are the learning-rate parameter of the back-propagation algorithm, local gradient, the nonlinear function at layer k, and the weighted sum of the layer, respectively. The model accuracy is improved with supervised learning by adjusting the adapted parameters to minimize the error with eq 9 9260


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In eq 11a, ncln (j) is the cluster number obtained from the clustering results of inputj utilizing the genetic information carried by the ith chromosome. In eq 11b, coni is the model predicted value, and cone,i is the calculation result from the measured density and the corresponding solution temperature. N is the number of data samples used to test the model accuracy of the ith ANFIS structure. Finally, in eq 11c, n1, n2, ..., ni are the rule numbers of the ith ANFIS structures in the current generation. The accuracy is the first criterion in evaluating the ANFIS structure. Those structures with small objective values are regarded as generated from high quality genes and will be selected preferentially during the offspring generating. When the structure has a satisfied accuracy, the sum of eq 11a and eq 11b will be assigned to the objective function, and in the condition that the value of constraint function is not in the acceptable range, the value of the objective function turns into the sum of eq 11b and eq 11c and will be assigned when the evaluation of this generation is finished. The final form of the objective function is

binary-coded decimal encoding result of {0.1845 0.9298 0.8817 0.2318 0.1548}.

Figure 5. An example of a chromosome.

The modified mountain clustering algorithm43 is applied to build up the fuzzy relationships from the genetic information carried by the chromosomes. The clustering algorithm extracts the implicated information contained in the training data, and the data with the same properties are clustered into one cluster. Each cluster can be translated into a fuzzy rule, and all these rules group into the fuzzy interference structure of the ANFIS.47,48 Objective Function of GA. To generate a simple yet accurate ANFIS model, a constraint objective function with three subfunctions is established. These subfunctions are denoted as the rule number function, constraint function, and extinction function as Rulenum(i) = ncln(j) 1 ConFun(i) = N

⎧Objfun(i) = Rulenum(i) ConFun(i) ≤ ε ⎪ ⎪ + ConFun(i), ⎨ ⎪Objfun(i) = ExticFun + ConF ConFun(i) > ε ⎪ ⎩ un(i),

(11a)

where i indicates the ith chromosome or the ith ANFIS structure in the current generation. Population and GA Operators. The randomly generated chromosomes are ranked based on the values of objective functions calculated from eq 12. Compared with the constraint

N 2

∑ (coni − cone ,i) i=1

ExticFun(i) = max(n1 , n2 , ..., ni)

(12)

(11b) (11c)

Figure 6. Flowchart of optimization. 9261


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Industrial & Engineering Chemistry Research function, the value of extinct function is significantly larger, and those unsatisfied structures with a large objective function value will be weakened or eliminated during the offspring generation. The parent chromosomes generate the offspring by selection, crossover, and mutation until the optimal chromosome is found in the evolution. The GA terminates when the average relative change between two generations is below the tolerance or the evolution reaches the maximal number of generation. After parameter tuning, this optimized structure is then validated subsequently with the offline calculated concentration values. The simplification method can be presented as follows: Step 1: Generate chromosomes randomly to initialize the GA population based on the proposed constraints; Step 2: Encode the genetic information to binary structures; Step 3: Cluster the collected data samples into different clusters;43 each cluster has a particular center and effective range and corresponds to a fuzzy rule; Step 4: Determine the optimal structure from the clustering results in step 347,48 based on the basic structure of Takagi− Sugeno ANFIS;49 Step 5: Evaluate the structure obtained in Step 4; Step 6: Rank the objective function values of the chromosomes in the current generation and generate the offspring with GA operators; Step 7: Reap from Step 2 until finding the optimal solution; Step 8: Decode the optimal chromosome to determine the preliminary ANFIS structure;43,47,48 Step 9: Tune the parameters of ANFIS by the backpropagation algorithm combining with the least-square method;45 Step 10: Validate the soft sensing model. The flowchart of the development steps is illustrated in Figure 6, and the parts with highlights are the steps in building up a conventional ANFIS model. To evaluate the effectiveness of the soft sensing model and simplification methods, three different structures are trained and verified. The first structure is the original data driven ANFIS, of which is developed as Section 5.1; the second structure is model-based ANFIS, utilizing the mass transfer model demonstrated in Section 4 for the input variable simplification; the last structure optimized the model-based ANFIS as clarified in Section 5.2. These three models are denoted as ANFIS, Mo-ANFIS, and Mo-Opt-ANFIS in the following statements.

Figure 7. Experimental rig of the LDDS: 1. fan; 2. heat exchanger; 3. heat pipes; 4. power cabinet; 5. data acquisition system; 6. solution storage tank; 7. dehumidfier working solution tank; 8. regeneration solution tank.

Table 1. Specifications of the Experimental Rig parameters

value

packing height packing corrugation angle solution buffer volume working solution tank regeneration solution tank

(m) (deg) (m3) (m3) (m3)

0.5 45 0.3 0.4 0.4

Table 2. Specifications of the Sensors in the Data Acquisition System name of the sensor

type

solution flow meter air flow meter density meter solution temperature air temperature/ humidity

accuracy

magnetic flow meter blade glass hydrometer 3-wire PT-1000 probe

range

±0.5%

0−50 L/min

±0.5% 1 kg/m3

0−600 m3/h 1100−1300 kg/m3

0.15 °C

0−100 °C

0.1 °C ± 0.5%

0−60 °C, 0−100%

the inlet and outlet temperature of desiccant solution, and the mass flow rate of the desiccant solution are all measured by the data acquisition system at a sample rate of 1 sample per second. The concentration of LiCl is derived from the density measured with the glass hydrometer and respective temperature information. In order to describe the effectiveness of the physical and soft sensing models, relative error (RE), mean relative error (MRE), and root-mean-square of relative error (RMSRE) are

6. VALIDATION AND DISCUSSION Experiments are performed on the LDDS shown in Figure 7 to verify the proposed soft sensing model. Following the operating scheme described in Section 2, the regenerator concentrates the diluted solution to the target concentration in a centralized form and stops when the desiccant concentration achieves the concentration set point value. The regenerator tower, which is made of polypropylene, is 1 m in height with a cylindrical structure packing, of which the dimension is 0.5 m. A sprayer is installed at the top of the column for solution distribution. The air and solution flow rates are regulated by the Variable Speed Drives installed on fans and pumps. Lithium chloride (LiCl) is used as the liquid desiccant in this experiment platform. The specifications of this experiment rig are explained in Table 1. Table 2 contains the specifications of sensors installed on this test bench. The inlet and outlet air temperature and humidity,

REi =

|DR − DC | × 100% DR

(13a)

M

MRE =

∑i = 1 REi (13b)

M M

RMSRE = 9262

∑i = 1

(

DRi − DCi DRi

M

2

)

(13c) DOI: 10.1021/acs.iecr.6b01988 Ind. Eng. Chem. Res. 2016, 55, 9256−9266

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Industrial & Engineering Chemistry Research where DR and DC are the real value measured from experiment data and calculated value from model prediction, respectively. The experiments are performed in the following conditions: a. The inlet air has a humidity ratio of 11−18 g/kg dry air and a temperature in the range of 20−25 °C; b. The same initial solution concentration of 26% for each round of the test; c. No solution exchanging during the whole regeneration period; d. The regeneration process ends automatically at the desiccant concentration at the preset concentration of 38%. With inlet solution temperatures in the range of 30 °C−55 °C and mass flow rates in the range of 0.4 kg/s−0.9 kg/s, the data samples are acquired in different regenerator operating conditions. Four databases have been built up for mass transfer model validation, parameter training, soft sensing model validation, and ANFIS structure optimization. The lumping parameters in eq 2 are identified with the mass transfer model database. This model is trained with the data samples covering the whole regenerator operating range. The values of c1, c2, c3, and c4 are 0.0100, 8.001, 5.029, and 4.9843, respectively. The relative errors of the model are illustrated in Figure 8, and the MRE and RMSRE are 5.70% and 0.01689, respectively.

mized model-based ANFIS (Mo-Opt-ANFIS), and the accuracy and simplicity of these models are discussed in this section. For the original data driven ANFIS, the eight inputs are the mass flow rate of air and solution, the solution outlet and inlet temperature, the inlet air humidity and temperature and the outlet air humidity and temperature, and the fuzzy membership functions are depicted in Figure S1. The model predicted and measured concentrations scatter over the regenerator operating range as described in Figure 9, and the results show a good accuracy of this model. This structure has 15 fuzzy rules generated from the clustering results and totally 375 parameters. With this meticulous structure, the relative errors are kept below 1.2%, and the MRE and RMSRE values are 0.5210% and 0.0071, respectively. Compared with the original data-driven ANFIS, the input dimension of the model-based ANFIS (Mo-ANFIS) decreases from 8 to 4, and the number of total parameters decreases to 156. From Figure 10, it can be observed that the soft sensing concentration values acquired by this model are consistent with the measured values. The relative errors are less than 3%, and the MRE and RMSRE are 0.7472% and 0.0103, respectively. The fuzzy membership functions are described as Figure S2. The GA serves as a method to further simplify the structure of the model-based ANFIS. The randomly generated initial population of GA has 500 chromosomes, and each determines a particular ANFIS structure. Every structure is evaluated by the constraint function with 20 data samples from random selections. The top-ranked chromosomes are selected to generate the new generation of offspring with a mutation probability of 0.8 and a two-point mutation method. The maximal generation number is 100, and the tolerance of the change between two generations is 10−6. The optimal ANFIS structures selected by GA are generated from a chromosome with a gene series as 0.2004 0.3019 0.2031 0.2143 0.3162, and the corresponding values of eq 11a, 11b, and 11c are 6, 0.0301, and 13, respectively. The validation results of this GA optimized model-based ANFIS (Mo-Opt-ANFIS) are described in Figure 11, and the MRE and RMSRE are 1.0230% and 0.1327, respectively. The optimal fuzzy membership functions obtained from GA are described as Figure S3. The values of performance indices and the structure characteristics are summarized in Table 3. Compared with the original ANFIS structure, the Mo-ANFIS model reduces

Figure 8. Relative error of regeneration mass transfer model.

As mentioned in Section 5, three different types of the softsensing model have been developed, i.e. data driven ANFIS (ANFIS), model-based ANFIS (Mo-ANFIS), and GA opti-

Figure 9. Regenerator soft sensing model validation and errors (ANFIS). 9263


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Figure 10. Regenerator soft sensing model validation and errors (Mo-ANFIS).

Figure 11. Regenerator soft sensing model validation and errors (Mo-Opt-ANFIS).

Table 3. Performance Indices of Different Methods model

input variables

Nfrn

nonlinear

linear

TotalPara

MRE

RMSRE

ANFIS Mo-ANFIS Mo-Opt-ANFIS

8 4 4

15 12 6

240 96 48

135 60 30

375 156 78

0.5210% 0.7472% 1.0230%

0.0099 0.0103 0.0133

most concise structure with a good accuracy (RMSER < 0.02), which proves the efficiency of the simplification method. This soft sensing model is imperative in providing the dehumidifiers with a preset solution concentration to guarantee controllability of the dehumidifier working concentration and also is beneficial in energy conservation to find an optimal regeneration temperature with respect to solution concentration.

58.4% of the total parameters, and the fuzzy rule number also decreases from 15 to 12. The parameter number of the MoOpt-ANFIS decreases 50% after GA optimization compared with the Mo-ANFIS model and reduces 70.2% with respect to the original ANFIS with only a slight loss of accuracy. This soft sensing model is developed for the concentration detection in a centralized regenerator, of which the solution temperature is between 30 °C and 55 °C, and the desiccant concentration is in the range of 26%−38%.

■

ASSOCIATED CONTENT

S Supporting Information *

7. CONCLUSION This work presents a soft sensing model to detect the regeneration concentration of a centralized regenerator in a distributed operating LDDS. Models with different input variable numbers and fuzzy rule numbers are developed, validated, and compared. According to the validation results, the predicted concentrations are consistent with the experimental values. By comparing the soft sensing accuracy and structural complexity, the model-based optimized ANFIS has a

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b01988.

■

Equations S1 and S2 and Figures S1−S3 (PDF)

AUTHOR INFORMATION

Corresponding Author

*Phone: +65 6790 6862. Fax: +65 6793 3318. E-mail: ewjcai@ ntu.edu.sg. 9264


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Industrial & Engineering Chemistry Research Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Research Foundation of Singapore under the grant NRF2011 NRF-CRP001-090 and the National Research Foundation of Singapore and Building and Construction Authority (BCA) under the grant NRF2013EWT-EIRP004-019. Their support is gratefully acknowledged.

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NOMENCLATURE c1−c4 = parameters of regenerator mass transfer rate model conre = desiccant concentration in regenerator (%) φa,in = relative humidity of regenerator inlet air (g/kg dry air) φa,out = relative humidity of regenerator outlet air (g/kg dry air) Ta,in = inlet air temperature (°C) Ta,out = outlet air temperature (°C) Ts,in = inlet solution temperature (°C) Ts,out = outlet solution temperature (°C) KG = mass transfer coefficient (kg/(m2.s·pa)) ṁ s = mass flow rate of LiCl solution in regenerator (kg/s) ṁ a = mass flow rate of air in regenerator (kg/s) ṁ re = mass transfer rate in regeneration process (kg/(m2.s)) pa,in = water vapor pressure of regenerating air (pa) ps,in * = water surface vapor pressure of LiCl solution (pa) psat,in = saturated water vapor pressure of the regenerating air (pa) psat,out = saturated water vapor pressure of the outlet air (pa) HRa,in = humidity ratio of the regenerating air (g/kg dry air) HRa,out = humidity ratio of the outlet air (g/kg dry air) α = specific surface area (m2/m3) V = regenerator tower volume (m3)

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