applied sciences

Article A Membership-Fusing Model for Characterizing the Shift of Methanogen Community in a Three-Stage Sludge-Treatment Process

Linna Cai 1,2, Hongyang Li 3 and Hong Yao 1,2,* 1 School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China; [email protected] 2 Beijing Key Laboratory of Typical Pollutant Control and Water Quality Protection in Water, Beijing 100044, China 3 Science and Technology on Space Physics Laboratory, Beijing 100076, China; [email protected] * Correspondence: [email protected]; Tel.: +86-1336-673-8735



Received: 17 May 2020; Accepted: 17 June 2020; Published: 22 June 2020


Abstract: Anaerobic digestion (AD) is an economical and effective method to treat sludge. AD with several pretreatments is the prior process to treat surplus sludge for a wastewater treatment plant. During a sludge-treatment process, various methanogens play their specific role in each sludge-processing stage where different methanogens predominate. Therefore, an expert in the shift of methanogen community could facilitate the workers in a plant to understand the efficiency of the sludge-treatment process. In this paper, a membership-fusing model is established to characterize the shift of methanogen community in a three-stage sludge-treatment process. The introduction of fuzzy sets clarifies the vagueness of the methanogen community structure between two processing stages. Dempster–Shafer (DS) evidence theory effectively alleviates the data error generated among paralleling samples. The accuracy of the model was verified, and the result shows the model could clearly distinguish the methanogen community structure of the three stages and make accurate judgment on the processing stage affiliation. The reliability of the model in dealing with different numbers of conflict data was proved and the experiment indicates the model could make a reliable judgment on the processing stage affiliation by reasonably fusing the interference data.

Keywords: anaerobic digestion (AD); shift of methanogen community; fuzzy sets; Dempster–Shafer (DS) evidence theory; data conflict

1. Introduction A large amount of surplus sludge, as by-product, is generated from the primary and secondary sedimentation tanks in a wastewater treatment plant every day [1]. The sludge is mainly composed of organic materials, water, nitrogen, and phosphorous nutrients, heavy metals, and pathogens [2]. Resources would be wasted, and harmful substances would be discharged into the environment if the sludge were not treated properly. Anaerobic digestion (AD) is proved to be an environmental-friendly and cost-effective treatment compared with other methods in realizing sludge reduction, stabilization, and harmlessness. The biogas produced in AD process could be used as a type of biofuel to generate energy, replacing above 86% of the energy derived from traditional fossil fuels [3]. Nutrients, such as nitrogen, phosphorous, and potassium, could also be recovered and used in AD process [4]. Basically, AD is a serious of interrelated complex biochemical reactions participated by various microorganisms, interacting with each other, to degrade organic compounds [5]. AD is usually divided into four procedures: hydrolysis, acidification, acetogenesis, and methanogenesis [6]. Complex organic materials are first hydrolyzed to soluble organic molecules, which then are fermented into short-chain fatty acids by hydrolytic and acidogenic bacteria in hydrolysis and acidification. Afterwards, the

Appl. Sci. 2020, 10, 4274; doi:10.3390/app10124274 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 4274 2 of 17

fatty acids are oxidized to H2 and acetate by acetogenic bacteria during acetogenesis. In the final methanogenesis, two metabolic paths exist. One is H2 used by hydrogenotrophic methanogens as the electron donor to reduce CO2 to methane [7]. The other is acetate decomposed by acetotrophic methanogens to methane [8]. As most of the organic compounds of the sludge are distributed in microbial cells in solid form, cell walls and membranes form firm barriers prohibiting the release of the organic compounds, and the hydrolysis rates of the hydrolytic enzymes outside microbial cells towards complex organic materials are relatively low, hydrolysis is considered to be the control step in AD process [9]. Physical, chemical, and biological pretreatments have been adopted to accelerate the speed of hydrolysis and alleviate the burden on AD process [10]. Enzymes are usually applied in the biological method as biocatalysts to degrade organic compounds [11], but they are less effective in treating surplus sludge as they easily degrade themselves before hydrolysis starts. Alkalization and acidification are commonly adopted chemical pretreatments to solubilize microbial cell walls and release intracellular organic matter [12]; however, the quality of the produced biogas pretreated by these methods needs to be further guaranteed. Physical pretreatments, such as ultrasonic and microwave, demand much more energy than other methods although the biogas yields can be greatly improved. Taking comprehensive consideration, thermal hydrolysis has been considered to be the prior selection for the surplus sludge pretreatment, because it is a high potential pretreatment in enhancing both the degradability of organic compounds and the yields of biogas with no extra energy input [13,14]. For a wastewater treatment plant, a commonly adopted sludge-treatment process consists of pretreatments, AD and posttreatments aiming to compress the sludge volume for final disposal [1]. Various types of microorganisms are involved in different biochemical reactions in both pretreatments and AD process, and the microbial metabolic viability could affect the efficiency and stability of the sludge-treatment process [15,16]. Methanogens have more strict growing requirements and longer doubling times than other microorganisms participating in the sludge-treatment process, which is widely concerned as the control microbial community in AD process [17]. Most previous studies regarding AD have been focused on the influence of environmental factors, such as temperature, pH, volatile fatty acids, ammonia, and the feedstock composition, on the shift of methanogen community. A change from mesophilic (30–40 ◦C) to thermophilic (50–60 ◦C) condition has exerted a significant impact on the methanogen community structure [18,19]. Improper pH might impair the microbial viability by restraining the activity of hydrolytic enzymes and producing ionic toxicity to microorganisms [20], and methanogens always require a strict range of pH for growth [21]. Jiang et al. [22] demonstrated the selective inhibition of ammonia on methanogens, and found the more susceptible characteristics of acetotrophic methanogens than hydrogenotrophic methanogens. Researchers have found the different effects of various feedstock, either positive or negative, on the growth of microorganisms in AD process [23,24], and that the adding of trace elements to feedstock could facilitate the metabolism and growth of methanogens [25]. As for the research on thermal hydrolysis pretreatment, much attention has been payed to the effect of temperature and heating time on the efficiency of hydrolysis and biogas yields. The optimal temperature and heating time vary greatly from 160 to 180°C and 30 to 60 mins, respectively [26–30]. Westerholm et al. [31] further confirmed thermal hydrolysis changed the composition and species abundance of the microbial community compared with the un-pretreated one. However, study on the shift of methanogen community in a sludge-treatment process has not been investigated yet. For a wastewater treatment plant, a clear characterization of the shift of methanogen community could reflect the efficiency and environmental condition of different processing stage, which could provide workers an advisable instruction to regulate the sludge-treatment process. In each sludge-processing stage, the structure of methanogen community is unique and in a relative stable range of change because of the heterogeneous and relatively steady environmental condition each stage provides. Therefore, the boundary of the methanogen community structure between two processing stages could not be such clear. Furthermore, the data error caused by sample contamination and faults Appl. Sci. 2020, 10, 4274 3 of 17 occurring in data measurement and analysis processes has not been fully taken into consideration when analyzing the microbial information in previous research. Although paralleling samples were collected to weaken the data error, the method to process the paralleling data is just taking the average value. If the paralleling data deviated extremely, the average value could not represent the authentic one. Fuzzy sets are good at describing the vagueness of a certain phenomenon and uncertainty caused by data error [32–34], and Dempster-Shafer (DS) evidence theory is adept at fusing imprecise and conflict data from multi-sources [35,36]. Both theories are combined to resolve the problem of the uncertain boundary of the methanogen community structure between two sludge-processing stages and data error generated among paralleling data. This paper aims to propose a membership-fusing model combing fuzzy sets and DS evidence theory to properly characterize the shift of methanogen community in different processing stages of a three-stage sludge-treatment process and reasonably determine which stage the tested paralleling sludge samples most likely come from by measuring the shift of methanogen community. The organization of this paper is as follows: In Section2, the three-stage sludge-treatment process is abstracted and the main functional methanogens able to characterize the shift of methanogen community are selected. Then the membership-fusing model is established based on fuzzy sets and DS evidence theory. In Section3, a sampling scheme and methods of data measurement and analysis are put forward, and undetermined parameters of the model are set up statistically with the measurement data from past several years. In Section4, the membership-fusing model is verified by a group of new data, and different numbers of interference data have been investigated to confirm the reliability of the model in addressing conflict and imprecise data brought by paralleling samples. Final conclusions are made in Section5.

2. Membership-Fusing Model of Sludge-Treatment Process The membership-fusing model is proposed below to characterize the variation of methanogen community in the three-stage sludge-treatment process, which is applied to determining the specific processing stage of a group of examined paralleling sludge samples. The procedure to establish the model consists of two parts, as is shown in Figure1. The first part is to abstract a sludge-treatment technical route into the three-stage process illustrated in Section 2.1, and the corresponding sampling points representing each stage are set to collect sludge samples. Then, the methanogens characterizing the variation of methanogen community are selected, and high-throughput sequencing technology is used to measure the gene sequences of each sludge sample to quantify the selected methanogens. The second part is to establish fuzzy sets SI, SII, SIII, and Sun to describe the affiliation of the processing stage of the sludge sample. The probability of the stage affiliation is assessed by the corresponding basic membership functions A(SI), A(SII), A(SIII) and A(Sun), which are then normalized as B(SI), B(SII), B(SIII) and B(Sun). The normalized memberships are subsequently fused to obtain the integrated memberships C(SI), C(SII), C(SIII) and C(Sun). The maximum among the four integrated memberships indicates which processing stage the tested paralleling sludge samples most likely belong to.

2.1. Sludge-Treatment Process and Representative Methanogen The prior technical route to treat surplus sludge for a wastewater treatment plant in China is thickening, thermal hydrolysis, AD, dewatering and final disposal [1], as is shown in Figure2. To be specifically, thickening, either gravity, or floatation, or mechanical thickening, aims to reduce water content of the sludge to be about 95%, which benefits the subsequent steps. Thermal hydrolysis purposes to improve the efficiency of AD process by enhancing the degradability of organic compounds and methane yields [13,14]. AD is the critical processing stage to degrade sludge. Dewatering, belt dewatering, centrifugal dewatering, and plate-frame dewatering included, is designed to compress the sludge volume, which alleviates the burden on the final disposal. To understand the efficiency of the sludge-treatment process, AD processing stage is widely considered to be the essential point [5,6]. As is shown in Figure2, the three stages—two stages before AD which could a ffect the effect of AD, and AD Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 18

Sludge treatment process abstraction and methanogens selection the three-stages sludge treatment process

sampling points

representative methanogens

gene sequencing

Appl. Sci. 2020, 10, 4274 shift of methanogen community 4 of 17

Membership-fusing model establishment stage, defined as Stage I, II, and III—must be the concernedfuzzy sets processing stages in the sludge-treatment fuzzy sets S , S , S , S process. Sampling points are set at the exit of eachI processingII III un stage among the three stages to collect

sludge samples for further analysisbasic membership on methanogen functions A(SI), community, A(SII), A(SIII), A(Sun as) is shown in Figure2. Sludge samples from sampling point I, after thickening and before thermal hydrolysis, could characterize the normalized membership functions B(S ), B(S ), B(S ), B(S ) feature of sludge in stage I. Sampling point II and III, afterI thermalII III hydrolysisun and before AD, and after Appl. Sci. 2020, 10, x FOR PEER REVIEW DS evidence theory 4 of 18 AD and before dewatering, couldintegrated represent memberships stage C II(SI and), C(SII III,), C( respectively.SIII), C(Sun) Paralleling sludge samples with a certain number, usually ranging from 3 to 10, are gathered from each processing stage. Maximum among C(S ), C(S ), C(S ) and C(S ) I II III un Sludge treatment process abstraction and methanogens selection 138 Figure 1. Procedurethe three-stages to build sludge the treatmentmembership-fusing process model.

139 2.1. Sludge-Treatment Process and Representativesampling Methanogen points

140 The prior technical route to treatrepresentative surplus sludge methanogens for a wastewater treatment plant in China is 141 thickening, thermal hydrolysis, AD, dewatering and final disposal [1], as is shown in Figure 2. To 142 be specifically, thickening, either gravity, geneor floa sequencingtation, or mechanical thickening, aims to reduce 143 water content of the sludge to be about 95%, which benefits the subsequent steps. Thermal shift of methanogen community 144 hydrolysis purposes to improve the efficiency of AD process by enhancing the degradability of 145 organic compounds and methane yields [13,14]. AD is the critical processing stage to degrade Membership-fusing model establishment 146 sludge. Dewatering, belt dewatering, centrifugal dewatering, and plate-frame dewatering included, fuzzy sets 147 is designed to compress the sludge volume, which alleviates the burden on the final disposal. To fuzzy sets S , S , S , S 148 understand the efficiency of the sludge-treatmeI II ntIII process,un AD processing stage is widely 149 considered to be the essential point [5,6]. As is shown in Figure 2, the three stages—two stages basic membership functions A(SI), A(SII), A(SIII), A(Sun) 150 before AD which could affect the effect of AD, and AD stage, defined as Stage I, II, and III—must be 151 the concerned processing stages in the sludge-treatment process. Sampling points are set at the exit normalized membership functions B(SI), B(SII), B(SIII), B(Sun) 152 of each processing stage among the three stages toDS collect evidence sludge theory samples for further analysis on

153 methanogen community, asintegrated is shown memberships in Figure C (2.SI), Sludge C(SII), C (samplesSIII), C(Sun from) sampling point I, after 154 thickening and before thermal hydrolysis, could characterize the feature of sludge in stage I.

155 Sampling point II and III,Maximum after thermal among Chydrolysis(SI), C(SII), Cand(SIII ) beforeand C(S unAD,) and after AD and before 156 dewatering, could represent stage II and III, respectively. Paralleling sludge samples with a certain 157 number, usually rangingFigure from 1. 3Procedure to 10, are togathered build the from membership-fusing each processing model. stage. 138 Figure 1. Procedure to build the membership-fusing model. The three-stages sludge treatment process 139 2.1. Sludge-Treatment Processparalleling and samplesRepresentative Methanogenparalleling samples paralleling samples 140 The prior technical route to treat surplus sludge for a wastewater treatment plant in China is Stage I Stage II Stage III 141 thickening, thermalThickening hydrolysis, unit AD,Thermal dewatering hydrolysis unit and finalAnaerobic disposal digestion [1], unitas is shown in Figure 2. To 142 be specifically, thickening,Sampling either point gravity, I or floaSamplingtation, point or II mechanicalSampling thic pointkening, III aims to reduce 143 water content of the sludge to be about 95%, which benefits the subsequent steps. Thermal 144 hydrolysis purposes to improve the efficiencyFinal of disposal AD processDewatering by enhancing unit the degradability of

145 organic compounds andFigure methane 2. Sludge-treatment yields [13,14]. process and AD distribution is the ofcritical sampling processing points. stage to degrade 146 sludge.158 Dewatering, beltFigure dewatering, 2. Sludge-treatment centrifugal process dewatering, and distribution andof sampling plate-frame points. dewatering included, The quantity ratio of Methanosaeta to Methanobacterium could represent the shift of methanogen 147 is designed to compress the sludge volume, which alleviates the burden on the final disposal. To community, defined as the independent variable x, calculated by Equation (1): 148 understand the efficiency of the sludge-treatment process, AD processing stage is widely R 149 considered to be the essential point [5,6]. As xis= shown1 in Figure 2, the three stages—two(1) stages R 150 before AD which could affect the effect of AD, and AD2 stage, defined as Stage I, II, and III—must be 151 the concernedwhere processingR1 and R2 stand stages for thein readsthe sludge-treat of genes of thement genera process. of Methanosaeta Samplingand Methanobacteriumpoints are set ,at the exit 152 respectively. High-throughput sequencing technology is applied to measure the quantities of the of each processingtwo genera ofstage methanogens. among Eachthe three sludge stages sample generatesto collect a great sludge deal ofsamples reads of genesfor further pertaining analysis on 153 methanogen community, as is shown in Figure 2. Sludge samples from sampling point I, after 154 thickening and before thermal hydrolysis, could characterize the feature of sludge in stage I. 155 Sampling point II and III, after thermal hydrolysis and before AD, and after AD and before 156 dewatering, could represent stage II and III, respectively. Paralleling sludge samples with a certain 157 number, usually ranging from 3 to 10, are gathered from each processing stage.

The three-stages sludge treatment process paralleling samples paralleling samples paralleling samples

Stage I Stage II Stage III Thickening unit Thermal hydrolysis unit Anaerobic digestion unit Sampling point I Sampling point II Sampling point III

Final disposal Dewatering unit

158 Figure 2. Sludge-treatment process and distribution of sampling points. Appl. Sci. 2020, 10, 4274 5 of 17 to various methanogens by the gene sequencing. Summing the reads of genes belonging to genus Methanosaeta and genus Methanobacterium up, respectively, and then do the ratio of the two sums to generate a certain value of x. The representative role of Methanosaeta [8] and Methanobacterium [37] is clarified as follow: first, previous studies have found that acetotrophic methanogen Methanosaeta and hydrogenotrophic methanogen Methanobacterium are the two main functional methanogens in AD process [37,38]. Secondly, their relative shift in quantity varies greatly in each sludge-processing stage, owing to the different growing requirements of these two genera of methanogens and the specific environment each stage provides [7,8,37]. Lastly, the relative variation of these two genera of methanogens is in a dynamic stable range of change in each stage due to the relatively steady surrounding of each processing stage. Consequently, a specific x value could reflect a specific state of the methanogen community, characterize a sludge-processing stage among the three stages, and reveal the efficiency and environmental condition of the representative processing stage. The value of x is distributed in a certain range for the three-stage sludge-treatment process and x also has a relative stable value range for each processing stage. Specifically, for stage I, the physical treatment provides the same environmental stress for the two genera of methanogens and the x value is usually below 10. The increase of the temperature in stage II is more favorable for hydrogenotrophic methanogen Methanobacterium to grow and the x value is lower than that of stage I [18]. Acetotrophic methanogenesis is the major path to produce methane compared with hydrogenotrophic methanogenesis in AD process, and x is supposed to be much greater than 10 for stage III [39].

2.2. Membership-Fusing Model Based on the three-stage sludge-treatment process and the quantity ratio x, the membership-fusing model is established by combing fuzzy sets and DS evidence theory. First, four fuzzy sets SI, SII, SIII, and Sun are put forward to elucidate the affiliation of the processing stage of a sludge sample being Stage I, Stage II, Stage III, and stage uncertain. SI, SII, and SIII contain x values belonging to Stage I, II, and III, respectively. Sun clarifies the indetermination of the processing stage of a sludge sample, considering of both the vague boundary of the methanogen community structure between two processing stages, and the absence of x values around 10. The data error generated among paralleling samples caused by sample contamination and incidental and instrumental errors occurring in data measurement and analysis processes would lead to the appearance of x values outside the fuzzy sets representing the three stages. The degree of the probability of a sludge sample from Stage I, II, III, and uncertain is described by the corresponding basic membership function of each fuzzy set, A(SI), A(SII), A(SIII), and A(Sun), respectively, established in Equation (2), referring to the traditional normally distributed membership function:

 (x u )2  − − 1  2σ 2  A(SI) = e 1  1  τ1(x c1)  A(SII) = (1 + e − )−  1 (2)  τ2(x c2) −  A(SIII) = (1 + e− − )  (x u )2  − − 2  2σ 2  A(Sun) = e 2 where parameters τ1, c1 and τ2, c2 reflect the trends of A(SII) and A(SIII), respectively. Parameters τ1 and τ2 indicate the changing gradients of the uncertainties of the two basic membership functions, while c1 and c2 clarify the limits of the x value where the two basic membership functions become uncertainly. Values of c1 and c2 are equal to the values of x when A(SII) and A(SIII) equal 0.5. Parameters u1 and u2 are the average values of SI and Sun and describe the most probable x values belonging to Stage I and stage uncertain. Parameters σ1 and σ2 are the standard deviation of SI and Sun and reveal the degree of the deviation of x values away from the average x value. Parameters mentioned above should satisfy condition (3) and are determined by statistics method elucidated in Section 3.3: Appl. Sci. 2020, 10, 4274 6 of 17

  u1 = xIaver   = x  σ1 Isd   c1 = xIImax   c = x  2 IIImin  τ (x c ) 1 (3)  (1 + e 1 IImin− 1 )− > 0.999   τ (x c ) 1  (1 + e− 2 IIImax− 2 )− > 0.999   =  u2 2σ2 xIaver  −  u2 + 2σ2 = xIIIaver where xjaver, xjsd, xjmax, and xjmin are the average value, standard deviation, maximum and minimum of x of Sj (j = I, II, III). 2σ principle [40] means the probability of the value of the normally distributed function is 0.95443 when the independent variable distributes in (u-2σ, u+2σ). In other words, x outside (u 2σ, u+2σ) is most unlikely to exist, which is applied to determine the values of u and σ . − 2 2 Considering of the vagueness of the critical state of methanogen community structure between two sludge-processing stages, the average value of x is chosen to be the boundary value. Then the basic membership functions are normalized in Equation (4):

 (x u )2 − − 1  2  2σ1  B(S ) = e  I (x u )2 (x u )2  − − 1 − − 2  2σ 2 τ (x c ) 1 τ (x c ) 1 2σ 2  e 1 +(1+e 1 − 1 )− +(1+e− 2 − 2 )− +e 2  1  ( +eτ1(x c1))−  B(S ) = 1 −  II (x u )2 (x u )2  − − 1 − − 2  2σ 2 τ (x c ) 1 τ (x c ) 1 2σ 2  e 1 +(1+e 1 − 1 )− +(1+e− 2 − 2 )− +e 2  1 (4)  (1+e τ2(x c2))−  B(S ) = − −  III (x u )2 (x u )2  − − 1 2  2 1 1 − − 2  2σ1 +( + τ1(x c1))− +( + τ2(x c2))− + 2σ2  e 1 e − 1 e− − e  2  (x u2)  − − 2  2σ2  B(S ) = e  un (x u )2 (x u )2  − − 1 − − 2  2σ 2 τ (x c ) 1 τ (x c ) 1 2σ 2 e 1 +(1+e 1 − 1 )− +(1+e− 2 − 2 )− +e 2

Sample contamination might occur, possibly brought from improper operations of sampling persons, or from samples transfer process, or from the inconsistency of the environmental condition of each sampling time. Instrumental and incidental data errors brought by measurement instruments and human operations are inevitable in data measurement and analysis processes [41]. All these circumstances could result in several imprecise and conflict x values generated from a group of paralleling sludge samples, so that the paralleling normalized memberships of a certain fuzzy set might deviated extremely. DS evidence theory is introduced to address such problem of data error brought by multi-sources. The four types of normalized memberships obtained from a group of paralleling sludge samples are fused together to generate the integrated membership C(S) of each fuzzy set in Equation (5):   S = S1 S2 ... SM  ∩P ∩ ∩  ( ) = B(S1)B(S2)...B(SM) (5)  C S 1 K f or S , ∅  P −  K = B(S1)B(S2) ... B(SM) f or S = ∅ where M stands for the number of the paralleling sludge samples. S1, S2, ... , SM represent any one of the four fuzzy sets, either SI, or SII, or SIII, or Sun, and are obtained from the M paralleling sludge samples, respectively. B(Sm)(m = 1, 2, ... , M) are the corresponding normalized memberships. K stands for the total conflict results generated from the M paralleling samples. S obeys the intersection operation in condition (6): Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 18

224 Where M stands for the number of the paralleling sludge samples. S1, S2, …, SM represent any 225 one of the four fuzzy sets, either SI, or SII, or SIII, or Sun, and are obtained from the M paralleling 226 sludge samples, respectively. B(Sm) (m = 1, 2, …, M) are the corresponding normalized 227 Appl.memberships. Sci. 2020, 10, 4274K stands for the total conflict results generated from the M paralleling samples.7 of 17S 228 obeys the intersection operation in condition (6):

 SSSjjj = ( j =I, II, III)  Sj Sj = Sj ( j = I, II, III)  ∩SSSun un= un  S S = S  un un un (6)  SS∩jj un = S ( j =I, II, III) (6)  Sj Sun = Sj ( j = I, II, III)  ∩    = ∅≠  Sj SSjkSk = ∅ ( j ,( k jk= , I, =I, II, II,III; III;j jk, k ) ∩ 229 For M paralleling x values of a certain fuzzy set, if severalseveral data not belonging to this fuzzy set 230 appeared, thethe integrated integrated membership membershipC(Sun C) would(Sun) would be higher. be Thehigher. other threeThe integratedother three memberships integrated 231 wouldmemberships be more would reliable be more by considering reliable by theconsiderin existenceg the of existence the null setof the when null two set conflictwhen two data conflict from 232 twodata stagesfrom two occur, stages and occur, eliminating and eliminating the influence the of influenceSun when of intersecting Sun when intersecting with other with three other fuzzy three sets. 233 Thefuzzy unreliability sets. The unreliability regarding the rega judgmentrding the on thejudgment specific on processing the specific stage processing would be weakenedstage would more be 234 reasonablyweakened more compared reasonably with just compared averaging with the just paralleling averaging data the [paralleling42]. data [42]. 235 The maximummaximum amongamong CC((SSII), CC((SSIIII), C(SIII),), and and C((Sun)) elucidates elucidates the the most most probable probable state of thethe 236 examined paralleling sludge samples, either to be Stage I, or II, or III, or uncertain,uncertain, based on the 237 maximum principle of fuzzy sets.sets.

238 3. Experiment and Parameter Setup

239 3.1. Sampling Scheme 240 The membership-fusingmembership-fusing model model was was applied applied to theto three-stagethe three-stage sludge-treatment sludge-treatment process process in Beijing in 241 GaobeidianBeijing Gaobeidian Wastewater Wastewater Treatment Treatment Plant, a Plant, municipal a municipal wastewater wastewater treatment treatment plant in plant Beijing, in Beijing, China. 242 TheChina. sludge-treatment The sludge-treatment technical routetechnical was abstracted route wa intos abstracted the three-stage into processthe three-stage in consistent process with that in 243 illustratedconsistent inwith Figure that2 illustrated, as is shown in inFigure Figure 2,3 .as As is centrifugalshown in Figure thickening 3. As and centrifugal pre-dewatering thickening are theand 244 twopre-dewatering physical operations are the withtwo thephysical same pressureoperations on with the environmental the same pressure condition, on the which environmental makes little 245 dicondition,fference onwhich the methanogen makes little community difference structure, on the thesemethanogen two processing community stages structure, are both includedthese two in 246 Stageprocessing I. Sampling stages pointsare both were included set at the in exit Stage of each I. Sampling processing points stage. were Six paralleling set at thesamples exit of wereeach 247 collectedprocessing for stage. one samplingSix paralleling point atsamples each sampling were collected time. Sludgefor one samples sampling were point collected at each once sampling a day 248 intime. the Sludge morning samples in every were September collected withonce 30a day days in from the morning the past sixin every years, September 2014 to 2019. with Eighteen 30 days samples obtained each day were kept away from light and stored at 20 C within three days for the 249 from the past six years, 2014 to 2019. Eighteen samples obtained each− ◦ day were kept away from 250 genelight sequencing.and stored at -20°C within three days for the gene sequencing.

paralleling samples paralleling samples a b c d e f a b c d e f Sampling point I Sampling point II

Thickening unit Pre-dewatering unit Thermal hydrolysis unit Anaerobic digestion unit

centrifugal thickener centrifugal dehydrator thermal hydrolysis reaction tank anaerobic digestor Stage I Stage II Stage III

Sampling point III Dewatering unit

Final disposal paralleling samples

plate-frame dehydrator a b c d e f

Figure 3. Sludge-treatment process and distribution of sampling points of Beijing Gaobeidian Wastewater Treatment Plant. Appl. Sci. 2020, 10, 4274 8 of 17

3.2. High-throughput Sequencing Technology

3.2.1. DNA Extraction DNA was extracted with Fast DNA™ Spin Kit for Soil (MP Biomedicals). DNA quality and concentration were measured by a NanoDrop Spectrophotometer (Nano-100, Aosheng Instrument Co Ltd.) to ensure the absorbance ratios of 260/280 nm was approximately 1.8 and that of 260/230 nm was above 1.7.

3.2.2. Polymerase Chain Reaction (PCR) Amplification, Sequencing, Quantification Methyl coenzyme M reductase (mcrA) gene was chosen to be the target gene to study methanogens [43–46]. Amplicon sequencing was performed on a MiSeq platform to collect raw sequencing data (Illumina, San Diego, CA, USA). Primers for amplifying had the following gene sequences: MLf, GGTGGTGTMGGATTCACACARTAYGCWACAGC, and MLr, TTCATTGCRTAGTTWGGRTAGTT [43]. The procedure of polymerase chain reaction (PCR) was as follows: Each sample was run in triplicates for PCR amplification using a Bori LineGene9600plus real-time PCR instrument (Hangzhou Langji Scientific Instrument Co., Ltd., China) with Taq DNA Enzyme, template DNA, primers, 10 PCR buffer × and dNTP mixture. The PCR cycling program was as follows: an initial denaturation at 95 ◦C for 3 mins and 35 cycles consisting of denaturizing at 95 ◦C for 30 secs, annealing at 56 ◦C for 30 secs and extension at 72 ◦C for 40 secs. Subsequently, the PCR products were confirmed by agarose gel electrophoresis, purified with the Gel Extraction Kit, and quantified through an ultra-trace visible ultra-violet (UV) spectrophotometer (ND5000, BioTeke Corporation). The PCR products generated contained barcodes and primers.

3.2.3. Sequence Analysis Raw sequences were conducted quality control by the Galaxy-based pipeline in Denglab (http://mem.rcees.ac.cn:8080) with default parameters to get rid of barcodes and primers, and guarantee the length of the mcrA gene sequences was above 400bp [45]. Then operational taxonomic units (OTUs) were clustered at the 97% similarity level by Unoise to generate ZOTU to produce the OTU table. A library of the mcrA gene was constructed by first downloading all mcrA gene sequences from Functional Gene Repository (http://fungene.cme.msu.edu). Then the sequences of each gene were verified in the National Center for Biotechnology Information (NCBI) non-redundant database. Finally, 80% and 85%, corresponding to the 16S rDNA sequence identity of 95% and 97%, were set as the cut-off of genus and species, respectively, when assigning taxonomic to produce the species classifier table of methanogens [44,45].

3.3. Model Parameter Statistical methods were used to determine the unknown parameters of the membership functions. For one stage, 900 paralleling x values were obtained from the corresponding paralleling sludge samples in every September from 2014 to 2018. All 2700 x values from the three stages were made statistical analysis. Values of xIaver, xIsd, xIImin, xIImax, xIIImin, xIIIaver, and xIIImax are 4.8, 2.3, 0.0, 2.0, 15.8, 17.2 and 20.0, respectively. The value of x is speculated to range from 0.0 to 20.0 based on the minimum and maximum. According to condition (3)., parameters u1 and σ1 are expected to be 4.8 and 2.3. Parameters u2 and σ2 are required to satisfy the conditions of u2-2σ2 and u2+2σ2 equaling 4.8 and 17.2, respectively, thus, u2 and σ2 were calculated to be 11.0 and 3.1. Parameters c1 and c2 are 2.0 and 15.8, and τ1 and τ2 should be above 3.45 and 1.64 based on condition (3). To further analysis the effect of τ1 and τ2 on the gradients of basic membership functions A(SII) and A(SIII), τ1 was set to be 2.5, 3.5, 5.0, 10.0 and 18.0, and τ2 was set to be 1.0, 1.7, 3.5, 6.0 and 10.0, respectively. Curves of the four basic membership functions in Equation (2) are drawn in Figure4. Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 18

281 non-redundant database. Finally, 80% and 85%, corresponding to the 16S rDNA sequence identity 282 of 95% and 97%, were set as the cut-off of genus and species, respectively, when assigning 283 taxonomic to produce the species classifier table of methanogens [44,45].

284 3.3. Model Parameter 285 Statistical methods were used to determine the unknown parameters of the membership 286 functions. For one stage, 900 paralleling x values were obtained from the corresponding paralleling 287 sludge samples in every September from 2014 to 2018. All 2700 x values from the three stages were 288 made statistical analysis. Values of xIaver, xIsd, xIImin, xIImax, xIIImin, xIIIaver, and xIIImax are 4.8, 2.3, 0.0, 2.0, 289 15.8, 17.2 and 20.0, respectively. The value of x is speculated to range from 0.0 to 20.0 based on the 290 minimum and maximum. According to condition (3)., parameters u1 and σ1 are expected to be 4.8 291 and 2.3. Parameters u2 and σ2 are required to satisfy the conditions of u2-2σ2 and u2+2σ2 equaling 4.8 292 and 17.2, respectively, thus, u2 and σ2 were calculated to be 11.0 and 3.1. Parameters c1 and c2 are 2.0 293 and 15.8, and τ1 and τ2 should be above 3.45 and 1.64 based on condition (3). To further analysis the 294 effect of τ1 and τ2 on the gradients of basic membership functions A(SII) and A(SIII), τ1 was set to be 295 2.5, 3.5, 5.0, 10.0 and 18.0, and τ2 was set to be 1.0, 1.7, 3.5, 6.0 and 10.0, respectively. Curves of the Appl. Sci. 2020, 10, 4274 9 of 17 296 four basic membership functions in equation (2) are drawn in Figure 4.

SI SII (τ1=2.5)

SII (τ1=3.5)

SII (τ1=5.0) SII (τ1=10.0) SII (τ1=18.0) (2.0,0.5) (15.8,0.5) SIII (τ2=1.0) SIII (τ2=1.7)

SIII (τ2 =3.5) Basic membership SIII (τ2=6.0)

SIII (τ2=10.0) Sun

Quantity ratio x

Figure 4. Basic membership functions with the change of parameters τ1 and τ2. 297 Figure 4. Basic membership functions with the change of parameters τ1 and τ2.

As is shown in Figure4, the relatively low x produces the higher membership of SII compared 298 As is shown in Figure 4, the relatively low x produces the higher membership of SII compared with memberships of SI, SIII, and Sun, while the relatively large x generates the bigger A(SIII) compared 299 with memberships of SI, SIII, and Sun, while the relatively large x generates the bigger A(SIII) with other three memberships. With the increase of x, A(SII) falls rapidly to 0, while A(SIII) climbs 300 compared with other three memberships. With the increase of x, A(SII) falls rapidly to 0, while A(SIII) lately to 1. As x increases, A(SI) goes up to 1 fast and then goes down, while A(Sun) rises slowly to 301 climbs lately to 1. As x increases, A(SI) goes up to 1 fast and then goes down, while A(Sun) rises 1 and then descends. A(SII), or A(SI), or A(Sun), or A(SIII) predominates within a certain range of x. 302 slowly to 1 and then descends. A(SII), or A(SI), or A(Sun), or A(SIII) predominates within a certain Furthermore, the larger the values of τ1 and τ2, the bigger the gradients of A(SII) and A(SIII), and the 303 range of x. Furthermore, the larger the values of τ1 and τ2, the bigger the gradients of A(SII) and smaller the uncertainties of fuzzy sets SII and SIII. When τ1 and τ2 exceed 10.0 and 6.0, respectively, 304 A(theSIII), two and fuzzy the smaller sets almost the uncertainties convert to the of fuzzy non-fuzzy sets S setsII and with SIII. the When threshold τ1 and ofτ2 xexceedvalues 10.0 being and 2.0 6.0, and 305 respectively, the two fuzzy sets almost convert to the non-fuzzy sets with the threshold of x values 15.8. In this model, 3.5 and 1.7 are set to be the values of τ1 and τ2. Figure5 describes the trends of the 306 beingnormalized 2.0 and 15.8. membership In this model, functions 3.5 inand Equation 1.7 are set (4) to with be thethe parametersvalues of τ1 determined and τ2. Figure above. 5 describes As can be 307 the trends of the normalized membership functions in equation (4) with the parameters determined Appl.seen, Sci. 2020SII ,is 10 predominant, x FOR PEER REVIEW when x is below 2.01, SI and Sun play decisive role when 2.01 < x <107.45 of 18 and 308 above. As can be seen, SII is predominant when x is below 2.01, SI and Sun play decisive role when 7.45 < x < 15.45, respectively, and it is most probable of x values belonging to SIII when x is above 15.45. 309 2.01 < x < 7.45 and 7.45 < x < 15.45, respectively, and it is most probable of x values belonging to SIII 310 when x is above 15.45. SI

SII

SIII (2.01,0.5) (7.45,0.5) (15.45,0.5) Sun Normalized membership Normalized

Quantity ratio x

Figure 5. Normalized membership functions with the determined parameters. 311 Figure 5. Normalized membership functions with the determined parameters. 4. Results and Discussion 312 4. Results and Discussion 4.1. Variation of Membership of Different Stage 313 4.1. Variation of Membership of Different Stage To prove the accuracy of the membership-fusing model, characterized by Equations (2), (4) and (5) 314 withTo theprove determined the accuracy parameters, of the membership-fusing a group of 18 sludge model, samples characterized collected in by the equation first day (2), in September,(4) and 315 (5) 2019with was the chosendetermined to measure parameters, the mcrA a group gene sequencesof 18 sludge to verify samples whether collected the sequencing in the first data day satisfy in 316 September,the membership 2019 was functions. chosen to Figure measure6a exhibitsthe mcrA the gene distribution sequences of to the verify relative whether abundance the sequencing of di fferent 317 datagenera satisfy methanogens the membership from functions. all samples Figure of the 6(a) three exhibits stages, the from distribution which the of the value relative of quantity abundance ratio of 318 of Methanosaetadifferent generato Methanobacterium methanogens fromcould all besample obtaineds of accordingthe three stages, to Equation from (1).which The the six value paralleling of 319 quantityx values ratio of of stage Methanosaeta I were calculated to Methanobacterium to be 7.15, 7.09, could 7.01, be 7.26,obtained 7.08 according and 6.98, betweento equation 2.01 (1). and The 7.45, 320 sixwithin paralleling the range x values of x whereof stage the I membershipwere calculated function to be of 7.15,SI predominates. 7.09, 7.01, 7.26, This 7.08 result and demonstrates6.98, between the 321 2.01processing and 7.45, stagewithin a ffitheliation range of of the x where tested parallelingthe membership samples function being of Stage SI predominates. I, which in turn This reveals result the 322 demonstratesapplicability the of processingB(SI) and A stage(SI). Theaffiliation six paralleling of the testedx values paralleling obtained samples from samples being Stage of Stage I, which II are in 1.63, 323 turn1.58, reveals 1.62, the 1.57, applicability 1.71 and 1.69, of B ranging(SI) and A from(SI). 0The to 2.01,six paralleling indicating x thesevalues samples obtained are from most samples likely fromof 324 Stage II are 1.63, 1.58, 1.62, 1.57, 1.71 and 1.69, ranging from 0 to 2.01, indicating these samples are 325 most likely from Stage II and the feasibility of B(SII) and A(SII). The six paralleling x values of Stage 326 III are 15.69, 15.61, 15.73, 15.72, 15.70 and 15.65, all above 15.45, reflecting these samples most 327 probably belong to Stage III and the fitness of B(SIII) and A(SIII). All x values generated from the 18 328 sludge samples distribute outside the range, from 7.45 to 15.45, showing the rationality of B(Sun) and 329 A(Sun). These three results indicate the accuracy of the membership functions was verified in the 330 aspect of the rational distribution of x values and the unique methanogen structure of each 331 processing stage could also be properly distinguished by the model. 332 For each processing stage, the four integrated memberships generated from the six paralleling 333 samples are shown in Figure 6(b), from which the judgment on the stage affiliation of a group of 334 paralleling sludge samples could be made. The determined stage could then be checked to test if it 335 corresponds to the stage where this group of paralleling samples were collected. For Stage I, the 336 integrated memberships of SI, SII, SIII, and Sun are 0.99, 0.00, 0.00 and 0.01, respectively, whose total 337 value is 1.00 and C(SI) is the maximum. This consequence confirms that this group of paralleling 338 samples most likely belong to Stage I, in consistent with the stage where the six paralleling samples 339 were collected. The 99% possibility of this group of paralleling samples collected from Stage I reveals 340 the vague boundary of the methanogen community structure owing to the relatively steady change 341 of the inlet quality and running operation condition of different sampling time. The integrated 342 memberships of SI, SII, SIII, and Sun for Stage II are 0.02, 0.98, 0.00 and 0.00, whose sum is 1.00 and 343 C(SII) is the largest. This result indicates that the judgment on the processing stage affiliation of these 344 six paralleling sludge samples being Stage II, corresponding with where these samples were 345 gathered. The possibility of 98% belonging to Stage II rather than 100% uncovers the relatively small 346 fluctuation of the wastewater quality treated by thermal hydrolysis of different sampling time. The 347 2% possibility being Stage I elucidates the higher similarity of the methanogen community 348 structure between Stage I and II compared with that between Stage II and III, or Stage I and III. The Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 18

349 same phenomenon is also illustrated in Figure 6(a). The integrated memberships generated from 350 paralleling samples of Stage III are 0.00, 0.00, 0.99 and 0.01 for SI, SII, SIII, and Sun, whose total value is 351 1.00 and C(SIII) is the biggest. It could be made a conclusion that the model could make a correct 352 judgment on the processing stage affiliation of this group of paralleling samples being Stage III, and 353 there is a little fluctuation of the wastewater quality in the anerobic digestor of different sampling 354 Appl.time. Sci. In2020 general,, 10, 4274 the four integrated memberships generated from any group of paralleling samples10 of 17 355 aggregate to 1, paralleling samples from one stage could generate the corresponding largest C(S) 356 representing the same stage. Therefore, the membership functions could make an accurate 357 Stagejudgment II and on the the feasibility processing of B stage(SII) and affiliationA(SII). Theof the six examined paralleling parallelingx values of sludge Stage IIIsamples, are 15.69, and 15.61, the 358 15.73,vagueness 15.72, and 15.70 uniqueness and 15.65, of all the above methanogen 15.45, reflecting community these structure samples mostof one probably processing belong stage to Stagecould 359 IIIbe andcharacterized the fitness ofproperlyB(SIII) and by Athe(SIII model.). All x valuesBy analyzing generated both from the the x18 values sludge and samples the integrated distribute 360 outsidememberships the range, of fromthe paralleling 7.45 to 15.45, samples showing belonging the rationality to the of Bthree(Sun) andstages,A(S unthe). Theserationality three resultsof the 361 indicatemembership the accuracy function of format, the membership the statistical functions meth wasod to verified determine in the parameters, aspect of the and rational the methodology distribution 362 ofto xprocessvalues andparalleling the unique data methanogen are all proved, structure which of each in processing turn verifies stage couldthe accuracy also be properly of the 363 distinguishedmembership-fusing by the model. model.

others Methanosphaera Methanoculleus Aaa Methanothermobacter Methanosarcina Methanobrevibacter Methanospirillum Methanolinea Methanosaeta Methanosphaerula Methanofollis Methanobacterium ) S ( C

C(SI)

C(SII)

C(SIII)

C(Sun) Integrated membershipIntegrated Genera relative abundance (100%) Genera relative abundance

Processing stage Samples from different processing stages Aaa

(a) (b)

Figure 6. Variation of x values and integrated memberships of different sludge-processing stages: (a) 364 Figure 6. Variation of x values and integrated memberships of different sludge-processing stages: (a) Relative abundance of different genera of methanogens (letters a to f represent the six paralleling sludge 365 Relative abundance of different genera of methanogens (letters a to f represent the six paralleling samples from one stage, roman numerals I, II, and III represent Stage I, Stage II and Stage III of the 366 sludge samples from one stage, roman numerals I, II, and III represent Stage I, Stage II and Stage III three-stage sludge-treatment process); (b) Integrated memberships of different processing stages. (Stage 367 of the three-stage sludge-treatment process); (b) Integrated memberships of different processing I stands for the state of sludge samples after treated by centrifugal thickening and pre-dewatering, 368 stages. (Stage I stands for the state of sludge samples after treated by centrifugal thickening and Stage II stands for the state of sludge samples after treated by thermal hydrolysis, Stage III stands for 369 pre-dewatering, Stage II stands for the state of sludge samples after treated by thermal hydrolysis, the state of sludge samples after experiencing anaerobic digestion, and stage uncertain stands for the 370 Stage III stands for the state of sludge samples after experiencing anaerobic digestion, and stage uncertainty of the processing stage affiliation of a sludge sample.) 371 uncertain stands for the uncertainty of the processing stage affiliation of a sludge sample.) For each processing stage, the four integrated memberships generated from the six paralleling 372 samples4.2. Variation are shownof Membership in Figure with6b, Different from which Number the of judgment Interference on Data the stage a ffiliation of a group of 373 parallelingThe existence sludge samplesof sample could contamination be made. The and determined incidental and stage instrumental could then bedata checked errors toresulted test if 374 itfrom corresponds data measurement to the stage and where analysis this groupis inevitable, of paralleling therefore, samples the x werevalue collected. of Sun from For which Stage could I, the 375 integratednot make a memberships determinate judgment of SI, SII, SonIII ,the and processing Sun are 0.99, stage 0.00, among 0.00 andthe three 0.01, respectively,stages most likely whose exists. total 376 valueThis type is 1.00 of x and value,C(S knownI) is the as maximum. the interference This consequencedata, would impair confirms the that reliability this group of the of model paralleling when 377 samplesdeciding most the specific likely belong sludge-processing to Stage I, in consistentstage. DS withevidence the stage theory where is introduced the six paralleling to address samples such 378 wereproblem collected. of data The impreciseness 99% possibility and of conflict this group among of paralleling paralleling samples data. To collected verify fromthe performance Stage I reveals of 379 thethe vaguemodel boundaryin dealing of with the different methanogen numbers community of interference structure data, owing a group to the of relatively interference steady data change with 380 ofthe the number inlet qualitybelow the and number running of operationthe total parallelin conditiong data of di wasfferent introduced sampling to time.one processing The integrated stage. 381 membershipsEighteen x values, of SI, theSII, SsameIII, and withSun thatfor in Stage Section II are 4.1, 0.02, were 0.98, chosen 0.00 and to be 0.00, the whose non-interference sum is 1.00 data and C(SII) is the largest. This result indicates that the judgment on the processing stage affiliation of these six paralleling sludge samples being Stage II, corresponding with where these samples were gathered. The possibility of 98% belonging to Stage II rather than 100% uncovers the relatively small fluctuation of the wastewater quality treated by thermal hydrolysis of different sampling time. The 2% possibility being Stage I elucidates the higher similarity of the methanogen community structure between Stage I and II compared with that between Stage II and III, or Stage I and III. The same phenomenon is Appl. Sci. 2020, 10, 4274 11 of 17 also illustrated in Figure6a. The integrated memberships generated from paralleling samples of Stage III are 0.00, 0.00, 0.99 and 0.01 for SI, SII, SIII, and Sun, whose total value is 1.00 and C(SIII) is the biggest. It could be made a conclusion that the model could make a correct judgment on the processing stage affiliation of this group of paralleling samples being Stage III, and there is a little fluctuation of the wastewater quality in the anerobic digestor of different sampling time. In general, the four integrated memberships generated from any group of paralleling samples aggregate to 1, paralleling samples from one stage could generate the corresponding largest C(S) representing the same stage. Therefore, the membership functions could make an accurate judgment on the processing stage affiliation of the examined paralleling sludge samples, and the vagueness and uniqueness of the methanogen community structure of one processing stage could be characterized properly by the model. By analyzing both the x values and the integrated memberships of the paralleling samples belonging to the three stages, the rationality of the membership function format, the statistical method to determine parameters, and the methodology to process paralleling data are all proved, which in turn verifies the accuracy of the membership-fusing model.

4.2. Variation of Membership with Different Number of Interference Data The existence of sample contamination and incidental and instrumental data errors resulted from data measurement and analysis is inevitable, therefore, the x value of Sun from which could not make a determinate judgment on the processing stage among the three stages most likely exists. This type of x value, known as the interference data, would impair the reliability of the model when deciding the specific sludge-processing stage. DS evidence theory is introduced to address such problem of data impreciseness and conflict among paralleling data. To verify the performance of the model in dealing with different numbers of interference data, a group of interference data with the number below the number of the total paralleling data was introduced to one processing stage. Eighteen x values, the same with that in Section 4.1, were chosen to be the non-interference data group. The interference data group was generated through computer random selection. For Stage I, the interference data were generated from x values obtained from paralleling sludge samples of Stage I collected from 2014 to 2018. The specific values were determined by computer randomly selecting five x values whose maximal normalized memberships were B(Sun), which could not indicate a determinate processing stage among the three stages. One interference data was brought to the six paralleling non-interference data each time, five interference data were brought in in total and the number of the total paralleling data was maintained to be six. The same operation was conducted to the other two groups x values belonging to Stage II and III, respectively. For one stage, five interference data were generated, and one data was introduced one time. The non-interference data together with the five groups x values generated by introducing one to five interference data in turn for Stage I are shown in Figure7a. All interference data are distributed in Sun. The corresponding integrated memberships of each fuzzy set calculated from these six groups of data are exhibited in Figure7b. C(SI) are 0.99, 0.98, 0.97, 0.93, 0.85 and 0.65, and C(Sun) are 0.01, 0.02, 0.03, 0.07, 0.15 and 0.35 with the increasing number of interference data. C(SII) and C(SIII) are in a negligible range of change approximately around 0. As is shown in Figure7b, as the number of interference data increases, the integrated membership of SI goes down and that of Sun goes up, and C(SI) is the largest among the six groups. This consequence indicates that with the increasing number of interference data, the probability of this group of paralleling sludge samples belonging to Stage I declines, the uncertainty of which stage these paralleling samples are from rises, which reveals that the credibility of the five data groups with interference data descends and sample contamination and faults occurring in data measurement and analysis might appear. Furthermore, interfering x values with the number below the total paralleling data could not change the maximal integrated memberships being C(SI). In other words, the interference data could not play a decisive role in determining the stage affiliation of a group of paralleling samples, but could weaken the belief degree on the judgment on the processing stage affiliation being stage I. When only one non-interference data left for Stage I, C(SI), Appl. Sci. 2020, 10, 4274 12 of 17

C(SII), C(SIII) and C(Sun) are 0.65, 0.00, 0.00 and 0.35, close to 0.60, 0.00, 0.00 and 0.40, values of B(SI), B(SII), B(SIII) and B(Sun) when x value is 6.98, the last non-interfering x in this data group. This result reflects that the calculation of integrated memberships would depend more on x values of SI than x values of Sun, indicating the stage affiliation judgment would more rely on the valid information rather than the uncertain one. Condition (6) explains this situation. When intersecting with any other fuzzy set, Sun does not work, so that the influence brought by the interference information would be eliminated, and the interference data could be reasonably fused to make a reliable stage affiliation judgment. It could be concluded that the smaller the number of interference data belonging to SI, the higher the integrated membership of SI, the more credible this group of data, and the more reliable the judgment on the processing stage affiliation being stage I. When x values belonging to Sun appear, the determination of the processing stage would be more dependent on valid x values belonging to SI than invalid x values pertaining to Sun. Consequently, the model could authentically reflect the appearance of imprecise and conflict data, fusing all the information reasonably and make a reasonable judgment on the processing stage affiliation for stage I. The reliability of the model in addressing Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 18 different numbers of interference data is guaranteed.

Aaa non-interference data interference data

C(SI)

C(SII) )

S C(SIII) ( C x C(Sun) Quantity ratio Integrated membership

Number of interference data of stage I 0 1 2 3 4 5 Aaa

(a) (b)

423 FigureFigure 7.7.Performance Performance of of the the model model fusing fusing different different numbers numbers of interference of interference data of Stagedata of I: (aStage) Quantity I: (a) 424 ratiosQuantity of Methanosaeta ratios of Methanosaetato Methanobacterium to Methanobacteriumof Stage I withof Stage diff erentI with numbers different ofnumbers interference of interference data (For 425 thedata x-coordinate, (For the x-coordinate, letters a to fletters represent a to the f represen six parallelingt the six data, paralleling numbers data, 0 to 5numbers represent 0 theto 5 number represent of 426 interferencethe number data.)of interference (b) Integrated data.) memberships (b) Integrated of memberships Stage I with di offf erentStage numbers I with different of interference numbers data. of (Stage I stands for the state of sludge samples after treated by centrifugal thickening and pre-dewatering, 427 interference data. (Stage I stands for the state of sludge samples after treated by centrifugal Stage II stands for the state of sludge samples after treated by thermal hydrolysis, Stage III stands for 428 thickening and pre-dewatering, Stage II stands for the state of sludge samples after treated by the state of sludge samples after experiencing anaerobic digestion, and stage uncertain stands for the 429 thermal hydrolysis, Stage III stands for the state of sludge samples after experiencing anaerobic uncertainty of the processing stage affiliation of a sludge sample.) 430 digestion, and stage uncertain stands for the uncertainty of the processing stage affiliation of a 431 sludge sample.) The five groups of quantity ratios of Methanosaeta to Methanobacterium by introducing one to five interference data together with the non-interference quantity ratios for Stage II and III are shown in 432 The five groups of quantity ratios of Methanosaeta to Methanobacterium by introducing one to Figures8a and9a, and the corresponding integrated memberships of the four fuzzy sets are exhibited 433 five interference data together with the non-interference quantity ratios for Stage II and III are in Figures8b and9b. All the interfering x values belong to S . For Stage II, C(S ) descends, C(S ) 434 shown in Figure 8(a) and Figure 9(a), and the correspondingun integrated membershipsII of the fourun rises and C(SII) is the largest as the number of the interfering x increases, in consistent with the shifts of 435 fuzzy sets are exhibited in Figure 8(b) and Figure 9(b). All the interfering x values belong to Sun. For C(SI) and C(Sun) of Stage I. Owing to the initial value of C(Sun) obtained from the non-interference data 436 Stage II, C(SII) descends, C(Sun) rises and C(SII) is the largest as the number of the interfering x group of Stage II being too small, the increase of C(Sun) does not appear such apparently, but is still in 437 increases, in consistent with the shifts of C(SI) and C(Sun) of Stage I. Owing to the initial value of an order of magnitude of growth. The range of the fluctuation of C(SIII) is negligible, corresponding to 438 C(Sun) obtained from the non-interference data group of Stage II being too small, the increase of that of Stage I. The apparent increase of C(SI) could be attributed to the relatively high initial value 439 C(Sun) does not appear such apparently, but is still in an order of magnitude of growth. The range of of C(SI), but is still below C(SII). For Stage III, C(SIII) declines, C(Sun) raises up and C(SIII) is the 440 the fluctuation of C(SIII) is negligible, corresponding to that of Stage I. The apparent increase of C(SI) 441 could be attributed to the relatively high initial value of C(SI), but is still below C(SII). For Stage III, 442 C(SIII) declines, C(Sun) raises up and C(SIII) is the maximal as the number of interference data 443 increases, which is the same with the trends of C(SI) and C(Sun) of Stage I. C(SII) and C(SI) are in a 444 relatively small range of change around 0, the same shifts as C(SII) and C(SIII) of Stage I. For the data 445 group with five interfering x values of Stage II or III, the integrated memberships generated are 446 close to the normalized memberships obtained from the last non-interfering x value in this data 447 group of Stage II or III, being 1.69 or 15.65. For Stage II and III, the results demonstrate that the more 448 the data belonging either to SII or SIII, the more reliable the stage affiliation judgment could be made. 449 The increasing number of interference data could only weaken the belief degree on the processing 450 stage affiliation judgment, but could not change the stage affiliation being Stage II or III. It could be 451 drawn the conclusion that a reliable judgment on the processing stage affiliation could be made for 452 Stage II or III by the model when conflict and imprecise data exist. The more similar methanogen 453 community structure between Stage I and II than that between Stage I and III, or Stage II and III 454 could also be reflected by the model as C(SI) values change apparently. Analyzing the results of the 455 three stages, it could come to conclusion that the bigger the number of data from one fuzzy set, in 456 other words, supporting each other, the more credible this group of data, and the more reliable the 457 judgment on the processing stage affiliation. When several interference x values of Sun appear, the Appl. Sci. 2020, 10, 4274 13 of 17

maximal as the number of interference data increases, which is the same with the trends of C(SI) and C(Sun) of Stage I. C(SII) and C(SI) are in a relatively small range of change around 0, the same shifts as C(SII) and C(SIII) of Stage I. For the data group with five interfering x values of Stage II or III, the integrated memberships generated are close to the normalized memberships obtained from the last non-interfering x value in this data group of Stage II or III, being 1.69 or 15.65. For Stage II and III, the results demonstrate that the more the data belonging either to SII or SIII, the more reliable the stage affiliation judgment could be made. The increasing number of interference data could only weaken the belief degree on the processing stage affiliation judgment, but could not change the stage affiliation being Stage II or III. It could be drawn the conclusion that a reliable judgment on the processing stage affiliation could be made for Stage II or III by the model when conflict and imprecise data exist. The more similar methanogen community structure between Stage I and II than that between Stage I and III, or Stage II and III could also be reflected by the model as C(SI) values change apparently. Analyzing the results of the three stages, it could come to conclusion that the bigger the number of data from one fuzzy set, in other words, supporting each other, the more credible this group of data, and the more Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 18 reliable the judgment on the processing stage affiliation. When several interference x values of Sun 458 determinationappear, the determination tends to rely tends more to on rely the more x values on the belongingx values to belonging fuzzy sets to representing fuzzy sets representing a valid stage a 459 amongvalid stage the three among stages the threethan stagesthat to thanSun. In that other to Swords,un. In otherthe appearance words, the of appearance interfering ofx values interfering couldx 460 notvalues change could the not affiliation change the of atheffiliation processing of the stage processing of the stagetested of paralleling the tested parallelingsludge samples, sludge but samples, could 461 increasebut could the increase uncertainty the uncertainty of the judgment. of the judgment. In hence, In the hence, model the could model reflect could the reflect credibility the credibility of a group of a 462 ofgroup measured of measured data, data,and advisably and advisably deal dealwith with the theinterference interference data data to todetermine determine the the most most probable probable 463 processing stagestage wherewhere this this data data group group come come from from and and how how likely likely are theseare these data data to belong to belong to this to stage. this 464 stage.The reliability The reliability of the modelof the model in addressing in addressi datang impreciseness data impreciseness and conflict and conflict are proved. are proved.

Aaa non-interference data interference data

C(SI)

C(SII) ) x S

( C(SIII) C C(Sun) Quantity ratio Integrated membership

Number of interference data of stage II 0 1 2 3 4 5 Aaa

(a) (b)

Figure 8. Performance of the model fusing different numbers of interference data of Stage II: (a) 465 Figure 8. Performance of the model fusing different numbers of interference data of Stage II: (a) Quantity ratios of Methanosaeta to Methanobacterium of Stage II with different numbers of interference 466 Quantity ratios of Methanosaeta to Methanobacterium of Stage II with different numbers of data (For the x-coordinate, letters a to f represent the six paralleling data, numbers 0 to 5 represent 467 interference data (For the x-coordinate, letters a to f represent the six paralleling data, numbers 0 to 5 the number of interference data.) (b) Integrated memberships of Stage II with different numbers of 468 represent the number of interference data.) (b) Integrated memberships of Stage II with different interference data. (Stage I stands for the state of sludge samples after treated by centrifugal thickening 469 numbers of interference data. (Stage I stands for the state of sludge samples after treated by and pre-dewatering, Stage II stands for the state of sludge samples after treated by thermal hydrolysis, 470 centrifugal thickening and pre-dewatering, Stage II stands for the state of sludge samples after Stage III stands for the state of sludge samples after experiencing anaerobic digestion, and stage 471 treated by thermal hydrolysis, Stage III stands for the state of sludge samples after experiencing uncertain stands for the uncertainty of the processing stage affiliation of a sludge sample.) 472 anaerobic digestion, and stage uncertain stands for the uncertainty of the processing stage affiliation 473 of a sludge sample.)

Aaa non-interference data interference data

C(SI)

C(SII)

) C(SIII) x S (

C C(Sun) Quantity ratio Integrated membership

Number of interference data of stage III 0 1 2 3 4 5 Aaa

(a) (b) Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 18

458 determination tends to rely more on the x values belonging to fuzzy sets representing a valid stage 459 among the three stages than that to Sun. In other words, the appearance of interfering x values could 460 not change the affiliation of the processing stage of the tested paralleling sludge samples, but could 461 increase the uncertainty of the judgment. In hence, the model could reflect the credibility of a group 462 of measured data, and advisably deal with the interference data to determine the most probable 463 processing stage where this data group come from and how likely are these data to belong to this 464 stage. The reliability of the model in addressing data impreciseness and conflict are proved.

Aaa non-interference data interference data

C(SI)

C(SII) ) x S

( C(SIII) C C(Sun) Quantity ratio Integrated membership

Number of interference data of stage II 0 1 2 3 4 5 Aaa

(a) (b)

465 Figure 8. Performance of the model fusing different numbers of interference data of Stage II: (a) 466 Quantity ratios of Methanosaeta to Methanobacterium of Stage II with different numbers of 467 interference data (For the x-coordinate, letters a to f represent the six paralleling data, numbers 0 to 5 468 represent the number of interference data.) (b) Integrated memberships of Stage II with different 469 numbers of interference data. (Stage I stands for the state of sludge samples after treated by 470 centrifugal thickening and pre-dewatering, Stage II stands for the state of sludge samples after 471 treated by thermal hydrolysis, Stage III stands for the state of sludge samples after experiencing 472 anaerobic digestion, and stage uncertain stands for the uncertainty of the processing stage affiliation 473 Appl.of Sci. a 2020sludge, 10, sample.) 4274 14 of 17

Aaa non-interference data interference data

C(SI)

C(SII)

) C(SIII) x S (

C C(Sun) Quantity ratio Integrated membership

Number of interference data of stage III 0 1 2 3 4 5 Aaa

(a) (b)

Figure 9. Performance of the model fusing different numbers of interference data of Stage III: (a) Quantity ratios of Methanosaeta to Methanobacterium of Stage III with different numbers of interference data (For the x-coordinate, letters a to f represent the six paralleling data, numbers 0 to 5 represent the number of interference data.) (b) Integrated memberships of Stage III with different numbers of interference data. (Stage I stands for the state of sludge samples after treated by centrifugal thickening and pre-dewatering, Stage II stands for the state of sludge samples after treated by thermal hydrolysis, Stage III stands for the state of sludge samples after experiencing anaerobic digestion, and stage uncertain stands for the uncertainty of the processing stage affiliation of a sludge sample.)

5. Conclusions The membership-fusing model is built in this paper to properly characterize the shift of methanogen community in the three-stage sludge-treatment process, and reasonably make judgment on the processing stage affiliation of a tested group of paralleling samples. First, the three-stage sludge-treatment process is abstracted, and the representative genera of methanogens are selected to quantify the methanogen community variation. Then, fuzzy sets and DS evidence theory is applied to clarify the stage affiliation of a sludge sample and address data error generated among paralleling data. Finally, the accuracy and reliability of the model are both proved. The accuracy of the model is verified by a group of new data. The experiment shows that the membership-fusing model could properly reflect the vagueness of the methanogen community structure of one processing stage and its uniqueness among the three stages by analyzing the correctness of both values of quantity ratios of Methanosaeta to Methanobacterium and the maximal integrated memberships of each stage. The reliability of the model in dealing with imprecise and conflict data among paralleling data is proved by introducing different numbers of interference data to each stage. The experiment demonstrates that the model could make more reliable judgment on the processing stage affiliation when more data supporting each other exist. The model could also reflect the occurrence of interference data clearly, fuse the influence brought by these data reasonably and make a reliable judgment on the processing stage affiliation of a group of paralleling samples. In hence, an accurate and reliable information regarding the effect of the sludge treatment could be provided to workers in Beijing Gaobeidian Wastewater Treatment Plant by quantifying any group of the shift of methanogen community of examined paralleling sludge samples, which could facilitate them to control the sludge-treatment process and realize sludge reduction, stabilization, and harmlessness.

Author Contributions: Conceptualization, L.C.; methodology, L.C. and H.L.; software, L.C. and H.L.; validation, L.C.; formal analysis, L.C. and H.L.; investigation, L.C.; resources, H.Y.; data curation, L.C.; writing—original draft preparation, L.C.; writing—review and editing, H.Y.; visualization, L.C.; supervision, H.Y.; project administration, H.Y. All authors have read and agreed to the published version of the manuscript. Appl. Sci. 2020, 10, 4274 15 of 17

Funding: This research was funded by Beijing University Outstanding Young Scientist Program, grant number BJJWZYJH01201910004016, and National Natural Science Foundation of China, grant number 51908029. Conflicts of Interest: The authors declare no conflict of interest.

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