Maximum Absolute Percentage Error Research Articles

Improved anti-noise adaptive long short-term memory neural network modeling for the robust remaining useful life prediction of lithium-ion batteries

Safety assurance is essential for lithium-ion batteries in power supply fields, and the remaining useful life (RUL) prediction serves as one of the fundamental criteria for the performance evaluation of energy and storage systems. Based on an improved dual closed-loop observation modeling strategy, an improved anti-noise adaptive long short-term memory (ANA-LSTM) neural network with high-robustness feature extraction and optimal parameter characterization is proposed for accurate RUL prediction. Then, an adaptive state parameter feedback correction strategy is constructed through multiple feature collaboration with its internal coupling mechanism characterization, which considers varying current rates, ambient temperatures, and other influencing parameters. Subsequently, a collaborative multi-parameter optimization is carried out along with the model training and meta-structure fine-tuning. Compared with other optimal existing methods, the maximum root mean square error decreases by 51.80%, the mean absolute error reduces by 26.95%, the maximum mean absolute percentage error decreases by 33.87%, and the R-squared increases by 4.11%. The established multiple-feature collaboration model realizes multi-scale parameter optimization and robust RUL prediction, thus advancing the industrial application of lithium-ion batteries.

Solar Irradiance Forecasting with Transformer Model

Solar energy is one of the most popular sources of renewable energy today. It is therefore essential to be able to predict solar power generation and adapt energy needs to these predictions. This paper uses the Transformer deep neural network model, in which the attention mechanism is typically applied in NLP or vision problems. Here, it is extended by combining features based on their spatiotemporal properties in solar irradiance prediction. The results were predicted for arbitrary long-time horizons since the prediction is always 1 day ahead, which can be included at the end along the timestep axis of the input data and the first timestep representing the oldest timestep removed. A maximum worst-case mean absolute percentage error of 3.45% for the one-day-ahead prediction was obtained, which gave better results than the directly competing methods.

Application of Finite‐Element Simulation and Neural Networks in the Prediction of Metal Flow Behavior during the Sizing Press Process

A dog‐bone profile is developed by inhomogeneous deformation of a slab, whose parameters can be used to describe the metal flow rule during the width reduction process by a sizing press. The accuracy of a dog‐bone profile is essential to ensure the high width precision of the roughing process. However, the existing equipment cannot satisfy the requirements of online measurement. To solve this problem, herein, a prediction model for dog‐bone parameters based on the finite‐element simulation and a neural network is presented. The finite‐element simulation can reproduce the field production process, revealing variations in the dog‐bone profile parameters. In addition, based on the simulation data, a neural network model is constructed to predict the dog‐profile parameters. By adjusting the hyperparameters, the prediction accuracy of the constructed deep neural network model with two hidden layers is improved. For the dog‐bone profile parameters, the mean squared error is less than 3 mm, the mean absolute percentage error is less than 2%, the maximum absolute percentage error is less than 9%, and the root mean squared error is less than 4 mm. Thus, an accurate prediction of the dog‐bone profile parameters is achieved, which can guide subsequent high‐precision width control.

Prediction of battery charging process based on aggregation neural network

An online sequence extreme learning machine neural network prediction model based on sample aggregation method (AOSELM) is proposed, which is used to solve the prediction of the charging process of lead-acid batteries. The model is based on the online sequence extreme learning machine (OSELM) neural network and finds the similar samples of the test samples based on the mean influence value (MIV) algorithm. Similar samples are used for temporary incremental learning of the neural network, then the updated neural network makes predictions on the test samples. Taking the terminal voltage prediction of the battery charging process as an example, the BP neural network, the OSELM neural network and the AOSELM neural network are used to compare the predictions, and the charging process of the battery is predicted based on the AOSELM neural network. The comparison results show that the AOSELM neural network has higher prediction accuracy and adaptive ability than the BP neural network, and reduces the maximum absolute percentage error and the maximum absolute error of the prediction result when compared with the OSELM neural network. The prediction shows that the charging process of lead-acid batteries can be accurately predicted by the AOSELM neural network.

Heat transfer analysis of a borehole heat exchanger array in a layered subsurface

In the engineering design of borehole heat exchanger arrays, the subsurface is generally regarded as homogeneous, which leads to a large deviation in the prediction of actual performance. An analytical model with good flexibility describing the heat transfer behavior of BHE array in a layered subsurface is introduced using the Green’s function. The Green’s function which is the exact solutions to the temperature response of a ring coil heat source imbedded in a layered ground domain is obtained directly from the governing equations of the problem by the separation of variables techniques. Meanwhile, the nonuniformity of the heat flow rate along the borehole wall depth is addressed in the analytical layered model. Then, a numerical model of BHE array heat transfer in a layered subsurface is proposed based on the modified pipeline flow model. The numerical model is systematically verified with three experiment tests from the literatures and one test performed by the authors. The maximum RSM error and mean absolute percentage error for four test cases are 0.66 °C and 3.25%, showing a good agreement between the proposed numerical model and the measurements. Then, the accuracy of the analytical solution is validated with the existing simple homogeneous model and the proposed numerical model for multiple BHEs and multiple layers scenarios. The effects of the BHEs array and ground stratification on the temperature response are examined in details employing the analytical and numerical models, with the analytical model focusing on the thermal responses of the layered ground and the numerical model on the circulating fluid in the U-tubes. Results show that the presence of the BHE array increases the magnitude of the discrepancy in the temperature prediction between the layered and homogeneous model, particularly in the layers with low thermal diffusivities at large timescales. For the simulated case, the dimensionless temperature difference between the layered and homogeneous scenarios at the borehole wall in the BHE array is 0.35, while it is only 0.11 in a single BHE, resulting in an increase by 218%. Moreover, the ground stratification could affect the prediction of fluid temperature profile along the BHE depth, thus influencing the thermal circuiting between the two pipes of the U-tube. Compared with the homogeneous model, the coefficient of the thermal circuiting increases by up to 11.6% when the ground stratification is considered. Using the homogeneous model with equivalent thermal properties to design the ground source heat pump system in a layered subsurface would underestimate the short circuiting of the U-pipes and undersize the BHE system. The results of this study provide analytical formalism and numerical method to understand better how the design and operation of actual ground source heat pump is engineered.

Machine learning prediction of bottomhole flowing pressure as a time series in the volve field

Bottomhole flowing pressure (BHFP) is a critical parameter in analyzing oil and gas well performance, production forecasting and reservoir management. This study is focused on obtaining feature combinations towards low-error prediction of time-series BHFP in two wells in the Volve field. Three machine learning (ML) models (support vector regression (SVR), a distance-based model; random forest (RF), a tree-based ensemble model and Long Short-Term Memory (LSTM), a type of recurrent neural network) are used for BHFP prediction in two wells of the Volve field. The data for each well was split such that the first 70% is used in training the model, the next 15% as validation data for selecting the optimal hyperparameters and the last 15% for testing the models. The train and validation sets were used to train the models before making predictions on the test sets. While the SVR and RF models reasonably predicted the BHFP in both wells with a maximum Mean Absolute Percentage Error (MAPE) of 5.0% and 4.3% respectively, the LSTM model performed best across both wells with the MAPE less than 2.9% in both wells. ML model performance was superior for the well with the data distributed more uniformly. The three feature combinations with superior ML model performance for BHFP prediction all have five features in common namely: bottomhole temperature, oil flow rate, gas flow rate, choke size, onstream hours. The workflow in this work can be adopted for fieldwide BHFP prediction.

A novel hybrid Machine learning model to forecast ionospheric TEC over Low-latitude GNSS stations

Understanding the ionospheric variability caused by the solar and geomagnetic space weather can be achieved using the ionospheric Total Electron Content (TEC) parameter. Developing a novel artificial intelligence-based machine learning model that can forecast the TEC parameter would primarily benefit Global Positioning System (GPS) users. This paper holds one such a novel hybrid empirical model that exploits nonlinear autoregressive neural network with external input (NARX) for a one hour in advance TEC forecasting over the Hyderabad (17.45°N,78.47°E) and Bengaluru (12.95°N, 77.68°E) GPS stations. The 11-year GPS data spans from 2009 to 2019 corresponding to the 24th solar cycle obtained over these GPS stations operated by the International GNSS Service (IGS) center. The performance of this multiple input data model, which accepts TEC, Ap index, Solar flux index, time of the day, geographical coordinates, and others, have been evaluated during both High Solar Activity (HSA) year 2014 and Low Solar Activity (LSA) period 2019. A comprehensive evaluation of the proposed model has been carried out in comparison with the International Reference Ionosphere 2016 (IRI-2016) model, NeQuick-G model, Auto Regressive Moving Average (ARMA), Neural Network (NN), and combined NN with ARMA models. Results reveal that the proposed hybrid ML model could forecast the ionospheric well. The proposed hybrid ML model's root-mean-square error (RMSE) ranges in 0.5–1 TECU during the LSA period and 1.63–2.2 TECU during the HSA period. The proposed model's Maximum Absolute Percentage Error (MAPE) is between 1.6% and 4.5%, with a 0.99 correlation coefficient (R 2 ) value consistently. Thus, the proposed ML model provides promising ionospheric TEC forecasting results.

Distribution Feeder Parameter Estimation Without Synchronized Phasor Measurement by Using Radial Basis Function Neural Networks and Multi-Run Optimization Method

In practice, the performance of distribution feeder parameter estimation is limited by the measurement conditions in distribution networks. An accurate mathematical model that considers limited phasor measurements in distribution networks is necessary to estimate feeder parameters. This paper presents a set of modified parameter estimation models for unbalanced three-phase distribution feeders that only require the measurements of voltage amplitudes and power flows. To simplify the calculation process and improve the estimated results, a method combined with a radial basis function neural network (RBFNN) and multi-run optimization method (MRO), namely RBFNN-MRO, is proposed to calculate the parameters of distribution feeders. The relationship between the feeder parameters and the measurement data from the two terminals of the feeder can be mapped perfectly using the RBFNN. Furthermore, the random errors in the measurement device were eliminated using the proposed RBFNN-MRO algorithm. The RBFNN-MRO algorithm can limit the number of neurons in the hidden layer and substantially reduce the training time for each RBFNN. The feasibility of the proposed method was verified using four IEEE test systems. The proposed RBFNN-MRO and RBFNN methods were compared using the maximum absolute percentage error (MAPE) curves. The results reveal that the proposed RBFNN-MRO method has excellent potential for improving the accuracy of feeder parameter estimation even without synchronized phasor measurement.

Application of Optimized Grey-Markov Model to Land Subsidence Monitoring With InSAR

Land subsidence prediction in mining areas is one of the most important applications of land deformation monitoring, which is significance for safe production. We used interferometric point target analysis (IPTA) timing series interferometry synthetic aperture radar (InSAR) processing technology to analyze the land subsidence results for the Xinfa mining area from 2017 to 2020; and compared them to global positioning system (GPS) static monitoring data. We proposed a residual correction theory based on deviation coefficient using the grey prediction and Markov models, and an optimized Grey-Markov model (RGM-M model) was established to predict the land subsidence of the mining area. Our results show that: (1) The maximum difference between InSAR timing processing results and GPS monitoring data in the same period is 10.91mm; they have roughly the same subsidence trend, indicating that IPTA timing series InSAR technology are strongly reliable in mining deformation. (2) Compared to the traditional Grey-Markov model, the improved residual correction and dynamic assignment of the Grey-Markov model improves the prediction accuracy. The optimized residual correction and dynamic empowerment of the Grey-Markov model prediction results are more suitable for the actual fluctuation of land subsidence value in the mining area. The maximum root mean square error of the prediction results is 0.751mm, and the maximum average absolute percentage error is 7.46%, which has a certain guiding significance for the work of monitoring, prediction and safety management of land deformation in the mining area.

Short-Term Prediction of Photovoltaic Power Based on Fusion Device Feature-Transfer

To attain the goal of carbon peaking and carbon neutralization, the inevitable choice is the open sharing of power data and connection to the grid of high-permeability renewable energy. However, this approach is hindered by the lack of training data for predicting new grid-connected PV power stations. To overcome this problem, this work uses open and shared power data as input for a short-term PV-power-prediction model based on feature transfer learning to facilitate the generalization of the PV-power-prediction model to multiple PV-power stations. The proposed model integrates a structure model, heat-dissipation conditions, and the loss coefficients of PV modules. Clear-Sky entropy, characterizes seasonal and weather data features, describes the main meteorological characteristics at the PV power station. Taking gate recurrent unit neural networks as the framework, the open and shared PV-power data as the source-domain training label, and a small quantity of power data from a new grid-connected PV power station as the target-domain training label, the neural network hidden layer is shared between the target domain and the source domain. The fully connected layer is established in the target domain, and the regularization constraint is introduced to fine-tune and suppress the overfitting in feature transfer. The prediction of PV power is completed by using the actual power data of PV power stations. The average measures of the normalized root mean square error (NRMSE), the normalized mean absolute percentage error (NMAPE), and the normalized maximum absolute percentage error (NLAE) for the model decrease by 15%, 12%, and 35%, respectively, which reflects a much greater adaptability than is possible with other methods. These results show that the proposed method is highly generalizable to different types of PV devices and operating environments that offer insufficient training data.

Heart Rate and Distance Measurement of Two Multisport Activity Trackers and a Cellphone App in Different Sports: A Cross-Sectional Validation and Comparison Field Study.

Options for monitoring sports have been continuously developed by using activity trackers to determine almost all vital and movement parameters. The aim of this study was to validate heart rate and distance measurements of two activity trackers (Polar Ignite; Garmin Forerunner 945) and a cellphone app (Polar Beat app using iPhone 7 as a hardware platform) in a cross-sectional field study. Thirty-six moderate endurance-trained adults (20 males/16 females) completed a test battery consisting of walking and running 3 km, a 1.6 km interval run (standard 400 m outdoor stadium), 3 km forest run (outdoor), 500/1000 m swim and 4.3/31.5 km cycling tests. Heart rate was recorded via a Polar H10 chest strap and distance was controlled via a map, 400 m stadium or 50 m pool. For all tests except swimming, strong correlation values of r > 0.90 were calculated with moderate exercise intensity and a mean absolute percentage error of 2.85%. During the interval run, several significant deviations (p < 0.049) were observed. The swim disciplines showed significant differences (p < 0.001), with the 500 m test having a mean absolute percentage error of 8.61%, and the 1000 m test of 55.32%. In most tests, significant deviations (p < 0.001) were calculated for distance measurement. However, a maximum mean absolute percentage error of 4.74% and small mean absolute error based on the total route lengths were calculated. This study showed that the accuracy of heart rate measurements could be rated as good, except for rapid changing heart rate during interval training and swimming. Distance measurement differences were rated as non-relevant in practice for use in sports.

THERMAL STATE OF THE AIR - GROUND HEAT EXCHANGER PREDICTION BASED ON ARTIFICIAL NEURAL NETWORK

The work aim is to predict the thermal state of the air-ground heat exchanger based on an artificial neural network. Training, testing and validation of the proposed model were made on experimental data obtained in the thermophysical laboratory of the Institute of Engineering Thermophysics of the National Academy of Sciences of Ukraine. A simple neural network is used in this work. The air temperature at the inlet to the heat exchanger, and its relative humidity are selected as input parameters for the neural network. The MATLAB (R2016a) and Levenberg-Markwatt model were used in this article's calculations. One hidden layer and 10 neurons were presented in the model. The array of analysed data was divided into ratios of 70%, 15%, 15% for neural network training, validation and testing, respectively. As a result, it is obtained that the forecasting takes place with acceptable accuracy in all models. The root mean square error for the whole data set for different models varies from 0.105 to 2.323°С. The maximum mean absolute percentage error was the largest for CFD model and was 11.2%. The minimum mean bias error of the predicted data from the experimentally measured ones was found in the model using temperature, humidity, and air temperature at the outlet of the air-ground heat exchanger for the previous hour and was 0.02%. The training and testing of the proposed models based on an artificial neural network are satisfactory enough to predict the temperature taking into account the influence of weather conditions. Artificial neural networks can be used to predict the thermal state of the air-ground heat exchanger. Data representing the description of a real system are required for forecasting the parameters based on the ANN.

A combined deep learning load forecasting model of single household resident user considering multi-time scale electricity consumption behavior

With the growth of residential load and the popularity of intelligent devices, resident users have become important target customers for demand response (DR). However, due to the strong volatility of individual household load and the large difference in user’s behavior, the accuracy of residential load forecasting is generally low and the forecasting effect is unstable, which is not conductive to the implementation of DR. To improve the accuracy of residential load forecasting, this paper proposes a combined deep learning load forecasting model considering multi-time scale electricity consumption behavior of single household resident user to achieve high-accuracy and stable load forecasting. Aiming at the electricity consumption behavior, the multi-time scale similarity analysis is carried out. For the time scale of one year, Normalized Dynamic Time Warping (N-DTW) and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) are used to analyze the significance of single user's long-term electricity consumption behavior. For the time scale of 7 days, behavior similarity is used to analyze the consistency of single user's short-term electricity consumption behavior. Then, Mutual Information (MI) and Principal Component Analysis (PCA) are used to select features and reduce dimensions of multi-dimensional weather influencing factors, so as to avoid the interference of irrelevant factors and improve the calculation speed. On this basis, combined with Back Propagation (BP) neural network, Extreme Gradient Boosting (XGBoost) and Long Short-Term Memory (LSTM) neural network, a combined deep learning network load forecasting model (Co-LSTM) is constructed by using multi-model and multi-variable method to achieve stable and high-accuracy load forecasting. Finally, based on the actual load data from the American Pecan Street Energy Project, the forecasting accuracy of the proposed model of resident user is evaluated. From the performance of load forecasting for 42 target users, the minimum, maximum and average Mean Arctangent Absolute Percentage Error (MAAPE) of Co-LSTM is 18.70%, 45.95% and 31.20% (the average MAAPE is 4.97% less than the traditional LSTM model) respectively.

Real-time heat dissipation model of electronic equipment for determining the dynamic cooling demand of office buildings

Internal heat gains are necessary inputs for determining the required cooling demand of Heating, Ventilation, and Air-Conditioning (HVAC) systems in office buildings. Electronic equipment is one of the main indoor thermal sources which needs to be carefully investigated because of its large heat dissipation and significant impact on the HVAC system. So far, very few studies about calculating the real-time heat dissipation of the equipment have been conducted. To address this problem, a real-time heat dissipation model of electronic equipment in office buildings is proposed in this paper. First, the structure of real-time heat dissipation model of electronic equipment was studied according to energy conservation laws, Laplace transform method, etc., and the model structure was determined as an eleventh-order transfer function. Second, an experimental setup was established to collect data on the heat dissipation and electric power consumption of typical electronic equipment, which were used for the parameter identification and model verification processes. Third, the unknown parameters in the real-time heat dissipation model were identified, and after order reduction analysis, a third-order transfer function was chosen as the heat dissipation model. Finally, experimental data and the designer's simulation toolkits were used to evaluate the proposed model's accuracy, yielding a maximum mean absolute percentage error of 9.13%. The presented model not only describes the dynamic and stochastic characteristics of the heat dissipation of electronic equipment, but also exhibits great importance in calculating instantaneous cooling demand and saving energy.

A transfer function model of lighting heat dissipation for detecting time-delay effect and dynamic cooling demand during the real-time operation of buildings

Monitoring real-time heat dissipation of lighting, a major indoor heat source, is essential for determining the dynamic cooling demand of buildings, and it provides a reliable basis for sizing air-conditioning systems and saving energy. Contemporary models cannot be used to obtain the accurate real-time heat dissipation of lighting or the time-delay effect, because of which these models have critical limitations in precisely detecting dynamic cooling demand of buildings. To address this problem, a transfer function model is proposed for calculating the real-time heat dissipation of lighting in this paper. First, the model structure is determined according to the energy conservation law, heat transfer principles, and so on. Second, an experiment is conducted using a nearly adiabatic test chamber. Third, parameter identification and order reduction analyses are performed, and the real-time heat dissipation model of lighting is determined as a third-order transfer function. Experimental data of the same and different types of lighting are employed to verify the proposed model, and the maximum mean absolute percentage error (MAPE) is 7.83%. Comparing with the fixed ratio method, the proposed transfer function model not only reduces MAPE by 66.05% within 1 h after lighting is turned on but also describes a time-delay effect in the stability of lighting heat dissipation. The results of this study exhibit the promising applicability for accurately determining the cooling demand of a building during real-time operation, thus improving the indoor thermal environment and reducing energy consumption.

Three‐phase feeder parameter estimation using radial basis function neural networks and multi‐run optimisation method with bad data preparation

The difference between the actual feeder parameters and feeder parameter data stored in a database or offered by manufacturers is significant owing to the ambient environment, temperature, and skin effect. Here, a parameter estimation method is proposed for unbalanced three-phase distribution feeders based on the bus voltages and branch power flows measured from two terminals of the feeder. In the proposed method, a high-precision phasor measurement unit is not required to estimate the magnitude and phase angle of the phasor quantity using a common time source for synchronisation. A radial basis function neural network with multi-run optimisation (RBFNN-MRO) is proposed to map the complex nonlinear relations between the distribution feeder parameters and electrical quantities. The feasibility and performance of the proposed RBFNN-MRO method were verified using the four IEEE test systems. The comparison between the proposed RBFNN-MRO method and the multi-run method based on the quasi-Newton method is implemented via the maximum absolute percentage error (MAPE) curves. The results reveal that the proposed RBFNN-MRO method has excellent potential for improving the accuracy of feeder parameter estimation, even for bad data preparation.

Short-Term Electric Load Forecasting Using Auto Regressive-Candidates Area Shifting Technique

Electric power load forecasting is needed to be used as a consideration in providing electricity in the future. A combination of the Auto Regressive model and the Candidates Area Shifting Technique is proposed to predict the demand for electrical loads. The results of the proposed method are compared with the ones of the hybrid Particle Swarm Optimization-Support Vector Regression and FCM Clustering Technique methods. The results show that the proposed method provides better performance than the other ones. The three methods provide mean absolute percentage error and maximum absolute percentage error respectively as follows: Particle Swarm Optimization-Support Vector Regression Method 2.859% and 9,516%, FCM Clustering 1.032% and 2.798%, and Auto Regressive-Candidates Area Shifting Technique 0.298% and 0.872%, respectively.

Dynamic mathematical model development and validation of in vitro Mycobacterium smegmatis growth under nutrient- and pH-stress

Mycobacterium tuberculosis can exist within a host for lengthy periods, tolerating even antibiotic challenge. This non-heritable, antibiotic tolerant “persister” state, is thought to underlie latent Tuberculosis (TB) infection and a deeper understanding thereof could inform treatment strategies. In addition to experimental studies, mathematical and computational modelling approaches are widely employed to study persistence from both an in vivo and in vitro perspective. However, specialized models (partial differential equations, agent-based, multiscale, etc.) rely on several difficult to determine parameters. In this study, a dynamic mathematical model was developed to predict the response of Mycobacterium smegmatis (a model organism for M. tuberculosis) grown in batch culture and subjected to a range of in vitro environmental stresses. Lag phase dynamics, pH variations and internal nitrogen storage were mechanistically modelled. Experimental results were used to train model parameters using global optimization, with extensive subsequent model validation to ensure extensibility to more complex modelling frameworks. This included an identifiability analysis which indicated that seven of the thirteen model parameters were uniquely identifiable. Non-identifiable parameters were critically evaluated. Model predictions compared to validation data (based on experimental results not used during training) were accurate with less than 16% maximum absolute percentage error, indicating that the model is accurate even when extrapolating to new experimental conditions. The bulk growth model can be extended to spatially heterogeneous simulations such as an agent-based model to simulate in vitro granuloma models or, eventually, in vivo conditions, where distributed environmental conditions are difficult to measure.

CGA: An image processing based software for surface strain analysis in sheet metal forming

Strain analysis is an essential step in sheet forming applications to understand the deformation behaviour of the material. The strain analysis is conventionally performed by Circle Grid Analysis (CGA). In CGA, a grid of circles with 2 mm–5 mm diameter is printed on a flat sheet and deformed into the required shape. The length of major and minor axes of the deformed ellipses are measured to estimate the strains at different locations of the formed component. The major and minor axes length of the deformed ellipses are measured either by using a manual method or automatic methods. The automated methods are faster and accurate compared to manual methods, but to perform strain measurement using commercially available automatic strain measurement system, is very expensive. Therefore, in this paper, an image processing based software has been developed with user-friendly Graphical User Interface (GUI) for strain measurement and analysis in sheet metal forming operations. The software has been tested on images obtained by printing the ellipses of known dimensions on the flat sheet by laser etching, electrochemical etching and screen printing, which are generally used for printing circular grids on flat sheets for strain analysis in sheet metal forming. It is observed that the edges of the laser engraved ellipse are very slim and easily detected by software compared to other grid printing methods. The developed software can measure the ellipse dimensions with a maximum absolute percentage error of 1.975%. Further, the results of CGA software has been compared with the commercial strain measurement system called Grid Pattern Analyzer (GPA). The mean absolute error in strain measurement using CGA and GPA was found to be 0.0106 and 0.0178, respectively. The statistical test results reveal that there is no evidence to support a claim that there is a difference in mean performance between the two methods.

A machine learning algorithm for retrieving the geometrical characteristic parameters of soot fractal aggregates from polarized light signal

Polarized light measurement technology is provided to study geometric characteristics of soot fractal aggregates. The inverse problem is solved by two mature applications of machine learning, i.e. stacked ensemble model and deep network. A new Fractal Aggregates Generative Adversarial Network (FAGAN) is proposed to generate synthetic data to solve the class imbalance problem. The results show that compared with the stacked ensemble model which is sensitive to noise, the performance of the deep network is still satisfactory even under 10 % Gaussian noise, and the maximum mean absolute percentage error is not more than 3.87 %, which means that the synthetic data generated by FAGAN is very similar to the real data. As a whole, the combination of deep network and FAGAN has important guiding significance for complex and time-consuming experiments and engineering applications where noise is difficult to control or continuous and regular data cannot be obtained.