Identification of release sources in advection–diffusion system by machine learning combined with Green’s function inverse method

Abstract The identification of sources of advection–diffusion transport is based usually on solving complex ill-posed inverse models against the available state-variable data records. However, if there are several sources with different locations and strengths, the data records represent mixtures rather than the separate influences of the original sources. Importantly, the number of these original release sources is typically unknown, which hinders reliability of the classical inverse-model analyses. To address this challenge, we present here a novel hybrid method for identification of the unknown number of release sources. Our hybrid method, called HNMF, couples unsupervised learning based on Non-negative Matrix Factorization (NMF) and inverse-analysis Green’s functions method. HNMF synergistically performs decomposition of the recorded mixtures, finds the number of the unknown sources and uses the Green’s function of advection–diffusion equation to identify their characteristics. In the paper, we introduce the method and demonstrate that it is capable of identifying the advection velocity and dispersivity of the medium as well as the unknown number, locations, and properties of various sets of synthetic release sources with different space and time dependencies, based only on the recorded data. HNMF can be applied directly to any problem controlled by a partial-differential parabolic equation where mixtures of an unknown number of sources are measured at multiple locations.

[1]  Shih-Ming Lin,et al.  A sequential algorithm and error sensitivity analysis for the inverse heat conduction problems with multiple heat sources , 2011 .

[2]  Pier Luigi Dragotti,et al.  Spatio-temporal sampling and reconstruction of diffusion fields induced by point sources , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[3]  Martin A. Fischler,et al.  The Representation and Matching of Pictorial Structures , 1973, IEEE Transactions on Computers.

[4]  Amin Rasekh,et al.  Machine Learning Approach for Contamination Source Identification in Water Distribution Systems , 2012 .

[5]  Amvrossios C. Bagtzoglou,et al.  Pollution source identification in heterogeneous porous media , 2001 .

[6]  Stanley Osher,et al.  Heat source identification based on l1 constrained minimization , 2014 .

[7]  David T. W. Jones,et al.  Signatures of mutational processes in human cancer , 2013, Nature.

[8]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[9]  Huayong Wu,et al.  Analytical solutions of three-dimensional contaminant transport in uniform flow field in porous media: A library , 2009 .

[10]  Guido Cervone,et al.  The case of arsenic contamination in the Sardinian Geopark, Italy, analyzed using symbolic machine learning , 2013 .

[11]  P. Paatero,et al.  Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values† , 1994 .

[12]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[13]  Adel Hamdi,et al.  Inverse source problem in a one-dimensional evolution linear transport equation with spatially varying coefficients: application to surface water pollution , 2013 .

[14]  Hirotugu Akaike,et al.  Akaike's Information Criterion , 2011, International Encyclopedia of Statistical Science.

[15]  Lars Kai Hansen,et al.  Tuning pruning in sparse non-negative matrix factorization , 2009, 2009 17th European Signal Processing Conference.

[16]  V. Borukhov,et al.  Identification of a time-dependent source term in nonlinear hyperbolic or parabolic heat equation , 2015 .

[17]  Andreas Kerschbaumer,et al.  A new structure identification scheme for ANFIS and its application for the simulation of virtual air pollution monitoring stations in urban areas , 2015, Eng. Appl. Artif. Intell..

[18]  Velimir V. Vesselinov,et al.  Analytical solutions for anomalous dispersion transport , 2014 .

[19]  Guohe Huang,et al.  Artificial intelligence for management and control of pollution minimization and mitigation processes , 2003 .

[20]  P. Rousseeuw.  Silhouettes: a graphical aid to the interpretation and validation of cluster analysis , 1987 .

[21]  Eungyu Park,et al.  Analytical solutions of contaminant transport from finite one-, two-, and three-dimensional sources in a finite-thickness aquifer. , 2001, Journal of contaminant hydrology.

[22]  R. Jackson,et al.  A critical review of the risks to water resources from unconventional shale gas development and hydraulic fracturing in the United States. , 2014, Environmental science & technology.

[23]  Velimir V. Vesselinov,et al.  Blind source separation for groundwater pressure analysis based on nonnegative matrix factorization , 2014 .

[24]  David T.W. Lin,et al.  The estimation of the strength of the heat source in the heat conduction problems , 2007 .

[25]  Dmitry Yarotsky,et al.  Univariate interpolation by exponential functions and Gaussian RBFs for generic sets of nodes , 2012, J. Approx. Theory.

[26]  Mustafa M. Aral,et al.  Identification of Contaminant Sources in Water Distribution Systems Using Simulation-Optimization Method: Case Study , 2006 .

[27]  Yen-Hsi Richard Tsai,et al.  Point source identification in nonlinear advection–diffusion–reaction systems , 2012, 1202.2373.

[28]  Mac McKee,et al.  Applicability of statistical learning algorithms in groundwater quality modeling , 2005 .

[29]  Krishnan Balachandran,et al.  Inverse problem for the reaction diffusion system by optimization method , 2011 .

[30]  V. V. Vesselinov,et al.  Model Analysis of Complex Systems Behavior using MADS , 2016 .

[31]  Vincent Y. F. Tan,et al.  Automatic Relevance Determination in Nonnegative Matrix Factorization with the /spl beta/-Divergence , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.