Application of Artificial Neural Network for Prediction of Key Indexes of Corn Industrial Drying by Considering the Ambient Conditions

Abstract

Uncontrollable ambient conditions are the main factors limiting the self-adaption control of an industrial drying system. To achieve the goal of accurate control of the drying process, the influence of the ambient conditions on the drying behavior should be taken into consideration when modeling the drying process. Present work introduced an industrial drying system with a loading capacity of 50 t, two artificial neural network prediction models with (IANN) and without (OANN) considering the ambient conditions were established using artificial neural network modeling approach. The ambient conditions on the moisture content (MC), exergy efficiency of the heat exchanger (η_ex,h) and specific recovered radiant energy (Er) of the drying process were also investigated. The results showed that the η_ex,h and Er increase with the increase of ambient temperature while the drying time decrease with the increase of the ambient temperature. The IANN model has a better prediction performance that that of OANN model. An optimal architecture of 9-2-12-3 artificial neuron network model was developed and the best prediction performance of the artificial neural network (ANN) model were found at a training epoch number of 30, and a momentum coefficient of 0.4, where the coefficient of determination of moisture content, exergy efficiency of heat exchanger, and the specific recovered radiant energy, respectively are 0.998, 0.992, and 0.980, indicating that the model has an excellent prediction performance and can be used in engineering practice.

1. Introduction

Drying is the process of removing the moisture from natural products (e.g., agricultural products, wood, and fruits) or industrial materials (e.g., lignite, ceramics, and medical materials) down to a specific moisture content, while ensuring at the same time prime product quality, high throughput, and minimal operational costs [1,2]. Industrial drying is an effective approach to achieve the efficient and economic production of the agricultural product, while the real-time detecting and controlling technology plays a very important role in the production. However, the drying is a typical nonlinear complex process and there are various variables coupled with each other during the drying process. The real-time measurement of the drying process has hysteresis and is interfered by many factors [3]. Therefore, it is very difficult to establish a mathematical model that is in line with the actual drying process in industrial production.

In the last few decades, researchers have done a lot of works on the mathematical modeling of grain drying process, which mainly focus on the modeling of single particle drying [4,5,6], thin layer drying [7,8], and deep bed drying [9,10,11], of which the deep bed drying model is generally used in industrial drying. The typical deep bed drying model is partial differential equation (PDE), which is based on the principle of heat and mass transfer. The kind of model are mainly adopted to simulate the drying process, so as to understand the variation law of various parameters in the drying process, and provide theoretical basis for simplifying the model. However, owing to the fact that this kind of model is complex and difficult to solve, it cannot be used for real-time control in drying process [12]. Liu, Q et al. [13] established a predictive and control model by combining the prediction model, rolling optimization algorithm and feedback correction algorithm, the problems of hysteresis and multi disturbance in the control process of grain dryer were solved. Though the mathematical model is considered to be one of the best control methods for industrial-scale grain dryers when the hot air temperature is in the range of 85–120 °C, and the moisture content of 21–32% w.b., the control and predicting effects are still affected by the analytical accuracy of the deep drying process as well as the accuracy of moisture on-line detection. Based on the analysis above, a simple and sensitive prediction model is necessary to realize the automatic control of drying process and achieve the goal of high efficiency, high quality, and energy saving drying.

Artificial neural network (ANN) methodology has great application potential in the classification and prediction of complex systems [14,15]. Generally, the methodology identifies the system by collecting certain input and output data to get the model without revealing the mathematical equation in advance [16]. Owing to the advantages of the self-learning, self-adaptation, and flexibility, ANN methodology was also widely applied in identification and modeling of grain drying system. A. Dai et al. established a 8-10-1 back propagation (BP) neural network prediction model for the drying process of the combined side-heat infrared radiation and convection grain dryer. The input of the model is eight variables of the grain dryer, and the output of the model is the moisture ratio (or drying rate) of grain material. The results showed that the model has an excellent prediction performance (coefficient of determination R² = 0.9989), and the feasibility of the application of ANN methodology in drying the drying process are also verified [17]. Farkas, I et al. applied the ANN methodology to an agricultural fixed-bed dryer, the relationship between the moisture distribution of the dried grain and the physical parameters of the drying air temperature, humidity, and air flow rate were determined; the results showed that ANN methodology can be effective for modelling of the grain drying process [18]. Momenzadeh et al. [19] established an ANN model to predict the drying characteristics of shelled corn drying in a fluidized bed dryer, and the results showed that a network with the Tansig transfer function and trainrp back propagation algorithm made the best prediction performance (R = 0.9991). Zare et al. [20] studied the drying characteristics of rough rice drying in a hot air dryer assisted by infrared heating, ANN methodology was also adopted to predict the bending strength of brown rice kernel, percentage of cracked kernels and moisture content, the simulation results showed that the established model has an excellent prediction performance. Based on the literature review, it can be inferred that the ANN methodology can be adopted to predict the drying behavior of the corn drying in an industrial scale drying system. Though the ANN modeling approach has been widely used predicting the drying process, few reports have taken the ambient conditions into consideration when establishing the ANN model. However, the ambient conditions are the main factors affecting prediction accuracy of the established ANN model; therefore, the ambient conditions should be fully considered especially for the outdoor installed drying system.

For an industrial scale grain drying plant, the drying system is usually installed outdoors [17,21,22]; however, the installed method is difficult to control the ambient factors. As analysis above, though the ambient conditions are difficult to be controlled, the influences of ambient conditions on the drying performance should be taken into consideration when analyzing the drying process. The present work aims to verify that the ambient conditions should be taken into consideration when analyzing and modeling the drying process for the outdoor installed industrial scale corn drying system and, accordingly, establish an ANN model for predicting the moisture content of corn, exergy efficiency of the heat exchanger, and the specific recovered exergy—hoping to lay some theoretical basis for guiding the practical production.

2. Materials and Methods

2.1. Materials

The corn (Changcheng 799#) was freshly harvested from a local farm at Xinzhou City, Shanxi Province, China. The threshed corn kernel were stored on the open yard and the average initial moisture content of the corn kernel is ascertained to be 32.2% dry basis (d.b.) by using the 105 °C constant weight methodology [7]. The impurity content is less than 5%.

2.2. Equipment Description

The scene graph of the outdoor installed industrial drying system is shown in Figure 1. As can be seen from the figure, the system mainly consisted of 11 components, including the conveyor belt (CB), dust removal chamber, discharging device (DD), induced draft fan (IDF), drying chamber (DC), preheating room (PR), hoist (HST), grain discharging pipeline (GDP), flue gases pipeline (FGP), heat exchanger (HE), combustion chamber (CC), heat exchanger (HE). Of which the CC, IDF, HST, and DD are the electrical energy consumed components while the CC is the biomass energy consumed component, the PR consisted of eight far-infrared radiators. The details of the electric energy consumed components are listed in

Table 1. Details of the instruments.

Component	Number	Power
Induced draft fan	2	18.5 kW
Discharging device	1	3.5 kW
Hoist	1	5.5 kW
Conveyor belt	1	3.5 kW
Data acquisition system	1	2.5 kW

.

2.3. Working Principle of the System

Figure 2 depicts the workflow and the schematic diagram of the drying system. As can be seen from the left of the figure, the whole drying operation experiences three periods. Feeding period (P₁): the threshed corn kernel is conveyed to the HST by the CB and further lifted by the HST, the period lasts almost 90 min under the hypothesis of the drying chamber holds up 50,000 kg. Drying period (P₂): after the drying chamber is full filled, the CC, IDF, and the DD are sequentially operated and then the corn material begins the cycle drying process. Discharging period (P₃): when the moisture content is about 14% d.b., the IDF and the CC are shut down, the grain discharge valve on the top of the dryer is opened, and the dried corn is discharged through the grain-discharging pipeline, as shown in the Figure 2, this period lasts about 90 min. During the drying process, the ambient temperature (T₀), ambient relative humidity (RH₀), outlet air relative humidity (RH_a,out), temperatures of inlet air (T_a,in), outlet air (T_a,out), outlet corn (T_c), inlet flue gas (T_fg,in), and the far-infrared radiator (T_r) were measured by the corresponding temperature and humidity sensors, as shown in Figure 2. The details of the instruments adopted in the present work are tabulated in

Table 2. The details of the experimental instruments.

Devices	Model	Measurement Range	Precision
Thermal resistance	PT100	−200–450 °C	±0.1 °C
Thermocouple	WRN-130/230	0–1300 °C	±0.1 °C
Anemometer	DT-8893	0.001–45 m/s	0.01 m/s
Temperature and humidity sensors	AM2301	0–100%/−40–80 °C	±3%/±0.5 °C
Data acquisition system	Self-developed	-	-

.

2.4. Drying Kinetics

In the present work, the dry basis moisture content (MC) of the corn can be calculated followed by Equation (1) [23]:

$$MC=\frac{m_i-m_d}{m_d}\times 100\%$$

(1)

where m_t is the weight of the material at time t, g; m_d is the weight of absolute dry matter, which can be determined using the 105 °C constant weight methodology [7].

2.5. Exergy Recovery Performance

In order to investigate the heat recovery behavior of the far-infrared radiator, the Wien Displacement Law [24] was adopted to compute the far-infrared wavelength (λ) and the specific recovered radiant energy (Er), which can be, respectively, determined followed by Equations (2) and (3):

$$\lambda \cdot T_r=2897.6 \mathrm{um}\cdot \mathrm{K}$$

(2)

$$Er=\sigma \cdot T_r^4$$

(3)

where λ is the far-infrared wavelength, um; T_r is the absolute temperature of the radiator, K; Er is the specific recovered energy, W; σ is the black body radiant constant, 5.67 × 10⁻⁸ W/(m²·K⁴).

2.6. Exergy Efficiency of the Heat Exchanger

As can be seen from the Figure 2, the exergetic efficiency of the heat exchanger (η_ex,h) can be expressed as:

$${\eta }_{ex,h}=\frac{{\dot{Ex}}_a}{{\dot{Ex}}_{fg,in}-{\dot{Ex}}_{fg,out}}$$

(4)

where the $\dot{E{x}_{fg,in}}$ and $\dot{E{x}_{fg,out}}$ are the specific exergy inlet and outlet of the heat exchanger; $\dot{E{x}_{a,in}}$ is the specific exergy outlet of the heat exchanger, which can be calculated followed by Equation (5) [25,26,27]:

$${\dot{Ex}}_a=\dot{m_a}\left\{\begin{array}{l}\left(C_a+{\omega }_a{C}_v\right)\left(T_a-T_0\right)-T_0\left[\left(C_a+{\omega }_a{C}_v\right)\ln \left(\frac{T_a}{T_0}\right)-\left(R_a+{\omega }_a{R}_v\right)\ln \left(\frac{P_a}{P_0}\right)\right]\\ +T_0\left[\left(R_a+{\omega }_a{R}_v\right)\ln \left(\frac{1+1.6078{\omega }_0}{1+1.6078{\omega }_a}\right)+1.6078{\omega }_a{R}_a\ln \left(\frac{{\omega }_a}{{\omega }_0}\right)\right]\end{array}\right\}$$

(5)

where the mass flow rate of the dry air ($\dot{m_a}$) can be calculated followed by Equation (6) [28]:

$${\dot{m}}_a={\rho }_a{V}_a{A}_{dc}$$

(6)

where ρ_a is the density of the dry air, which can be determined using Equation (7) [29]:

$${\rho }_a=101.325/0.287T$$

(7)

The humidity ratio of the air (ω_a) in Equation (5) can be determined by using the following Equation (8) [30]:

$${\omega }_a=0.622\frac{\varphi P_{vs,a}}{P_a-\varphi P_{vs,a}}$$

(8)

Considering the flue gas is the mixture of many chemical compositions, the specific heat, and exergy depending on the chemical composition of fuels, excess air ratio, and gas temperature. The exergy calculation model developed by C. Coskun et al. was adopted to calculate the exergy of the flue gas [31]:

$${\dot{Ex}}_{fg}=c_{p,fg}\dot{m_{fg}}\left[\left(T_{fg}-T_0\right)-T_0\left(\ln \frac{T_{fg}}{T_0}\right)\right]$$

(9)

$$c_{p,fg}=\frac{c_{p,C{O}_2}}{a_C+b_N+c_H+d_S}\cdot \frac{m_{tot,steo}}{m_{fg}}+f_A$$

(10)

$$c_{p,C{O}_2}=0.1874\times {1.000061}^{T_{fg}}\times T_{fg}^{0.2665}$$

(11)

2.7. ANN Modeling

To ascertain the influence of the ambient conditions on the prediction performance of the drying process, two artificial neuron network models with (IANN) and without (OANN) considering the ambient conditions were established.

2.7.1. The Input Layer Neurons

The present work regards the drying time (t), ambient temperature(T₀), ambient relative humidity (RH₀), outlet air relative humidity (RH_a,out), temperatures of inlet air (T_a,in), outlet air(T_a,out), outlet corn (T_c), inlet flue gas (T_fg,in), and the far-infrared radiator (T_r) as the input layer neurons. The number of the input layer neurons for IANN and OANN are 9 and 7, respectively.

2.7.2. The Output Layer Neurons

The present work considers the corn moisture content (MC), exergetic efficiency of the heat exchanger (η_ex,h), and the energy recovery rate of the radiator (Er) as the output layer neurons; therefore, the output layer neurons for the two models are 3.

2.7.3. The Hidden Layer Neurons

According to some open literature [7,17,18], the hidden layer neurons of IANN and OANN can be ascertained by the following Equation (12):

$$n=\sqrt{a+b}+m$$

(12)

where, n is the number of hidden layer neurons, a is the number of neurons in the input layer, a = 9 for the IANN model and for the OANN, a = 7; b is the number of neurons in the output layer, b = 3; m is a constant between 1 to 10, so the number of hidden layer neurons for the IANN and OANN can be ascertained to be both in the range of 4 < n < 14. Therefore, the number of hidden neurons for the two ANN models can be determined by iteratively changing the number from 5 to 13 and monitoring the reliability of the response with respect to the validation set, as recommended by Furferi, R et al. [32].

2.7.4. The Transfer and Train Functions

The present work adopted the Tansig function as the transfer function of the hidden layer. Compared with the traditional BP algorithm, the Levenberg–Marquardt algorithm has a faster gradient descent and can meet the error requirement with less epochs [33]. Therefore, the Levenberg–Marquardt algorithm is adopted to be the training function of the established network.

2.7.5. The Physical Structure of the Models

Based on the analysis above, the physical structure of the IANN and OANN models are described in Figure 3, and the training process is shown in Figure 4.

2.7.6. Experimental Data

The experimental test was conducted from 16 October to 19 November, 2019, in Xinzhou, Shanxi Province, China. During the test period, the local ambient temperature changed a lot (e.g., the T₀ on 16 October varies from 8.6 to 12.8 °C while the T₀ on 17 November varies from −6.2 to 0.32 °C). In order to investigate the influences of ambient conditions on the drying behavior of the drying system, 327 groups of drying data for three days (17 October, 30 October, and 19 November) with significant T₀ difference were selected to be analyzed in the present work. The experimental data were measured every 5 min interval, and the data with obvious errors (e.g., the imprecise measurement of the grain moisture sensor caused by the ice phenomenon inside the grain at the beginning of the test, or the random error caused by the system failures) were eliminated during the process. The selected data were normalized followed by Equation (13) before the ANN modeling. The partial experiment data and the related calculation results are tabulated in

Table 3. Partial experiment data and the related calculation results.

Day	Input Neurons									Output Neurons
	t/min	T0	RH0	Ta,in	Ta,out	Tc	Tfg,in	RHa,out	Tr	MC	ηex,h	Er
17 October	40	8.65	44.76	102.6	34.1	30.8	927.5	99.9	97.6	29.5	0.43	19.39
	75	9.21	54.8	108.2	32.3	28.2	861.1	99.9	102.5	28.1	0.52	20.44
	125	9.5	54.8	117.7	38.8	30.3	930.7	99.2	97.8	24.3	0.51	19.43
	270	12.56	55.54	114.4	35.3	31.2	867.1	77.6	96.6	17.2	0.54	19.18
	435	8.53	53.32	107.7	46.1	35.4	880.9	64.2	104.1	14.8	0.51	20.79
30 October	25	3.83	63.25	92.1	32.9	25.8	867.5	99.9	95.5	31.2	0.44	18.95
	105	5.01	57.02	102.6	30.2	24.8	930.7	99.9	96.3	26.4	0.44	19.12
	185	6.84	53.21	103.5	32.6	27.6	898.4	94.1	96.6	22.9	0.47	19.18
	355	8.14	51.26	100.3	32.1	28.8	892.6	74.2	97.3	18.9	0.45	19.33
	500	5.27	48.25	96.3	33.6	30.7	961.5	64.2	98.6	14.2	0.39	19.60
19 November	15	0.24	43.55	85	19.1	18	950.6	99.8	92.9	31.7	0.36	18.43
	85	1.72	49.7	85.3	23.8	18.7	973.2	99.9	87.5	29.3	0.34	17.36
	165	2.26	45.77	95	25.7	18.9	987.7	99.9	90.5	25.3	0.38	17.95
	415	1.98	55.55	74.8	28.7	20.6	838.1	76.8	91.3	17.2	0.37	18.11
	545	0.7	41.47	82.5	28.6	23	876.1	56.8	92.8	14.2	0.39	18.41

.

$$X=\frac{X_i-X_{\min }}{X_{\max }-X_{\min }}$$

(13)

2.8. Statistical Analysis

In the present work, the predicting performance of the established ANN models are estimated by the statistic indexes including: coefficient of determination (R²), mean squared error (MSE), and mean absolute error (MAE), which can be, respectively, calculated followed by Equations (14)–(16) [34]:

$$R^2=1-{\displaystyle \sum _{i=1}^N{(x_i-y_i)}^2}/{\displaystyle \sum _{i=1}^N{(\overline{x}-y_i)}^2}$$

(14)

$$MSE=\frac{1}{N}{\displaystyle \sum _{i=1}^N{(x_i-y_i)}^2}$$

(15)

$$MSE=\frac{1}{N}{\displaystyle \sum _{i=1}^N\left(|x_i-y_i|\right)}$$

(16)

where N is the number of the data points, x is the experimental results; $\overline{x}$ is the mean value of the experimental data, and y is the results predicted by the established ANN model.

2.9. Uncertainty Analysis

In the present study, the experimental errors and uncertainties mainly arose from convective dryer, instruments accuracy, observation, and the test planning. Uncertainties of the experimental in this work were ascertained by the following Equations (17) and (18) [35] and the results were presented in

Table 4. Uncertainties of the experimental parameters.

Parameters	Unit	Uncertainties
Inlet air temperature	°C	±0.5
Outlet air temperature	°C	±0.3
Outlet corn temperature	°C	±0.2
Radiator temperature	°C	±0.2
Ambient temperature	°C	±0.1
Ambient relative humidity	%	±0.3
Flue gas temperature	°C	±0.2
Outlet air relative humidity	RH	±0.3
Corn moisture content	%	±0.2

:

$$N={\displaystyle {\sum }_{i=1}^{r}Ni/r}$$

(17)

$$u=\left(\frac{1}{r-1}\right){\displaystyle {\sum }_{i=1}^r(Ni-N)}$$

(18)

where N is the result, r is the number of runs, i is integer, and u is uncertainty.

3. Results and Discussion

3.1. The Influence of Ambient Temperature on the Energy and Exergy Performance of the Drying System

In order to fully investigate the influence of ambient temperature on the drying behavior of the drying system, the experimental data in three days with different ambient temperatures and similar relative humidity (17 October: 8.07 °C ≤ T₀ ≤ 13.41 °C, 42.51% ≤ RH₀ ≤ 56.36%; 30 October: 3.26 °C ≤ T₀ ≤ 8.87 °C, 47.26% ≤ RH₀ ≤ 65.22%; 19 November: −0.74 °C ≤T₀ ≤ 5.18 °C, 40.35% ≤ RH₀ ≤ 63.22%) are adopted for the analysis. The variations of corn moisture content and corn temperature with drying time are shown in Figure 5.

The loading capacity of the dryer is considered to be 50,000 kg accuracy and the initial moisture content of the corn were also determined to be 32% d.b. for the three experimental days. As shown in Figure 5, MC decreases with the increase of t while T_c slightly increases with the increase of t for the three sets of experimental data. The MC decreases in a stepped way owing to the fact that corn drying is the circulate drying process, and the circulate time for each circle was ascertained to be 90 min. Similar drying process for agricultural product industrial drying were reported by Ma X.Z. et al. in 2017 [36]. The total drying time for a unit drying operation in 17 October, 30 October, and 19 November, are, respectively, ascertained to be 480, 540, and 600 min, indicating that the T₀ has a great influence on the drying kinetics of the corn industrial drying. The T_c for the three sets of experimental data are less than 38 °C, as recommended by Skoneczna-Łuczków, J. et al. [37]. Moreover, it can be obvious found that the T_c under the same drying time for the three days, in ascending order of values, are as follows: T_c in 19 November, T_c in 30 October, T_c in 17 October, which might be caused by the heat change efficiency of the heat exchanger.

The exergy efficiency of the heat exchanger was calculated followed by Equation (4), and the results are depicted in Figure 6. As can be seen from the figure, even if the η_ex,h fluctuates a lot with the drying time, which might be caused by the fluctuating inlet flue gas temperature, it can be obviously found that η_ex,h in 17 October is higher than that in 30 October and 19 November. The η_ex,h for the three days, respectively, ranges from 0.391 to 0.648, 0.350 to 0.601, and 0.249 to 0.434. It is interesting that there is a clear upward trend of the η_ex,h for three days after 260 min owing to the fact that T₀ rose up at noon for the three days. Accordingly, it can be concluded that the T₀ has a significant influence on the heat exchange performance of the heat exchanger, as well as the drying performance of the whole drying process. Moreover, for the present industrial-scale drying system, the ambient conditions should not be considered as the dead state, the ambient temperature should be take into consideration when analyzing the energy and exergetic performance of the dryer. Similar findings have been reported by Jörg Schemminger et al. [38] for ambient air cereal grain drying; they developed a model for predicting the drying behavior based on the climatic data parameters (ambient temperature and relative humidity).

Waste heat recovery is an effective approach to improve the energy efficiency of an energy consumption system. In the present work, eight far-infrared radiators inserted into the drying chamber were adopted to recover the waste heat in outlet flue gas. As can be seen from Figure 6, the values of γ in 19 November, 30 October, and 17 October, respectively, vary from 7.61 to 7.90 um, 7.77 to 7.92 um, and 7.81 to 8.15 um, which are all closed to the optimized absorption far-infrared wavelength (9 µm) of cereal grain, as recommend by Zhu W et al. in 2003 [39]. The Er under the same drying time for the three days, in ascending order of values, are as follows: Er in 17 October, Er in 30 October, Er in 19 November, owing to the fact that the Er is directly proportional to the T_r, as described in Equation (7). The total recovered exergy by the radiators for 17 October, 30 October, and 19 November are, respectively, ascertained to be 571.12, 621.17, and 650.43 MJ, as shown in the Figure 7b.

3.2. Analysis of Prediction Results of BP Neural Network

Based on the analysis in Section 2.7, the number of input layers of the IANN and OANN models were, respectively, ascertained to be 9 and 7; the outlet layers of the two models are 3, while the other key parameters, such as numbers of hidden layers, neurons, training epochs, and the momentum coefficient, should be further determined. The variation range of the key parameters of the two models are tabulated in

Table 5. Configurations of the artificial neural network (ANN) models.

Parameters of the ANN Models	Range
Number of hidden layers	1–3
Number of neurons	5–13
Momentum coefficient	0.1–0.4
Number of training epochs	300–1500

.

Based on the configurations of the ANN models, the 327 experimental data sets were used for the training (training epoch number of 1000, learning rate of 0.1). The variation of MSE values with different ANN configurations for the two models are tabulated in

Table 6. The variation of mean squared error (MSE) values with different ANN configurations.

Number of Hidden Layer	Neuron Number	MSE Values for Momentum Coefficient (×10−4)
		0.1		0.2		0.3		0.4
		IANN	OANN	IANN	OANN	IANN	OANN	IANN	OANN
1	6	3.2503	5.2432	2.802	4.2535	3.2214	5.3265	2.4048	3.8654
	8	3.4358	4.9585	4.9191	4.3254	2.8923	4.8659	3.3991	3.5462
	10	3.0859	5.2153	2.8526	5.3215	1.7918	4.8654	1.4452	3.5412
	12	2.9181	4.5241	1.4097	3.2546	1.7174	5.2136	1.6129	3.2654
2	6	2.5645	4.6235	3.0270	5.2365	2.9827	5.0231	2.9694	3.1205
	8	5.1399	5.6865	3.5683	4.9565	3.2241	4.8654	3.9953	3.6215
	10	1.9517	3.6542	2.3201	5.3214	2.5523	4.5621	2.212	3.0365
	12	2.1699	4.2156	1.8036	4.2356	2.6759	4.3562	1.3876	2.9654
3	6	3.7975	4.3655	5.4039	5.2142	4.1843	4.8654	2.7318	2.8542
	8	2.2898	4.3568	2.6400	4.3652	1.7453	4.2154	3.246	2.7321
	10	3.8677	4.6856	2.1785	4.1025	2.7466	4.0354	2.587	2.6245
	12	2.6241	3.2345	1.6469	3.8695	1.6639	3.9564	1.5512	2.5324

Training epoch number of 1000 and learning rate of 0.1. The bold number in the table is the lowest MSE value.

. As can be seen from the Table 6, the lowest MSE value of the IANN model is ascertained to be 1.3876 × 10⁻⁴ when the hidden layer number is 2, neuron number is 12, and momentum coefficient is 0.4, while the MSE value of the OANN model is ascertained to be 2.5324 × 10⁻⁴ when the hidden layer number is 2, neuron number is 12 and momentum coefficient is 0.4. In order to further investigate the influence of the training epochs on the MSE of the ANN models, the different training epochs (300–1500) and neuron numbers (5–13) are selected to train the IANN model with the hidden layer number of 2 and momentum coefficient of 0.4, and OANN model, with the hidden layer number of 3, and momentum coefficient of 0.4. The results are shown in

Table 7. Influence of epochs and neuron number of established IANN model on MSE values.

Epochs	MSE Values for Neuron Number (×10−4)
	5	6	7	8	9	10	11	12	13
300	3.7578	4.5403	2.4953	3.5101	2.3489	4.7521	2.7562	1.7478	2.1324
400	2.9890	2.6727	2.5036	3.7639	1.7403	2.4159	2.2206	0.97334	1.3887
500	5.8078	1.6159	3.2015	2.5594	2.2823	3.0795	2.1183	0.89931	2.1599
600	4.5154	2.6319	2.0265	1.2636	1.8356	1.3300	2.1651	1.2676	1.4908
700	4.1400	2.6848	3.0314	1.6838	1.2706	2.0658	2.0319	1.3243	1.4640
800	3.9628	2.6995	2.4877	1.7637	1.8480	1.2178	2.5307	1.3522	1.0449
900	3.1647	3.5374	2.5379	1.9526	1.2983	1.3416	2.1309	1.8244	0.79806
1000	3.7801	2.387	2.8735	3.3274	2.3157	1.6443	1.7539	1.1109	1.2262
1100	3.3921	2.6832	2.2898	1.7675	2.8269	1.7395	1.7649	1.2327	1.3550
1200	3.6763	2.7611	2.2023	2.1266	2.0861	2.7173	2.0194	1.0018	0.99515
1300	3.6221	2.4292	2.0158	3.3011	1.8011	1.6036	2.0977	1.1542	0.8389
1400	4.1916	2.5568	1.8191	1.4018	1.9659	1.7178	1.5259	1.3142	1.1663
1500	3.4770	2.8762	4.7773	1.7395	1.789	1.4142	2.0901	0.75975	1.7163

and

Table 8. Influence of epochs and neuron number of established OANN model on MSE values.

Epochs	MSE Values for Neuron Number (×10−4)
	5	6	7	8	9	10	11	12	13
300	6.3524	5.9654	5.6548	5.1264	4.9546	3.6584	3.2345	3.215	4.3254
400	6.1256	5.8645	5.3642	4.2568	3.9564	2.8645	3.3654	2.9564	3.9584
500	6.5426	6.2153	5.2648	4.8654	4.2315	3.6524	3.9654	2.9852	4.6524
600	6.1546	5.6425	5.1265	4.0365	4.2125	2.9952	2.8675	3.2465	3.6584
700	5.8642	5.3549	5.0365	4.2156	3.6584	2.3654	3.3264	3.2156	3.4528
800	5.6521	5.6842	4.9564	3.2156	3.9654	3.1257	3.6542	3.6214	4.1253
900	5.5215	5.1265	4.8542	3.6879	2.9654	2.6584	3.3215	2.8654	3.6254
1000	5.2698	5.3216	4.6245	3.6954	3.2564	2.6542	3.0215	2.8654	3.2154
1100	5.3165	4.9632	4.3568	4.0264	3.9854	2.9548	2.3652	2.6854	2.9548
1200	4.9632	4.8654	4.3564	4.2565	2.6584	1.6548	3.8654	1.9654	2.6458
1300	4.8652	4.5687	4.0215	3.8652	3.2152	2.2154	3.6584	2.6542	2.3254
1400	4.8652	4.5324	4.3265	3.3264	3.6542	1.6854	3.2548	2.3254	2.6542
1500	4.6624	4.2156	4.2364	3.9862	3.2644	1.4542	3.6524	1.8824	2.0312

Hidden layer number of 2 and learning rate of 0.4. The bold number in the table is the lowest MSE value.

. It obviously can be seen from the Table 7 that the IANN model displays the best prediction performance (MSE = 0.75975 × 10⁻⁴) when the training epochs are 1500 and the hidden layer neuron numbers are 12, while the OANN model displays the best prediction performance (MSE = 1.4542 × 10⁻⁴) when the training epochs are 1500 and the hidden layer neuron numbers are 10. Accordingly, the architecture of the IANN model is ascertained to be 9-2-12-3, while the OANN model is 7-2-10-3.

Based on the obtained architecture of the two models, the data sets were trained by the models and the training results are shown in Figure 8. As can be seen from the Figure 8a, the IANN model gets the best prediction performance when the training epochs are 30, where the model gets the lowest MSE value (2.1252 × 10⁻⁴) and the R-values for the data sets used for training, validating, and testing the model are 0.99852, 0.99623, and 0.99788, respectively. On the other hand, the OANN model gets performs a best prediction performance when the epochs are 31, where the model gets the lowest MSE value (2.1125 × 10⁻⁴) and the R-values for the data sets used for training, validating, and testing the model are 0.99779, 0.99225, and 0.99231, respectively. Indicating that the established models have sufficient reliability and can be used for predicting the MC, η_ex,h, and Er. However, compared with the OANN model, the IANN model has a better prediction performance with the higher values of MSE and R-values, indicating that the IANN model has a better prediction performance. It can be summarized that the ambient conditions should be taken into consideration when establishing the prediction model. Moreover, in order to achieve the repeatability of the model, the weights of the established IANN model are listed in

Table 9. The weights of the established model.

Weight	Matrix
$iw\{1,1\}$	${\left[\begin{array}{cccccccccccc}-0.13887& -1.4159& -0.59037& 0.1114& -0.75533& -0.065606& -0.40298& 0.10036& 0.048895& 0.31505& -0.11427& -2.9315\\ -0.043673& 0.88573& 0.40884& -0.11595& -1.6174& 0.19736& 0.21143& -0.1711& -0.38451& -0.9736& -0.18843& -0.21793\\ -0.029184& -0.94861& -0.04776& -0.072804& 0.67878& 0.10712& -0.10786& 0.016793& 1.1512& 0.43835& -0.12774& -0.27362\\ 1.325& 0.87228& 1.2523& -0.36426& 0.69924& 0.28796& -0.014829& 0.32952& -0.31587& 0.72732& 1.6455& -0.12686\\ -0.20193& 0.43779& -0.13525& 0.17093& -0.16529& -0.13133& -0.23734& 0.091524& -0.16368& 0.039253& -0.10292& 0.25585\\ 0.035035& -0.29962& 1.2988& -0.41771& 0.019629& -0.50672& -0.9173& -0.10148& -0.56316& 0.55246& 0.016416& -0.146\\ -0.42221& 0.14413& 0.19538& 0.036047& -0.11686& 0.18668& -0.097933& 0.21095& -0.32161& -0.050346& -0.87703& -0.022803\\ -0.13902& 0.23502& -0.025627& 0.1226& 0.10235& 0.10235& -0.34015& 0.064227& -1.1691& -0.61913& -0.062187& 0.15284\\ -0.044179& 0.4277& 1.0711& 0.0056514& 0.17523& 0.17523& -1.0477& -0.21919& 0.56578& 0.29425& -0.049908& 0.083461\end{array}\right]}^T$
$iw\{2,1\}$	$\left[\begin{array}{cccccccccccc}-0.19737& 0.6332& -0.64687& -1.095& 1.0386& 0.95262& -0.48395& 0.016947& 0.18969& -1.5994& -0.11055& 2.0895\\ 1.1872& 0.020194& 0.055515& -0.51733& -0.033498& -0.1982& -0.17442& 0.88639& -0.0037144& -0.021703& 1.2493& 0.014532\\ 0.22659& 0.015762& 0.13859& -0.93039& 0.041831& -0.71062& -0.82429& -1.0963& -0.0062919& 0.059516& 0.000596& 0.035423\end{array}\right]$
$b\{1\}$	${\left[\begin{array}{}1.5332& 0.7684& -0.18591& 0.20253& 1.0812& 0.078345& 0.11536& 0.011221& -0.51627& -1.1868& -2.0232& -3.1241\end{array}\right]}^T$
$b\{2\}$	${\left[\begin{array}{}-0.5767& 0.052421& 0.11789\end{array}\right]}^T$

.

3.3. The Application of the IANN Model

To further verify the practicability of the established IANN model, the 117 experimental data sets acquired in 12 November (−3.01 °C ≤ T₀ ≤ 5.94 °C, 40.35% ≤ RH₀ ≤ 63.23%) were trained by the model. The comparison between experimental values and predicting results of the MC, Er, and η_ex,h are depicted in the following Figure 9. Obviously, it can be seen from the figure that the regression coefficient of determination (R²) for MC, Er, and η_ex,h, respectively, are 0.998, 0.992, and 0.980, mean squared error (MSE) of 0.067, 0.00296, and 0.0057, mean absolute error (MAE) of 0.16, 0.04, and 0.0063. The values of the above statistic indexes indicate that the 9-2-12-3 IANN model has an excellent prediction performance and can be used in engineering practice. Moreover, the prediction results of the first cycle (the measured MC between 28.9% d.b. and 32% d.b.) are slightly deviated from the experimental results, which might be caused by the fact that there is a measurement error for the on-line moisture meter in the high moisture region of cereal grains [40].

Based on the established 9-2-12-3 IANN model, a control model of the drying process is proposed, as shown in the Figure 10. During the drying process, the experimental data collected by the corresponding sensor are used to train, and get, the optimal IANN model. As can be seen from Figure 2 and Figure 10, the drying process is controlled by the DD and the flue gas valve on the flue gas pipeline. When one of the inputted factors changes, the established IANN model can automatically calculate and analyze the predicted corresponding output indexes at the same time. Accordingly, the intelligent optimized controller optimizes and calculates the grain discharging electric motor (or flue gas valve), and the optimal rotational speed of the electric motor (or optimal openness of the valve) is given to the frequency converter, so as to control the drying process, and realize the optimal control of the MC, Er, and η_ex,h. The proposed control model based on the IANN model may strengthen the practical implications.

4. Conclusions

The present work considers the ambient temperature as one of the key parameters affecting the drying performance of the industrial corn drying. The artificial neuron network was applied to predict the drying performance of the drying system. The drying kinetics, the exergy exchange performance, as well as the heat recovery performance of the drying system were investigated. The detailed conclusions depending on the results are listed as follow:

(1)

the exergy efficiency of the heat exchanger is significantly affected by the ambient temperature, where the exergy efficiency is proportion to the ambient temperature. Moreover, the exergy efficiency of the heat exchanger varies from 0.249 to 0.648 for the whole drying process;

(2)

the far-infrared wavelength of the radiators are found to be ranged from 7.61 to 8.15 um, and the recovered radiant exergy for 17 October, 30 October, and 19 November are, respectively, ascertained to be 571.12, 621.17, and 650.43 MJ;

(3)

based on the analysis of the ambient conditions on the drying performance of the drying system, two prediction models with (IANN) and without (OANN) considering the ambient conditions were established and compared with each other. The results showed that IANN model has a better prediction performance, which indicates that the ambient conditions should be taken into consideration when establishing the prediction model;

(4)

the best performance for prediction of moisture content, specific recovered exergy, and exergy efficiency for corn industrial drying are found to be at the training epochs of 30, where the regression coefficient of determination for MC, Er, and η_ex,h, respectively, are 0.998, 0.992, and 0.980; mean squared error of 0.067, 0.00296, and 0.0057; mean absolute error of 0.16, 0.04, and 0.0063. This indicates that the established IANN model has excellent prediction performance and can be used in engineering practices.