Improved Levenberg-Marquardt Algorithm Research Articles

Soft sensor modeling based on self-organizing fuzzy neural network with clustering, merging, and splitting scheme

Abstract As a pivotal role in the control, optimization, and monitoring of contemporary industrial processes, soft sensors are frequently employed in the prediction of key quality variables. To achieve accurate prediction of key quality variables in industrial processes, a soft sensor modeling method based on the self-organizing fuzzy neural network with the clustering, merging, and splitting scheme (SOFNN-CMS) is proposed. First, the supervised fuzzy C-means clustering algorithm is proposed to identify the appropriate initial center and width of the fuzzy neural network, obtaining appropriate initial fuzzy rules. Then, a neuron merging and splitting strategy is designed to adjust the structure of the fuzzy neural network, by merging and splitting the hidden neurons according to the distance of clusters, increasing the adaptability of the fuzzy neural network. Besides, to accelerate the convergence of estimation errors, an improved Levenberg Marquardt algorithm is utilized to update neural network parameters in the training phase, realizing the soft sensor modeling of key quality variables. The effectiveness of the proposed SOFNN-CMS neural network is demonstrated on two benchmark problems and an industrial debutanizer column. Finally, the experiments showcase that the proposed SOFNN-CMS neural network can obtain better soft sensor modeling performance with a compact structure.

Application of self-learning interval type-2 fuzzy neural network in PM2.5 concentration prediction

Abstract The change of PM2.5 concentration in air quality is nonlinear and difficult to predict. Therefore, a self-learning interval type-2 fuzzy neural network (SLIT2FNN) is proposed. SLIT2FNN has two parts: online structure learning and parameter learning. In structure learning, to improve the training accuracy and speed of the model, the Possibilistic Fuzzy C-Means (PFCM) algorithm is used to process the input data and obtain the number of initial rules before model training. The PFCM algorithm introduces the concept of possibility P to Fuzzy C-Means (FCM), allowing PFCM to overcome the shortcomings of FCM that cannot accurately cluster a large number of nonlinear problems. SLIT2FNN can establish an appropriate number of rules in the preparation stage, and then use the firing strength of the antecedents of the rules to judge whether to generate fuzzy rules for online self-learning, thereby optimizing its network structure. Then, the improved Levenberg–Marquardt (ILM) algorithm is used to modify the relevant parameters of SLIT2FNN. The ILM algorithm can address the challenge of numerous parameters in the Jacobian matrix and complex calculations and improve the calculation speed and adaptive ability of SLIT2FNN parameter learning. Finally, SLIT2FNN is applied to the prediction of air quality PM2.5 concentration, and the performance is compared with other models. The experiment proves that SLIT2FNN has a high prediction accuracy and fast convergence.

Point cloud registration of arrester based on scale-invariant points feature histogram

Arrester is an important lightning protection device in the electrical field. The parameters of arrester such as creepage distance, umbrella distance and diameter are important for product quality, but they are difficult to measure because the shape of arrester is irregular. However, the three-dimensional (3D) reconstruction technique is efficient in measuring arrester parameters. The uniform distributed structure of umbrella skirt on the arrester surface restrict the registration of point cloud. In this paper, a scale-invariant points features histogram (SIPFH) descriptor is proposed; the descriptor combines the characteristics of Scale-invariant Feature Transform (SIFT) and fast point feature histogram (FPFH). Moreover, the improved Levenberg-Marquardt (LM) algorithm is presented, the maximum distance of corresponding points in the iterative process is adjusted to realize the local optimization. The point cloud registration method consists of two parts: primary registration method based on SIPFH, and secondary registration method based on improved LM algorithm. Point clouds of different arresters are collected to establish datasets, some of which have interference. Experimental results indicate that the root mean square error of the method is less than 0.02 m; the average running time is 2.7 s, which is 41.4% of the conventional method based on FPFH.

An Efficient Multi-parameter Synchronous Identification Method for Fiber-Reinforced Laminated Structure Based on Improved Levenberg–Marquardt Algorithm and Modal Data

An Efficient Multi-parameter Synchronous Identification Method for Fiber-Reinforced Laminated Structure Based on Improved Levenberg–Marquardt Algorithm and Modal Data

An improved Levenberg–Marquardt method for nonsmooth equations with application to multi-stream heat exchangers

Systems of nonsmooth equations are very useful in the study of nonlinear complementarity problems, variational inequality problems, bilevel programming problems, and arise in the mathematical modeling of many problems in chemical processing, mechanics and engineering. In this paper, we introduce a hybrid method for solving systems of nonsmooth equations, which combines the idea of Levenberg–Marquardt–type methods with bundle techniques, while avoiding the hypothesis of differentiability of the least squares merit function. Some numerical results comparing the proposed method with LP-Newton method indicate that the improved Levenberg–Marquardt algorithm works quite well in practice. As an application of the proposed algorithm, we consider the multi-stream heat exchanger network problem, where a heat exchange network must be designed to meet a specified exit temperature for a given set of streams.

Fuzzy Wavelet Neural Network with the Improved Levenberg–Marquardt Algorithm for the AC Servo System

In this study, a fuzzy wavelet neural network with the improved Levenberg–Marquardt algorithm (FWNN-LM) is proposed to conquer nonlinearity and uncertain disturbance problems in the AC servo system. First of all, use the particle swarm optimization algorithm based on Levenberg–Marquardt (LM) to optimize parameters in the FWNN controller. Second, the potentiality of fuzzy rules (PFR) method is developed to optimize the structure of the FWNN by error reduction ratio (ERR). Furthermore, stability of FWNN-LM is proved by the Lyapunov method. Finally, simulation and prototype test results show that this method can improve the accuracy and robustness of the system in presence of load disturbances and parameter perturbations.

Prediction of SLM-NiTi transition temperatures based on improved Levenberg–Marquardt algorithm

In this study, we have obtained the corresponding relationship between SLM-NiTi alloy transition temperatures and energy density, and realized the accurate prediction and inverse prediction of SLM process parameters and NiTi alloy transition temperatures. And we verify the accuracy of the prediction model through DSC, XRD and SEM. Secondly, B19′NiTi and B2NiTi are successfully obtained through the prediction model. Finally, a composite gradient NiTi is established based on the idea of rigid-flexible coupling, which successfully achieved the simultaneous improvement of the strength and toughness of the SLM-NiTi alloy. The compressive fracture strength reached 2668 MPa, and the fracture strain reached 55.51%.

Static analysis and verification of flexible riser for underwater compressed air energy storage system with different boundary conditions

ABSTRACT In an underwater compressed air energy storage system, fracture of the flexible riser often occurs. To solve this problem, we proposed a static analysis method for a flexible riser based on Cosserat theory. Bending and torsion deformation of a flexible riser were described. Using Euler parameters, static equilibrium differential equations were established. Finite element discretization, finite difference, and an improved Levenberg–Marquardt algorithm were used to perform the numerical calculations. Based on the similarity principle, experiments with three different boundary conditions were performed. Our static model and the OrcaFlex simulations were compared with experiments, and the average error of our static model was 2.9% smaller than that of the simulation. The results showed that the static model presented in this paper was more accurate than the OrcaFlex simulation calculation. This model is useful for estimating the mechanical characteristics and determining the strengths of flexible risers.

The atmospheric model of neural networks based on the improved Levenberg-Marquardt algorithm

Abstract Traditional atmospheric models are based on the analysis and fitting of various factors influencing the space atmosphere density. Neural network models do not specifically analyze the polynomials of each influencing factor in the atmospheric model, but use large data sets for network construction. Two traditional atmospheric model algorithms are analyzed, the main factors affecting the atmospheric model are identified, and an atmospheric model based on neural networks containing various influencing factors is proposed. According to the simulation error, the Levenberg-Marquardt algorithm is used to iteratively realize the rapid network weight correction, and the optimal neural network atmospheric model is obtained. The space atmosphere is simulated and calculated with an atmospheric model based on neural networks, and its average error rate is lower than that of traditional atmospheric models such as the DTM2013 model and the MSIS00 model. At the same time, the calculation complexity of the atmospheric model based on the neural networks is significantly simplified than that of the traditional atmospheric model.

Modeling of energy consumption and effluent quality using density peaks-based adaptive fuzzy neural network

Modeling of energy consumption &#x0028 EC &#x0029 and effluent quality &#x0028 EQ &#x0029 are very essential problems that need to be solved for the multiobjective optimal control in the wastewater treatment process &#x0028 WWTP &#x0029. To address this issue, a density peaks-based adaptive fuzzy neural network &#x0028 DP-AFNN &#x0029 is proposed in this study. To obtain suitable fuzzy rules, a DP-based clustering method is applied to fit the cluster centers to process nonlinearity. The parameters of the extracted fuzzy rules are fine-tuned based on the improved Levenberg-Marquardt algorithm during the training process. Furthermore, the analysis of convergence is performed to guarantee the successful application of the DPAFNN. Finally, the proposed DP-AFNN is utilized to develop the models of EC and EQ in the WWTP. The experimental results show that the proposed DP-AFNN can achieve fast convergence speed and high prediction accuracy in comparison with some existing methods.

Improvement of Levenberg-Marquardt algorithm during history fitting for reservoir simulation

Abstract In order to estimate reservoir parameters more effectively by history fitting, DE (Differential Evolution) was proposed to estimate the optimum damping factor so that the standard Levenberg-Marquardt algorithm was improved, and the improved algorithm was validated by analysis of examples. The standard LM algorithm uses trial-and-error method to estimate the damping factor and is less reliable for large scale inverse problems. DE can solve this problem and eliminate the use of line search for an appropriate step length. The improved Levenberg-Marquardt algorithm was applied to match the histories of two synthetic reservoir models with different scales, and compared with other algorithms. The results show that: DE speeds up the convergence rate of the LM algorithm and reduces the residual errors, making the algorithm suitable for not only small and medium scale inverse problems, but also large scale inverse problems; if the iteration termination criteria of LM algorithm is preset, the improved algorithm will save the number of iterations and reduce the total time greatly needed for the LM algorithm, leading to higher efficiency of history matching.

Inverse analysis of non-uniform temperature distributions using multispectral pyrometry

Optical diagnostics can be used to obtain sub-pixel temperature information in remote sensing. A multispectral pyrometry method was developed using multiple spectral radiation intensities to deduce the temperature area distribution in the measurement region. The method transforms a spot multispectral pyrometer with a fixed field of view into a pyrometer with enhanced spatial resolution that can give sub-pixel temperature information from a “one pixel” measurement region. A temperature area fraction function was defined to represent the spatial temperature distribution in the measurement region. The method is illustrated by simulations of a multispectral pyrometer with a spectral range of 8.0–13.0μm measuring a non-isothermal region with a temperature range of 500–800K in the spot pyrometer field of view. The inverse algorithm for the sub-pixel temperature distribution (temperature area fractions) in the “one pixel” verifies this multispectral pyrometry method. The results show that an improved Levenberg–Marquardt algorithm is effective for this ill-posed inverse problem with relative errors in the temperature area fractions of (–3%, 3%) for most of the temperatures. The analysis provides a valuable reference for the use of spot multispectral pyrometers for sub-pixel temperature distributions in remote sensing measurements.

Accurate modification methodology of universal machine tool settings for spiral bevel and hypoid gears

Universal machine tool settings with higher-order motion coefficients are developed to make accurate modification considering the actual machine geometric error compensation for spiral bevel and hypoid gears. First, the universal machine tool settings are exploited for the identification of the real tooth flank form error. Furthermore, the error sensitivity analysis method and an improved Levenberg–Marquardt algorithm with a trust-region strategy are utilized to obtain the solution of modification amount. Finally, a higher-order modification methodology for the universal machine tool settings is proposed which mainly covers three vital parts: (a) optimized selection of the modification settings, (b) modification of universal machine tool settings, and (c) machine geometric error compensation. Especially, a higher-accuracy fitting method for the form error tooth flank is investigated. Some numerical examples verify that the tooth flank form error after higher-order modification can reach less than 0.5 µm or even a smaller one, and the position error after compensating process spindle can be reduced from 0.0044861° to 0.0009232°. In addition, given experimental result can validate the feasibility of the proposed methodology.

Improved extreme learning machine for multivariate time series online sequential prediction

Multivariate time series has attracted increasing attention due to its rich dynamic information of the underlying systems. This paper presents an improved extreme learning machine for online sequential prediction of multivariate time series. The multivariate time series is first phase-space reconstructed to form the input and output samples. Extreme learning machine, which has simple structure and good performance, is used as prediction model. On the basis of the specific network function of extreme learning machine, an improved Levenberg–Marquardt algorithm, in which Hessian matrix and gradient vector are calculated iteratively, is developed to implement online sequential prediction. Finally, simulation results of artificial and real-world multivariate time series are provided to substantiate the effectiveness of the proposed method.

Research on the NNARX Model Identification of Hydroelectric Unit Based on Improved L-M Algorithm

Its hard to use traditional ways to set up a hydroelectric power plant model due to its complex, time-varying and nonlinear characteristics. This article uses the neural network autoregressive with exogenous input (NNARX) to identify and model hydro-turbine generating unit which is the key in the hydroelectric power plant modeling. The random guide vain signal is used to train NNARX in this paper and the other two working conditions are used to check its generalization ability. In order to improve identification accuracy, generalization performance and training speeds, an improved Levenberg-Marquardt algorithm is proposed in this article which is based on the L-M algorithm that widely used in artificial neural network weights adjustment. Simulation results indicate that NNARX model with improved L-M algorithm can reach high recognition accuracy and have good generalization ability. It can provide a good simulation model for intelligent controller design in the future.

An improved Levenberg–Marquardt algorithm for extracting the features of Brillouin scattering spectrum

To extract the features of the Brillouin scattering spectrum in distributed sensing systems, an improved Levenberg–Marquardt (L-M) algorithm based on finite element analysis (FEA-LM algorithm) is proposed. The simulation data of different linewidth and signal-to-noise ratio (SNR) are analyzed by using the FEA-LM algorithm and the Brillouin center frequency shifts are extracted. The operational precision of the L-M and FEA-LM algorithms are compared in a certain range of initial value. The result shows that the FEA-LM algorithm can be appropriate for extracting the feature of the Brillouin scattering spectrum with different linewidth and SNR. Moreover, it has an advantage in precision by comparing with the L-M algorithm.

Identification de piézoviscosité en lubrification

In order to design better mechanisms, the piezoviscosity, i.e., the sensitivity of lubricant viscosity to pressure changes, needs to be accounted for. A strategy for identifying piezoviscosity based on image analysis and numerical identification is devised in two steps. Firstly, the identifiability of three piezoviscosity models (Barus, Roelands and WLF) is analyzed by minimizing a least squares distance between pressure–viscosity responses. Numerical difficulties stem from magnitude differences between parameters and from the wide range of viscosity/pressure values. A strategy based on an improved Levenberg–Marquardt algorithm is proposed. Improvements concern respect of parameter bounds and scaling. The non-identifiability of the WLF piezoviscosity model at constant temperature is proved. Secondly, the piezoviscosity identification strategy is applied to data for noisy lubricant thickness and pressure fields. In this case, piezoviscosity can be recovered by minimizing the Reynolds equations residual globally in the field. A method for smoothing and numerical differentiation of the measurements is described. It is based on building a local polynomial approximation to the field. Using noisy field measurements, piezoviscosity parameters are finally estimated within 5% accuracy.

Modern photographic developments

Optical diagnostics can be used to obtain sub-pixel temperature information in remote sensing. A multispectral pyrometry method was developed using multiple spectral radiation intensities to deduce the temperature area distribution in the measurement region. The method transforms a spot multispectral pyrometer with a fixed field of view into a pyrometer with enhanced spatial resolution that can give sub-pixel temperature information from a “one pixel” measurement region. A temperature area fraction function was defined to represent the spatial temperature distribution in the measurement region. The method is illustrated by simulations of a multispectral pyrometer with a spectral range of 8.0–13.0 μm measuring a non-isothermal region with a temperature range of 500–800 K in the spot pyrometer field of view. The inverse algorithm for the sub-pixel temperature distribution (temperature area fractions) in the “one pixel” verifies this multispectral pyrometry method. The results show that an improved Levenberg–Marquardt algorithm is effective for this ill-posed inverse problem with relative errors in the temperature area fractions of (–3%, 3%) for most of the temperatures. The analysis provides a valuable reference for the use of spot multispectral pyrometers for sub-pixel temperature distributions in remote sensing measurements.