Nonlinear Least-squares Technique Research Articles

Temperature dependences of N2-broadening and shift coefficients in the ν6 perpendicular band of 12CH3D

The temperature-dependences of line broadening and shift parameters for many 12CH3D transitions have been determined using six high-resolution, high signal-to-noise ratio, room-temperature CH3D (98% purity) and CH3D-N2 spectra recorded with 25cm path length ( at 0.01cm−1 unapodized resolution) using the McMath−Pierce FTS located on Kitt Peak, Arizona, and 17 additional high quality, pure CH3D (99% purity) and CH3D-N2 spectra recorded between 79 and 296K with the 20.38cm path coolable cell (at 0.0056cm−1 unapodized resolution) with the Bruker 125HR FTS at the Jet Propulsion Laboratory (JPL), Pasadena, California. The spectra have been fitted simultaneously applying a multispectrum nonlinear least-squares technique. In the analysis, the Lorentzian N2-broadened half-width coefficients and the corresponding pressure-shift coefficients as well as their temperature dependences are extracted for about 400 transitions (0≤J″≤19, K″≤16) in the perpendicular (ΔK=±1) ν6 band. At 296K, the measured N2-broadened half-width coefficients range from 0.0209 to 0.0782cm−1atm−1 whereas the majority of the associated N2-induced shift coefficients are negative, and the values are between -0.016 and 0.005cm−1atm−1. The temperature dependence exponents for N2-broadened half-widths range between 0.264 and 0.924, whereas the temperature dependence coefficients for N2-induced shifts are between 0 and 0.00011cm−1atm−1K−1. The N2-broadened half-width coefficients have been also calculated using a semi-classical approach based on a rigorous treatment of the active molecule as a symmetric top, a model intermolecular potential comprising both short- and long-range interactions, and exact classical trajectories. The role of the various high-order multipoles in the line-broadening at low, middle and high values of the rotational quantum number J″ has been investigated and the main features of the K-dependences analyzed. The calculations performed for 296, 240 and 190K have allowed to deduce the half-width temperature-dependence exponents, completing the general comparison of our new experimental results with those which are available in the literature.

Self- and air-broadened line shapes in the 2ν3 P and R branches of 12CH4

In this paper we report line shape parameters of 12CH4 for several hundred 2ν3 transitions in the spectral regions 5891–5996cm−1 (P branch) and 6015–6115cm−1 (R branch). Air- and self-broadening coefficients were measured as a function of temperature; line mixing via off-diagonal relaxation matrix element coefficients was also obtained for 47 transition pairs. In total, nearly 1517 positions and intensities were retrieved, but many transitions were too weak for the line shape study. For this analysis, we used 25 high-resolution (0.0056 and 0.0067cm−1) and high signal-to-noise (S/N) spectra of high-purity 12CH4 and the same high-purity 12CH4 broadened by dry air recorded at different sample temperatures between 130K and 295K with the Bruker IFS 125HR Fourier transform spectrometer at JPL. Three different absorption cells were used (1) a White cell set to a path length of 13.09m for room temperature data, (2) a single-pass 0.2038m long coolable cell (for self-broadening) and (3) a multipass cell with 20.941m total path coolable Herriott cell (for air-broadening). In total there were 13 spectra with pure 12CH4 (0.27–599Torr) and 12 air-broadened spectra with total sample pressures of 80–805Torr and volume mixing ratios (VMR) of methane between 0.18 and 1.0. An interactive multispectrum nonlinear least-squares technique was employed to fit the individual P10–P1 and R0–R10 manifolds in all the spectra simultaneously. Results obtained from the present analysis are compared to other recent measurements.

Creep Characterization of Ni-Based Superalloy IN-792 Using the 4- and 6-θ Projection Method

This paper studies the accuracy of a technique which is capable of predicting and modeling a wide range of creep life in Ni-based superalloys. The θ-projection method was applied to characterize the creep behavior of the Ni-based superalloy IN-792 at 800 °C. Constant load creep tests have been carried out over a wide range of loads at the constant operating temperature. Creep curves were fitted using either 4-θ or 6-θ equation by the use of a nonlinear least-square technique. The results showed that both 4- and 6-θ projection parameters revealed a good linearity as a function of stress. Comparison of experimental creep curves with those predicted using both of the utilized θ-projection techniques showed that the techniques fit the experimental data at high strain values very well while the 6-θ approach describes much better the creep curves at low strain region.

Generalized separable parameter space techniques for fitting 1K‐5K serial compartment models

Kinetic modeling is widely used to analyze dynamic imaging data, estimating kinetic parameters that quantify functional or physiologic processes in vivo. Typical kinetic models give rise to nonlinear solution equations in multiple dimensions, presenting a complex fitting environment. This work generalizes previously described separable nonlinear least-squares techniques for fitting serial compartment models with up to three tissue compartments and five rate parameters. The approach maximally separates the linear and nonlinear aspects of the modeling equations, using a formulation modified from previous basis function methods to avoid a potential mathematical degeneracy. A fast and robust algorithm for solving the linear subproblem with full user-defined constraints is also presented. The generalized separable parameter space technique effectively reduces the dimensionality of the nonlinear fitting problem to one dimension for 2K-3K compartment models, and to two dimensions for 4K-5K models. Exhaustive search fits, which guarantee identification of the true global minimum fit, required approximately 10 ms for 2K-3K and 1.1 s for 4K-5K models, respectively. The technique is also amenable to fast gradient-descent iterative fitting algorithms, where the reduced dimensionality offers improved convergence properties. The objective function for the separable parameter space nonlinear subproblem was characterized and found to be generally well-behaved with a well-defined global minimum. Separable parameter space fits with the Levenberg-Marquardt algorithm required fewer iterations than comparable fits for conventional model formulations, averaging 1 and 7 ms for 2K-3K and 4K-5K models, respectively. Sensitivity to initial conditions was likewise reduced. The separable parameter space techniques described herein generalize previously described techniques to encompass 1K-5K compartment models, enable robust solution of the linear subproblem with full user-defined constraints, and are amenable to rapid and robust fitting using iterative gradient-descent type algorithms.

Efficient implementation of power-law attenuation of elastic waves in time-domain numerical simulations

Numerical simulation of wave propagation in the time domain is easily parallelizable on high performance computing systems due to the spatially local nature of the governing equations. The disadvantage of working in the time domain arises when lossy media must be modeled which generally gives rise to convolution-type loss terms in the governing time-domain equations. Computation of these convolutions usually requires the storage of several solution fields at thousands of previous time steps. This requirement can be memory prohibitive in three-dimensions. In this talk we present a recursive convolution approach to computing lossy (power-law) elastic wave propagation that is an extension of the one-way, one-dimensional acoustic wave equation work done by Liebler [Liebler et al., J. Acoust. Soc. Am. 116 (2004)] in order to handle multiple dimensions and shear waves. Convolutions are computed recursively by first using a nonlinear least-squares technique to fit the kernel of the convolution with a series of decaying exponentials. We demonstrate how graphical processing units (GPUs) can be used to obtain speed-up factors as high as 35 on a test computation of time-domain scattering from a highly resonant but lossy elastic cylinder. [Work sponsored by the Office of Naval Research.]

Calibration of Vector Magnetograms with the Chromospheric Mg b2 Line

Stokes polarization profiles of the Mg b2 5172.68 A spectral line on two simple sunspots are obtained with the Multi-Channel Solar Telescope (MCST) at the Huairou Solar Observing Station (HSOS). This is done by means of scanning this line over the wavelength interval from 200 mA redward of the line center to 200 mA blueward, in steps of 10 mA. A generalized analytic solution to the transfer equation for polarized radiation is presented. With a nonlinear least-square fitting technique, the linear calibration coefficients for the low-chromospheric longitudinal magnetic field is obtained in the weak-field case. We also discuss the problems in calibrating the transverse field with this line. It is shown that the weak-field approximation is not applicable to the chromospheric Mg b2 line for the transverse component of the magnetic field.

A Study of the Phenomenon of Mass Increased by Coal Oxidation Prior to 400 ℃: Governing Mechanism and the Associated Chemical Kinetics

The reaction mechanism and kinetics of coal oxidation at temperatures prior to 400 °C were studied theoretically, with a focus on the phenomenon of mass increase observed by thermo-gravimetric analysis (TGA). In light of the existing understanding on coal oxidation, chemical reactions taking place at moderate temperatures were simplified into three parallel but competitive reaction sequences, including water release, oxygen adsorption and decomposition of the oxygenated compounds, as well as the direct “burn-off” reaction. Using the non-linear least-square fitting technique, the kinetic parameters of all the reactions occurring within the temperature range studied were determined by fitting the sets of TG and DTG data collected at the oxygen concentrations of 10%, 21% and 40% in volume, respectively. The modeling results are in excellent agreement with the experimental data, confirming the reliability of the model established. It is proved that the mass increase during coal oxidation at moderate temperatures is primarily contributed by the oxygen adsorption and the subsequent decomposition reactions, while influence of the direct “burn-off” reaction on this phenomenon is relatively trivial. Since the mass increase phenomenon is a compromised result of the principal reactions involved, and the kinetic parameters of the oxygen adsorption reaction cannot be determined with accuracy based upon this phenomenon with a utilization of a single-reaction assumption. Enrichment of O2 in the reaction medium speeds up the rates of oxygen adsorption reaction and the decomposition reaction. However, we did not observe the significant effect of the oxygen concentration on the direct “burn-off” reaction, solely due to the nature of the experimental data selected No. 8 战 婧等:煤氧化增重现象中的控制反应及其动力学解析 981 and the techniques utilized for retrieving the kinetic data for the reactions involved.

A numerical and experimental hybrid approach for the investigation of aerodynamic forces on stay cables suffering from rain-wind induced vibration

The aerodynamic forces on a stay cable under a rain-wind induced vibration (RWIV) are difficult to measure directly in a wind tunnel test. This paper presents a hybrid approach that combines an experiment with computational fluid dynamics (CFD) for the investigation on aerodynamic forces of a stay cable under a RWIV. The stay cable and flow field were considered as two substructures of the system. The oscillation of the stay cable was first measured by using a wind tunnel test of a RWIV under an artificial rainfall condition. The oscillation of the cable was treated as a previously known moving boundary condition and applied to the flow field. Only the flow field with the known moving cable boundary was then numerically simulated by using a CFD method (such as Fluent 6.3). The transient aerodynamic forces of the stay cable with a predetermined cable oscillation were obtained from numerical calculations. The characteristics of the aerodynamic forces in the time domain and frequency domain were then analysed for various cases. To verify the feasibility and accuracy of the proposed hybrid approach, the transient aerodynamic forces were applied to a single-degree-of-freedom model (SDOF) of the stay cable to calculate the RWIV of the cable. A comparison was performed between the oscillation responses of the stay cable obtained from the calculated (SDOF model) and experimental results, and the results indicate that the hybrid approach accurately simulates the transient aerodynamic forces of the stay cable. The equivalent damping ratios induced by the aerodynamic forces were obtained for various wind speeds. Furthermore, a nonlinear model of the aerodynamic force is proposed based on the calculation results, and the coefficients in the model were identified by a nonlinear least-squares technique.

Equivalent Electric Circuit Modeling and Performance Analysis of a PEM Fuel Cell Stack Using Impedance Spectroscopy

In this paper, equivalent electric circuit models of a commercial 1.2-kW proton exchange membrane (PEM) fuel cell stack are proposed based on AC impedance studies. The PEM fuel cell stack was operated using room air and pure hydrogen (99.995%). Using electrochemical impedance spectroscopy (EIS) technique, impedance data were collected in the laboratory under various loading conditions. Impedance data were analyzed and circuit models developed using basic circuit elements like resistors and inductors, and distributed elements such as Warburg and constant-phase elements. A nonlinear least-square fitting technique is employed to obtain the circuit parameters by fitting a curve to the experimental impedance data. Two circuit models of the fuel cell, one for low and one for high currents are proposed. The average ohmic resistance for the whole stack is estimated to be 41 mΩ. Double-layer capacitances are determined at anode and cathode at various current densities. As expected, cathode charge transfer resistance turns out to be much higher than the anode charge transfer resistance because of slower kinetics of the oxygen reduction reaction. At higher load currents, a significant increase in mass transfer resistance as well as low-frequency inductive effects is observed. These low-frequency inductive effects are recognized and modeled in the fuel cell models of this work. Finally, a semiquantitative analysis was used to determine the contribution of individual performance factors to the overall fuel cell voltage drop. The transient response of the fuel cell circuit models is simulated using MATLAB/Simulink and their performance is validated by comparison with experimental data.

The combination of GNSS-levelling data and gravimetric (quasi-) geoid heights in the presence of noise

We propose a methodology for the combination of a gravimetric (quasi-) geoid with GNSS-levelling data in the presence of noise with correlations and/or spatially varying noise variances. It comprises two steps: first, a gravimetric (quasi-) geoid is computed using the available gravity data, which, in a second step, is improved using ellipsoidal heights at benchmarks provided by GNSS once they have become available. The methodology is an alternative to the integrated processing of all available data using least-squares techniques or least-squares collocation. Unlike the corrector-surface approach, the pursued approach guarantees that the corrections applied to the gravimetric (quasi-) geoid are consistent with the gravity anomaly data set. The methodology is applied to a data set comprising 109 gravimetric quasi-geoid heights, ellipsoidal heights and normal heights at benchmarks in Switzerland. Each data set is complemented by a full noise covariance matrix. We show that when neglecting noise correlations and/or spatially varying noise variances, errors up to 10% of the differences between geometric and gravimetric quasi-geoid heights are introduced. This suggests that if high-quality ellipsoidal heights at benchmarks are available and are used to compute an improved (quasi-) geoid, noise covariance matrices referring to the same datum should be used in the data processing whenever they are available. We compare the methodology with the corrector-surface approach using various corrector surface models. We show that the commonly used corrector surfaces fail to model the more complicated spatial patterns of differences between geometric and gravimetric quasi-geoid heights present in the data set. More flexible parametric models such as radial basis function approximations or minimum-curvature harmonic splines perform better. We also compare the proposed method with generalized least-squares collocation, which comprises a deterministic trend model, a random signal component and a random correlated noise component. Trend model parameters and signal covariance function parameters are estimated iteratively from the data using non-linear least-squares techniques. We show that the performance of generalized least-squares collocation is better than the performance of corrector surfaces, but the differences with respect to the proposed method are still significant.

Nonlinear Stochastic Galerkin and Collocation Methods: Application to a Ferromagnetic Cylinder Rotating at High Speed

The objective of this paper is to reviewrecent developments in numerical re- construction methods for inverse transport problems in imaging applications, mainly optical tomography, fluorescence tomography and bioluminescence tomography. In those inverse problems, one aims at reconstructing physical parameters,suchas the ab- sorption coefficient, the scattering coefficient and the fluorescence light source, inside heterogeneous media, frompartialknowledge oftransport solutions onthe boundaries of the media. The physical parameters recovered can be used for diagnostic purpose. Numerical reconstruction techniques for those inverse transport problems can be roughly classified into two categories: linear reconstruction methods and nonlinear re- construction methods. In the first type of methods, the inverse problems are linearized around some known background to obtain linear inverse problems. Classical regular- ization techniques are then applied to solve those inverse problems. The second type of methods are either based on regularized nonlinear least-square techniques or based on gradient-driven iterative methods for nonlinear operator equations. In either case, the unknown parameters are iteratively updated until the solutions of the transport equations with the those parameters match the measurements to a certain extent. We reviewlinear and nonlinear reconstruction methods for inverse transport problems in medical imaging with stationary, frequency-domain and time-dependent data. The materials presented include both existing and new results. Meanwhile, we attempt to present similar algorithms for different problems in the same framework to make it more straightforward to generalize those algorithms to other inverse (transport) prob- lems.

Experimental Study of Damage Detection by Data-Driven Subspace Identification and Finite-Element Model Updating

The need to identify the physical properties of a structure given its force-response (input-output) relationship is driven primarily by the need to validate the approximate solution models, such as finite-element models. This paper proposes a method, which combines the structural system identification and model updating techniques, for the damage detection of a steel frame structure and a RC frame. The damage detection procedure consists of two steps: (1) identifying the system dynamic characteristics using the subspace identification (SI) technique from input/output measurements and (2) developing a damage assessment method for structural members (including joints) based on a progressive finite-element model updating and a large-scale optimization using a nonlinear least-square technique. The proposed method was verified through a shaking table experimental study using: (1) a 1/4-scale six-story steel frame structure by loosening the connection bolts for damage simulations and (2) a two-story RC frame subject to different levels of ground excitations back to back. As demonstrated by experimental results, the proposed damage detection method, based on the combination of SI technique and the model updating approach, is very effective for the damage assessment of frame structures. The method not only can detect the damage locations but also can quantify the damage severities.

Temperature dependences for air-broadened Lorentz half-width and pressure shift coefficients in the 30013←00001 and 30012←00001 bands of CO2near 1600 nm This article is part of a Special Issue on Spectroscopy at the University of New Brunswick in honour of Colan Linton and Ron Lees.

In this study, 39 high-resolution spectra of pure and air-broadened CO2recorded at temperatures between 215 and 294 K were analyzed using a multispectrum nonlinear least-squares technique to determine temperature dependences of air-broadened Lorentz half-width and air-induced pressure shift coefficients for over 100 individual12C16O2transitions in the 30012←00001 (at 6348 cm–1) and 30013←00001 (at 6228 cm–1) bands. Data were recorded with two different Fourier transform spectrometers (Kitt Peak FTS at the National Solar Observatory in Arizona and the Bomem FTS at NRC, Ottawa), with absorption path lengths ranging between 25 and 121 m. The sample pressures varied between 11 torr (pure CO2) and 924 torr (CO2-air) with volume mixing ratios of CO2in air between ∼1.5% and 11% (1 torr = 133.322 4 Pa). To minimize systematic errors and increase the accuracy of the retrieved parameters, a constrained multispectrum nonlinear least-squares fitting technique was used to include theoretical quantum mechanical expressions for the rovibrational energies and intensity parameters rather than retrieving the individual positions and intensities line by line. The results suggest no detectable vibrational dependence for the temperature dependences for the air-broadened Lorentz half-width coefficients and the air-induced pressure shift coefficients. The half-width coefficients and temperature dependence exponents were modeled using semiclassical calculations based upon the Robert–Bonamy formalism. A good agreement is seen between the measurements and theoretical calculations. Beyond |m| = 26, a simple scaling factor (0.96) has been applied to the calculated half-width coefficients to match the experimental measurements.

Constrained multispectrum analysis of CO2–Ar broadening at 6227 and 6348 cm–1 This article is part of a Special Issue on Spectroscopy at the University of New Brunswick in honour of Colan Linton and Ron Lees.

We report the first extensive experimental measurements of Ar-broadened half-width and pressure-induced shift coefficients, speed dependence parameters, and line mixing coefficients for the 30013←00001 and 30012←00001 bands of 16O12C16O centered near 6227 and 6348 cm–1, respectively. These parameters were determined from 15 self-broadened and six Ar-broadened CO2 spectra recorded at room temperature with long absorption path lengths (25 to 121 m) using the McMath–Pierce Fourier transform spectrometer (FTS) at the National Solar Observatory. All 21 spectra were fit simultaneously using a multispectrum nonlinear least-squares technique. The line positions and line intensities were constrained to quantum mechanical expressions to obtain maximum accuracies in the retrieved parameters. Speed-dependent line shapes with line mixing (via the relaxation matrix formalism) were required to remove systematic errors in the fit residuals using only the Voigt profile. Remaining fit residuals were minimized by adjusting the half-width and pressure-induced shift coefficients of the overlapping 31113←01101 and 31112←01101 hot bands. We compare the Ar-broadening parameters with those recently determined for self- and air-broadening in the 30012←00001 and 30013←00001 bands and also with other Ar-broadening values from the literature, as appropriate.

Fluorescence lifetime discrimination using expectation-maximization algorithm with joint deconvolution

The fluorescence lifetime technique offers an effective way to resolve fluorescent components with overlapping emission spectra. The presence of multiple fluorescent components in biological compounds can hamper their discrimination. The conventional method based on the nonlinear least-squares technique is unable to consistently determine the correct number of fluorescent components in a fluorescence decay profile. This can limit the applications of the fluorescence lifetime technique in biological assays and diagnoses where more than one fluorescent component is typically encountered. We describe the use of an expectation-maximization (EM) method with joint deconvolution to estimate the fluorescence decay parameters, and the Bayesian information criterion (BIC) to accurately determine the number of fluorescent components. A comprehensive simulation and experimental study is carried out to compare the performance and accuracy of the proposed method. The results show that the EM-BIC method is able to accurately identify the correct number of fluorescent components in samples with weakly fluorescing components.

A numerical solution based parameter estimation method for flash thermal diffusivity measurements

Abstract A data reduction method based on numerical solutions of the heat conduction equation has been developed for obtaining thermal diffusivity values from thermal flash measurements. Using the new method, the computed evolution in temperature is fitted to the measured temperature evolution instead of using the t1/2 point alone, as is done in many other analyzes. The numerical solutions used are based on the finite-difference technique applied to the heat conduction equation including all the boundary conditions. A nonlinear least-squares regression technique is used to estimate simultaneously the thermal diffusivity, the heat transfer coefficient and the absorbed energy. Also, the effect of a finite pulse-width can be corrected without knowing the exact shape of the heat pulse.

AN ANALYTIC FORM FOR THE INTERRESPONSE TIME ANALYSIS OF SHULL, GAYNOR, AND GRIMES WITH APPLICATIONS AND EXTENSIONS

Shull, Gaynor and Grimes advanced a model for interresponse time distribution using probabilistic cycling between a higher-rate and a lower-rate response process. Both response processes are assumed to be random in time with a constant rate. The cycling between the two processes is assumed to have a constant transition probability that is independent of bout length. This report develops an analytic form of the model which has a natural parametrization for a higher-rate within-bout responding and a lower-rate visit-initiation responding. The analytic form provides a convenient basis for both a nonlinear least-squares data reduction technique to estimate the model's parameters and Monte Carlo simulations of the model. In addition, the analytic formulation is extended to both a refractory period for the rats' behavior and, separately, the strongly-banded behavior seen with pigeons.

Integrated geophysical mapping of the Ifewara transcurrent fault system, Nigeria

Integrated geophysical methods involving magnetic and dipole–dipole resistivity (DDR) were conducted across a prominent zone of weakness clearly observable in Landsat MSS and SLAR images in the Precambrian basement complex of southwestern Nigeria. Up till now, the location and existence of this megascopic structure have not been confirmed using geophysical methods. With the objective of delineating this weak zone and its structural attributes, three traverses were established at 500 m intervals across it, and geophysical measurements were made at 10 m intervals along these traverses. Qualitative interpretation of the magnetic data obtained shows a diagnostic signature of a near-vertical fault, trending along a NNE–SSW direction. Also, the quantitative interpretation of the data using the non-linear least-squares regression technique indicates that the width of the magnetic anomaly ranges from 90 to 150 m, its dip angle varies between 75° and 85°; the anomaly is concealed by a regolith of approximately 15 m thickness. Furthermore, a 2D resistivity inversion of the field resistivity data reveals a three-layer model, representing thin resistive topsoil underlain by weathered bedrock, resistive bedrock with a distinct low resistivity zone located within the bedrock. The most plausible explanation for this low resistivity zone is that it was formed by shearing activities during Late Precambrian times. Conclusively, the integrated approach employed in this research confirms the existence of the supposed Ifewara shear zone (ISZ).

Quantitative sonoelastography for the in vivo assessment of skeletal muscle viscoelasticity

A novel quantitative sonoelastography technique for assessing the viscoelastic properties of skeletal muscle tissue was developed. Slowly propagating shear wave interference patterns (termed crawling waves) were generated using a two-source configuration vibrating normal to the surface. Theoretical models predict crawling wave displacement fields, which were validated through phantom studies. In experiments, a viscoelastic model was fit to dispersive shear wave speed sonoelastographic data using nonlinear least-squares techniques to determine frequency-independent shear modulus and viscosity estimates. Shear modulus estimates derived using the viscoelastic model were in agreement with that obtained by mechanical testing on phantom samples. Preliminary sonoelastographic data acquired in healthy human skeletal muscles confirm that high-quality quantitative elasticity data can be acquired in vivo. Studies on relaxed muscle indicate discernible differences in both shear modulus and viscosity estimates between different skeletal muscle groups. Investigations into the dynamic viscoelastic properties of (healthy) human skeletal muscles revealed that voluntarily contracted muscles exhibit considerable increases in both shear modulus and viscosity estimates as compared to the relaxed state. Overall, preliminary results are encouraging and quantitative sonoelastography may prove clinically feasible for in vivo characterization of the dynamic viscoelastic properties of human skeletal muscle.

Parameter optimization for differential equations in asset price forecasting

A system of nonlinear asset flow differential equations (AFDE) gives rise to an inverse problem involving optimization of parameters that characterize an investor population. The optimization procedure is used in conjunction with daily market prices (MPs) and net asset values to determine the parameters for which the AFDE yield the best fit for the previous n days. Using these optimal parameters, the equations are computed and solved to render a forecast for MPs for the following days. For a number of closed-end funds, the results are statistically closer to the ensuing MPs than the default prediction of random walk (RW). In particular, we perform this optimization by a nonlinear computational algorithm that combines a quasi-Newton weak line search with the Broyden–Fletcher–Goldfarb–Shanno formula. We develop a nonlinear least-square technique with an initial value problem (IVP) approach for arbitrary stream data by focusing on the MP variable P since any real data for the other three variables B, ζ1, and ζ2 in the dynamical system is not available explicitly. We minimize the sum of exponentially weighted squared differences F[[Ktilde]] between the true trading prices from Day i to Day i+n−1, and the corresponding computed MPs obtained from the first row vector of the numerical solution U of the IVP with AFDE for ith optimal parameter vector, where [Ktilde] is an initial parameter vector. Here, the gradient (∇ F(x)) is approximated by using the central difference formula, and step length s is determined by the backtracking line search. One of the novel components of the proposed asset flow optimization forecast algorithm is a dynamic initial parameter pool that contains most recently used successful parameters, besides the various fixed parameters from a set of grid points in a hyper-box.