Maximum Mean Absolute Percentage Error Research Articles

Combining Multi-Indirect Features Extraction and Optimized GPR Algorithm for Online State of Health Estimation of Lithium-ion Batteries

Abstract With the wide application of lithium batteries (LIBs) in electrified transportation and smart grids, especially in the pure electric vehicle industry, the accurate health maintenance monitor of LIBs has emerged as critical for safe battery operation. Although many data-driven methods with state of health (SOH) estimation for LIBs have been proposed, the problems of industrial generation and computational cost still need to be improved further. In contrast, this paper carried out a low-complexity SOH estimation method for LIBs. Specifically, the seven health indicators are extracted firstly to characterize battery health status from voltage, current, temperature and other data that can be obtained online. Then, the optimized gaussian process regression (GPR) algorithm is proposed with proper computational cost. Ultimately, combining a multi-indirect features extraction and optimized GPR algorithm, the online SOH estimation for LIBs was established and verified with NASA experiment data. The experimental results show that the maximum Mean Absolute Percentage Error (MAPE) of SOH estimation from the proposed method is 1.4496 and the minimum MAPE only reaches 0.5635. More importantly, the optimized GPR for SOH estimation can achieve a maximum 65.37% improvement under multiple evaluation criteria compared to traditional GPR. The method proposed in this paper is helpful for realizing on-line SOH estimation in battery management systems.

Inverse design of cellular structures with the geometry of triply periodic minimal surfaces using generative artificial intelligence algorithms

Triply periodic minimal surfaces (TPMS) exhibit excellent mechanical and energy absorption properties due to their structural advantages. However, existing porous TPMS structural design methods are constrained to a forward process from structural parameters to mechanical properties. This study proposed an inverse design method that combines bidirectional generative adversarial networks (BiGAN) and mechanical performance targets, resulting in a combined TPMS structure of Primitive and IWP types with superior buffering and energy absorption capabilities. The results show that under a single load value target condition of the designed structure, the minimum deviation index (R2) between the load value corresponding to the displacement point and the target load value is only 0.987, and the maximum mean absolute percentage error (MAPE) is only 5.92 %. When considering the elastic modulus target, the approach successfully conducts two sets of combined structural designs meeting the requirements of both high and low elastic moduli. When targeting the specified load-displacement curve conditions, specifically when combining high elastic modulus with ascending plasticity, the designed structures exhibit an error of only 2.2 % compared to the target property. Moreover, the quasi-static uniaxial compression experiments conducted on additively manufactured designed structures confirm that the experimental curves match the target curves in terms of deformation trends and load value ranges. The success of this inverse design approach for cellular TPMS structures has the potential to expedite new structural material development processes.

Short-term wind speed prediction of wind farm based on TSO-VMD-BiLSTM

Aiming at the random and intermittent characteristics of wind speed, a short-term wind speed prediction (SWSP) method based on TSO-VMD-BiLSTM is proposed in this article. Firstly, open-source historical data from a certain region in 2022, including wind speed, direction, pressure, and temperature is analyzed. The data is processed through variational mode decomposition (VMD) to fully extract feature data from historical wind speed records. Secondly, taking historical wind speed, direction, pressure, and temperature as inputs and wind speed as output, a SWSP model based on long short-term memory (LSTM) network is constructed. Thirdly, the tuna swarm optimization (TSO) algorithm is utilized for parameters optimization, and a bi-directional long short-term memory (BiLSTM) network is incorporated to enhance prediction accuracy for micrometeorological parameters. The proposed TSO-VMD-BiLSTM model is validated through comparison with other models, demonstrating its higher accuracy with the maximum absolute error of only 2.52 m/s, the maximum root mean square error of 0.81, the maximum mean absolute error of only 0.54, and the maximum mean absolute percentage error of 6.89%.

Forecasting electricity demand of municipalities through artificial neural networks and metered supply point classification

This study develops a methodology to characterise and forecast large consumers’ electricity demand, particularly municipalities, with hundreds of different metered supply points based on the previous characterisation of facilities’ consumption. Demand forecasting allows consumers to improve their participation in electricity markets and manage their electricity consumption. The method considers a classification by different types of metered supply points combined with artificial neural networks to obtain hourly forecasts using well-known parameters such as day types, hourly temperature, the last hour of electricity consumption, and sunrise and sunset time. We apply the methodology to the municipality of Valencia using over five hundred hourly load profiles for a year during 2017 and 2018. Our results present aggregated forecasts with a maximum Mean Absolute Percentage Error of 3.8% per day, outperforming the same forecast without classifying Metered Supply Points. We conclude that a correct electricity demand forecast for a consumer with different types of consumption does not need submetering, but characterising Metered Supply Points is an option with lower costs that allows for better predictions.

Construction and Estimation of Battery State of Health Using a De-LSTM Model Based on Real Driving Data

Electric vehicles (EVs) have considerable potential in promoting energy efficiency and carbon neutrality. State of health (SOH) estimations for battery systems can be effective for avoiding accidents involving EVs. However, existing methods have rarely been developed using real driving data. The complex working environments of EVs and their limited data acquisition capability increase the challenges for estimating SOH. In this study, a novel battery SOH definition for EVs was established by analyzing and extracting six potential SOH indicators from driving data. The definition proposed using the entropy weight method (EWM) described the degradation trend for different EV batteries. Combined with a denoising autoencoder, a novel long short-term memory neural network model was established for SOH prediction. It can learn robust features using noisy input data without being affected by different environments or driver behaviors. The network achieved a maximum mean absolute percentage error (MAPE) of 0.8827% and root mean square error (RMSE) of 0.9802%. The results have shown that the proposed method has a higher level of accuracy and is more robust than existing methods in the field.

A robust approach for the derivation of rating curves using minimum gauging data

Rating curves are robust tools for continuously evaluating streamflows by gauging water levels. This paper introduces a procedure to derive rating curves by combining a stage-discharge relationship proposed by Maghrebi et al. and the inverse-distance weighting (IDW) method. In order to determine the appropriate value of the α parameter in IDW, a trial-and-error procedure using different values of α from 0 to 5 is implemented. To this end, 2000 subsamples in different sizes selected randomly from the observed data of four cross-sections are generated, and the corresponding rating curves are delivered. The mean absolute percentage error (MAPE) and the root mean square error (RMSE) are used to evaluate the results. The results from four cross-sections demonstrated that α = 0 corresponds to the least favorable results, while α = 1 is the most appropriate value. The Maximum MAPE and RMSE, observed in the Trent River section, were 22.5 % and 13.1 m3/s using Maghrebi’s relation, respectively. These values decreased to 13.5 % and 8.6 m3/s when applying the proposed method using 7 points. Additional cross-sections from the Tiber River are used to validate the method and to compare it with the classical model. The results demonstrated that MAPE and RMSE values are reduced with increasing sample size, and the proposed model outperforms the classical one for small sample sizes. RMSE values declined from 62, 27.4, 46, 76.7 m3/s to 32.8, 14.4, 23.5, 33.9 m3/s using seven observed points in Ponte Nuovo, Santa Lucia, Ponte Felcino, and Ponte Rosciano cross-sections, respectively. The proposed model illustrated a notable decline in the uncertainty bands, which diminished significantly with increasing sample sizes. The proposed method is advantageous in constructing rating curves in new sites, specifically in the case of limited funding, and building more reliable rating curves in gauged sites.

Data-Driven State of Health Estimation for Lithium-Ion Batteries Based on Universal Feature Selection

A simple yet effective health indicator (HI)-based data-driven model forecasting the state of health (SOH) of lithium-ion batteries (LIBs) and thus enabling their efficient management is developed. Five HIs with high physical significance and predictive power extracted from voltage, current, and temperature profiles are used as model inputs. The generalizability and robustness of the proposed ridge regression–based linear regularization model are assessed using three NASA datasets containing information on the behavior of batteries over a wide range of temperatures and discharge rates. The maximum mean absolute error, maximum root-mean-square error, and maximum mean absolute percentage error of the SOH for the three groups of batteries are determined as 0.7%, 0.86%, and 2.1%, respectively. Thus, the developed model exhibits high accuracy in estimating the SOH of LIBs under multiworking conditions and is sufficiently robust to be applicable to low-quality datasets obtained under other conditions.

Transfer Learning With Deep Neural Network for Capacity Prediction of Li-Ion Batteries Using EIS Measurement

In this study, transfer learning (TL) technique is used in conjunction with deep neural network (DNN) to predict the capacity of lithium-ion batteries. First, the base DNN model is trained and validated based on the source dataset containing electrochemical impedance spectroscopy (EIS) measurement at temperatures of 25 °C and 35 °C. Then, the base DNN model is retrained and validated using different proportions, i.e., the first 50% and 20% of the target dataset, which contains EIS measurement at the temperature of 45 °C. This will create a new model called DNN-TL carrying the knowledge from the base model. The DNN-TL model is used to predict the second proportions, i.e., the second 50% and 80% of the target dataset considered as missing data. The maximum mean absolute percentage error (MAPE), when the first 50% and 20% of the target dataset are used for retraining DNN-TL with no fixed-layer, is found to be 0.605% and 0.999%, respectively, which indicates the accuracy of the model to estimate the capacity of batteries. The average <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula> -squared of 0.9683 is achieved by DNN-TL with no fixed-layer indicating the goodness of its fit and its capability to follow the actual missing datasets.

Comparative study of seasonal autoregressive integrated moving average and Holt–Winters modeling for forecasting monthly ground-level ozone

In this study, ground-level ozone is modeled using Seasonal Autoregressive Integrated Moving Average (SARIMA) and additive Holt–Winters models over the North-Western cluster of Ethiopia using four homogeneous series of more than 13 years of data from the European Center for Medium-Range Weather Forecasts. We split the dataset into training and testing sets. We used the data during the period 2007–2019 for model formulation and parameter estimation and the one year data in 2020 to test model forecasts. More than 60 SARIMA models have been generated for the time series. The goodness of fit of these models has been assessed using the Akaike information criterion and Bayesian information criterion. After rigorous assessment, the seasonal ARIMA(2,0,4)(1,1,2)[12], ARIMA(3,1,0)(2,0,0)[12], ARIMA(0,1,2)(0,0,2)[12], and ARIMA(2,0,0)(2,1,0)[12] models have been identified as best predictive models for Addis Ababa, Ras Dashen, Danakil Depression, and Bahir Dar, respectively. We applied model evaluation metrics, such as root mean square error, mean absolute error, and Mean Absolute Percentage Error (MAPE) to compare the accuracy between seasonal ARIMA and Holt–Winters models. Among the SARIMA and Holt–Winters models, our findings show that the best model for forecasting surface-level ozone is ARIMA(2,0,4)(1,1,2)[12] and ARIMA(3,1,0)(2,0,0)[12] for Addis Ababa and Ras Dashen stations, respectively. However, for Danakil Depression and Bahir Dar stations, the Holt–Winters model with α = 0.346, β = 0.023, γ = 0.36 and α = 0.302, β = 0.019, γ = 0.266, respectively, are found to be best models than the SARIMA. Moreover, the maximum MAPE were found to be less than 7.86% in the study, and hence all the forecasts are acceptable.

A machine learning framework for evaluating the biodiesel properties for accurate modeling of spray and combustion processes

The environment-friendly nature of biodiesel coupled with its inherent compression ignition fuel characteristics like better ignition quality, and fuel bound oxygen may reduce sooting combustion, and attract wide attention. The variation of thermophysical properties with temperature is essential for accurately modeling the combustion and emission characteristics of biodiesel fuelled diesel engines. Hence, the current paper attempts to predict the thermo-physical properties such as density, viscosity, specific heat, thermal conductivity, latent heat of vaporization, vapor pressure, mass diffusivity etc., and their variation with respect to the temperature following a machine learning approach for biodiesel fuels. Twenty feedstock samples are chosen for predicting the biodiesel thermo-physical properties and are validated with the available experimental data within a maximum error of 14 %. To evaluate the thermo-physical properties of a variety of feedstock, the predicted data are used for training an artificial neural network (ANN) and the developed ANN function is used for generating the various thermophysical properties of biodiesel fuels based on their composition and temperature. A good agreement is observed between the predicted and ANN results with a maximum mean absolute percentage error of 10 %. Hence in the current work, a collective mathematical modeling approach is proposed to accurately determine the spray and combustion-related fuel properties. The proposed model provides the various liquid and vapor properties and their variation with temperature which could be effectively employed for detailed spray and biodiesel-combustion modeling. An exhaustive data generation of eleven major liquid and vapour properties of twenty biodiesel fuels within the actual temperature range from 300 K to their respective critical temperature is presented.

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.

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 new correlation for performance prediction of small and large capacity single-effect vapor absorption refrigeration systems

Vapor absorption refrigeration (VAR) enables cleaner cooling by exploiting waste or renewable heat, hence avoiding the use of fossil-based electricity employed by conventional chillers. A new correlation is developed for the prediction of the coefficient of performance (COP) of single-effect VAR systems under different operating conditions, considering 27 different working fluids and 1,568 literature data points. The developed correlation incorporates for the first-time fluid parameters such as the boiling points of absorbents and refrigerants, the latent heat of vaporization of refrigerants, and the specific heat of absorbents together with the generator, condenser, absorber and evaporator temperatures. It is further applied for the first time in both small- and large-scale VAR systems, with the former validated based on results from literature and the latter based on ASPEN Plus simulation data, derived from rigorous VAR system models. The small-scale, literature results reveal that the developed COP model is applicable for all data sets with a mean absolute percentage error (MAPE) of 12.25%, for 93.78% of the data that appear within a ± 30% error range. The developed model is also applied to the simulation of large-scale VAR cycles that use ammonia-water (NH3-water) and water-lithium bromide (water-LiBr) for different cooling loads (100 TR, 1000 TR, and 10,000 TR), to evaluate its suitability for high-capacity systems. The maximum MAPE among the model-predicted and ASPEN Plus-generated data is 13.51% for the 100 TR water-LiBr system, with all data found within a ± 30% error band. The developed model can be applied to predict the COP of numerous fluids for single effect VAR cycles, paving the way for the investigation of VAR application in large scale, district cooling systems.

Real-time estimation of patient-specific dose distributions for medical CT using the deep dose estimation.

With the rising number of computed tomography (CT) examinations and the trend toward personalized medicine, patient-specific dose estimates are becoming more and more important in CT imaging. However, current approaches are often too slow or too inaccurate to be applied routinely. Therefore, we propose the so-called deep dose estimation (DDE) to provide highly accurate patient dose distributions in real time METHODS: To combine accuracy and computational performance, the DDE algorithm uses a deep convolutional neural network to predict patient dose distributions. To do so, a U-net like architecture is trained to reproduce Monte Carlo simulations from a two-channel input consisting of a CT reconstruction and a first-order dose estimate. Here, the corresponding training data were generated using CT simulations based on 45 whole-body patient scans. For each patient, simulations were performed for different anatomies (pelvis, abdomen, thorax, head), different tube voltages (80kV, 100kV, 120kV), different scan trajectories (circle, spiral), and with and without bowtie filtration and tube current modulation. Similar simulations were performed using a second set of eight whole-body CT scans from the Visual Concept Extraction Challenge in Radiology (Visceral) project to generate testing data. Finally, the DDE algorithm was evaluated with respect to the generalization to different scan parameters and the accuracy of organ dose and effective dose estimates based on an external organsegmentation. DDE dose distributions were quantified in terms of the mean absolute percentage error (MAPE) and a gamma analysis with respect to the ground truth Monte Carlo simulation. Both measures indicate that DDE generalizes well to different scan parameters and different anatomical regions with a maximum MAPE of 6.3% and a minimum gamma passing rate of 91%. Evaluating the organ dose values for all organs listed in the International Commission on Radiological Protection (ICRP) recommendation, shows an average error of 3.1% and maximum error of 7.2% (bone surface). The DDE algorithm provides an efficient approach to determine highly accurate dose distributions. Being able to process a whole-body CT scan in about 1.5s, it provides a valuable alternative to Monte Carlo simulations on a graphics processing unit (GPU). Here, the main advantage of DDE is that it can be used on top of any existing Monte Carlo code such that real-time performance can be achieved without major adjustments. Thus, DDE opens up new options not only for dosimetry but also for scan and protocoloptimization.

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.

Daily production prediction for coalbed methane based on Bayesian temporal matrix factorization

Effective and accurate daily production prediction of coalbed methane (CBM) is significant for enhancing CBM recovery and developing economic evaluations of CBM exploitation. As production time increases, CBM well data gradually show some characteristics of big data and is susceptible to incomplete data and noise data. Traditional geological modeling, however, requires a variety of input factors. In the present study, we apply a time series analysis method based on Bayesian temporal matrix factorization (BTMF) without the deletion of exceptional values to investigate the characteristics of CBM development. In addition, different from the widely used data preprocessing, we innovatively scale the multidimensional data to accomplish the analysis and prediction of different attributive data. By studying the temporal and attributive characteristics of the CBM production curve, the model is applied to a CBM block in China to impute the production data and perform a multi-step rolling prediction of daily gas production.Evaluation metrics, including the mean absolute percentage error (MAPE) and the root mean square error (RMSE), are applied to evaluate the performance. It is found that the imputation by the application of BTMF achieves highly satisfactory estimates (in all tested CBM wells, the maximum MAPE and RMSE are 0.1182 and 245.5882, respectively) and is comparable to the other factorization models. Results also show that BTMF is able to account for the variance in gas production with different multi-step rolling predictions and different predicting scenarios, with the MAPE matrix of five CBM wells of different predicting strategies varies from 0.051 to 0.208, 0.121 to 0.307, 0.099 to 0.221, 0.062 to 0.224 and 0.054 to 0.135, respectively. Because of the similar mechanisms of CBM development, this method can provide a reference for predicting the daily gas production of other CBM wells.

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.