Modified Levenberg-Marquardt Algorithm Research Articles

A Modified Levenberg Marquardt Algorithm for Simultaneous Learning of Multiple Datasets

A Modified Levenberg Marquardt Algorithm for Simultaneous Learning of Multiple Datasets

B-145 An R Shiny App for Automated Peak Deconvolution, Interpretation, and Quantitation of Monoclonal Proteins Using Capillary Electrophoresis Immunotyping Data

Abstract Background Machine learning methods have been utilized to train algorithms for interpretation of immunofixation electrophoresis. This work developed an R Shiny app for immunotyping (IT) data capable of deconvoluting discrete peaks in overlapping backgrounds and automatic quantitation of monoclonal proteins. Unlike machine learning which obfuscates decision making, each step of this deconvolution and quantitation process is displayed to the end user. Methods Individual traces for 1315 previously interpreted IT results were used in the study. A modified Levenberg-Marquardt algorithm using 50 sets of randomized start parameters was used for deconvolution. Primitive peak features such as height, FWHM, AUC and retention time were used to match heavy and light chain deconvoluted peaks for interpretation. The matched peak with the largest AUC was compared to reviewer interpretation and peak quantitation. Repeatability of quantitation was evaluated through 10 consecutive rounds of deconvolution. Code was written for end user visualization in Shiny or batch processing in base R. Results Deconvolution was successful for 97.2% (1279/1315) of specimens. Agreement between the software and reviewer interpretation was 90.6% (11 927/13 150) across all deconvolutions and was consistent for 84.7% of samples in all 10 rounds of deconvolution. Discordant interpretation in 15.3% of samples was often attributed to splitting of large peaks with sharp maximums, large percentage (but small absolute) changes in calculated AUC for monoclonal proteins under 0.5 g/dL, or drifting baseline signal between channels. Mean and median percent CV for consecutive rounds of monoclonal quantitation was 5.9% and 1.16% respectively (protein range 0.02–4.5 g/dL). Deming regression of reviewer vs software quantitation had a calculated slope of 0.728 and Pearson’s r coefficient of 0.933. Conclusion Deconvolution and automatic quantitation of monoclonal protein peaks is possible using the Levenberg-Marquardt algorithm for immunotyping data. Future work aims to improve interpretation agreement with reviewers using more advanced ranking of matched peaks.

Application of Group Method of Data Handling via a Modified Levenberg-Marquardt Algorithm in the Prediction of Compressive Strength of Oilwell Cement with Reinforced Fly Ash Based on Experimental Data

SummaryThe experimental design of well cement with durable compressive strength (CS) is challenging and time-consuming. The current research predicts CS using the enhanced group method of data handling via a modified Levenberg-Marquardt algorithm (GMDH-LM) with experimental data. Class F fly ash (CFFA) is used as a supplementary material to cement at various proportions. Experimental tests of CS, thermogravimetric (TG) analysis, rheology, and scanning electron microscopy (SEM) are applied. Experimental findings revealed that the addition of fly ash (FA) enhances CS with curing time as an outcome of pozzolanic action. CS for 20% FA reinforcement after curing for 28 days was 42.95 MPa, compared with 41.53 MPa for 50%. This indicates that a higher addition of FA lowers CS. The rheological findings revealed that FA enhanced the viscosity of the cement slurry. The SEM images demonstrated that the incorporation of CFFA with cement modified the contexture of hardened cement. Cement, water, oilwell cement (OWC), curing time, dispersant, and FA were assigned as input variables for GMDH-LM while CS from the experimental analysis was set as output. Machine learning (ML) findings indicated that GMDH-LM can effectively estimate the CS of OWC. GMDH-LM performed better than backpropagation neural network (BPNN), support vector machine (SVM), and normal GMDH models in predicting CS; it provided higher linearity during training as GMDH-LM gave R2 = 0.958, GMDH = 0.946, SVM = 0.925, BPNN = 0.897, and the least loss functions of mean square error (MSE) = 0.238, MSE = 1.685, MSE = 2.567, and MSE = 4.032, respectively. Similarly, good results were ascertained during testing GMDH-LM provided R2 = 0.928, GMDH = 0.907, SVM = 0.895, BPNN = 0.878, and the lowest loss functions of MSE = 0.304, MSE = 2.650, MSE = 3.494, and MSE = 5.678, respectively. Therefore, the comparative results of all experiments and predictions reveal that GMDH-LM can be deployed as an advanced approach for the estimation of cement hydration in oil and gas wells.

Convergence rate of the modified Levenberg-Marquardt method under Hölderian local error bound

Abstract In this article, we analyze the convergence rate of the modified Levenberg-Marquardt (MLM) method under the Hölderian local error bound condition and the Hölderian continuity of the Jacobian, which are more general than the local error bound condition and the Lipschitz continuity of the Jacobian. Under special circumstances, the convergence rate of the MLM method coincides with the results presented by Fan. A globally convergent MLM algorithm by the trust region technique will also be given.

Optimization of number of microphones and microphone spacing using time delay based multilateration approach for explosive sound source localization

The use of microphone array for sound source localization has been a trending area of research in speech source recognition, battlefield acoustics, etc. For such applications, the localization accuracy is significantly influenced by the number of microphones and their arrangement on the ground surface. Thus, this paper proposes optimized microphone array geometries with the optimized number of microphones for positioning near and distant sound sources. Moreover, this paper also discusses the significance of the reference microphone selection on positioning accuracy. Here, the time-delay-based multilateration approach is used to formulate the governing nonlinear hyperbolic equations for sound source localization. The resulting equations are solved using the least square optimizer, the modified Levenberg Marquardt algorithm. The source results for several customized array structures are validated through simulation and experimental studies. Based on the results, this paper proposes that at least six microphones are required to identify a source position (<1800 m) with 97 % accuracy at lower noise thresholds (SNR: (6 to 20) dB) and 95 % accuracy at higher noise thresholds (SNR: -6 to 0 dB). Moreover, the paper suggests that microphone spacing should be a minimum of 0.34 times the source range for localization of distant sound sources to improve accuracy at higher and lower noise levels.

Prediction of blasting induced air-overpressure using a radial basis function network with an additional hidden layer

Blasting operations are the most conventional and frequently used rock breakage approach in the field of Civil and Mining Engineering. However, the side effects induced by blasting may cause severe damages to surrounding areas. Air-overpressure (AOp) is one of the side effects induced by blasting operations, which is defined as the air pressure wave generated by blasting operation that exceeds normal atmospheric pressure. It can result in potential structural damage and glass breaking and therefore needs to be well predicted and subsequently minimized. In this study, 76 sets of blasting data were collected to develop a predictive model to estimate AOp value. However, due to the small size of dataset, it is hard to determine the complexity of the model. Therefore, for the purpose of developing a machine learning model with appropriate complexity, a radial basis function network with an additional second hidden layer (RBF-2) is proposed, which is trained by incremental design principle and modified Levenberg–Marquardt algorithm. The performance of the proposed RBF-2 is compared with those of five other machine learning techniques, i.e., multilayer perceptron (MLP), RBF, MLP optimized by genetic algorithm (GA-MLP), multi adaptive regression spline (MARS) and random forest (RF). The results demonstrate that the proposed RBF-2 network outperforms other models with RMSE of 2.02/1.98, MAPE of 1.32%/1.40%, and R of 0.9828/0.9735 in training/testing stage. Findings revealed that the proposed RBF-2 network emerged as the most efficient, powerful and robust technique in predicting blast induced AOp compared with other machine learning models.

A parameter identification technique for traffic speed deflectometer tests of pavements

The structural evaluation of existing pavements forms the basis for formulating cost-effective maintenance and rehabilitation strategies. A promising tool for pavement structural evaluation at network level is the Traffic Speed Deflectometer (TSD) test. However, the application of the TSD test is hindered by the lack of a robust and efficient parameter identification technique. To solve this problem, a theoretical model for the TSD test is first formulated. Then, a minimisation algorithm which works best with the theoretical TSD model for parameter identification is selected. Finally, the performance of this combination in processing field TSD measurements is studied. The results show that the modified Levenberg-Marquardt algorithm using all the 9 detection points is most suitable to be combined with the theoretical TSD model for parameter identification, which gives a promising parameter identification technique for TSD tests of pavements. The presented work contributes to the development of technologies for pavement structural evaluation.

A new method for identifying temperature-dependent thermal conductivity in transient heat conduction problems based on element differential method

In order to accurately identify the temperature-dependent thermal conductivity of solids, a novel method which combines the element differential method (EDM) with the modified Levenberg-Marquardt algorithm (LMA) is firstly proposed to solve the inverse heat conduction problems, where complex variable derivative method (CVDM) is introduced to obtain the derivatives of the observed temperature with respect to the unknown variables. In this paper, the conventional EDM is transformed from the real domain to the complex domain, and then the transient heat conduction problems with complex-variable temperature-dependent thermal conductivity are solved to obtain the numerical temperature solutions of the measuring points using the EDM. The real part of numerical temperature and the corresponding measured temperature are used to build the objective function, and the imaginary part of numerical temperature is used to calculate the sensitivity coefficients of the LMA using the CVDM. Thus, the LMA is modified to stably obtain the sensitivity of the temperature to the unknown variables, and it is used to iteratively optimize the unknown temperature-dependent thermal conductivity by minimizing the objective function. Finally, three numerical examples with the different forms of temperature-dependent thermal conductivity are considered in this paper, and the effects of the different initial values and measurement errors on the inversion results are fully investigated. The results show that the proposed method shows good accuracy, efficiency and robustness in identifying the temperature-dependent thermal conductivity with specific function and that without function form in 2D and 3D models.

Explosive sound source localization in indoor and outdoor environments using modified Levenberg Marquardt algorithm

In this paper, a modified Levenberg-Marquardt algorithm (MLMA) is proposed to localize the ‘point of burst’ of an explosive sound source over the range of (0.5–2500) m. The objective function for minimization is formulated through the time difference of arrival based multilateration approach. The developed method uses four exclusive steps to satisfy global convergence along with fast computational speed. The performance of the proposed method is validated through both indoor-outdoor experiments and simulation studies and compared to other well-known methods. The experimental results show that the non-iterative approaches perform satisfactorily only if the ratio of microphone spacing to source rangeris greater than 0.30. However, the iterative approaches outperform non-iterative approaches for anyr. It is also observed that the MLMA converges globally at least five times faster than other algorithms. The numerical simulation results also demonstrate that the MLMA provides optimal solutions at lower and higher noise thresholds.

Investigation of Electrochemical Processes in Solid Oxide Fuel Cells by Modified Levenberg–Marquardt Algorithm: A New Automatic Update Limit Strategy

Identification of ongoing processes in solid oxide fuel cells (SOFC) enables both optimizing the operating environment and prolonging the lifetime of SOFC. The Levenberg–Marquardt algorithm (LMA) is commonly used in the characterization of unknown electrochemical processes within SOFC by extracting equivalent electrical circuit (EEC) parameter values from electrochemical impedance spectroscopy (EIS) data. LMA is an iteration optimization algorithm regularly applied to solve complex nonlinear least square (CNLS) problems. The LMA convergence can be boosted by the application of an ordinary limit strategy, which avoids the occurrence of off-limit values during the fit. However, to additionally improve LMA descent properties and to discard the problem of a poor initial parameters choice, it is necessary to modify the ordinary limit strategy. In this work, we designed a new automatic update (i.e., adaptive) limit strategy whose purpose is to reduce the impact of a poor initial parameter choice. Consequently, the adaptive limit strategy was embedded in a newly developed EIS fitting engine. To demonstrate that the new adaptive (vs. ordinary) limit strategy is superior, we used it to solve several CNLS problems. The applicability of the adaptive limit strategy was also validated by analyzing experimental EIS data collected by using industrial-scale SOFCs.

Apparent temperature in temperature-sensitive paint measurement and its effect on surface heat flux determination for hypersonic flows

Non-zero temperature gradients in temperature-sensitive paint (TSP) cause the apparent temperature (the temperature measured by the TSP) to correspond to the temperature somewhere inside the TSP, which does not equal the top surface temperature. Treating the apparent temperature as the average temperature across the TSP layer is not always accurate, especially when there is a large temperature gradient in the TSP. In this paper, the apparent temperature is theoretically derived by integrating the luminescent intensity across the TSP layer and numerically determined using a Monte Carlo ray-tracing method. The results of a simulation show that the difference between the apparent and average temperatures increases with the temperature gradient in the TSP layer, which leads to a non-negligible error when determining the surface heat flux based on the average temperature. A modified Levenberg–Marquardt algorithm is used to accurately recover the surface heat flux based on the apparent temperature for typical optical conditions in the measurement system. The results are compared with those obtained using the average temperature of the TSP. The effects of heat flux, TSP thickness and base material on the errors in the determination of the heat flux are investigated in detail.

Diesel Generator Model Parameterization for Microgrid Simulation Using Hybrid Box-Constrained Levenberg-Marquardt Algorithm

Existing generator parameterization methods, typically developed for large turbine generator units, are difficult to apply to small kW-level diesel generators in microgrid applications. This article presents a model parameterization method that estimates a complete set of kW-level diesel generator parameters simultaneously using only load-step-change tests with limited measurement points. This method provides a more cost-efficient and robust approach to achieve high-fidelity modeling of diesel generators for microgrid dynamic simulation. A two-stage hybrid box-constrained Levenberg-Marquardt (H-BCLM) algorithm is developed to search the optimal parameter set given the parameter bounds. A heuristic algorithm, namely Generalized Opposition-based Learning Genetic Algorithm (GOL-GA), is applied to identify proper initial estimates at the first stage, followed by a modified Levenberg-Marquardt algorithm designed to fine tune the solution based on the first-stage result. The proposed method is validated against dynamic simulation of a diesel generator model and field measurements from a 16kW diesel generator unit.

Stability Analysis of the Modified Levenberg-Marquardt Algorithm for the Artificial Neural Network Training.

The Levenberg-Marquardt and Newton are two algorithms that use the Hessian for the artificial neural network learning. In this article, we propose a modified Levenberg-Marquardt algorithm for the artificial neural network learning containing the training and testing stages. The modified Levenberg-Marquardt algorithm is based on the Levenberg-Marquardt and Newton algorithms but with the following two differences to assure the error stability and weights boundedness: 1) there is a singularity point in the learning rates of the Levenberg-Marquardt and Newton algorithms, while there is not a singularity point in the learning rate of the modified Levenberg-Marquardt algorithm and 2) the Levenberg-Marquardt and Newton algorithms have three different learning rates, while the modified Levenberg-Marquardt algorithm only has one learning rate. The error stability and weights boundedness of the modified Levenberg-Marquardt algorithm are assured based on the Lyapunov technique. We compare the artificial neural network learning with the modified Levenberg-Marquardt, Levenberg-Marquardt, Newton, and stable gradient algorithms for the learning of the electric and brain signals data set.

Conductivity Profiling of Graphite Moderator Bricks From Multifrequency Eddy Current Measurements

This paper presents a novel system for mapping the through-wall electrical conductivity profiles of graphite moderator bricks that make up the core of an Advanced Gas-Cooled Reactor. Multi-frequency eddy current measurements were used to reconstruct the conductivity profiles as a function of depth from the bores of different graphite bricks. The study was carried out using a modified Levenberg Marquardt algorithm, along with a finite element based forward model. First, the algorithm was tested using a laboratory graphite sample with known electrical conductivity profile. Secondly, real datasets from one of the operating Advanced Gas-Cooled Reactors was collected and then used for reconstruction. The results in this study were compared with measurements from trepanned graphite samples taken from the reactor cores, and showed reasonable agreement in multiple cases, suggesting that this method could be a viable tool for non-destructively assessing the condition of the graphite core in Advanced Gas-Cooled Reactors.

Heuristic Strategies of Modified Levenberg–Marquardt Algorithm for Fitting Transition Curves

AbstractHorizontal curve identification is important both for road safety management and railway maintenance. Parameters of a transition curve are introduced to perform an orthogonal least-squares ...

Solution of the Adiabatic Sound Wave Equation as a Nonlinear Least Squares Problem

A new method for deriving accurate thermodynamic properties of gases and vapors (the compression factor and heat capacities) from the speed of sound is recommended. A set of PDEs connecting speed of sound with other thermodynamic properties is solved as a nonlinear least squares problem, using a modified Levenberg–Marquardt algorithm. In supercritical domain, boundary values of compression factor are imposed along two isotherms (one slightly above Tc and another several times Tc) and two isochores (one at zero density and another slightly above ρc). In subcritical domain, the upper isochore is replaced by the saturation line, the lower isotherm is slightly above the triple point, and the upper isotherm is slightly below the critical point. Initial values of compression factor inside the domains are obtained from the boundary values by a cubic spline interpolation with respect to density. All the partial derivation with respect to density and temperature, as well as speed of sound interpolation with respect to pressure, is also conducted by a cubic spline. The method is tested with Ar, CH4 and CO2. The average absolute deviation of compression factor and heat capacities is better than 0.002 % and 0.1 %, respectively.

Non-kinematic calibration of industrial robots using a rigid–flexible coupling error model and a full pose measurement method

Abstract This study addresses the non-negligible flexibility problem of industrial robots and describes a rigid–flexible coupling error model for robot non-kinematic calibration. Simulation confirms that compliance errors are major sources of inaccuracies and affect robot accuracy with geometric errors. To reduce the impact of measurement noise and improve calibration performance, an enhanced approach is proposed for full pose measurement and identification optimisation. This approach is based on the self-adaption particle swarm optimisation (SAPSO) algorithm with a dual-index (i.e. observability index O1 and identification accuracy index Omin) and a modified Levenberg–Marquardt algorithm, which considers external constraints (i.e. structural interference and angular limitation). Simulation results illustrate that the 36 error parameters of the proposed error model can be identified with improved accuracy and stability using the proposed approach. Finally, experimental results obtained with a Staubli TX60L robot with a FARO laser tracker are introduced to demonstrate the practical effectiveness of our approach in robot accuracy improvement.

Power Market Load Forecasting on Neural Network With Beneficial Correlated Regularization

In day-ahead market (DAM), load serving entities (LSEs) are required to submit their future load schedule to market operator. Due to the cost computation, we have found the inconformity between load accuracy and cost of power purchase. It means that more accurate load forecasting model may not lead to a lower cost for LSEs. Accuracy pursuing load forecast model may not target a solution with optimal benefit. Facing this issue, this paper initiates a beneficial correlated regularization (BCR) for neural network (NN) load prediction. The training target of NN contains both accuracy section and power cost section. Also, this paper establishes a virtual neuron and a modified Levenberg–Marquardt algorithm for network training. A numerical study with practical data is presented and the result shows that NN with BCR can reduce power cost with acceptable accuracy level.

3D Moving Sound Source Localization via Conventional Microphones

In this paper, we present an approach to sound localization for moving sound sources. We use four conventional microphones and a multi-channel sound recording device for capturing sound signals. A database with different types of moving sound source scenarios is created and one of the scenarios is analysed in this paper. This scenario involves walking of a person and creating sounds simultaneously at certain positions in a room, and our aim is to determine the location of the person as three dimensions. We use time difference of arrival for 3D sound source localization. The time delays between sounds channels are obtained by excitation source information based time-delay estimation algorithm. In addition, signal processing methods are used for increasing the success of moving sound source localization. Savitzky-Golay and threshold filters are utilized to pre-filter the recorded sounds and removing the background noise signals, respectively. The non-linear equation of the sound localization is solved by using the modified Levenberg–Marquardt Algorithm (LMA) on the Time Difference of Arrival (TDOA) process. The results for the 3D localization of the moving sound source are obtained by measuring the differences between the real and estimated positions of the person.DOI: http://dx.doi.org/10.5755/j01.eie.23.4.18724

SPIN: An Inversion Code for the Photospheric Spectral Line

Inversion codes are the most useful tools to infer the physical properties of the solar atmosphere from the interpretation of Stokes profiles. In this paper, we present the details of a new Stokes Profile INversion code (SPIN) developed specifically to invert the spectro-polarimetric data of the Multi-Application Solar Telescope (MAST) at Udaipur Solar Observatory. The SPIN code has adopted Milne–Eddington approximations to solve the polarized radiative transfer equation (RTE) and for the purpose of fitting a modified Levenberg–Marquardt algorithm has been employed. We describe the details and utilization of the SPIN code to invert the spectro-polarimetric data. We also present the details of tests performed to validate the inversion code by comparing the results from the other widely used inversion codes (VFISV and SIR). The inverted results of the SPIN code after its application to Hinode/SP data have been compared with the inverted results from other inversion codes.