Feed-forward Neural Network Algorithm Research Articles

Memetic algorithms for training feedforward neural networks: an approach based on gravitational search algorithm

The backpropagation (BP) algorithm is a gradient-based algorithm used for training a feedforward neural network (FNN). Despite the fact that BP is still used today when FNNs are trained, it has some disadvantages, including the following: (i) it fails when non-differentiable functions are addressed, (ii) it can become trapped in local minima, and (iii) it has slow convergence. In order to solve some of these problems, metaheuristic algorithms have been used to train FNN. Although they have good exploration skills, they are not as good as gradient-based algorithms at exploitation tasks. The main contribution of this article lies in its application of novel memetic approaches based on the Gravitational Search Algorithm (GSA) and Chaotic Gravitational Search Algorithm (CGSA) algorithms, called respectively Memetic Gravitational Search Algorithm (MGSA) and Memetic Chaotic Gravitational Search Algorithm (MCGSA), to train FNNs in three classical benchmark problems: the XOR problem, the approximation of a continuous function, and classification tasks. The results show that both approaches constitute suitable alternatives for training FNNs, even improving on the performance of other state-of-the-art metaheuristic algorithms such as ParticleSwarm Optimization (PSO), the Genetic Algorithm (GA), the Adaptive Differential Evolution algorithm with Repaired crossover rate (Rcr-JADE), and the Covariance matrix learning and Bimodal distribution parameter setting Differential Evolution (COBIDE) algorithm. Swarm optimization, the genetic algorithm, the adaptive differential evolution algorithm with repaired crossover rate, and the covariance matrix learning and bimodal distribution parameter setting differential evolution algorithm.

Congestion Prediction System With Artificial Neural Networks

Software Defined Network (SDN) is a programmable network architecture that provides innovative solutions to the problems of the traditional networks. Congestion control is still an uncharted territory for this technology. In this work, a congestion prediction scheme has been developed by using neural networks. Minimum Redundancy Maximum Relevance (mRMR) feature selection algorithm was performed on the data collected from the OMNET++ simulation. The novelty of this study also covers the implementation of mRMR in an SDN congestion prediction problem. After evaluating the relevance scores, two highest ranking features were used. On the learning stage Nonlinear Autoregressive Exogenous Neural Network (NARX), Nonlinear Autoregressive Neural Network, and Nonlinear Feedforward Neural Network algorithms were executed. These algorithms had not been used before in SDNs according to the best of the authors knowledge. The experiments represented that NARX was the best prediction algorithm. This machine learning approach can be easily integrated to different topologies and application areas.

Quantitative assessment of forest ecosystem stress caused by cement plant pollution using in situ measurements and Sentinel-2 satellite data in a part of the UNESCO World Heritage Site

Anthropogenic industrial dust decreases productivity and slows down the growth of plants. Quantifying the effects of industrial dust on vegetation and determining the distance over which factories scatter dust are of paramount importance for biodiversity conservation and sustaining ecosystem services. This study aims at quantifying the effect of dust emitted by the Neka cement plant (NCP), Mazandaran province, northern Iran, on the surrounding Hyrcanian forests based on an analysis of the Leaf Area Index (LAI) retrieved from Sentinel-2 imagery. An Inductively Coupled Plasma Mass Spectrometer (ICP-MS) was used to quantify the concentrations of cadmium (Cd), chromium (Cr), copper (Cu), lead (Pb), calcium (Ca), magnesium (Mg), sodium (Na), silicon (Si) and zinc (Zn) in leaves of the dominant Chestnut-leaved Oak (Quercus castaneifolia). A feed-forward neural network algorithm and field measurements were used to retrieve the leaf area index (LAI) from Sentinel-2 data with a RMSE of 0.42 (m2/m2). MODIS-NDVI and EVI time series spanning 17 years (2000 to 2017) were analysed to ensure the independence of the variation in the condition of the vegetation from drought or other environmental factors. The results indicate that Sentinel-2 data can be used to map degradation due to pollution from the cement plant and quantify the effect of the dust spatially. Dust from the cement plant (dust source) was carried approximately 4700 meters in the direction of the prevailing wind. A significant correlation of 0.849 was recorded between LAI and distance from the NCP. It is concluded that dust from the NCP had adverse ecological effects on the neighbouring forest ecosystems recently designated a UNESCO World Heritage Site.

An efficient background calibration technique for analog-to-digital converters based on neural network

This paper introduces a background digital calibration algorithm based on neural network, which can adaptively calibrate multiple non-ideal factors in a single-channel ADC, such as gain error, mismatch, offset and harmonic distortion. It enables an efficient background calibration through a simple feed forward neural network and LM gradient descent algorithm. The simulation results show that in the case of a signal input close to the Nyquist frequency, for a 14-bit 500 MS/s prototype ADC, only about 40,000 data needed, the ENOB of the ADC can be increased from 7.81 to 13.06 and the SFDR from 49.7 dB to 106.8 dB assisted by a lower speed reference ADC.

Design and Implementation of Intelligent Hybrid Neuro Controller for Automatic Voltage Regulator

In this paper, we presented a hybrid controller by combining the advantages of both PID and Neuro controllers for automatic voltage regulator (AVR) system. A Neuro controller is designed using multilayer feedforward neural network and Levenberg-Marquardt backpropagation algorithm is used for training the network. Also, hybrid controller is achieved by blending the characteristics of classical PID and proposed Neuro controller using a switching mechanism based on the error. The proposed PID, Neuro and Hybrid controllers are simulated in MATLAB environment and their transient response parameters are compared. The simulation results clearly indicated the improvement in the transient output of the automatic voltage regulator system with proposed hybrid controller even in the presence of uncertainties in the system.

An online self-organizing algorithm for feedforward neural network

Feedforward neural network (FNN) is the most popular network model, and the appropriate structure and learning algorithms are the key of its performance. This paper proposes an online self-organizing algorithm for feedforward neural network (OSNN) with a single hidden layer. The proposed OSNN optimizes the structure of FNN for time-varying system including structure design and parameter learning. In structure design, this paper measures the contribution ratios of hidden nodes by local sensitivity analysis based on differentiation method. OSNN merges hidden nodes with the others that have the highest correlation when their contribution ratios are almost zero and adds new hidden nodes by error reparation. For parameter learning, an improved online gradient method (OGM), called online gradient method with fixed memory (FMOGM), is proposed to improve the convergence speed and accuracy of OGM. In addition, this paper calculates the contribution ratios and the network error and estimates the local minima by using the fixed-sized training set of FMOGM instead of one sample at the current time, which can obtain more effective local information and a compact network structure. Finally, the proposed OSNN is verified using a number of benchmark problems and a practical problem for biochemical oxygen demand prediction in wastewater treatment. The experimental results show that OSNN has better convergence speed and accuracy than other algorithms.

Insights into Potent Therapeutical Antileukemic Agent L-glutaminase Enzyme Under Solid-state Fermentation: A Review.

To review the applications and production studies of reported antileukemic drug L-glutaminase under Solid-state Fermentation (SSF). An amidohydrolase that gained economic importance because of its wide range of applications in the pharmaceutical industry, as well as the food industry, is L-glutaminase. The medical applications utilized it as an anti-tumor agent as well as an antiretroviral agent. L-glutaminase is employed in the food industry as an acrylamide degradation agent, as a flavor enhancer and for the synthesis of theanine. Another application includes its use in hybridoma technology as a biosensing agent. Because of its diverse applications, scientists are now focusing on enhancing the production and optimization of L-glutaminase from various sources by both Solid-state Fermentation (SSF) and submerged fermentation studies. Of both types of fermentation processes, SSF has gained importance because of its minimal cost and energy requirement. L-glutaminase can be produced by SSF from both bacteria and fungi. Single-factor studies, as well as multi-level optimization studies, were employed to enhance L-glutaminase production. It was concluded that L-glutaminase activity achieved by SSF was 1690 U/g using wheat bran and Bengal gram husk by applying feed-forward artificial neural network and genetic algorithm. The highest L-glutaminase activity achieved under SSF was 3300 U/gds from Bacillus sp., by mixture design. Purification and kinetics studies were also reported to find the molecular weight as well as the stability of L-glutaminase. The current review is focused on the production of L-glutaminase by SSF from both bacteria and fungi. It was concluded from reported literature that optimization studies enhanced L-glutaminase production. Researchers have also confirmed antileukemic and anti-tumor properties of the purified L-glutaminase on various cell lines.

Implementation of artificial neural networks for very short range weather prediction

Weather conditions are a significant factor for various sectors such as transportation safety, development, health, etc. Therefore, high development is needed in forecasting future weather conditions. Many ways are used to predict weather conditions. Along with the development of technology now, weather prediction can be made using Artificial Intelligence (AI) technology or artificial intelligence so that the results obtained are more optimal. In this study, the artificial neural network used has a feedforward neural network algorithm using training data consisting of temperature, air pressure, air humidity, wind speed, hourly wind speed at the Juanda Meteorological Station in Surabaya in Januari 2019 with the target is intensity of rainfall. Furthermore, the data was released in the period of 1 January 2019 to 31 Januari 2019. Based on the analysis results, the Artificial Neural Network model has a fairly good performance in predicting an increase in rainfall in Surabaya. The best model is considered by a model with architecture 7 - 60 - 1 with an estimate correlation is 0.87, with an error value of -0.03. With this model, it is expected to become one of the forecaster considerations in making special weather forecasts at intervals every hour.

Equilibrium, kinetics and artificial intelligence characteristic analysis for Zn (II) ion adsorption on rice husks digested with nitric acid

The use of low-cost adsorbents produced from rice husks that can selectively remove zinc (II) ion from wastewater effluent has been investigated. The disorder and fatal diseases can be triggered in living organisms by accumulating the heavy metals in the wastewater. Adsorption is an operative cleansing and separation method used in the industry to remove contaminants from effluents. In order to convert the rice husk to the adsorbent, digestion and carbonization processes were performed. Rice husks digested nitric acid at 1.0 M to reduce the organic constituents and further carbonized at 400, 600 and 800 °C to eliminate the non-carbon element in rice husks. The physiochemical characteristics of the digested and carbonized rice husks were analyzed using scanning electron microscope (SEM), X-ray diffraction (XRD) and atomic adsorption spectrophotometer (AAS). The SEM morphological characteristics showed the high pyrolysis effect on the organic matter left the samples with more pores and cavities, which enhanced the surface area and uptake, especially for 800 °C carbonized samples. The samples’ physical characteristics using XRD showed that the treatment with HNO3 illustrated a pattern close to the activated carbon with slightly lower intensities. The applied feed-forward back-propagation neural network algorithm showed high validity (R2 ≈ 0.9686) for the tested experimental data sets and hence can be applied for forthcoming studies with nearby conditions. The outcomes showed that the increment of the carbonization temperature is correlated with the contact time and can increase the metal uptake percentage and adsorption capacity. The adsorption followed the Langmuir isotherm, which indicates monolayer coverage. The data showed that adsorption kinetics follow the pseudo-second-order rate expression.

Data-Driven Modeling of Smartphone-Based Electrochemiluminescence Sensor Data Using Artificial Intelligence.

Understanding relationships among multimodal data extracted from a smartphone-based electrochemiluminescence (ECL) sensor is crucial for the development of low-cost point-of-care diagnostic devices. In this work, artificial intelligence (AI) algorithms such as random forest (RF) and feedforward neural network (FNN) are used to quantitatively investigate the relationships between the concentration of luminophore and its experimentally measured ECL and electrochemical data. A smartphone-based ECL sensor with /TPrA was developed using disposable screen-printed carbon electrodes. ECL images and amperograms were simultaneously obtained following 1.2-V voltage application. These multimodal data were analyzed by RF and FNN algorithms, which allowed the prediction of concentration using multiple key features. High correlation (0.99 and 0.96 for RF and FNN, respectively) between actual and predicted values was achieved in the detection range between 0.02 µM and 2.5 µM. The AI approaches using RF and FNN were capable of directly inferring the concentration of using easily observable key features. The results demonstrate that data-driven AI algorithms are effective in analyzing the multimodal ECL sensor data. Therefore, these AI algorithms can be an essential part of the modeling arsenal with successful application in ECL sensor data modeling.

Integration of synthetic aperture radar and optical satellite data for corn biomass estimation

Efforts to use satellites to monitor the condition and productivity of crops, although extensive, can be challenging to operationalize at field scales in part due to low frequency revisit of higher resolution space-based sensors, in the context of an actively growing crop canopy. The presence of clouds and cloud shadows further impedes the exploitation of high resolution optical sensors for operational monitoring of crop development. The objective of this research was to present an option to facilitate greater temporal observing opportunities to monitor the accumulation of corn biomass, by integrating biomass products from Synthetic Aperture Radar (SAR) and optical satellite sensors. To accomplish this integration, a transfer function was developed using a Neural Network algorithm to relate estimated corn biomass from SAR to that estimated from optical data. With this approach, end users can exploit biomass products to monitor corn development, regardless of the source of satellite data.•The Water Cloud Model (WCM) was calibrated or parametrized for horizontal transmit and horizontal received (HH) and horizontal transmit and vertical received (HV) C-band SAR backscatter using a least square algorithm.•Biomass and volumetric soil moisture were estimated from dual-polarized RADARSAT-2 images without any ancillary input data.•A feed forward backpropagation Neural Network algorithm was trained as a transfer function between the biomass estimates from RADARSAT-2 and the biomass estimates from RapidEye.

Machine learning facilitated business intelligence (Part I)

PurposeThe purpose of this paper is to conduct a comprehensive review of the noteworthy contributions made in the area of the Feedforward neural network (FNN) to improve its generalization performance and convergence rate (learning speed); to identify new research directions that will help researchers to design new, simple and efficient algorithms and users to implement optimal designed FNNs for solving complex problems; and to explore the wide applications of the reviewed FNN algorithms in solving real-world management, engineering and health sciences problems and demonstrate the advantages of these algorithms in enhancing decision making for practical operations.Design/methodology/approachThe FNN has gained much popularity during the last three decades. Therefore, the authors have focused on algorithms proposed during the last three decades. The selected databases were searched with popular keywords: “generalization performance,” “learning rate,” “overfitting” and “fixed and cascade architecture.” Combinations of the keywords were also used to get more relevant results. Duplicated articles in the databases, non-English language, and matched keywords but out of scope, were discarded.FindingsThe authors studied a total of 80 articles and classified them into six categories according to the nature of the algorithms proposed in these articles which aimed at improving the generalization performance and convergence rate of FNNs. To review and discuss all the six categories would result in the paper being too long. Therefore, the authors further divided the six categories into two parts (i.e. Part I and Part II). The current paper, Part I, investigates two categories that focus on learning algorithms (i.e. gradient learning algorithms for network training and gradient-free learning algorithms). Furthermore, the remaining four categories which mainly explore optimization techniques are reviewed in Part II (i.e. optimization algorithms for learning rate, bias and variance (underfitting and overfitting) minimization algorithms, constructive topology neural networks and metaheuristic search algorithms). For the sake of simplicity, the paper entitled “Machine learning facilitated business intelligence (Part II): Neural networks optimization techniques and applications” is referred to as Part II. This results in a division of 80 articles into 38 and 42 for Part I and Part II, respectively. After discussing the FNN algorithms with their technical merits and limitations, along with real-world management, engineering and health sciences applications for each individual category, the authors suggest seven (three in Part I and other four in Part II) new future directions which can contribute to strengthening the literature.Research limitations/implicationsThe FNN contributions are numerous and cannot be covered in a single study. The authors remain focused on learning algorithms and optimization techniques, along with their application to real-world problems, proposing to improve the generalization performance and convergence rate of FNNs with the characteristics of computing optimal hyperparameters, connection weights, hidden units, selecting an appropriate network architecture rather than trial and error approaches and avoiding overfitting.Practical implicationsThis study will help researchers and practitioners to deeply understand the existing algorithms merits of FNNs with limitations, research gaps, application areas and changes in research studies in the last three decades. Moreover, the user, after having in-depth knowledge by understanding the applications of algorithms in the real world, may apply appropriate FNN algorithms to get optimal results in the shortest possible time, with less effort, for their specific application area problems.Originality/valueThe existing literature surveys are limited in scope due to comparative study of the algorithms, studying algorithms application areas and focusing on specific techniques. This implies that the existing surveys are focused on studying some specific algorithms or their applications (e.g. pruning algorithms, constructive algorithms, etc.). In this work, the authors propose a comprehensive review of different categories, along with their real-world applications, that may affect FNN generalization performance and convergence rate. This makes the classification scheme novel and significant.

A Novel Orthogonal Extreme Learning Machine for Regression and Classification Problems

An extreme learning machine (ELM) is an innovative algorithm for the single hidden layer feed-forward neural networks and, essentially, only exists to find the optimal output weight so as to minimize output error based on the least squares regression from the hidden layer to the output layer. With a focus on the output weight, we introduce the orthogonal constraint into the output weight matrix, and propose a novel orthogonal extreme learning machine (NOELM) based on the idea of optimization column by column whose main characteristic is that the optimization of complex output weight matrix is decomposed into optimizing the single column vector of the matrix. The complex orthogonal procrustes problem is transformed into simple least squares regression with an orthogonal constraint, which can preserve more information from ELM feature space to output subspace, these make NOELM more regression analysis and discrimination ability. Experiments show that NOELM has better performance in training time, testing time and accuracy than ELM and OELM.

Automatic defects detection in CFRP thermograms, using convolutional neural networks and transfer learning

Recent advancements in the field of Artificial Intelligence can support the post-processing of thermographic data, efficiently, especially for nonlinear or complex thermography scanning routines. This study proposes the implementation of an autonomous/intelligent post-processor that is capable of automatically detecting defects from given thermograms via a Convolutional Neural Networks (CNN) coding, in tandem with a Deep Feed Forward Neural Networks (DFF-NN) algorithm to estimate the defect depth as well. Thus, the proposed NN combination will process (detect and quantify) the defects from acquired thermograms in real-time, and without any human (inspector) intervention. The study shows that employing a pre-trained network, using a relatively small dataset of thermograms for training, can detect and quantify defects in thermographic sequences. In this paper, pre-trained networks with CIFAR-10 and ImageNet databases are used, and followed by a fine-tuning step of the later layers in the network; using a relatively small thermograms dataset. This text will also provide several in-depth studies to compare how transfer learning, state of the art object detection architectures, and the convolutional neural networks influence the performance of the trained post-processing system. The proposed post-processor applied to thermograms obtained from a pulsed-thermography setup testing a Carbon Fiber Reinforced Polymer (CFRP) sample with artificially created sub-surface defects validates the CNN approach.

Two noise tolerant incremental learning algorithms for single layer feed-forward neural networks

This paper focuses on noise resistant incremental learning algorithms for single layer feed-forward neural networks (SLFNNs). In a physical implementation of a well trained neural network, faults or noise are unavoidable. As biological neural networks have ability to tolerate noise, we would like to have a trained neural network that has certain ability to tolerate noise too. This paper first develops a noise tolerant objective function that can handle multiplicative weight noise. We assume that multiplicative weight noise exist in the weights between the input layer and the hidden layer, and in the weights between the hidden layer and the output layer. Based on the developed objective function, we propose two noise tolerant incremental extreme learning machine algorithms, namely weight deviation incremental extreme learning machine (WDT-IELM) and weight deviation convex incremental extreme learning machine (WDTC-IELM). Compared to the original extreme learning machine algorithms, the two proposed algorithms have much better ability to tolerate the multiplicative weight noise. Several simulations are carried out to demonstrate the superiority of the two proposed algorithms.

Transformed Secure Feed Forward Supervised Learning Method for Authentication in Multi-Model Biometric System

Biometric is an automated detection of the characteristics of an individual on the basis of the biological and social features. Detection of the uni-modal biometric system is based on the biometric data of an individual. Some issue of distortion level spoofing threats are more accessible to biometric data. Some of the issues overcome by multimodal biometric scheme in which signature of the biometric data are determine for better security of the data. Multimodal biometric is used on variety of the application areas which are human computer interface, detection of the sensor through unique method. The physical and social characteristics are used for the identification of an individual using multimodal biometric system. Multi-model biometric system applications are security system developed in banking sectors, business phase and Industry (MNC) companies. In existing work, using ESVM method to recognize the biometric traits and problem occurs in existing phase is distortion and degrades the image quality present and reduces the recognition rate and high error rates. In proposed research, determined the biometric features finger print, face and iris through CASIA dataset. Then, distortion rate is recognised through salt and pepper method and removal of interference using filtration technique. After that, discrete wavelet transformation is used for the extraction of the features of the biometric system through face, fingerprint and eye that determine the graphical features. Along with that, feed forward neural network algorithm developed for classification and recognition of multi modal biometric behaviour characteristics. The Encrypted NN method conducts simulation work on the metrics like as a recognition rate, true positive rate and computation time. The experimental results demonstrate that Encrypted NN method is able to enhance the image quality, recognition rate and TPR and reduces the computational time of Multi-model Biometric System when compared with existing work and simulation tool used MATLAB 2016a.

A Heterogeneous AdaBoost Ensemble Based Extreme Learning Machines for Imbalanced Data

Extreme learning machine (ELM) is an effective learning algorithm for the single hidden layer feed-forward neural network (SLFN). It is diversified in the form of kernels or feature mapping functions, while achieving a good learning performance. It is agile in learning and often has good performance, including kernel ELM and Regularized ELM. Dealing with imbalanced data has been a long-term focus for the learning algorithms to achieve satisfactory analytical results. It is obvious that the unbalanced class distribution imposes very challenging obstacles to implement learning tasks in real-world applications, including online visual tracking and image quality assessment. This article addresses this issue through advanced diverse AdaBoost based ELM ensemble (AELME) for imbalanced binary and multiclass data classification. This article aims to improve classification accuracy of the imbalanced data. In the proposed method, the ensemble is developed while splitting the trained data into corresponding subsets. And different algorithms of enhanced ELM, including regularized ELM and kernel ELM, are used as base learners, so that an active learner is constructed from a group of relatively weak base learners. Furthermore, AELME is implemented by training a randomly selected ELM classifier on a subset, chosen by random re-sampling. Then, the labels of unseen data could be predicted using the weighting approach. AELME is validated through classification on real-world benchmark datasets.

Abnormal Behavior Recognition Based on Transfer Learning

In order to identify abnormal behavior in image samples, a transfer learning recognition model based on Inception-V3 neural network is proposed in this paper. The whole process consists of two parts: 1) Inception-V3 neural network is used to extract the features of image samples.2) The abnormal behavior recognition model is established to classify the obtained features. In this paper, three-layer feedforward neural network algorithm is used to compare with other common machine learning classification models (k-nearest neighbor algorithm, random forest, LightGBM, SVM, two-layer feedforward neural network).The results show that the performance of anomalous behavior recognition based on three-layer feedforward neural network is better than other classification models.

Artificial Neural Networks Approach for a Multi-Objective Cavitation Optimization Design in a Double-Suction Centrifugal Pump

Double-suction centrifugal pumps are widely used in industrial and agricultural applications since their flow rate is twice that of single-suction pumps with the same impeller diameter. They usually run for longer, which makes them susceptible to cavitation, putting the downstream components at risk. A fast approach to predicting the Net Positive Suction Head required was applied to perform a multi-objective optimization on the double-suction centrifugal pump. An L32 (84) orthogonal array was designed to evaluate 8 geometrical parameters at 4 levels each. A two-layer feedforward neural network and genetic algorithm was applied to solve the multi-objective problem into pareto solutions. The results were validated by numerical simulation and compared to the original design. The suction performance was improved by 7.26%, 3.9%, 4.5% and 3.8% at flow conditions 0.6Qd, 0.8Qd, 1.0Qd and 1.2Qd respectively. The efficiency increased by 1.53% 1.0Qd and 1.1% at 0.8Qd. The streamline on the blade surface was improved and the vapor volume fraction of the optimized impeller was much smaller than that of the original impeller. This study established a fast approach to cavitation optimization and a parametric database for both hub and shroud blade angles for double suction centrifugal pump optimization design.

Incremental Multiple Hidden Layers Regularized Extreme Learning Machine Based on Forced Positive-Definite Cholesky Factorization

The theory and implementation of extreme learning machine (ELM) prove that it is a simple, efficient, and accurate machine learning method. Compared with other single hidden layer feedforward neural network algorithms, ELM is characterized by simpler parameter selection rules, faster convergence speed, and less human intervention. The multiple hidden layer regularized extreme learning machine (MRELM) inherits these advantages of ELM and has higher prediction accuracy. In the MRELM model, the number of hidden layers is randomly initiated and fixed, and there is no iterative tuning process. However, the optimal number of hidden layers is the key factor to determine the generalization ability of MRELM. Given this situation, it is obviously unreasonable to determine this number by trial and random initialization. In this paper, an incremental MRELM training algorithm (FC-IMRELM) based on forced positive-definite Cholesky factorization is put forward to solve the network structure design problem of MRELM. First, an MRELM-based prediction model with one hidden layer is constructed, and then a new hidden layer is added to the prediction model in each training step until the generalization performance of the prediction model reaches its peak value. Thus, the optimal network structure of the prediction model is determined. In the training procedure, forced positive-definite Cholesky factorization is used to calculate the output weights of MRELM, which avoids the calculation of the inverse matrix and Moore-Penrose generalized inverse of matrix involved in the training process of hidden layer parameters. Therefore, FC-IMRELM prediction model can effectively reduce the computational cost brought by the process of increasing the number of hidden layers. Experiments on classification and regression problems indicate that the algorithm can be effectively used to determine the optimal network structure of MRELM, and the prediction model training by the algorithm has excellent performance in prediction accuracy and computational cost.