Influence Coefficient Algorithm Research Articles

Watershed model calibration framework developed using an influence coefficient algorithm and a genetic algorithm and analysis of pollutant discharge characteristics and load reduction in a TMDL planning area

Manual calibration is common in rainfall-runoff model applications. However, rainfall-runoff models include several complicated parameters; thus, significant time and effort are required to manually calibrate the parameters individually and repeatedly. Automatic calibration has relative merit regarding time efficiency and objectivity but shortcomings regarding understanding indigenous processes in the basin. In this study, a watershed model calibration framework was developed using an influence coefficient algorithm and genetic algorithm (WMCIG) to automatically calibrate the distributed models. The optimization problem used to minimize the sum of squares of the normalized residuals of the observed and predicted values was solved using a genetic algorithm (GA). The final model parameters were determined from the iteration with the smallest sum of squares of the normalized residuals of all iterations. The WMCIG was applied to a Gomakwoncheon watershed located in an area that presents a total maximum daily load (TMDL) in Korea. The proportion of urbanized area in this watershed is low, and the diffuse pollution loads of nutrients such as phosphorus are greater than the point-source pollution loads because of the concentration of rainfall that occurs during the summer. The pollution discharges from the watershed were estimated for each land-use type, and the seasonal variations of the pollution loads were analyzed. Consecutive flow measurement gauges have not been installed in this area, and it is difficult to survey the flow and water quality in this area during the frequent heavy rainfall that occurs during the wet season. The Hydrological Simulation Program-Fortran (HSPF) model was used to calculate the runoff flow and water quality in this basin. Using the water quality results, a load duration curve was constructed for the basin, the exceedance frequency of the water quality standard was calculated for each hydrologic condition class, and the percent reduction required to achieve the water quality standard was estimated. The R2 value for the calibrated BOD5 was 0.60, which is a moderate result, and the R2 value for the TP was 0.86, which is a good result. The percent differences obtained for the calibrated BOD5 and TP were very good; therefore, the calibration results using WMCIG were satisfactory. From the load duration curve analysis, the WQS exceedance frequencies of the BOD5 under dry conditions and low-flow conditions were 75.7% and 65%, respectively, and the exceedance frequencies under moist and mid-range conditions were higher than under other conditions. The exceedance frequencies of the TP for the high-flow, moist and mid-range conditions were high and the exceedance rate for the high-flow condition was particularly high. Most of the data from the high-flow conditions exceeded the WQSs. Thus, nonpoint-source pollutants from storm-water runoff substantially affected the TP concentration in the Gomakwoncheon.

An overview of quantification methods in energy-dispersive X-ray fluorescence analysis

This paper reviews the major factors influencing the accuracy of the energy-dispersive X-ray fluorescence (EDXRF) analysis including physical and chemical matrix effects (resulting from particle size, surface irregularity, mineralogy, moisture, absorption and enhancement) as well as the correction procedures with emphasis on the analysis of unprepared samples. Quantification methods for thin samples, samples with intermediate thickness and thick samples are presented including fundamental parameter methods, influence coefficient algorithms, empirical coefficient algorithms and quantification methods based on scattered primary radiation. Quality control procedures are also reviewed.

Parameter optimization of the QUAL2K model for a multiple-reach river using an influence coefficient algorithm

An influence coefficient algorithm and a genetic algorithm (GA) were introduced to develop an automatic calibration model for QUAL2K, the latest version of the QUAL2E river and stream water-quality model. The influence coefficient algorithm was used for the parameter optimization in unsteady state, open channel flow. The GA, used in solving the optimization problem, is very simple and comprehensible yet still applicable to any complicated mathematical problem, where it can find the global-optimum solution quickly and effectively. The previously established model QUAL2Kw was used for the automatic calibration of the QUAL2K. The parameter-optimization method using the influence coefficient and genetic algorithm (POMIG) developed in this study and QUAL2Kw were each applied to the Gangneung Namdaecheon River, which has multiple reaches, and the results of the two models were compared. In the modeling, the river reach was divided into two parts based on considerations of the water quality and hydraulic characteristics. The calibration results by POMIG showed a good correspondence between the calculated and observed values for most of water-quality variables. In the application of POMIG and QUAL2Kw, relatively large errors were generated between the observed and predicted values in the case of the dissolved oxygen (DO) and chlorophyll-a (Chl-a) in the lowest part of the river; therefore, two weighting factors (1 and 5) were applied for DO and Chl-a in the lower river. The sums of the errors for DO and Chl-a with a weighting factor of 5 were slightly lower compared with the application of a factor of 1. However, with a weighting factor of 5 the sums of errors for other water-quality variables were slightly increased in comparison to the case with a factor of 1. Generally, the results of the POMIG were slightly better than those of the QUAL2Kw.

Study of epitaxial selective area growth In1−xGaxAs films by synchrotron μ-XRF mapping

We present an analytical method allowing to quantitatively extract, from a space resolved Synchrotron Radiation X-Ray Fluorescence (SR-XRF) map, the variation of the thickness and chemical composition of a In1−xGaxAs ternary semiconductor film, in which a gradient in the growth plane of both composition and thickness is obtained using the Selective Area Growth (SAG) method. This advanced growth technique allows the realization of monolithic integrated laser/modulator devices for long distance fiber optics communication at high frequency, which have recently come to the market as high performance products. In a SAG growth, the optimization of the growth parameters is usually done by an empirical approach since a spatially resolved compositional characterization is not possible with conventional laboratory techniques. Exploiting the μ-X-ray beam available at the ID22 beamline of the European Synchrotron Radiation Facility (ESRF), we performed a 2D micrometric resolved (1.7 × 5.3 μm2) XRF study of a In1−xGaxAs ternary semiconductor film. The purposed method is a theoretical influence coefficient algorithm based on the use of only few reference materials coupled with the fundamental parameter (FP) approach and it is optimized for intermediate thickness samples. Reported values agree quantitatively with independent High Resolution X-Ray Diffraction (HRXRD) analysis within 1%.

Study on the influence of X-ray tube spectral distribution on the analysis of bulk samples and thin films: Fundamental parameters method and theoretical coefficient algorithms

Knowledge of X-ray tube spectral distribution is necessary in theoretical methods of matrix correction, i.e. in both fundamental parameter (FP) methods and theoretical influence coefficient algorithms. Thus, the influence of X-ray tube distribution on the accuracy of the analysis of thin films and bulk samples is presented. The calculations are performed using experimental X-ray tube spectra taken from the literature and theoretical X-ray tube spectra evaluated by three different algorithms proposed by Pella et al. (X-Ray Spectrom. 14 (1985) 125–135), Ebel (X-Ray Spectrom. 28 (1999) 255–266), and Finkelshtein and Pavlova (X-Ray Spectrom. 28 (1999) 27–32). In this study, Fe–Cr–Ni system is selected as an example and the calculations are performed for X-ray tubes commonly applied in X-ray fluorescence analysis (XRF), i.e., Cr, Mo, Rh and W. The influence of X-ray tube spectra on FP analysis is evaluated when quantification is performed using various types of calibration samples. FP analysis of bulk samples is performed using pure-element bulk standards and multielement bulk standards similar to the analyzed material, whereas for FP analysis of thin films, the bulk and thin pure-element standards are used. For the evaluation of the influence of X-ray tube spectra on XRF analysis performed by theoretical influence coefficient methods, two algorithms for bulk samples are selected, i.e. Claisse–Quintin (Can. Spectrosc. 12 (1967) 129–134) and COLA algorithms (G.R. Lachance, Paper Presented at the International Conference on Industrial Inorganic Elemental Analysis, Metz, France, June 3, 1981) and two algorithms (constant and linear coefficients) for thin films recently proposed by Sitko (X-Ray Spectrom. 37 (2008) 265–272).

Determination of thickness and composition of thin films by x‐ray fluorescence spectrometry using theoretical influence coefficient algorithms

AbstractX‐ray fluorescence radiation intensity from analyte in thin film is a complex function of matrix composition and film thickness. Nevertheless, the complicated problem of matrix correction in XRF analysis of these materials can be simply solved by using the concept of theoretical influence coefficients. In this article, two algorithms based on the previous published equation for intermediate‐thickness samples are proposed. In the first algorithm, the coefficients are treated as constants; in the second one, the coefficients are linear functions of sample thickness and concentration of all matrix elements. The coefficients are calculated from composition and relative radiation intensity (calculated from theory) of hypothetical pure element films and binary films. The calculations are presented in detail on Fe‐Cr‐Ni ternary films as an example. The capability of the algorithms is demonstrated with hypothetical Fe‐Cr‐Ni ternary systems and binaries Fe‐Cr, Fe‐Ni and Cr‐Ni of thickness from 0.01 to 2 mg cm−2. Diverse compositions of these specimens are in the range 5–95% (m/m) of each element. The algorithms are also verified using experimental data of Fe‐Ni binary system films and Cu films taken from literature. Obtained results indicate the usefulness of the proposed algorithms for simultaneous and accurate determination of the chemical composition and thickness of thin film materials. Moreover, the calibration procedure is very clear and interpretation of the data is easy for the analyst, which is a serious advantage of the proposed algorithms over fundamental parameters methods. Copyright © 2008 John Wiley & Sons, Ltd.

Influence of X-ray tube spectral distribution on uncertainty of calculated fluorescent radiation intensity

The relative radiation intensity ( R i ) defined as fluorescent radiation intensity of analyte in specimen to fluorescent radiation intensity of pure element or compound, e.g., oxide is used in calculation in both fundamental parameter methods and in theoretical influence coefficient algorithms. Accuracy of calculated R i is determined by uncertainties of atomic parameters, spectrometer geometry and also by X-ray tube spectral distribution. This paper presents the differences between R i calculated using experimental and theoretical X-ray tube spectra evaluated by three different algorithms proposed by Pella et al., Ebel, and Finkelshtein–Pavlova. The calculations are performed for the most common targets, i.e., Cr, Mo, Rh and W. In this study, R i is calculated for V, Cr, Mn, Fe, Co, Ni, Cu and Mo in steels as an example. The differences between R i calculated using different X-ray tube spectrum algorithms are presented when pure element standard, multielement standard similar to the analyzed material and one pure element standard for all analytes is used in X-ray fluorescence analysis. The differences between R i for intermediate-thickness samples (and also for thin films) and for X-ray tube, which ran for many hours, are also evaluated.

Use of Cm and cross product coefficients in influence coefficient algorithms for quantitative XRF analysis

AbstractThe use of influence coefficients in algorithms for the correction of matrix effects in quantitative XRF analysis is discussed. In principle, multi‐element influence coefficients should be used. In practice, many algorithms are based on the use of binary influence coefficients, even when dealing with multi‐component specimens. This involves approximations which may affect the accuracy of the analysis. It is shown that the effects of this approximation can be reduced, provided that the binary influence coefficients are calculated for the correct composition (this involves the use of Cm, where Cm is the sum of the concentrations of the matrix elements, i.e. Cm = 1 − Ci) and by applying cross‐product coefficients. Copyright © 2004 John Wiley & Sons, Ltd.

Comparison between some common influence coefficient algorithms

The quality of the results obtainable from a number of different algorithms available in modern manufacturers' software has been compared using data for a single sample of Ni–Fe–Cr, for considerations of space. The conclusions reached are based on similar comparisons using many samples of different compositions. The aim was to demonstrate that, when all criteria (variable theoretical influence coefficients; total concentration of all elements equals 100%; homogeneous, flat and infinitely thick samples) relating to emission theory are met, a number of valid mathematical expressions are available to the user. The mathematical expressions (algorithms) examined are Lucas-Tooth and Price, Rasberry–Heinrich and Lachance–Traill, all using empirical influence coefficients; Claisse–Quintin and COLA using linear and hyperbolic variable theoretical influence coefficients, respectively; and Broll–Tertian, Rousseau, Lachance–Claisse and de Jongh, using variable theoretical influence coefficients based on fundamental parameters. The last four algorithms give exactly the same results, despite the fact that the ‘structures’ of the algorithms are all very different and that the magnitudes of the influence coefficients are also very different (except that the magnitudes and signs of influence coefficients are the same for the Broll–Tertian and Rousseau algorithms). If any of the four algorithms is used correctly, each will give acceptable results. Copyright © 2004 John Wiley & Sons, Ltd.

General Influence Coefficient Algorithm in Balancing of Rotating Machinery

General Influence Coefficient Algorithm in Balancing of Rotating Machinery

General Influence Coefficient Algorithm in Balancing of Rotating Machinery

The General Influence Coefficient Algorithm (GICA), developed in this article, is a new calculation method for Influence Coefficients (ICs) with a general formula. Compared to the traditional calculation method, GICA can solve the ICs' calculation task when the group of trial weights are installed on the rotor each time, the trial weights are retained on the rotor systems, or there is redundant trial balancing data, when even part of the ICs is known. GICA is also a powerful tool for refining the ICs from redundant balancing data or historical balancing data and serves as a general algorithm. With the general matrix formula, GICA is ready to be applied in a computer-aided balancing system as the key part of calculation software. Examples in industry are also presented to demonstrate the aplication of this new algorithm.

The concordance of algorithms and influence coefficients for the correction for matrix effects in XRF

The development of influence coefficient algorithms has retained the attention of XRF analysts given that their goal seeks to combine the theoretical exactness of the fundamental parameters approach for quantifying fluorescence missions and the flexibility of simple mathematical models that convert experimentally measured fluorescence intensities to concentrations. By definition, the purpose underlying the use of influence coefficients is to quantify or condense in one value the magnitude of absorption and/or enhancement effects. This presentation examines the concordance underlying a number of algorithms and their influence coefficients which have been proposed over some 50 years. Initially, influence coefficients were defined only in the context of binary absorption and monochromatic excitation sources. Subsequently, the coefficients were defined explicitly for the more comprehensive context, namely, polychromatic excitation sources, absorption and enhancement effects defined separately or combined as 'matrix effects' in multi-element specimens. Thus, on close examination, it can be shown that contrary to algorithms, influence coefficients are direct explicit functions of analytical contexts and that algorithms, often contested when interpreted in the original context for which they were developed, retain their validity when subsequent advancements in the definition of influence coefficients are taken into consideration.

A Versatile Fundamental Alphas Program for Use with Either Tube or Secondary Target Excitation

During this decade, several influence-coefficient algorithms have been published which utilize fundamental parameter equations to correct interelement effects in bulk samples. The Comprehensive Algorithm of Lachance (COLA) is one such algorithm and is used in the program NBSGSC(l). Another COLA-based computer program called FLY-FPM has been developed in China by one of the authors (L. Feng). Using FLY-FPM as a starting point, we developed a new COLA-based program as part of a Cooperative Research Agreement with Kevex Instruments. This program was designed for use with x-ray spectrometers that employ both tube and secondary targets for excitation. For direct tube excitation, the NIST tube spectral distribution algorithm is used in this program (2). For secondary target excitation, the radiation is usually treated as being monochromatic, and fundamental parameter expressions are formulated with this in mind.

Optimal Identification of Parameters in an Inhomogeneous Medium With Quadratic Programming

Abstract The paper develops a new algorithm for parameter identification in a partial differential equation associated with an inhomogeneous aquifer system. The parameters chosen for identification are the storage coefficient, a constant, and transmissivities, functions of the space variable. An implicit finite-difference scheme is used to approximate the solutions of the governing equation. A least-squares criterion is then established. Using distributed observations on the dependent variable within the system, parameters are identified directly by solving a sequence of quadratic programming problems such that the final solution converges to the original problem. The advantages of this new algorithm problem. The advantages of this new algorithm include rapid rate of convergence, ability to handle any inequality constraints, and easy computer implementation. The numerical example presented demonstrates the simultaneous identification of 12 parameters in only seconds of computer time. parameters in only seconds of computer time Introduction Simulation and mathematical models are often used in analyzing aquifer systems. Physically based mathematical models are implemented by high-speed computers. Most models are of a parametric type, in which parameters used in parametric type, in which parameters used in deriving the governing equation are not measurable directly from the physical point of view and, therefore, must be determined from historical records. The literature dealing with parameter identification in partial differential equations has become available only within the last decade. The approaches include gradient searching procedures, the balanced error-weighted gradient method, the classical Gauss-Newton least-squares procedure, optimal control and gradient optimization, quasi linearization, influence coefficient algorithm, linear programming, maximum principle, and regression analysis allied with the steepest-descent algorithm. Yeh analyzed a typical parameter identification problem governed by a second-order, nonlinear, parabolic partial differential equation using five different methods (the gradient method, quasilinearization, maximum principle, influence coefficient method, and linear programming) and then compared these methods. The problem under consideration is that of an unsteady radial flow in a confined aquifer system. The governing equation is(1)1 h h--- --- rT(r) ----- = S ------ + Q, r r r t subject to the following initial and boundary conditions:0t = 0, h = h, 0 < r < re(2)r= 0, h = h (t), t >00Bhr = r ----- = 0, t >0e r Eq. 1 represents a distributed system in which parameters are functions of the space variable. The parameters are functions of the space variable. The assumptions used in deriving Eq. 1 include (1) the aquifer is confined with a constant depth, b; (2) the aquifer overlays on an infinite horizontal impermeable bed; (3) the Dupuit-Forchheimer assumptions are valid; and (4) water is released instantaneously because of the change of the flow potential. SPEJ P. 371

Linear Programming and Channel Flow Identification

A method is developed for the optimal identification of parameters in unsteady open channel flow. The parameters chosen for the identification are two constants embedded in the generalized friction slope expression which encompasses both the Manning and Chezy equations. A minimax error criterion is formulated and solution is obtained by the use of the influence coefficient algorithm and linear programming. The required information is a set of concurrent input and output measurements and appropriate initial and boundary conditions of the system. Numerical results are presented which demonstrate the efficiency of the formulation and the rapidity of the rate of convergence. The advantage of this approach is also considered.

Identification of multiple reach channel parameters

The previously developed influence coefficient algorithm for the solution of the parameter identification problem is extended to multiple reach channel flows, and the stage hydrograph and velocity data and observation station location requirements for an effective determination of the parameters are discussed. The specific application chosen here involves the identification of the individual reach friction parameters, which are not physically measurable and which have to be determined from the mathematical model by the use of concurrent input and output measurements. The influence coefficient algorithm is incorporated with numerical solutions of the unsteady equations of flow through explicit finite difference formulations of these equations. The explicit formulations simplify the computer program but necessitate special precautions to avoid computational instabilities. The stability criteria, which must be observed, are indicated.

Identification of parameters in unsteady open channel flows

This paper introduces the influence coefficient algorithm, a simple, easily implemented, and rapidly convergent computational procedure for the solution of the parameter identification problem in unsteady open channel flow from field observations on stage hydrograph and velocity distribution at one or more points along the channel. (Identification is a mathematical process whereby the parameters embedded in a differential equation defining a system are determined from observations of system input and output.) The parameters specifically chosen for identification are the two ‘friction slope’ characteristics: the channel roughness coefficient and the exponent of the hydraulic radius in the empirical friction slope relation, a number usually assumed to be 4/3. These parameters are not physically measurable and have to be determined from the solutions of the mathematical model using concurrent input and output measurements. This new procedure is related to both quasilinearization and gradient methods. Additionally, an effective formulation of the algorithm is shown to depend on certain stability and convergence features related to the finite difference solutions of the governing flow equations but often ignored or glossed over.