Three-layer Back-propagation Neural Network Research Articles

Social Media Marketing Optimization Method Based on Deep Neural Network and Evolutionary Algorithm

Under the background of the vigorous development of China’s market economy, the marketing mix is constantly updated, which promotes the all-round development of various industries. Social media marketing has formed a relatively solid theoretical and practical foundation, especially with the continuous updating and iteration of Internet technology and the improvement of people’s requirements for experience, and we must find ways to optimize the methods of social media marketing. This study mainly introduces several optimization methods of social media marketing based on deep neural networks and advanced algorithms, and the experiments of gradient-based back-propagation algorithm and adaptive Adam’s optimization algorithm show that the proposed optimization algorithm can easily achieve the global optimal state based on the combination of back-propagation algorithm and Adam’s optimization algorithm. Accuracy of marketing is very important, so we introduce a scheme of how to accurately market, and the scheme is effective. Firstly, the FCE model is constructed by a three-layer back-propagation neural network, and then, the data input layer is designed to achieve the effect of the model.

Study on neural network algorithm for detecting respirable dust in photoacoustic cavity

The traditional photoacoustic cavity has the advantages of simple structure, low cost, and easy integration with optical cavity technology, so it has significant advantages in the measurement of the optical characteristics of respirable dust. In order to meet the demand of high-precision respirable dust measurements in practical applications, it is necessary to improve the measurement accuracy of respirable dust by traditional photoacoustic spectroscopy technology. Therefore, the structure size of the photoacoustic cavity was determined by theoretical and simulation analysis. A system for measuring respirable dust by photoacoustic spectroscopy was designed, which was applied to the atmospheric respirable dust detection simultaneously with the cavity ring-down spectroscopy system. The results showed that the correlation between the two systems was poor. Therefore, the three-layer back propagation neural network algorithm was used to correct the photoacoustic response values, and the measured value of the cavity ring-down spectroscopy system was used as the reference truth value. The calibration results showed that the output value of the neural network model was in good agreement with the reference true value: the slope was above 0.96. The results showed that the neural network algorithm could effectively improve the measurement accuracy of the photoacoustic spectroscopy system to respirable dust, improve the linearity, and reduce the detection error.

Highly sensitive resistance-type flexible pressure sensor for cuffless blood-pressure monitoring by using neural network techniques

Blood pressure is an important parameter of a heart-pumping function, vascular peripheral resistance, and blood volume in human body. The non-invasive blood pressure measurement method has attracted tremendous attention due to its advantages of simple operation and comfort. In this paper, graft-modified MWCNTs and water-based polyurethane are used as filler and matrix, which are combined with simple dipping process to produce a resistance-type flexible pressure sensor with crack structure. The sensor with crack structure exhibits a high gauge factor (∼1582.7), fast response time (∼58 ms) and good repeatability (>2000 cycles) under 0–5% strain. By attaching the sensor to the radial artery of human wrist, the pulse waveform is accurately captured. By adopting the time-domain analysis method, in addition to the fast Fourier transform and threshold method which is employed to position and extract the characteristic value of pulse signal, a three-layer back propagation neural network is constructed to regress blood pressure value. The correlation coefficients of systolic blood pressure, diastolic blood pressure and mean blood pressure were 0.950, 0.875 and 0.947, respectively, which could meet the A-level standards of British Hypertension Society and Association for the Advancement of Medical Instrumentation. This study provides a good real-time and portable technology for home blood pressure measurement.

Computational model of grid cells based on back‐propagation neural network

To simulate the firing pattern of biological Grid cells (GCs), an efficient computational model based on back-propagation neural network (BPNN), which allows for the generation of regular hexagonal grids, is described. For each GC, it is associated with the output of a learned BPNN. The firing characteristics of GCs can be controlled by the adjustment factors (AFs) flexibly. During the vehicle's space exploration, GCs can exhibit hexagonal firing patterns with different characteristics according to the settings of the AFs. Simulation results validate the proposed model's accuracy as they are in agreement with GCs' biological experimental electroencephalogram results. Meanwhile, the application of the three-layer BPNN can greatly reduce the computational complexity, which lay a foundation for its application in realistic bio-inspired autonomous navigation systems.

A Data-Driven Investigation on Surface Electromyography Based Clinical Assessment in Chronic Stroke.

Background: Surface electromyography (sEMG) based robot-assisted rehabilitation systems have been adopted for chronic stroke survivors to regain upper limb motor function. However, the evaluation of rehabilitation effects during robot-assisted intervention relies on traditional manual assessments. This study aimed to develop a novel sEMG data-driven model for automated assessment.Method: A data-driven model based on a three-layer backpropagation neural network (BPNN) was constructed to map sEMG data to two widely used clinical scales, i.e., the Fugl–Meyer Assessment (FMA) and the Modified Ashworth Scale (MAS). Twenty-nine stroke participants were recruited in a 20-session sEMG-driven robot-assisted upper limb rehabilitation, which consisted of hand reaching and withdrawing tasks. The sEMG signals from four muscles in the paretic upper limbs, i.e., biceps brachii (BIC), triceps brachii (TRI), flexor digitorum (FD), and extensor digitorum (ED), were recorded before and after the intervention. Meanwhile, the corresponding clinical scales of FMA and MAS were measured manually by a blinded assessor. The sEMG features including Mean Absolute Value (MAV), Zero Crossing (ZC), Slope Sign Change (SSC), Root Mean Square (RMS), and Wavelength (WL) were adopted as the inputs to the data-driven model. The mapped clinical scores from the data-driven model were compared with the manual scores by Pearson correlation.Results: The BPNN, with 15 nodes in the hidden layer and sEMG features, i.e., MAV, ZC, SSC, and RMS, as the inputs to the model, was established to achieve the best mapping performance with significant correlations (r > 0.9, P < 0.001), according to the FMA. Significant correlations were also obtained between the mapped and manual FMA subscores, i.e., FMA-wrist/hand and FMA-shoulder/elbow, before and after the intervention (r > 0.9, P < 0.001). Significant correlations (P < 0.001) between the mapped and manual scores of MASs were achieved, with the correlation coefficients r = 0.91 at the fingers, 0.88 at the wrist, and 0.91 at the elbow after the intervention.Conclusion: An sEMG data-driven BPNN model was successfully developed. It could evaluate upper limb motor functions in chronic stroke and have potential application in automated assessment in post-stroke rehabilitation, once validated with large sample sizes.Clinical Trial Registration: www.ClinicalTrials.gov, identifier: NCT02117089.

Prediction model for the risk of osteoporosis incorporating factors of disease history and living habits in physical examination of population in Chongqing, Southwest China: based on artificial neural network

BackgroundOsteoporosis is a gradually recognized health problem with risks related to disease history and living habits. This study aims to establish the optimal prediction model by comparing the performance of four prediction models that incorporated disease history and living habits in predicting the risk of Osteoporosis in Chongqing adults.MethodsWe conduct a cross-sectional survey with convenience sampling in this study. We use a questionnaire From January 2019 to December 2019 to collect data on disease history and adults’ living habits who got dual-energy X-ray absorptiometry. We established the prediction models of osteoporosis in three steps. Firstly, we performed feature selection to identify risk factors related to osteoporosis. Secondly, the qualified participants were randomly divided into a training set and a test set in the ratio of 7:3. Then the prediction models of osteoporosis were established based on Artificial Neural Network (ANN), Deep Belief Network (DBN), Support Vector Machine (SVM) and combinatorial heuristic method (Genetic Algorithm - Decision Tree (GA-DT)). Finally, we compared the prediction models’ performance through accuracy, sensitivity, specificity, and the area under the receiver operating characteristic curve (AUC) to select the optimal prediction model.ResultsThe univariate logistic model found that taking calcium tablet (odds ratio [OR] = 0.431), SBP (OR = 1.010), fracture (OR = 1.796), coronary heart disease (OR = 4.299), drinking alcohol (OR = 1.835), physical exercise (OR = 0.747) and other factors were related to the risk of osteoporosis. The AUCs of the training set and test set of the prediction models based on ANN, DBN, SVM and GA-DT were 0.901, 0.762; 0.622, 0.618; 0.698, 0.627; 0.744, 0.724, respectively. After evaluating four prediction models’ performance, we selected a three-layer back propagation neural network (BPNN) with 18, 4, and 1 neuron in the input layer, hidden and output layers respectively, as the optimal prediction model. When the probability was greater than 0.330, osteoporosis would occur.ConclusionsCompared with DBN, SVM and GA-DT, the established ANN model had the best prediction ability and can be used to predict the risk of osteoporosis in physical examination of the Chongqing population. The model needs to be further improved through large sample research.

Technical and tactical diagnosis model of table tennis matches based on BP neural network

BackgroundThe technical and tactical diagnosis of table tennis is extremely important in the preparation for competition which is complicated by an apparent nonlinear relationship between athletes’ performance and their sports quality. The neural network model provides a high nonlinear dynamic processing ability and fitting accuracy that may assist in the diagnosis of table tennis players’ technical and tactical skill. The main purpose of this study was to establish a technical and tactical diagnosis model of table tennis matches based on a neural network to analyze the influence of athletes’ techniques and tactics on the competition results.MethodsA three-layer Back Propagation (BP) neural network model for table tennis match diagnosis were established. A Double Three-Phase evaluation method produced 30 indices that were closely related to winning table tennis matches. A data sample of 100 table tennis matches was used to establish the diagnostic model (n = 70) and evaluate the predictive ability of the model (n = 30).ResultsThe technical and tactical diagnosis model of table tennis matches based on BP neural network had a high-level of prediction accuracy (up to 99.997%) and highly efficient in fitting (R2 = 0.99). Specifically, the technical and tactical diagnosis results indicated that the scoring rate of the fourth stroke of Harimoto had the greatest influence on the winning probability.ConclusionThe technical and tactical diagnosis model of table tennis matches based on BP neural network was highly accurate and efficiently fit. It appears that the use of the model can calculate athletes’ technical and tactical indices and their influence on the probability of winning table tennis matches. This, in turn, can provide a valuable tool for formulating player’s targeted training plans.

Application of Rough Set and Neural Network in Water Energy Utilization

In water energy utilization, the damage of fault occurring in the power unit operational process to equipment directly affects the safety of the unit and efficiency of water power conversion and utilization, so fault diagnosis of water power unit equipment is especially important. This work combines a rough set and artificial neural network and uses it in fault diagnosis of hydraulic turbine conversion, puts forward rough set theory based on the tolerance relation and defines similarity relation between samples for the decision-making system whose attribute values are consecutive real numbers, and provides an attribute-reducing algorithm by making use of the condition that approximation classified quality will not change. The diagnostic rate of artificial neural networks based on a rough set is higher than that of the general three-layer back-propagation(BP) neural network, and the training time is also shortened. But, the network topology of an adaptive neural-fuzzy inference system is simpler than that of a neural network based on the rough set, the diagnostic accuracy is also higher, and the training time required under the same error condition is shorter. This algorithm processes consecutive failure data of the hydraulic turbine set, which has avoided data discretization, and this indicates that the algorithm is effective and reliable.

Robust neural-network-based quasi-sliding-mode control for spacecraft-attitude maneuvering with prescribed performance

This paper investigates the robust tracking control problem for spacecraft attitude maneuvering with prescribed performance. Firstly, a control scheme is studied based on a quasi-sliding-mode approach which can simultaneously restrict the convergence speed and the steady-state error of both Euler angle and relative angular velocity. Then, to reduce actuators' energy consumption, a three-layer back-propagation neural network is combined with the above control law to auto-tune the control gains. Finally, the performance and effectiveness of the control approach are demonstrated by numerical simulation.

Application of back-propagation neural networks in the distribution of oil sand reservoirs\u2014a case study from the western slope of the Songliao Basin, China

High-quality hydrocarbon source rocks are present in the upper Cretaceous layer in the western slope of the Songliao Basin. Oil and gas have accumulated in these rocks at the shallow edge of the basin, which has led to the formation of oil sand resources. This study uses the back-propagation (BP) neural network method to predict the distribution of oil sand reservoirs and is the first study of its kind in China. First, based on the basic data collected by core sample, well log and geochemical analyses, and the reasonable selection of samples, the cores are divided into mudstone, siltstone, fine sandstone, medium sandstone, and sand, according to lithology. Second, a three-layer BP neural network model is constructed with two hidden S-type layers and one linear output layer. Third, through a comparison of the effect of different numbers of training sessions of the sample data, we demonstrate that the accuracy of the model can be increased to 90% after training the network 100,000 times. Then, the log-derived data of rocks with unknown lithologies are input into the neural network to predict whether they contain oil sands. We show that the BP neural network method can predict the distribution of oil sand reservoirs in the target horizon of the study area, and the results are consistent with research results on the corresponding sand reservoirs and sedimentary facies. Thus, we conclude that it is feasible to use the BP neural network method to predict the distribution of oil sand reservoirs.

Pontryagin’s minimum principle based fuzzy adaptive energy management for hybrid electric vehicle using real-time traffic information

Pontryagin's minimum principle (PMP) based energy management strategy, which describes the optimal power distribution of hybrid electric vehicle as Hamiltonian minimization problem, gains the ability to ensure real-time performance and near-optimal solutions, but demonstrates poor cycle adaptability. Therefore, this paper proposes a novel fuzzy adaptive method for the PMP-based optimal strategy by utilizing real-time traffic information that is described by the average velocity and the standard deviation of the velocity on different road segments. The two velocity feature parameters are derived by the data of floating vehicles. A three-layer back-propagation neural network (BP-NN) is constructed to predict the average power with the velocity feature parameters. On the basis of battery charging sustainability, the fuzzy adaptive law is designed to calculate the co-state of the PMP-based strategy using the predicted average power and the actual battery SOC. Finally, the performance of the proposed strategy is evaluated by comparative simulation studies. It is validated that the average velocity and the standard deviation of the velocity can be well evaluated by the information of floating vehicles. Tested by the standard and practical sampled driving cycles, the BP-NN demonstrates good performance in predicting the average power with the selected velocity feature parameters. Compared with the strategy whose co-state is just corrected by the battery SOC in the feed-back manner, the proposed PMP-based fuzzy adaptive method demonstrates superiority in improving the vehicle fuel economy and maintaining the battery charging sustainability under various driving cycles.

Prediction of biogas production from food waste in a continuous stirred microbial electrolysis cell (CSMEC) with backpropagation artificial neural network

In this study, a three-layer backpropagation neural network (BPNN) model was utilised as an estimation model of biogas production from a continuous stirred microbial electrolysis cell (CSMEC) and a continuous stirred tank reactor (CSTR) treating food waste. The study focuses on the effects of several factors, such as chemical oxygen demand removal, oxidation reduction potential (ORP), volatile fatty acids (VFAs), organic loading rate (OLR), influent pH, effluent pH, and influent ammonium on biogas production. The biogas recovery target for the model was set at 75–85%. Levenberg Marquardt backpropagation algorithm was chosen as the algorithm for the model out of the seven-benchmark comparison. Determination coefficient (R2), index of agreement (IA) and fractional variance (FV) used for the exactitude of optimal BPANN model were 0.8902, 0.925 and 0.0715 in the CSMEC and 0.9414, 0.966 and 0.0484 in the CSTR, respectively. The results of this study showed a higher accuracy and dependability of BPANN in modelling and optimizing the process parameter interactions in relation to biogas production in both the CSMEC and CSTR.

Application of statistical analysis, Deng’s relevancy and BP neural network for predicting molten iron sulfur in COREX process

AbstractThe high and fluctuation property of sulfur content in hot metal (HM) is a prominent problem in COREX process. The precise prediction of sulfur content in HM of COREX can provide a theoretical basis and technical reference for stabilizing and reducing the sulfur content in HM. In this work, a three-layer back propagation (BP) neural network was developed to predict the sulfur content in HM of COREX. The main affecting factors regarded as input parameters of the model are determined by the statistical analysis, and the hysteretic heats corresponding to each input parameters are analyzed by calculating the Deng’s correlation degree. The final structure of the BP neural network model is 20-37-1. The results show that when the error of BP neural network model for predicting sulfur content in HM of COREX is ±0.1%, the hit rate is 86.7%. In order to further improve the prediction accuracy of the model, the time series process method is adopted to update the training samples in real time and optimize the model. When the prediction error of the improved model is ±0.1%, the hit rate increases to 96.7%. The improved BP model can provide technical guidance for judging the change of sulfur content in HM and subsequent operations.

Mechanical behavior prediction of CF/PEEK-titanium hybrid laminates considering temperature effect by artificial neural network

This paper focuses on the mechanical behaviors of carbon fiber-reinforced PEEK-titanium hybrid laminates (TiGr) under different temperatures. The tensile strength, flexural strength and inter-laminar shear strength (ILSS) of TiGr laminates with different stacking structures were investigated at room temperature, 80, 150 and 220 °C, respectively. The results show that the tensile strength, flexural strength and ILSS gradually decrease as the temperature increases, and reduced by 12.3%, 45.4% and 29.1% for Type I, 12.9%, 48.8% and 30.1% for Type II, 16.1%, 45.1% and 39.4% for Type III at 220 °C. Moreover, a three-layers back-propagation (BP) neural network was developed to predict the corresponding mechanical behaviors of TiGr laminates, then the genetic algorithm (GA) was introduced to optimize the established BP neural network and the accuracies of the two prediction models were compared. It is found that both the trained BP and GA-BP neural networks could predict the mechanical performances of TiGr laminates well while the GA optimized BP neural network has better prediction results, with average absolute errors of 1.78%, 1.92% and 2.41% for tensile, flexural and inter-laminar shear strengths, respectively. Furthermore, the predictability of the trained models was validated with data from published literature, providing a new concept for the application of BP neural networks to fiber metal laminates.

An Effect Analysis Model for Corporate Marketing Mix Based on Artificial Neural Network

Under the boom of market economy in China, marketing mix is being updated constantly to facilitate the all-round development of various industries. To accurate evaluate the effect of corporate marketing mix, this paper designs an effect analysis model for corporate marketing mix based on artificial neural network (ANN). Firstly, a complete evaluation index system (EIS) was created for corporate marketing mix, and the weight of each index was assigned through analytic hierarchy process (AHP). Then, a marketing mix of big marketing + service marketing was proposed, and subject to fuzzy comprehensive evaluation (FCE). Finally, an FCE model was constructed for the effect of corporate marketing mix, based on three-layer backpropagation neural network (BPNN). The effectiveness of the model was verified through experiments. The research findings provide a reference for the application of ANN in other fields of effect analysis.

Real-Time In-Situ Laser Ranging via Back Propagation Neural Network on FPGA

To increase the measurement rate and reduce the ranging error of real-time in-situ laser ranging in full-waveform light detection and ranging (LiDAR), a back propagation (BP) neural network-based online ranging method (BPO) implemented on FPGA is proposed. In BPO, a three-layer BP neural network model is trained and implemented on a Virtex-6 FPGA to estimate the parameters of laser pulses for ranging in real time. The training dataset is generated using the multi-pulse coherent average method combined with the B-spline interpolation method. In the implementation of BPO, the parallel-pipeline architecture is employed to accelerate the computational process. Simulations proved that BPO decreased the time consumption of a single measurement to $2.95~\mu \text{s}$ . The measurement rate was increased to 339 kHz by BPO, which was approximately as 1.2 times as the measurement rate of Gauss-Newton-based online ranging method (GNO). Experiments were conducted by an FPGA-based in-situ ranging system to evaluate the ranging error of BPO. The results revealed that the mean and standard deviation of ranging errors of BPO were 0.8 mm and 1.4 cm for a laser pulse with an SNR of 36.4 dB, respectively. For a laser pulse with an SNR of 21.8 dB, the mean and standard deviation of ranging errors of BPO were 1.7 cm and 5.5 cm, which decreased 0.8 cm and 1.7 cm from those of GNO, implying that the proposed method is capable of mapping the trailing laser pulse and reducing the ranging error caused by the trailing distortion.

A machine learning approach to improve ignition properties of high-ash Indian coals by solvent extraction and coal blending

Indian coals are of poor quality, having high ash content and lower calorific value as compared to foreign coal reserves. To circumvent the problems of high ash content and low calorific value in coal, this study endeavours to explore two methods of improving ignition characteristics of Indian coals: solvent extraction and coal blending. The thermal decomposition behaviour of four Indian coals with and without solvent extraction were investigated through a thermogravimetric analyser under non-isothermal conditions. Kinetic parameters and activation energies of the coals were determined by using Arrhenius, Coats-Redfern, Doyle-Ozawa and Friedman methods. It was found that solvent extraction of the coal reduced the activation energy by approximately 50%. Pearson correlation analysis performed on the chemical composition and ignition properties of 16 typical Chinese coals and 48 of their blends showed that moisture, volatile matter, fixed carbon, calorific value, oxygen, and carbon content of coals were the most relevant factor to ignition temperature and activation energy. Accordingly, three-layer back-propagation neural network models were trained and tested and found to be reasonably accurate. The selected neural networks were used to predict the ignition characteristics of 17 Indian coals. 16 Indian coals were then hypothetically blended with 84 coals from various other countries to form 1344 blends, whose ignition characteristics were further predicted using the trained neural network models. 220 of these 1344 blends were found to have better ignition properties than the original Indian coals. The maximum reductions observed in ignition temperature and activation energy were 79.08 K and 179.38 kJ/mol respectively.

Vertical handover algorithm based on multi-attribute and neural network in heterogeneous integrated network

A novel vertical handover algorithm based on multi-attribute and neural network for heterogeneous integrated network is proposed in this paper. The whole frame of the algorithm is constructed by setting the network environment in which we use the network resources by switching between UMTS, GPRS, WLAN, 4G, and 5G. Each network build their own three-layer BP (Back Propagation, BP) neural network model and then the maximum transmission rate, minimum delay, SINR (signal to interference and noise ratio, SINR), bit error rate, user moving speed, and packet loss rate which can affect the overall performance of the wireless network are employed as reference objects to participate in the setting of BP neural network input layer neurons and the training and learning process of subsequent neural network data. Finally, the network download rate is adopted as prediction target to evaluate performance on the five wireless networks and then the vertical handover algorithm will select the right wireless network to perform vertical handover decision. The simulation results on MATLAB platform show that the vertical handover algorithm designed in this paper has a handover success rate up to 90% and realizes efficient handover and seamless connectivity between multi-heterogeneous networks.

A Novel Approach for Energy Efficiency Prediction of Various Natural Draft Wet Cooling Towers Using ANN

Cooling tower is crucial equipment in the cool-end system of power plant and the natural draft counter-flow wet cooling tower (NDWCT) gets wide application. The artificial neural network (ANN) technique is becoming an effective method for the thermal performance investigation of cooling towers. However, the neural network research on the energy efficiency performance of NDWCTs is not sufficient. In this paper, a novel approach was proposed to predict energy efficiency of various NDWCTs by using Back Propagation (BP) neural network: Firstly, based on 638 sets of field test data within 36 diverse NDWCTs in power plant, a three-layer BP neural network model with structure of 8-14-2 was developed. Then the cooling number and evaporation loss of water of different NDWCTs were predicted adopting the BP model. The results show that the established BP neural network has preferable prediction accuracy for the heat and mass transfer performance of NDWCT with various scales. The predicted cooling number and evaporative loss proportion of the testing cooling towers are in good agreement with experimental values with the mean relative error in the range of 2.11%–4.45% and 1.04%–4.52%, respectively. Furthermore, the energy efficiency of different NDWCTs can also be predicted by the proposed BP model with consideration of evaporation loss of water in cooling tower. At last, a novel method for energy efficiency prediction of various NDWCTs using the developed ANN model was proposed. The energy efficiency index (EEI) of different NDWCTs can be achieved readily without measuring the temperature as well as velocity of the outlet air.

Backwashing behavior and hydrodynamic performances of granular activated carbon blends

Ozone-biological activated carbon (O3-BAC) process has been proved to be an efficient and cost-effective technology in advanced treatment of drinking water. However, O3-BAC raises strict requirements in adsorption, hydrodynamic and regeneration performances, which one single activated carbon could hardly all-sided meet. Blending activated carbons seems to be an appropriate and economically feasible method to deal with the issue. Thus, the uniformity and stability of activated carbon blends during water treatment, especially in backwashing process are of great importance. In this paper, cyclic experiments of downward adsorption and upward backwash on 11 typical commercial granular coal-based activated carbons and their blends were carried out in column test. Hydrodynamic performances such as bed expansion rate and bed pressure drop were measured. The uniformity and stability of activated carbon blends were investigated by determining iodine number of samples collected from different heights of activated carbon bed. Then, both traditional regression methods and back-propagation neural network model were utilized to predict superficial velocity at 30% bed expansion rate and maximum bed pressure drop of activated carbon blends. The results indicate that water backwashing process has no effect on the composition proportion of activated carbon blends, and slightly changes the particle distribution of activated carbon bed regarding pore structure and adsorption capacity. A three-layer back-propagation neural network model for superficial velocity at 30% bed expansion rate yields mean relative errors of 2.17%, which is much lower than that given by traditional regression methods such as 5.53% (weighted average), 4.08% (linear) and 4.06% (polynomial). Moreover, the back-propagation neural network model for maximum bed pressure drop yields mean relative errors of 1.37%, which is much lower than that given by traditional regression methods such as 4.31% (weighted average), 4.28% (linear) and 4.22% (polynomial). The non-linear relationships can be accurately identified by the back-propagation neural network model.