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A chaotic investigation on pollutant parameters of a wastewater treatment facility using false nearest neighbour algorithm

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Abstract

Investigation of the behaviour and complexity of hard-to-measure parameter time series is not explored to a greater extent before modelling a wastewater treatment facility (WWTF). In this context, A dynamic non-linear chaotic approach, namely the False nearest neighbour (FNN) algorithm, is employed for the first time to investigate the influent and effluent quality parameters of a WWTF. The primary objective of this research is to analyze the parameters of a WWTF located in India for its behaviour and complexity using the FNN algorithm. The autocorrelation function and average mutual information time lags are used as the delay time (τ) in the algorithm for phase space reconstruction and further FNN analysis. The optimum embedding dimensions (mopt) from FNN plots indicate the complexity or number of optimum variables required to model the time series. For influent and effluent parameters, the mopt values fall within a range of 4–15 and 4–17, respectively, and the τ value influences this range. Wastewater time series behaviour differs, such as pure stochastic or chaotic or chaotic series with noise, which is highly dependent on τ. The future scope of the study involves integrating the retrieved behaviour and complexity into state-of-the-art artificial intelligence or data-driven techniques to forecast hard-to-measure parameters.

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References

  • Aayog NITI (2022) Urban wastewater scenario in India. National institution for transforming India. Government of India Publication, New Delhi

    Google Scholar 

  • Alavi J, Ewees AA, Ansari S, Shahid S, Yaseen ZM (2022) A new insight for real-time wastewater quality prediction using hybridized kernel-based extreme learning machines with advanced optimization algorithms. Environ Sci Pollut Res 29(14):20496–20516

    Article  CAS  Google Scholar 

  • Alharbi M, Hong PY, Laleg-Kirati TM (2022) Sliding window neural network based sensing of bacteria in wastewater treatment plants. J Process Control 110:35–44

    Article  CAS  Google Scholar 

  • Andreides M, Dolejš P, Bartáček J (2022) The prediction of WWTP influent characteristics: good practices and challenges. J Water Process Eng Eng 49:103009

    Article  Google Scholar 

  • APHA (2005) Standard methods for the examination of water and wastewater, 21st edn. American Public Health Association, Washington

    Google Scholar 

  • Bărbulescu A, Barbeş L (2021) Statistical methods for assessing water quality after treatment on a sequencing batch reactor. Sci Total Environ 752:141991

    Article  Google Scholar 

  • Benmebarek S, Chettih M (2023) Chaotic analysis of daily runoff time series using dynamic, metric, and topological approaches. Acta Geophys 18:1–19

    Google Scholar 

  • CPCB (2021) National inventory of sewage treatment plants. Central pollution control board. Government of India Publication, Delhi

    Google Scholar 

  • Das VK, Singh SK, Sivakumar B, Debnath K (2023) Testing the complexity and chaotic nature of wave-dominated turbulent flows. Ocean Eng 285:115326

    Article  Google Scholar 

  • Datta P, Das S (2019) Analysis of long-term precipitation changes in West Bengal, India: an approach to detect monotonic trends influenced by autocorrelations. Dyn Atmo Oceans 88:101118

    Article  Google Scholar 

  • Delafrouz H, Ghaheri A, Ghorbani MA (2018) A novel hybrid neural network based on phase space reconstruction technique for daily river flow prediction. Soft Comput 22(7):2205–2215

    Article  Google Scholar 

  • Dhanya CT, Nagesh Kumar D (2010) Non-linear ensemble prediction of chaotic daily rainfall. Adv Water Resour 33(3):327–347

    Article  Google Scholar 

  • Do P, Chow CWK, Rameezdeen R, Gorjian N (2022) Wastewater inflow time series forecasting at low temporal resolution using SARIMA model: a case study in South Australia. Environ Sci Pollut Res 29(47):70984–70999

    Article  Google Scholar 

  • Ebrahimi M, Gerber EL, Rockaway TD (2017) Temporal performance assessment of wastewater treatment plants by using multivariate statistical analysis. J Environ Manage 193:234–246

    Article  CAS  Google Scholar 

  • El-Rawy M, Abd-Ellah MK, Fathi H, Ahmed AKA (2021) Forecasting effluent and performance of wastewater treatment plant using different machine learning techniques. J Water Process Eng 44:102380

    Article  Google Scholar 

  • Fathima TA, Jothiprakash V (2014) Behavioural analysis of a time series: a chaotic approach. Sadhana: Acad Proc Eng Sci 39(3):659–676

    Article  Google Scholar 

  • Ghorbani MA, Khatibi R, Danandeh MA, Asadi H (2018) Chaos-based multigene genetic programming: a new hybrid strategy for river flow forecasting. J Hydrol 562:455–467

    Article  Google Scholar 

  • Godini K, Azarian G, Kimiaei A, Niculina E, Curteanu S (2021) Modeling of a real industrial wastewater treatment plant based on aerated lagoon using a neuro-evolutive technique. Process Saf Environ Prot 148:114–124

    Article  CAS  Google Scholar 

  • Golabi MR, Farzi S, Khodabakhshi F, Sohrabi Geshnigani F, Nazdane F, Radmanesh F (2020) Biochemical oxygen demand prediction: development of hybrid wavelet-random forest and M5 model tree approach using feature selection algorithms. Environ Sci Pollut Res 27(27):34322–34336

    Article  CAS  Google Scholar 

  • Goswami B (2019) A brief introduction to nonlinear time series analysis and recurrence plots. Vibration 2(4):332–368

    Article  Google Scholar 

  • Henze M, Gujer W, Mino T, van Loosedrecht M (2006) Activated sludge models ASM1, ASM2, ASM2d and ASM3. IWA Publishing, ISBN electronic: 9781780402369

  • Hosseinzadeh A, Zhou JL, Altaee A, Li D (2022) Machine learning modeling and analysis of biohydrogen production from wastewater by dark fermentation process. Biores Technol 343:126111

    Article  CAS  Google Scholar 

  • Hvala N, Kocijan J (2020) Design of a hybrid mechanistic/Gaussian process model to predict full-scale wastewater treatment plant effluent. Comput Chem Eng 140:106934

    Article  CAS  Google Scholar 

  • Kennel MB, Brown R, Abarbanel HDI (1992) Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev Appl 45(6):3403–3411

    CAS  Google Scholar 

  • Khatibi R, Sivakumar B, Ghorbani MA, Kisi O, Koçak K, Farsadi ZD (2012) Investigating chaos in river stage and discharge time series. J Hydrol 414:108–117

    Article  Google Scholar 

  • Kim HS, Yoon YN, Kim JH (2001) Searching for strange attractor in wastewater flow. Stoch Env Res Risk Assess 15(5):399–413

    Article  Google Scholar 

  • Kraskov A, Stögbauer H, Grassberger P (2004) Estimating mutual information. Phys Rev E 69(6):066138

    Article  Google Scholar 

  • Liu H, Zhang Y, Zhang H (2020) Prediction of effluent quality in papermaking wastewater treatment processes using dynamic kernel-based extreme learning machine. Process Biochem 97:72–79

    Article  CAS  Google Scholar 

  • Lotfi K, Bonakdari H, Ebtehaj I, Delatolla R, Zinatizadeh AA, Gharabaghi B (2020) A novel stochastic wastewater quality modeling based on fuzzy techniques. J Environ Health Sci Eng 18(2):1099–1120

    Article  Google Scholar 

  • Man Y, Hu Y, Ren J (2019) Forecasting COD load in municipal sewage based on ARMA and VAR algorithms. Resourc Conserv Recycl 144:56–64

    Article  Google Scholar 

  • Matheri AN, Ntuli F, Ngila JC, Seodigeng T, Zvinowanda C (2021) Performance prediction of trace metals and cod in wastewater treatment using artificial neural network. Comput Chem Eng 149:107308

    Article  CAS  Google Scholar 

  • Metcalf E (2014) Wastewater engineering: treatment & reuse, 5th edn. McGraw-Hill, Boston

    Google Scholar 

  • Mihailović DT, Malinović-Milićević S, Han J, Singh VP (2023) Complexity and chaotic behavior of the U.S. Rivers and estimation of their prediction horizon. J Hydrol 30:129730

    Article  Google Scholar 

  • Mihály NB, Simon-Várhelyi M, Cristea VM (2022) Data-driven modelling based on artificial neural networks for predicting energy and effluent quality indices and wastewater treatment plant optimization. Optim Eng 23(4):2235–2259

    Article  Google Scholar 

  • MoHUA (2021) Swachh survekshan 2021 report, World’s largest urban Sanitation survey. Ministry of Housing and Urban Affairs, New Delhi, India. https://www.mygov.in/mygov-survey/swachh-survekshan-2021/

  • Najafzadeh M, Zeinolabedini M (2019) Prognostication of waste water treatment plant performance using efficient soft computing models: an environmental evaluation. Measurement 138:690–701

    Article  Google Scholar 

  • Newhart KB, Holloway RW, Hering AS, Cath TY (2019) Data-driven performance analyses of wastewater treatment plants: a review. Water Res 157:498–513

    Article  CAS  Google Scholar 

  • Nguyen NP, Duong TA, Jan P (2023) Strategies of multi-step-ahead forecasting for chaotic time series using autoencoder and LSTM neural networks: a comparative study. IN: Proceedings of the 2023 5th international conference on image processing and machine vision, pp 55–61

  • NMMC (2019) Environmental Status report of navi Mumbai municipal corporation 2018/2019. Navi Mumbai Municipal Corporation, Navi Mumbai

    Google Scholar 

  • Nourani V, Asghari P, Sharghi E (2021) Artificial intelligence based ensemble modeling of wastewater treatment plant using jittered data. J Clean Prod 291:125772

    Article  CAS  Google Scholar 

  • Ombadi M, Nguyen P, Sorooshian S, Kl H (2021) Complexity of hydrologic basins: a chaotic dynamics perspective. J Hydrol 597:126222

    Article  Google Scholar 

  • Packard NH, Crutchfield JP, Farmer JD, Shaw RS (1980) Geometry from a time series. Phys Rev Lett 45(9):712–716

    Article  Google Scholar 

  • Qambar AS, Al KMM (2022) Prediction of municipal wastewater biochemical oxygen demand using machine learning techniques: a sustainable approach. Process Saf Environ Prot 168:833–845

    Article  CAS  Google Scholar 

  • Qiao J, Hu Z, Li W (2016) Soft measurement modeling based on chaos theory for biochemical oxygen demand (BOD). Water (Switzerland) 8(12):581

    CAS  Google Scholar 

  • Ramadevi B, Bingi K (2022) Chaotic time series forecasting approaches using machine learning techniques: a review. Symmetry 14(5):955

    Article  CAS  Google Scholar 

  • Ramdani S, Bouchara F, Casties JF (2007) Detecting determinism in short time series using a quantified averaged false nearest neighbors approach. Phys Rev E 76(3):036204

    Article  Google Scholar 

  • Ramkumar D, Jothiprakash V, Patil BN (2022) Performance assessment of sewage treatment plants using compliance index. J Water Sanit Hyg Dev 12(6):485–497

    Article  Google Scholar 

  • Ramkumar D, Jothiprakash V (2022) Simulating influent & effluent BOD of Wastewater treatment facility using hybrid time series modelling. In: Proceedings of IWA world water congress, Copenhagen

  • Rani S (2022) Evaluating the regional disparities in safe drinking water availability and accessibility in India. Environ Dev Sustain 24(4):4727–4750

    Article  Google Scholar 

  • Rolim LZR, de Souza Filho FDA (2023) Exploring spatiotemporal chaos in hydrological data: evidence from Ceará, Brazil. Stoch Environ Res Risk Assess 5:1–25

    Google Scholar 

  • Ruskeepää H, Ferreira LN, Ghorbani MA, Kahya E, Golmohammadi G, Karimi V (2023) Nonlinear and periodic dynamics of chaotic hydro-thermal process of Skokomish river. Stochast Environ Res Risk Assess 37:2739–2756

    Article  Google Scholar 

  • Sadri Moghaddam S, Mesghali H (2023) A new hybrid ensemble approach for the prediction of effluent total nitrogen from a full-scale wastewater treatment plant using a combined trickling filter-activated sludge system. Environ Sci Pollut Res 30(1):1622–1639

    Article  CAS  Google Scholar 

  • Scarciglia A, Catrambone V, Bonanno C, Valenza G (2022) A Multiscale partition-based kolmogorov-sinai entropy for the complexity assessment of heartbeat dynamics. Bioengineering 9(2):1–15

    Article  Google Scholar 

  • Sin G, Al R (2021) Activated sludge models at the crossroad of artificial intelligence: a perspective on advancing process modeling. Npj Clean Water 4(1):16

    Article  Google Scholar 

  • Sivakumar B (2016) Chaos in hydrology: bridging determinism and stochasticity. In: Chaos in hydrology: bridging determinism and stochasticity. Springer Netherlands

  • Srivalli CNS, Jothiprakash V, Sivakumar B (2019) Complexity of streamflows in the west-flowing rivers of India. Stochast Environ Res Risk Assess 33(3):837–853

    Article  Google Scholar 

  • Su Y, Yang C, Qiao J (2022) Effluent ammonia nitrogen prediction using a phase space reconstruction method combining pipelined recurrent wavelet neural network. Appl Soft Comput 120:108602

    Article  Google Scholar 

  • Takens F (1981) Detecting strange attractors in turbulence. In: Rand D, Young LS (eds) Dynamical systems and turbulence, Warwick 1980. Lecture notes in mathematics, vol 898. Springer, Berlin, Heidelberg, pp 366–381

    Chapter  Google Scholar 

  • Tan E, Algar S, Corrêa D, Small M, Stemler T, Walker D (2023) Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology. Chaos: Interdiscip J Nonlinear Sci 33(3):032101

    Article  Google Scholar 

  • Thoradeniya B, Pinto U, Maheshwari B (2019) Perspectives on impacts of water quality on agriculture and community well-being: a key informant study from Sri Lanka. Environ Sci Pollut Res 26(3):2047–2061

    Article  Google Scholar 

  • Verma A, Wei X, Kusiak A (2013) Predicting the total suspended solids in wastewater: a data-mining approach. Eng Appl Artif Intell 26(4):1366–1372

    Article  Google Scholar 

  • Vignesh R, Jothiprakash V, Sivakumar B (2019) Spatial rainfall variability in peninsular India: a non-linear dynamic approach. Stochast Environ Res Risk Assess 33(2):465–480

    Article  Google Scholar 

  • Wang X, Kvaal K, Ratnaweera H (2019) Explicit and interpretable non-linear soft sensor models for influent surveillance at a full-scale wastewater treatment plant. J Process Control 77:1–6

    Article  CAS  Google Scholar 

  • Wu J, Lu J, Wang J (2009) Application of chaos and fractal models to water quality time series prediction. Environ Model Softw 24(5):632–636

    Article  Google Scholar 

  • Wu J, Cheng H, Liu Y, Huang D, Yuan L, Yao L (2020) Learning soft sensors using time difference–based multi-kernel relevance vector machine with applications for quality-relevant monitoring in wastewater treatment. Environ Sci Pollut Res 27(23):28986–28999

    Article  Google Scholar 

  • Yan B, Chan PW, Li Q, He Y, Shu Z (2021) Dynamic analysis of meteorological time series in Hong Kong: a nonlinear perspective. Int J Climatol 41(10):4920–4932

    Article  Google Scholar 

  • Zarra T, Galang MGK, Oliva G, Belgiorno V (2022) Smart instrumental odour monitoring station for the efficient odour emission management and control in wastewater treatment plants. Chemosphere 309:136665

    Article  CAS  Google Scholar 

  • Zeleňáková M, Jothiprakash V, Arjun S, Káposztásová D, Hlavatá H (2018) Dynamic analysis of meteorological parameters in košice climatic station in Slovakia. Water 10(6):702

    Article  Google Scholar 

  • Zhang Q, Li Z, Snowling S, Siam A, El-Dakhakhni W (2019) Predictive models for wastewater flow forecasting based on time series analysis and artificial neural network. Water Sci Technol 80(2):243–253

    Article  Google Scholar 

  • Zhou S, Wang X (2020) Simple estimation method for the second-largest Lyapunov exponent of chaotic differential equations. Chaos Solition Fract 139:109981

    Article  Google Scholar 

  • Zhou P, Li Z, Snowling S, Baetz BW, Na D, Boyd G (2019) A random forest model for inflow prediction at wastewater treatment plants. Stochast Environ Res Risk Assess 33(10):1781–1792

    Article  Google Scholar 

  • Zhou P, Li C, Li Z, Cai Y (2022) Assessing uncertainty propagation in hybrid models for daily streamflow simulation based on arbitrary polynomial chaos expansion. Adv Water Resour 160:104110

    Article  Google Scholar 

  • Zounemat-Kermani M, Alizamir M, Keshtegar B, Batelaan O, Hinkelmann R (2022) Prediction of effluent arsenic concentration of wastewater treatment plants using machine learning and kriging-based models. Environ Sci Pollut Res 29(14):20556–20570

    Article  CAS  Google Scholar 

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Funding

The research was funded by the Maharashtra Pollution control board (MPCB), Government of India, to perform technical and socio-economic analysis on wastewater treatment facilities of Maharashtra state (Grant No: RD/0119-MPCB009-001).

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  1. Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra, 400076, India

    D. Ramkumar & V. Jothiprakash

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  1. D. Ramkumar
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The conception and design of this research project resulted from the authors' joint efforts; DR drafted the initial version of the primary manuscript, and VJ provided feedback and made revisions. The final manuscript was reviewed and approved by both authors. DR: Methodology, investigation, data curation, software, analysis, visualization, writing—original draft, VJ: Conceptualizations, Funding acquisition, methodology, supervision, manuscript proofreading.

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Correspondence to V. Jothiprakash.

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Ramkumar, D., Jothiprakash, V. A chaotic investigation on pollutant parameters of a wastewater treatment facility using false nearest neighbour algorithm. Stoch Environ Res Risk Assess 38, 1–16 (2024). https://doi.org/10.1007/s00477-023-02559-1

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