Identification of pollution sources in rivers using a hydrodynamic diffusion wave model and improved Bayesian-Markov chain Monte Carlo algorithm

Water quality restoration in rivers requires identification of the locations and discharges of pollution sources,and a reliable mathematical model to accomplish this identification is essential.In this paper,an innovative framework is presented to inversely estimate pollution sources for both accident preparedness and normal management of the allowable pollutant discharge.The proposed model integrates the concepts of the hydrodynamic diffusion wave equation and an improved Bayesian-Markov chain Monte Carlo method(MCMC).The methodological framework is tested using a designed case of a sudden wastewater spill incident(i.e.,source location,flow rate,and starting and ending times of the discharge)and a real case of multiple sewage inputs into a river(i.e.,locations and daily flows of sewage sources).The proposed modeling based on the improved Bayesian-MCMC method can effectively solve high-dimensional search and optimization problems according to known river water levels at pre-set monitoring sites.It can adequately provide accurate source estimation parameters using only one simulation through exploration of the full parameter space.In comparison,the inverse models based on the popular random walk Metropolis(RWM)algorithm and microbial genetic algorithm(MGA)do not produce reliable estimates for the two scenarios even after multiple simulation runs,and they fall into locally optimal solutions.Since much more water level data are available than water quality data,the proposed approach also provides a cost-effective solution for identifying pollution sources in rivers with the support of high-frequency water level data,especially for rivers receiving significant sewage discharges.

A dynamic stiffness-based framework for harmonic input estimation and response reconstruction considering damage

In structural health monitoring(SHM),the measurement is point-wise but structures are continuous.Thus,input estimation has become a hot research subject with which the full-field structural response can be calculated with a finite element model(FEM).This paper proposes a framework based on the dynamic stiffness theory,to estimate harmonic input,reconstruct responses,and to localize damages from seriously deficient measurements.To begin,Fourier transform converts the dynamic equilibrium equation to an equivalent static one in the frequency domain,which is underdetermined since the dimension of measurement vector is far less than the FEM-node number.The principal component analysis has been adopted to“compress”the under-determined equation,and formed an over-determined equation to estimate the unknown input.Then,inverse Fourier transform converts the estimated input in the frequency domain to the time domain.Applying this to the FEM can reconstruct the target responses.If a structure is damaged,the estimated nodal force can localize the damage.To improve the damage-detection accuracy,a multi-measurement-based indicator has been proposed.Numerical simulations have validated that the proposed framework can capably estimate input and reconstruct multi-types of full-field responses,and the damage indicator can localize minor damages even with the existence of noise.