Modeling error identification of activated sludge models

1997 ◽  
Vol 36 (5) ◽  
pp. 81-88 ◽  
Author(s):  
Zhigou Yuan ◽  
Peter A. Vanrolleghem ◽  
Ghislain C. Vansteenkiste

Information about the location of modeling erros is crucial for the efficient improvement of an invalid model. This article discusses how to pinpoint modeling errors through comparison of experimental data with data obtained through simulation of the invalid model. An observer-based approach is presented. By designing a dedicated observer for the system using the invalid model, a signal vector is generated, on which each modeling error imposes an easily identifiable feature. An algorithm to analyze the featured signal is then presented. With this algorithm, the features of each of the modeling errors are extracted. The approach is illustrated for a denitrification reactor model in which errors in the dimension of the state vector, in the structure of the biokinetic relationship and in the values of the parameters could be identified.

2016 ◽  
pp. 4039-4042
Author(s):  
Viliam Malcher

The interpretation problems of quantum theory are considered. In the formalism of quantum theory the possible states of a system are described by a state vector. The state vector, which will be represented as |ψ> in Dirac notation, is the most general form of the quantum mechanical description. The central problem of the interpretation of quantum theory is to explain the physical significance of the |ψ>. In this paper we have shown that one of the best way to make of interpretation of wave function is to take the wave function as an operator.


2018 ◽  
Vol 15 (1) ◽  
pp. 12-22
Author(s):  
V. M. Artyushenko ◽  
D. Y. Vinogradov

The article reviewed and analyzed the class of geometrically stable orbits (GUO). The conditions of stability in the model of the geopotential, taking into account the zonal harmonics. The sequence of calculation of the state vector of GUO in the osculating value of the argument of the latitude with the famous Ascoli-royski longitude of the ascending node, inclination and semimajor axis. The simulation is obtained the altitude profiles of SEE regarding the all-earth ellipsoid model of the gravitational field of the Earth given 7 and 32 zonal harmonics.


1985 ◽  
Vol 17 (8) ◽  
pp. 1475-1478 ◽  
Author(s):  
A P. C. Warner ◽  
G. A. Ekama ◽  
G v. R. Marais

The laboratory scale experimental investigation comprised a 6 day sludge age activated sludge process, the waste sludge of which was fed to a number of digesters operated as follows: single reactor flow through digesters at 4 or 6 days sludge age, under aerobic and anoxic-aerobic conditions (with 1,5 and 4 h cycle times) and 3-in-series flow through aerobic digesters each at 4 days sludge age; all digesters were fed draw-and-fill wise once per day. The general kinetic model for the aerobic activated sludge process set out by Dold et al., (1980) and extended to the anoxic-aerobic process by van Haandel et al., (1981) simulated accurately all the experimental data (Figs 1 to 4) without the need for adjusting the kinetic constants. Both theoretical simulations and experimental data indicate that (i) the rate of volatile solids destruction is not affected by the incorporation of anoxic cycles and (ii) the specific denitrification rate is independent of sludge age and is K4T = 0,046(l,029)(T-20) mgNO3-N/(mg active VSS. d) i.e. about 2/3 of that in the secondary anoxic of the single sludge activated sludge stystem. An important consequence of (i) and (ii) above is that denitrification can be integrated easily in the steady state digester model of Marais and Ekama (1976) and used for design (Warner et al., 1983).


2003 ◽  
Vol 37 (12) ◽  
pp. 2893-2904 ◽  
Author(s):  
Britta Petersen ◽  
Krist Gernaey ◽  
Martijn Devisscher ◽  
Denis Dochain ◽  
Peter A. Vanrolleghem

1992 ◽  
Vol 25 (6) ◽  
pp. 167-183 ◽  
Author(s):  
H. Siegrist ◽  
M. Tschui

The wastewater of the municipal treatment plants Zürich-Werdhölzli (350000 population equivalents), Zürich-Glatt (110000), and Wattwil (20000) have been characterized with regard to the activated sludge model Nr.1 of the IAWPRC task group. Zürich-Glatt and Wattwil are partly nitrifying treatment plants and Zürich-Werdhölzli is fully nitrifying. The mixing characteristics of the aeration tanks at Werdhölzli and Glatt were determined with sodium bromide as a tracer. The experimental data were used to calibrate hydrolysis, heterotrophic growth and nitrification. Problems arising by calibrating hydrolysis of the paniculate material and by measuring oxygen consumption of heterotrophic and nitrifying microorganisms are discussed. For hydrolysis the experimental data indicate first-order kinetics. For nitrification a maximum growth rate of 0.40±0.07 d−1, corresponding to an observed growth rate of 0.26±0.04 d−1 was calculated at 10°C. The half velocity constant found for 12 and 20°C was 2 mg NH4-N/l. The calibrated model was verified with experimental dam of me Zürich-Werdhölzli treatment plant during ammonia shock load.


2010 ◽  
Vol 49 (6) ◽  
pp. 2790-2799 ◽  
Author(s):  
Anca Maria Nagy ◽  
Gilles Mourot ◽  
Benoît Marx ◽  
José Ragot ◽  
Georges Schutz

2010 ◽  
Vol 61 (4) ◽  
pp. 825-839 ◽  
Author(s):  
H. Hauduc ◽  
L. Rieger ◽  
I. Takács ◽  
A. Héduit ◽  
P. A. Vanrolleghem ◽  
...  

The quality of simulation results can be significantly affected by errors in the published model (typing, inconsistencies, gaps or conceptual errors) and/or in the underlying numerical model description. Seven of the most commonly used activated sludge models have been investigated to point out the typing errors, inconsistencies and gaps in the model publications: ASM1; ASM2d; ASM3; ASM3 + Bio-P; ASM2d + TUD; New General; UCTPHO+. A systematic approach to verify models by tracking typing errors and inconsistencies in model development and software implementation is proposed. Then, stoichiometry and kinetic rate expressions are checked for each model and the errors found are reported in detail. An attached spreadsheet (see http://www.iwaponline.com/wst/06104/0898.pdf) provides corrected matrices with the calculations of all stoichiometric coefficients for the discussed biokinetic models and gives an example of proper continuity checks.


2016 ◽  
Author(s):  
Jean M. Bergeron ◽  
Mélanie Trudel ◽  
Robert Leconte

Abstract. The potential of data assimilation for hydrologic predictions has been demonstrated in many research studies. Watersheds over which multiple observation types are available can potentially further benefit from data assimilation by having multiple updated states from which hydrologic predictions can be generated. However, the magnitude and time span of the impact of the assimilation of an observation varies according not only to its type, but also to the variables included in the state vector. This study examines the impact of multivariate synthetic data assimilation using the Ensemble Kalman Filter (EnKF) into the spatially distributed hydrologic model CEQUEAU for the mountainous Nechako River located in British-Columbia, Canada. Synthetic data includes daily snow cover area (SCA), daily measurements of snow water equivalent (SWE) at three different locations and daily streamflow data at the watershed outlet. Results show a large variability of the continuous rank probability skill score over a wide range of prediction horizons (days to weeks) depending on the state vector configuration and the type of observations assimilated. Overall, the variables most closely linearly linked to the observations are the ones worth considering adding to the state vector. The performance of the assimilation of basin-wide SCA, which does not have a decent proxy among potential state variables, does not surpass the open loop for any of the simulated variables. However, the assimilation of streamflow offers major improvements steadily throughout the year, but mainly over the short-term (up to 5 days) forecast horizons, while the impact of the assimilation of SWE gains more importance during the snowmelt period over the mid-term (up to 50 days) forecast horizon compared with open loop. The combined assimilation of streamflow and SWE performs better than its individual counterparts, offering improvements over all forecast horizons considered and throughout the whole year, including the critical period of snowmelt. This highlights the potential benefit of using multivariate data assimilation for streamflow predictions in snow-dominated regions.


2021 ◽  
Vol 13 (17) ◽  
pp. 3389
Author(s):  
Pei Ye ◽  
Meng-Dao Xing ◽  
Xiang-Gen Xia ◽  
Guang-Cai Sun ◽  
Yachao Li ◽  
...  

In a short observation time, after the range alignment and phase adjustment, the motion of a target can be approximated as a uniform rotation. The radar observing process can be simply described as multiplying an observation matrix on the ISAR image, which can be thought of as a linear system. It is known that the longer observation time is, the higher cross-range resolution is. In order to deal with the conflict between short observation time and high cross-range resolution, we introduce Kalman filtering (KF) into the ISAR imaging and propose a novel method to reconstruct a high-resolution image with short time observed data. As KF has excellent reconstruction performance, it leads to a good application in ISAR image reconstruction. At each observation aperture, the reconstructed image denotes the state vector in KF at the aperture time. It is corrected by a two-step KF process: prediction and update. As iteration continues, the state vector is gradually corrected to a well-focused high-resolution image. Thus, the proposed method can obtain a high-resolution image in a short observation time. Both simulated and real data are applied to demonstrate the performance of the proposed method.


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