# Predicting Multidimensional Environmental Factor Trends in Greenhouse Microclimates Using a Hybrid Ensemble Approach

Authors: Dayu Xu; Lei Ren; Xuyao Zhang
Journal: Journal of Sensors
 (2023)

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## Abstract

Trend prediction of greenhouse microclimate is crucial, as greenhouse crops are vulnerable to potential losses resulting from dramatic changes in greenhouse microclimate. Consequently, a precise greenhouse microclimate predictive model is required that can predict trends in greenhouse microclimates several weeks in advance to avoid financial losses. In the present study, we proposed a hybrid ensemble approach to predict greenhouse microclimate based on an Informer model that is optimized using improved empirical mode decomposition (IEMD). The dataset was decomposed using IEMD, and then all the decomposed datasets were predicted using the Informer model. Afterward, the predictions were combined. In the present study, five different environmental factor datasets of CO2 concentration, atmospheric pressure, light intensity, temperature, and humidity were predicted. The performance of the IEMD-Informer model was compared with other modeling approaches. The results demonstrate that the proposed method has outstanding performance and can predict the greenhouse microclimate environmental factors more accurately.


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## Body

## 1. Introduction

Greenhouse technology is progressively establishing itself as a viable and excellent crop production option [1]. Greenhouses are small-scale agricultural systems used to improve crop yields and quality. Growers can regulate parts or all of the greenhouse microclimate using various methods to reduce resource investment and improve yields and quality [2]. The growth, development, and final yields of greenhouse crops are all influenced by the microclimate in the greenhouse. Using a predictive model to anticipate future changes in the greenhouse microclimate can facilitate responses to changes in the greenhouse environment quickly, adjustment of the greenhouse environment, and avoidance of crop malnutrition or death caused by untimely regulation.Based on crop characteristics, the greenhouse environment, and exterior meteorological conditions, Rahman et al. [3] developed a model to estimate the greenhouse dehumidification demand (dehumreq), which enabled annual hourly predictions of changes in greenhouse dehumidification demand in cold regions. Gao et al. [4] suggested a deep bidirectional long short-term memory (bid-LSTM) network to predict soil moisture and conductivity based on a citrus orchard environmental data collection system that utilized the Internet of things and combined with environmental data. To anticipate greenhouse temperatures and humidity, Gharghory [5] proposed an improved recurrent neural network approach based on long short-term memory (LSTM). Although LSTM can handle some gradient difficulties, it cannot fully address the gradient vanishing problem. In addition, training an LSTM is very difficult and takes a long time. To estimate the air temperatures and heat load of a solar greenhouse, Huang et al. [6] proposed a dynamic thermal model based on the Laplace transform. Liu et al. [7] proposed a hierarchical optimization control technique based on a crop development model that divides the light environment optimization control problem into optimization and control levels, thereby reducing the computational complexity of light environment problems. To solve the problem of high greenhouse light environment control expenses, Li et al. [8] developed a photosynthetic rate prediction model based on the least squares support vector machine (LS-SVM) method. Altikat [9] estimated CO2 transport from the soil to the atmosphere in a greenhouse setting using artificial neural networks (ANNs), deep learning neural networks (DLNNs), and multiple linear regression (MLR). Hu et al. [10] used two cascade convolutional neural networks (CNN) for cancer cell detection and identification of stages in their life cycle, and the experimental results outperformed the conventional methods. In addition, Ji et al. [11] proposed a long short-term memory- (LSTM)- based abnormality detection method (LSTMAD) for discordant search of ECG data, and experiments showed that the method could detect abnormalities accurately.Currently, there is increasing demand for analysis and prediction of complex and large datasets. Therefore, the use of multiple algorithms to construct a combined model to address the shortcomings of a single algorithm is also increasing. To acquire wind speed characteristics, Ruiz-Aguilar et al. [12] used empirical mode decomposition (EMD) to break down wind speed data for wind speed prediction and combined EMD, permutation entropy (PE), and artificial neural networks (ANNs). In the predictive range of their experiments, the EMD-PE-ANN method outperformed a single ANN model [12]. However, the traditional EMD method has frequent modal mixing problems. Improved EMD approaches can address the problem. Yan et al. [13] proposed a method based on seasonal autoregressive integrated moving average (SARIMA), ensemble empirical mode decomposition (EEMD), and LSTM to predict wind speed. In addition, Kala et al. [14] proposed a rainfall forecasting model based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) combined with long short-term memory (LSTM). Guo et al. [15] trained a backpropagation (BP) neural network with an upgraded particle swarm optimization (PSO) algorithm and constructed a particle swarm optimization neural network air humidity prediction model, showcasing the effectiveness of the upgraded particle swarm neural network forecasting system. However, BP neural networks often stagnate in the flat area of the error gradient surface, and their convergence is slow or potentially unable to converge. Fan et al. [16] used the PSO algorithm to optimize support vector regression (SVR) super parameters, the results of which indicate that the improved SVR greenhouse temperature prediction model outperformed the classic BP neural network. Yuan et al. [17] combined the PSO algorithm with the LS-SVM algorithm, which has higher accuracy and performance for predicting photosynthetic rates than the traditional BP or SVM algorithms. Ouamane et al. [18] proposed an algorithm that combined principal component analysis (PCA) and seasonal autoregressive integrated moving average model with exogenous variables (SARIMAX) to fill in missing sensor data caused by greenhouse power failures. Ullah et al. [19] used ANNs to optimize and adjust the parameters of the Kalam filtering algorithm. Experiments have shown that the improved Kalam filtering algorithm had a higher accuracy than the traditional Kalam filtering algorithm; however, when the moving target is blocked for a long period of time, the target tracking may be lost.Large datasets, multiple dimensions, and nonlinearity are common properties of greenhouse microclimate data. Therefore, to anticipate and regulate a greenhouse environment for an extended period of time, a greater ability to capture long-term data dependence is required for greenhouse microclimate data prediction. The transformer model proposed by Vaswani et al. [20] in 2017 outperformed the recurrent neural network (RNN) model in terms of capturing the long-term dependence. Yao et al. [21] proposed an end-to-end transformer network with embedded random deviation queries for pedestrian trajectory prediction and achieved better performance.However, the transformer model has three problems related to predicting long-term time series data [22]. (1) Due to the atom action of the self-attention mechanism (the classical dot product), the time complexity and memory usage per layer are OL2, and L is the length of the input dataset. (2) The total memory use is OJ×L2 due to the stack of J encoder/decoder layers, which restricts the model scalability when receiving long sequence inputs. (3) Step-by-step inference is slow (as in an RNN-based model) because of the transformer model’s dynamic decoding.In order to address these problems, Zhou et al. [22] proposed the Informer model, which was an improvement of the transformer model. They used a probabilistic sparse self-attention mechanism to replace the transformer model’s original standardized self-attention mechanism, which lowered the time complexity and memory utilization. In addition, they also proposed a self-attention extraction operation and improved the decoder, both of which are helpful for receiving long sequences of data and avoiding cumulative error diffusion during the reasoning stage. Wang et al. [23] proposed a method for average wind power prediction based on convolutional neural network (CNN) and Informer model to improve prediction accuracy.Previous studies have not applied the Informer model for greenhouse environmental prediction, and some methods require extended training periods. Subsequent research has determined that the training time of the Informer algorithm is short for the long-term time series data prediction of greenhouse environments, but the prediction accuracy is insufficient. The Informer model therefore requires adjustment; however, the algorithm contains many parameters, and adjusting the algorithm is complicated. Therefore, we used the CEEMDAN method in this study, as it can decompose complex datasets. Our goals were to improve the effect of the Informer algorithm on feature extraction and reduce the parameter optimization requirements of the algorithm. Combining the CEEMDAN and Informer methods can expand the optimal parameter selection range of the Informer model, and improved results can be obtained without strict parameter selection, thereby reducing the time consumed in parameter debugging and optimization.The CEEMDAN method used in this paper can effectively decompose complex datasets and reduce the effect of modal mixing. The Informer method is suitable for predicting long time series data with high accuracy. Greenhouse environmental factor data happens to be complex nonlinear long time series data, which is very suitable for the application of the CEEMDAN and Informer methods. In the actual experimental process, the original datasets only need time dimension data and environmental factor data; the dataset requirement is simple, the Informer training time is short, and the hybrid model prediction accuracy is high.In agricultural production, the method can be applied to the prediction of greenhouse climate trends, which facilitates the prevention of greenhouse climate extremes, provide managers with a reference for maintaining suitable greenhouse environments, and reduce crop losses caused by unsuitable climate.The contributions of this study are as follows:The Informer network model is improved using the CEEMDAN method, and the two methods are combined to form a hybrid model. The CEEMDAN method can decompose a complex nonlinear dataset into several component datasets with simple features, and the addition of CEEMDAN can reduce the difficulty of predicting long time series data in the Informer network significantly and improve the prediction accuracy.A hybrid CEEMDAN and Informer network model is used for trend change prediction of greenhouse microclimate. The method predicts five long time series datasets of CO2 concentration, atmospheric pressure, light intensity, temperature, and humidity. The method shows good generalizability.The rest of this paper is organized as follows. Section2 provides a structural description of the method used, the flow structure of the hybrid model, and details of the experiments. Section 3 presents the decomposed images of the datasets, the predicted results, and the errors. Section 4 is a discussion of the experimental results. Section 5 summarizes the research and highlights prospective work.


## 2. Methodology

### 2.1. Original EMD Method

Huang et al. [24] was the first to propose the use of EMD, as it performs well when analyzing nonlinear and nonstationary time series data. EMD decomposes a signal based on the time scale properties of the data rather than using a fixed basis function and can describe the physical significance of the time series signal. EMD can deconstruct a complicated signal into a limited number of intrinsic mode functions (IMFs), each of which retains the original signal’s local characteristic signals at different time scales, and is its most important feature. EMD can make nonstationary data stationary, then uses the Hilbert transform to obtain the temporal spectrum and physical frequency. The IMFs must meet two essential requirements: (1) the zero-crossing and extreme numbers should be one apart or equal, and (2) the average value of the higher envelope established by the local maximum and the average value of the lower envelope created by the local minimum should both be zero.The EMD procedure is as follows:(1)
Local minimum and maximum values of the time series dataXt are determined(2)
The upper and lower envelopesemax1 and emin1 are created, and the local maximum and minimum are connected using a cubic spline. The average envelope emean1, which represents the first IMF, is then generated(3)
The (h1) difference between the data and the average envelope is calculated. The preintrinsic mode function is denoted by h1. This process is called the sifting technique(1)Xt−emean1=h1(4)
Steps 1–3 are repeatedk times, with h1k−1 being the new data(2)h1k−1−emean1k=h1k(5)
Steps 1–3 are repeated untilh1k meets the IMF requirements. Then, it is designated c1, the first IMF. The remaining part r1 is established by separating c1 from the other data(3)Xt−c1=r1(6)
The remainderr1 is regarded as fresh data, i.e., Xt=r1; then, the screening procedure is repeated. The following are the outcomes of this procedure:(4)r1−c2=r2,r2−c3=r3,⋯,rN−1−cN=rNOne of 4the termination requirements can halt this process: (1) the IMF cannot be extracted from the residualrN which becomes a monotonic function, or (2) the cN component or residual rN is less than a predefined threshold.Finally, as indicated in Equation (5), the time series Xt can be expressed as the sum of n IMF components, with the last residual term included.
(5)Xt=∑i=1Nci+rN.Each IMF is a distinct and concrete manifestation of the time seriesXt’s local properties. Despite the fact that this method is extremely beneficial, EMD still has several outstanding issues. One of the EMD algorithm’s major flaws is that it produces virtually identical oscillations in different IMFs or oscillations in a mode with very different amplitudes, which is a phenomenon known as “mode mixing.” The existence of the boundary effect is demonstrated by substantial oscillations at the start and end of the IMF, which is another drawback of this method. The boundary effect is due to the interpolation function used in the filtering process, which causes the decomposition result to be inconsistent with the original data.


### 2.2. CEEMDAN Method

The CEEMDAN method was originally proposed by Torres et al. [25]. Every phase of the decomposition process in CEEMDAN includes large amounts of white noise. Compared with EMD and ensemble empirical mode decomposition (EEMD), CEEMDAN can effectively address the mode mixing problem and precisely reconstruct the signal. The CEEMDAN method consists of the following steps:
(1)
To acquire the initial IMF of the noise-contaminated signal, a defined amount of white noise is introduced to the original signal. The EMD is repeatedN times with different noise, and the ensemble average of the total IMF1 corresponding to N tests is used to determine the initial IMF1 of the original signal:(6)IMF¯1t=1N∑n=1NE1Xt+εunt,where IMF¯1 is the incoming signal’s first EMD component X, un is the unit variance zero mean Gaussian white noise, ε is the fixed coefficient, E1 is the operator that yields the ith IMF component, and N is the implementation number. The first signal residual r1 is then calculated as follows:
(7)r1=X−IMF¯1(2)
The input for the second IMF isr1+εE1un,n=1,N. When EMD is used, the second IMF is the average of the first IMF generated:(8)IMF¯2t=1N∑n=1NE1r1t+εE1unt(3)
Thekth residual is calculated for k=2,3,⋯,K, rk=rk−1−IMFk¯, and the ensemble average of the first IMF obtained by EMD as k+1th IMF:(9)IMF¯k+1t=1N∑n=1NE1rkt+εEkunt(4)
The method is repeated until no more than two extremes are present in the last residual value:(10)R=X−∑k=1KIMF¯kwhere the ultimate residual value is R and the total number of IMFs isK(5)
The final decomposition result is as follows:(11)Xt=∑k=1KIMF¯kt+RtThis method can ensure accurate signal decomposition and reconstruction.


### 2.3. Informer Neural Network

The Informer model was proposed by Zhou et al. [22]. Figure 1 shows an overview of the components included in the Informer model.Figure 1
Overview of the Informer model.


#### 2.3.1. Typical Self-Attention Mechanism

Typical self-attention [10] is based on tuple input, which includes the key, value, and query, and uses the scaled dot product as AQ,K,V=SoftmaxQKT/dV, where Q∈ℝLQ×d, K∈ℝLK×d, V∈ℝLV×d, and d denotes the input dimensions. To go deeper into the self-attention mechanism, let qi, ki, and vi represent line I in Q, K, and V. The attention of the ith question is described as a kernel smoother in probability, according to Tsai et al. [26]:
(12)Aqi,K,V=∑jkqi,kj∑lkqi,klvj=Epkjqivj,where pkjqi=kqi,kl/∑lkqi,kl and kqi,kl choose the exponential asymmetric kernel exp qikjT/d. Self-attention integrates these variables and produces a result according to the likelihood determined pkjqi. It requires the calculation of quadratic time point products and the use of OLQLK memory, which is the fundamental disadvantage of boosting forecasting ability.The result of theith query is its composition with the value v, and the attention of the ith query to all keys is defined as its probability pkjqi. The dominant dot product pair pushes the accompanying query’s attention probability distribution away from a uniform distribution. If pkjqi resembles a uniform distribution, pkjqi=1/LK, then self-attention is reduced to a trivial sum of values V, which is unnecessary for residual input. The “similarity” between P and Q distributions might then be utilized to differentiate “important” queries. The Kullback-Leibler divergence is used to assess “similarity” KLqp=ln∑l=1LKeqiklT/d−1/Lk∑j=1LKqikjT/d−lnLk. After deleting the constant, the sparsity measure of the ith query is defined as:
(13)Mqi,K=ln∑j=1LKeqikjT/d−1LK∑j=1LKqikjTd,where the log-sum-exp (LSE) of qi on all keys is the first term. The arithmetic mean of these keys is the second term. If the ith query has a larger Mqi,K, its attention probability p is more “diversified,” and the primary point product pairs in the head domain of the long tail self-attention distribution have a higher chance of being included.


#### 2.3.2. ProbSparse Self-Attention

ProbSparse self-attention can be achieved by enabling each key to focus exclusively onu-dominant queries, according to the proposed measurement:
(14)AQ,K,V=SoftmaxQ¯KTdV,where Q¯ is a sparse matrix of the same size that includes only the top-u query according to the sparse metric. Under the direction of a constant sampling factor C, set u=c×lnLQ, and it only needs to compute the OlnLQ dot product of each query-key search, for which the layer memory usage is OLKlnLQ. This attention results in various sparse query-key pairs for each head in the multihead perspective, thereby avoiding substantial information loss.However, traversing all queries measuringMqi,K necessitates computing each dot product pair or quadratic OLQLK. In addition to LSE operation, there are potential numerical stability problems. Thus, an empirical approximation is used to effectively obtain the query sparsity measure.For each queryqi∈ℝd and kj∈ℝd in the key set K, it has the bound as lnLK≤Mqi,K≤maxjqikjT/d−1/LK∑j=1LKqikjT/d+lnLK. When qi∈K, it is also true.The maximum average measurement is:(15)M¯qi,K=maxjqikjTd−1LK∑j=1LKqikjTd.In the long tailed distribution, the method only requires a random sampleU=LKlnLQ dot product pairs to compute Mqi,K, that is, the other pairs are filled with zero. To calculate Mqi,K in the long tailed distribution, U=LKlnLQ point product pairs are sampled at random, leaving the other pairs as zero. Then, choose sparse top-u as Q¯. Mqi,K’s maximal operator is less affected by zero and has a more stable value. Since the query and key input lengths are frequently equal in practice LQ=LK=L, the overall ProbSparse self-attention space and time complexity is OLlnL.


#### 2.3.3. Encoder

The encoder extracts the robust long-term dependence of lengthy sequence inputs. Thetth sequence’s input χt is molded into a matrix Xent∈ℝLx×dmodel following the input representation. Figure 2 shows a schematic diagram of the encoder.Figure 2
A single stack in the encoder used in the Informer model. The overlapping red square indicates then-head weight matrix.The encoder’s characteristic graph has a redundant combination of valuesV as a natural result of the ProbSparse self-attention mechanism. In the next layer, the superior extraction operation of operation privileges is used with the dominant characteristics to produce a centralized self- attention feature graph. Figure 2 shows the n-head weight matrix of the attention block, which severely cuts the input time dimension. From the jth layer to j+1, the “extraction” method proceeds as follows:
(16)Xj+1t=MaxPoolELUConvldXjtAB.(1)
The horizontal stack represents an encoder replica (Figure1)(2)
The primary stack, which receives the entire input sequence, is the one proposed. The second stack then repeats the operation with a half slice of the input(3)
The red layers are dot product matrices that are reduced in order using self-attention distillation in every layer(4)
The function maps of all stacks are connected as the output of the encoderThe attention block is denoted by⋅AB and includes multihead active attention and basic operations such as conv1d·, which executes a one-dimensional convolution filter in the temporal dimension (kernel width is 3) using the ELU(·) activation function [27]. After stacking one layer, a maximum pool layer is added, and Xt is downsampled to the half layer, resulting in a total memory use of O2−εLlogL, where ε is a small number in this case. To improve the robustness of the distillation operation, the main stack that halves the input is replicated and the number of self-attention distillation levels is reduced gradually by removing each layer one at a time (Figure 1), so that their output dimensions are aligned. As a result, the outputs of all stacks are linked to obtain the encoder’s final hidden representation.


#### 2.3.4. Decoder

As shown in Figure1, the model uses a conventional decoder structure made up of two similar multihead attention layers. To compensate for the slower long-term prediction, generative reasoning is used. As a result, the decoder is given the following vectors:
(17)Xdet=ConcatXtokent,X0t∈ℝLtoken+Ly×dmodel,where Xtokent∈ℝLtoken×dmodel represents the start tag and X0t∈ℝLy×dmodel is a placeholder for the sequence that will be used as the target (the scalar is set to 0). By setting the masking dot product to −∞, the ProbSparse self-attention calculation uses masked multihead attention, which prevents each location from noticing the upcoming location and thereby avoids automatic regression.


### 2.4. Improved EMD-Informer Model

The execution of the improved EMD-Informer model proceeds as follows:Step 1. The greenhouse microclimate one-dimensional time series data containing time stamps are input, and the dataset is divided into training and test sets at a ratio of 9 : 1Step 2. The input data are preprocessed, including data integration and missing data recursionStep 3. The improved EMD method is used to decompose the preprocessed data, from which several IMFs and a residual are obtainedStep 4. The Informer model is used to forecast all IMFs and the residual to obtain the forecast dataset of the IMFs and the residualStep 5. All IMFs and residual forecast datasets are integrated, and the test set is used as the final forecast datasetStep 6. The error between the test and prediction sets is calculated and compared to obtain the final model prediction results and evaluationFigure3 shows the procedure used in the proposed CEEMDAN-Informer model.Figure 3
Procedures used in the proposed CEEMDAN-Informer model.


### 2.5. Experimental Methods

#### 2.5.1. Datasets

We investigated five one-dimensional greenhouse microclimate datasets in this study: CO2 concentrations (time series, 20000 data points, ppm), atmospheric pressure (time series, 20200 data points, Pa), light intensity (time series, 14400 data points, Lux), humidity (time series, 20000 data points, %), and temperature (time series, 20000 data points, °C). Each dataset contained target time series data and timestamp information. The datasets were obtained from the Internet of Things Laboratory at Zhejiang Agriculture and Forestry University and are private data.CO2 concentration is an important index for regulating greenhouse climates and environments. This dataset included data collected from May 3 to November 27, 2018, with a 15 min sampling interval.Atmospheric pressure is another important greenhouse climate indicator. This dataset included data collected from May 3 to November 30, 2018, with a 15 min sampling interval. Light intensity is an indicator that affects crop growth. This dataset included data collected from September 15, 2018, to February 12, 2019, with a 15 min sampling interval. The humidity and temperature datasets included data from April 8 to November 2, 2018, with a 15 min sampling interval.We used a ratio of 9 : 1 for the numbers of data points in the training and test sets in this study. Because the sampling interval was 15 minutes, a 9 : 1 ratio can provide sufficient training data for the network, as well as for obtaining predictive outcomes for approximately two to three weeks. A time period of this length can accurately compare the changes in the trends of predicted and actual values and can serve as a guideline for managing actual greenhouse environments.Figures4–8 show the original environmental monitoring datasets used in the experiment.Figure 4
CO2 concentration dataset.Figure 5
Atmospheric pressure dataset.Figure 6
Light intensity dataset.Figure 7
Humidity dataset.Figure 8
Temperature dataset.


#### 2.5.2. Experimental Details

In the present study, the CEEMDAN-Informer network was constructed in the Spyder software environment in anticipation of the use of greenhouse microclimate data.The original EMD algorithm of CEEMDAN does not have any hyper parameters to be set, but CEEMDAN adds a white noise addition step; thus, CEEMDAN has hyperparameters that require adjustment. These hyperparameters are the signal-to-noise ratio, number of noise additions, and maximum envelope number. The noise weight is generally between 0 and 1 for the signal-to-noise ratio, the number of noise additions is generally 50–100, and the maximum envelope number is the maximum number of decomposed IMFs. In general, there is no need to limit this parameter; therefore, it is set to a large number, such as 5000.Compared with other models, the Informer model has many hyperparameters. A total of 38 parameters must be set in the network training period. The main hyperparameters are the timestamp identification frequency, batch size, and training epochs. The time stamp identification frequency is modified according to the time stamp changes in the data. For example, if data are recorded every 15 min, the time stamp identification frequency is minutes. For batch size, a smaller value generally yields a longer training time and a smaller training error. The batch size selected by the model and used in this study was 32. For the training epochs, the number of epochs substantially affects the training time. Generally, a large value is used to ensure that the model can fully learn and converge. The number of training epochs selected by the model and used herein was 10.In the present study, mean square error (MSE), root mean square error (RMSE),R-squared (R2), mean absolute error (MAE), mean absolute percentage error (MAPE), and symmetric mean absolute percentage error (SMAPE) were used to assess the accuracy of the different forecasting models. The loss function used in this experiment was MSE.
(18)MSE=1n∑i=1ny−y∧2,RMSE=1n∑i=1ny−y∧2,R2=1−∑i=1ny∧−y2∑i=1ny¯−y2,MAE=1n∑i=1ny−y∧2,MAPE=100%n∑i=1ny^i−yiyi,SMAPE=100%n∑i=1ny^i−yiy^i+yi/2.


## 2.1. Original EMD Method

Huang et al. [24] was the first to propose the use of EMD, as it performs well when analyzing nonlinear and nonstationary time series data. EMD decomposes a signal based on the time scale properties of the data rather than using a fixed basis function and can describe the physical significance of the time series signal. EMD can deconstruct a complicated signal into a limited number of intrinsic mode functions (IMFs), each of which retains the original signal’s local characteristic signals at different time scales, and is its most important feature. EMD can make nonstationary data stationary, then uses the Hilbert transform to obtain the temporal spectrum and physical frequency. The IMFs must meet two essential requirements: (1) the zero-crossing and extreme numbers should be one apart or equal, and (2) the average value of the higher envelope established by the local maximum and the average value of the lower envelope created by the local minimum should both be zero.The EMD procedure is as follows:(1)
Local minimum and maximum values of the time series dataXt are determined(2)
The upper and lower envelopesemax1 and emin1 are created, and the local maximum and minimum are connected using a cubic spline. The average envelope emean1, which represents the first IMF, is then generated(3)
The (h1) difference between the data and the average envelope is calculated. The preintrinsic mode function is denoted by h1. This process is called the sifting technique(1)Xt−emean1=h1(4)
Steps 1–3 are repeatedk times, with h1k−1 being the new data(2)h1k−1−emean1k=h1k(5)
Steps 1–3 are repeated untilh1k meets the IMF requirements. Then, it is designated c1, the first IMF. The remaining part r1 is established by separating c1 from the other data(3)Xt−c1=r1(6)
The remainderr1 is regarded as fresh data, i.e., Xt=r1; then, the screening procedure is repeated. The following are the outcomes of this procedure:(4)r1−c2=r2,r2−c3=r3,⋯,rN−1−cN=rNOne of 4the termination requirements can halt this process: (1) the IMF cannot be extracted from the residualrN which becomes a monotonic function, or (2) the cN component or residual rN is less than a predefined threshold.Finally, as indicated in Equation (5), the time series Xt can be expressed as the sum of n IMF components, with the last residual term included.
(5)Xt=∑i=1Nci+rN.Each IMF is a distinct and concrete manifestation of the time seriesXt’s local properties. Despite the fact that this method is extremely beneficial, EMD still has several outstanding issues. One of the EMD algorithm’s major flaws is that it produces virtually identical oscillations in different IMFs or oscillations in a mode with very different amplitudes, which is a phenomenon known as “mode mixing.” The existence of the boundary effect is demonstrated by substantial oscillations at the start and end of the IMF, which is another drawback of this method. The boundary effect is due to the interpolation function used in the filtering process, which causes the decomposition result to be inconsistent with the original data.


## 2.2. CEEMDAN Method

The CEEMDAN method was originally proposed by Torres et al. [25]. Every phase of the decomposition process in CEEMDAN includes large amounts of white noise. Compared with EMD and ensemble empirical mode decomposition (EEMD), CEEMDAN can effectively address the mode mixing problem and precisely reconstruct the signal. The CEEMDAN method consists of the following steps:
(1)
To acquire the initial IMF of the noise-contaminated signal, a defined amount of white noise is introduced to the original signal. The EMD is repeatedN times with different noise, and the ensemble average of the total IMF1 corresponding to N tests is used to determine the initial IMF1 of the original signal:(6)IMF¯1t=1N∑n=1NE1Xt+εunt,where IMF¯1 is the incoming signal’s first EMD component X, un is the unit variance zero mean Gaussian white noise, ε is the fixed coefficient, E1 is the operator that yields the ith IMF component, and N is the implementation number. The first signal residual r1 is then calculated as follows:
(7)r1=X−IMF¯1(2)
The input for the second IMF isr1+εE1un,n=1,N. When EMD is used, the second IMF is the average of the first IMF generated:(8)IMF¯2t=1N∑n=1NE1r1t+εE1unt(3)
Thekth residual is calculated for k=2,3,⋯,K, rk=rk−1−IMFk¯, and the ensemble average of the first IMF obtained by EMD as k+1th IMF:(9)IMF¯k+1t=1N∑n=1NE1rkt+εEkunt(4)
The method is repeated until no more than two extremes are present in the last residual value:(10)R=X−∑k=1KIMF¯kwhere the ultimate residual value is R and the total number of IMFs isK(5)
The final decomposition result is as follows:(11)Xt=∑k=1KIMF¯kt+RtThis method can ensure accurate signal decomposition and reconstruction.


## 2.3. Informer Neural Network

The Informer model was proposed by Zhou et al. [22]. Figure 1 shows an overview of the components included in the Informer model.Figure 1
Overview of the Informer model.


### 2.3.1. Typical Self-Attention Mechanism

Typical self-attention [10] is based on tuple input, which includes the key, value, and query, and uses the scaled dot product as AQ,K,V=SoftmaxQKT/dV, where Q∈ℝLQ×d, K∈ℝLK×d, V∈ℝLV×d, and d denotes the input dimensions. To go deeper into the self-attention mechanism, let qi, ki, and vi represent line I in Q, K, and V. The attention of the ith question is described as a kernel smoother in probability, according to Tsai et al. [26]:
(12)Aqi,K,V=∑jkqi,kj∑lkqi,klvj=Epkjqivj,where pkjqi=kqi,kl/∑lkqi,kl and kqi,kl choose the exponential asymmetric kernel exp qikjT/d. Self-attention integrates these variables and produces a result according to the likelihood determined pkjqi. It requires the calculation of quadratic time point products and the use of OLQLK memory, which is the fundamental disadvantage of boosting forecasting ability.The result of theith query is its composition with the value v, and the attention of the ith query to all keys is defined as its probability pkjqi. The dominant dot product pair pushes the accompanying query’s attention probability distribution away from a uniform distribution. If pkjqi resembles a uniform distribution, pkjqi=1/LK, then self-attention is reduced to a trivial sum of values V, which is unnecessary for residual input. The “similarity” between P and Q distributions might then be utilized to differentiate “important” queries. The Kullback-Leibler divergence is used to assess “similarity” KLqp=ln∑l=1LKeqiklT/d−1/Lk∑j=1LKqikjT/d−lnLk. After deleting the constant, the sparsity measure of the ith query is defined as:
(13)Mqi,K=ln∑j=1LKeqikjT/d−1LK∑j=1LKqikjTd,where the log-sum-exp (LSE) of qi on all keys is the first term. The arithmetic mean of these keys is the second term. If the ith query has a larger Mqi,K, its attention probability p is more “diversified,” and the primary point product pairs in the head domain of the long tail self-attention distribution have a higher chance of being included.


### 2.3.2. ProbSparse Self-Attention

ProbSparse self-attention can be achieved by enabling each key to focus exclusively onu-dominant queries, according to the proposed measurement:
(14)AQ,K,V=SoftmaxQ¯KTdV,where Q¯ is a sparse matrix of the same size that includes only the top-u query according to the sparse metric. Under the direction of a constant sampling factor C, set u=c×lnLQ, and it only needs to compute the OlnLQ dot product of each query-key search, for which the layer memory usage is OLKlnLQ. This attention results in various sparse query-key pairs for each head in the multihead perspective, thereby avoiding substantial information loss.However, traversing all queries measuringMqi,K necessitates computing each dot product pair or quadratic OLQLK. In addition to LSE operation, there are potential numerical stability problems. Thus, an empirical approximation is used to effectively obtain the query sparsity measure.For each queryqi∈ℝd and kj∈ℝd in the key set K, it has the bound as lnLK≤Mqi,K≤maxjqikjT/d−1/LK∑j=1LKqikjT/d+lnLK. When qi∈K, it is also true.The maximum average measurement is:(15)M¯qi,K=maxjqikjTd−1LK∑j=1LKqikjTd.In the long tailed distribution, the method only requires a random sampleU=LKlnLQ dot product pairs to compute Mqi,K, that is, the other pairs are filled with zero. To calculate Mqi,K in the long tailed distribution, U=LKlnLQ point product pairs are sampled at random, leaving the other pairs as zero. Then, choose sparse top-u as Q¯. Mqi,K’s maximal operator is less affected by zero and has a more stable value. Since the query and key input lengths are frequently equal in practice LQ=LK=L, the overall ProbSparse self-attention space and time complexity is OLlnL.


### 2.3.3. Encoder

The encoder extracts the robust long-term dependence of lengthy sequence inputs. Thetth sequence’s input χt is molded into a matrix Xent∈ℝLx×dmodel following the input representation. Figure 2 shows a schematic diagram of the encoder.Figure 2
A single stack in the encoder used in the Informer model. The overlapping red square indicates then-head weight matrix.The encoder’s characteristic graph has a redundant combination of valuesV as a natural result of the ProbSparse self-attention mechanism. In the next layer, the superior extraction operation of operation privileges is used with the dominant characteristics to produce a centralized self- attention feature graph. Figure 2 shows the n-head weight matrix of the attention block, which severely cuts the input time dimension. From the jth layer to j+1, the “extraction” method proceeds as follows:
(16)Xj+1t=MaxPoolELUConvldXjtAB.(1)
The horizontal stack represents an encoder replica (Figure1)(2)
The primary stack, which receives the entire input sequence, is the one proposed. The second stack then repeats the operation with a half slice of the input(3)
The red layers are dot product matrices that are reduced in order using self-attention distillation in every layer(4)
The function maps of all stacks are connected as the output of the encoderThe attention block is denoted by⋅AB and includes multihead active attention and basic operations such as conv1d·, which executes a one-dimensional convolution filter in the temporal dimension (kernel width is 3) using the ELU(·) activation function [27]. After stacking one layer, a maximum pool layer is added, and Xt is downsampled to the half layer, resulting in a total memory use of O2−εLlogL, where ε is a small number in this case. To improve the robustness of the distillation operation, the main stack that halves the input is replicated and the number of self-attention distillation levels is reduced gradually by removing each layer one at a time (Figure 1), so that their output dimensions are aligned. As a result, the outputs of all stacks are linked to obtain the encoder’s final hidden representation.


### 2.3.4. Decoder

As shown in Figure1, the model uses a conventional decoder structure made up of two similar multihead attention layers. To compensate for the slower long-term prediction, generative reasoning is used. As a result, the decoder is given the following vectors:
(17)Xdet=ConcatXtokent,X0t∈ℝLtoken+Ly×dmodel,where Xtokent∈ℝLtoken×dmodel represents the start tag and X0t∈ℝLy×dmodel is a placeholder for the sequence that will be used as the target (the scalar is set to 0). By setting the masking dot product to −∞, the ProbSparse self-attention calculation uses masked multihead attention, which prevents each location from noticing the upcoming location and thereby avoids automatic regression.


## 2.3.1. Typical Self-Attention Mechanism

Typical self-attention [10] is based on tuple input, which includes the key, value, and query, and uses the scaled dot product as AQ,K,V=SoftmaxQKT/dV, where Q∈ℝLQ×d, K∈ℝLK×d, V∈ℝLV×d, and d denotes the input dimensions. To go deeper into the self-attention mechanism, let qi, ki, and vi represent line I in Q, K, and V. The attention of the ith question is described as a kernel smoother in probability, according to Tsai et al. [26]:
(12)Aqi,K,V=∑jkqi,kj∑lkqi,klvj=Epkjqivj,where pkjqi=kqi,kl/∑lkqi,kl and kqi,kl choose the exponential asymmetric kernel exp qikjT/d. Self-attention integrates these variables and produces a result according to the likelihood determined pkjqi. It requires the calculation of quadratic time point products and the use of OLQLK memory, which is the fundamental disadvantage of boosting forecasting ability.The result of theith query is its composition with the value v, and the attention of the ith query to all keys is defined as its probability pkjqi. The dominant dot product pair pushes the accompanying query’s attention probability distribution away from a uniform distribution. If pkjqi resembles a uniform distribution, pkjqi=1/LK, then self-attention is reduced to a trivial sum of values V, which is unnecessary for residual input. The “similarity” between P and Q distributions might then be utilized to differentiate “important” queries. The Kullback-Leibler divergence is used to assess “similarity” KLqp=ln∑l=1LKeqiklT/d−1/Lk∑j=1LKqikjT/d−lnLk. After deleting the constant, the sparsity measure of the ith query is defined as:
(13)Mqi,K=ln∑j=1LKeqikjT/d−1LK∑j=1LKqikjTd,where the log-sum-exp (LSE) of qi on all keys is the first term. The arithmetic mean of these keys is the second term. If the ith query has a larger Mqi,K, its attention probability p is more “diversified,” and the primary point product pairs in the head domain of the long tail self-attention distribution have a higher chance of being included.


## 2.3.2. ProbSparse Self-Attention

ProbSparse self-attention can be achieved by enabling each key to focus exclusively onu-dominant queries, according to the proposed measurement:
(14)AQ,K,V=SoftmaxQ¯KTdV,where Q¯ is a sparse matrix of the same size that includes only the top-u query according to the sparse metric. Under the direction of a constant sampling factor C, set u=c×lnLQ, and it only needs to compute the OlnLQ dot product of each query-key search, for which the layer memory usage is OLKlnLQ. This attention results in various sparse query-key pairs for each head in the multihead perspective, thereby avoiding substantial information loss.However, traversing all queries measuringMqi,K necessitates computing each dot product pair or quadratic OLQLK. In addition to LSE operation, there are potential numerical stability problems. Thus, an empirical approximation is used to effectively obtain the query sparsity measure.For each queryqi∈ℝd and kj∈ℝd in the key set K, it has the bound as lnLK≤Mqi,K≤maxjqikjT/d−1/LK∑j=1LKqikjT/d+lnLK. When qi∈K, it is also true.The maximum average measurement is:(15)M¯qi,K=maxjqikjTd−1LK∑j=1LKqikjTd.In the long tailed distribution, the method only requires a random sampleU=LKlnLQ dot product pairs to compute Mqi,K, that is, the other pairs are filled with zero. To calculate Mqi,K in the long tailed distribution, U=LKlnLQ point product pairs are sampled at random, leaving the other pairs as zero. Then, choose sparse top-u as Q¯. Mqi,K’s maximal operator is less affected by zero and has a more stable value. Since the query and key input lengths are frequently equal in practice LQ=LK=L, the overall ProbSparse self-attention space and time complexity is OLlnL.


## 2.3.3. Encoder

The encoder extracts the robust long-term dependence of lengthy sequence inputs. Thetth sequence’s input χt is molded into a matrix Xent∈ℝLx×dmodel following the input representation. Figure 2 shows a schematic diagram of the encoder.Figure 2
A single stack in the encoder used in the Informer model. The overlapping red square indicates then-head weight matrix.The encoder’s characteristic graph has a redundant combination of valuesV as a natural result of the ProbSparse self-attention mechanism. In the next layer, the superior extraction operation of operation privileges is used with the dominant characteristics to produce a centralized self- attention feature graph. Figure 2 shows the n-head weight matrix of the attention block, which severely cuts the input time dimension. From the jth layer to j+1, the “extraction” method proceeds as follows:
(16)Xj+1t=MaxPoolELUConvldXjtAB.(1)
The horizontal stack represents an encoder replica (Figure1)(2)
The primary stack, which receives the entire input sequence, is the one proposed. The second stack then repeats the operation with a half slice of the input(3)
The red layers are dot product matrices that are reduced in order using self-attention distillation in every layer(4)
The function maps of all stacks are connected as the output of the encoderThe attention block is denoted by⋅AB and includes multihead active attention and basic operations such as conv1d·, which executes a one-dimensional convolution filter in the temporal dimension (kernel width is 3) using the ELU(·) activation function [27]. After stacking one layer, a maximum pool layer is added, and Xt is downsampled to the half layer, resulting in a total memory use of O2−εLlogL, where ε is a small number in this case. To improve the robustness of the distillation operation, the main stack that halves the input is replicated and the number of self-attention distillation levels is reduced gradually by removing each layer one at a time (Figure 1), so that their output dimensions are aligned. As a result, the outputs of all stacks are linked to obtain the encoder’s final hidden representation.


## 2.3.4. Decoder

As shown in Figure1, the model uses a conventional decoder structure made up of two similar multihead attention layers. To compensate for the slower long-term prediction, generative reasoning is used. As a result, the decoder is given the following vectors:
(17)Xdet=ConcatXtokent,X0t∈ℝLtoken+Ly×dmodel,where Xtokent∈ℝLtoken×dmodel represents the start tag and X0t∈ℝLy×dmodel is a placeholder for the sequence that will be used as the target (the scalar is set to 0). By setting the masking dot product to −∞, the ProbSparse self-attention calculation uses masked multihead attention, which prevents each location from noticing the upcoming location and thereby avoids automatic regression.


## 2.4. Improved EMD-Informer Model

The execution of the improved EMD-Informer model proceeds as follows:Step 1. The greenhouse microclimate one-dimensional time series data containing time stamps are input, and the dataset is divided into training and test sets at a ratio of 9 : 1Step 2. The input data are preprocessed, including data integration and missing data recursionStep 3. The improved EMD method is used to decompose the preprocessed data, from which several IMFs and a residual are obtainedStep 4. The Informer model is used to forecast all IMFs and the residual to obtain the forecast dataset of the IMFs and the residualStep 5. All IMFs and residual forecast datasets are integrated, and the test set is used as the final forecast datasetStep 6. The error between the test and prediction sets is calculated and compared to obtain the final model prediction results and evaluationFigure3 shows the procedure used in the proposed CEEMDAN-Informer model.Figure 3
Procedures used in the proposed CEEMDAN-Informer model.


## 2.5. Experimental Methods

### 2.5.1. Datasets

We investigated five one-dimensional greenhouse microclimate datasets in this study: CO2 concentrations (time series, 20000 data points, ppm), atmospheric pressure (time series, 20200 data points, Pa), light intensity (time series, 14400 data points, Lux), humidity (time series, 20000 data points, %), and temperature (time series, 20000 data points, °C). Each dataset contained target time series data and timestamp information. The datasets were obtained from the Internet of Things Laboratory at Zhejiang Agriculture and Forestry University and are private data.CO2 concentration is an important index for regulating greenhouse climates and environments. This dataset included data collected from May 3 to November 27, 2018, with a 15 min sampling interval.Atmospheric pressure is another important greenhouse climate indicator. This dataset included data collected from May 3 to November 30, 2018, with a 15 min sampling interval. Light intensity is an indicator that affects crop growth. This dataset included data collected from September 15, 2018, to February 12, 2019, with a 15 min sampling interval. The humidity and temperature datasets included data from April 8 to November 2, 2018, with a 15 min sampling interval.We used a ratio of 9 : 1 for the numbers of data points in the training and test sets in this study. Because the sampling interval was 15 minutes, a 9 : 1 ratio can provide sufficient training data for the network, as well as for obtaining predictive outcomes for approximately two to three weeks. A time period of this length can accurately compare the changes in the trends of predicted and actual values and can serve as a guideline for managing actual greenhouse environments.Figures4–8 show the original environmental monitoring datasets used in the experiment.Figure 4
CO2 concentration dataset.Figure 5
Atmospheric pressure dataset.Figure 6
Light intensity dataset.Figure 7
Humidity dataset.Figure 8
Temperature dataset.


### 2.5.2. Experimental Details

In the present study, the CEEMDAN-Informer network was constructed in the Spyder software environment in anticipation of the use of greenhouse microclimate data.The original EMD algorithm of CEEMDAN does not have any hyper parameters to be set, but CEEMDAN adds a white noise addition step; thus, CEEMDAN has hyperparameters that require adjustment. These hyperparameters are the signal-to-noise ratio, number of noise additions, and maximum envelope number. The noise weight is generally between 0 and 1 for the signal-to-noise ratio, the number of noise additions is generally 50–100, and the maximum envelope number is the maximum number of decomposed IMFs. In general, there is no need to limit this parameter; therefore, it is set to a large number, such as 5000.Compared with other models, the Informer model has many hyperparameters. A total of 38 parameters must be set in the network training period. The main hyperparameters are the timestamp identification frequency, batch size, and training epochs. The time stamp identification frequency is modified according to the time stamp changes in the data. For example, if data are recorded every 15 min, the time stamp identification frequency is minutes. For batch size, a smaller value generally yields a longer training time and a smaller training error. The batch size selected by the model and used in this study was 32. For the training epochs, the number of epochs substantially affects the training time. Generally, a large value is used to ensure that the model can fully learn and converge. The number of training epochs selected by the model and used herein was 10.In the present study, mean square error (MSE), root mean square error (RMSE),R-squared (R2), mean absolute error (MAE), mean absolute percentage error (MAPE), and symmetric mean absolute percentage error (SMAPE) were used to assess the accuracy of the different forecasting models. The loss function used in this experiment was MSE.
(18)MSE=1n∑i=1ny−y∧2,RMSE=1n∑i=1ny−y∧2,R2=1−∑i=1ny∧−y2∑i=1ny¯−y2,MAE=1n∑i=1ny−y∧2,MAPE=100%n∑i=1ny^i−yiyi,SMAPE=100%n∑i=1ny^i−yiy^i+yi/2.


## 2.5.1. Datasets

We investigated five one-dimensional greenhouse microclimate datasets in this study: CO2 concentrations (time series, 20000 data points, ppm), atmospheric pressure (time series, 20200 data points, Pa), light intensity (time series, 14400 data points, Lux), humidity (time series, 20000 data points, %), and temperature (time series, 20000 data points, °C). Each dataset contained target time series data and timestamp information. The datasets were obtained from the Internet of Things Laboratory at Zhejiang Agriculture and Forestry University and are private data.CO2 concentration is an important index for regulating greenhouse climates and environments. This dataset included data collected from May 3 to November 27, 2018, with a 15 min sampling interval.Atmospheric pressure is another important greenhouse climate indicator. This dataset included data collected from May 3 to November 30, 2018, with a 15 min sampling interval. Light intensity is an indicator that affects crop growth. This dataset included data collected from September 15, 2018, to February 12, 2019, with a 15 min sampling interval. The humidity and temperature datasets included data from April 8 to November 2, 2018, with a 15 min sampling interval.We used a ratio of 9 : 1 for the numbers of data points in the training and test sets in this study. Because the sampling interval was 15 minutes, a 9 : 1 ratio can provide sufficient training data for the network, as well as for obtaining predictive outcomes for approximately two to three weeks. A time period of this length can accurately compare the changes in the trends of predicted and actual values and can serve as a guideline for managing actual greenhouse environments.Figures4–8 show the original environmental monitoring datasets used in the experiment.Figure 4
CO2 concentration dataset.Figure 5
Atmospheric pressure dataset.Figure 6
Light intensity dataset.Figure 7
Humidity dataset.Figure 8
Temperature dataset.


## 2.5.2. Experimental Details

In the present study, the CEEMDAN-Informer network was constructed in the Spyder software environment in anticipation of the use of greenhouse microclimate data.The original EMD algorithm of CEEMDAN does not have any hyper parameters to be set, but CEEMDAN adds a white noise addition step; thus, CEEMDAN has hyperparameters that require adjustment. These hyperparameters are the signal-to-noise ratio, number of noise additions, and maximum envelope number. The noise weight is generally between 0 and 1 for the signal-to-noise ratio, the number of noise additions is generally 50–100, and the maximum envelope number is the maximum number of decomposed IMFs. In general, there is no need to limit this parameter; therefore, it is set to a large number, such as 5000.Compared with other models, the Informer model has many hyperparameters. A total of 38 parameters must be set in the network training period. The main hyperparameters are the timestamp identification frequency, batch size, and training epochs. The time stamp identification frequency is modified according to the time stamp changes in the data. For example, if data are recorded every 15 min, the time stamp identification frequency is minutes. For batch size, a smaller value generally yields a longer training time and a smaller training error. The batch size selected by the model and used in this study was 32. For the training epochs, the number of epochs substantially affects the training time. Generally, a large value is used to ensure that the model can fully learn and converge. The number of training epochs selected by the model and used herein was 10.In the present study, mean square error (MSE), root mean square error (RMSE),R-squared (R2), mean absolute error (MAE), mean absolute percentage error (MAPE), and symmetric mean absolute percentage error (SMAPE) were used to assess the accuracy of the different forecasting models. The loss function used in this experiment was MSE.
(18)MSE=1n∑i=1ny−y∧2,RMSE=1n∑i=1ny−y∧2,R2=1−∑i=1ny∧−y2∑i=1ny¯−y2,MAE=1n∑i=1ny−y∧2,MAPE=100%n∑i=1ny^i−yiyi,SMAPE=100%n∑i=1ny^i−yiy^i+yi/2.


## 3. Experimental Results

### 3.1. CEEMDAN Decomposition Results

Figure9 shows the decomposition results for CO2 concentrations by CEEMDAN. The results are divided into 13 IMFs and one residual. CEEMDAN’s decomposition results for atmospheric pressure are shown in Figure 10, which include 10 IMFs and one residual. CEEMDAN’s light intensity decomposition results are shown in Figure 11, which include 12 IMFs and one residual. The CEEMDAN humidity decomposition results are shown in Figure 12, which include 12 IMFs and one residual. The CEEMDAN temperature decomposition results are shown in Figure 13, which include 12 IMFs and one residual.Figure 9
CEEMDAN-based decomposition of the CO2 concentration dataset.Figure 10
CEEMDAN-based decomposition of the atmospheric pressure dataset.Figure 11
CEEMDAN-based decomposition of the light intensity dataset.Figure 12
CEEMDAN-based decomposition of the humidity dataset.Figure 13
CEEMDAN-based decomposition of the temperature dataset.


### 3.2. Simulation Results

Figures14–18 show the predicted CO2 concentration, atmospheric pressure, light intensity, humidity, and temperature, respectively, compared with actual data in the test phase.Figure 14
CO2 prediction results and actual data in the test phase.Figure 15
Atmospheric pressure prediction results and actual data in the test phase.Figure 16
Light intensity prediction results and actual data in the test phase.Figure 17
Humidity prediction results and actual data in the test phase.Figure 18
Temperature prediction results and actual data in the test phase.Figures19–23 show the RMSE prediction errors between the actual data and the predicted values for CO2 concentration, atmospheric pressure, light intensity, humidity, and temperature, respectively, in the test phase. Figure 24 shows the single IMF training loss function for the CO2 dataset decomposed by CEEMDAN. We also compared many of the time series forecasting algorithms, including RNN [28], CNN [28], LSTM [28], BiLSTM, and the Informer model, with the model proposed herein. In addition, a model combining the above models with EMD and CEEMDAN was compared with the proposed CEEMDAN-Informer model. This study also used the CNN-LSTM method [29]. The predictive performances of the different models are presented in Table 1.Figure 19
CO2 prediction error in the test phase.Figure 20
Atmospheric pressure prediction error in the test phase.Figure 21
Light intensity prediction error in the test phase.Figure 22
Humidity prediction error in the test phase.Figure 23
Temperature prediction error in the test phase.Figure 24
Single IMF training loss function for the CO2 dataset decomposed by CEEMDAN.Table 1
Prediction errors of the different models.
MethodMetricCO2 concentrationAtmospheric pressureLight intensityHumidityTemperatureRNNMSE628.711978.899487481.8971.8580.982RMSE25.07431.287698.1991.3630.991R20.9730.9950.9510.9910.961MAE16.12522.015328.4860.9050.785MAPE2.253%0.023%——1.811%8.955%SMAPE2.216%0.023%——1.800%8.710%CNNMSE592.845957.548498524.8861.7840.799RMSE24.34830.944706.0631.3360.894R20.9740.9960.9500.9910.970MAE13.95321.783330.1530.8880.697MAPE2.107%0.022%——1.799%8.588%SMAPE2.098%0.022%——1.782%8.220%LSTMMSE607.908945.915471187.0781.6670.592RMSE24.65630.756686.4311.2910.769R20.9750.9960.9520.9900.975MAE14.24221.589325.5140.8460.565MAPE2.167%0.021%——1.780%7.979%SMAPE2.180%0.021%——1.743%7.444%BiLSTMMSE579.833696.083414738.0121.3790.468RMSE24.07926.383644.0021.1750.684R20.9740.9970.9530.9920.986MAE13.69617.867304.9430.7400.474MAPE2.077%0.018%——1.459%6.259%SMAPE2.056%0.018%——1.460%5.861%InformerMSE540.253589.742339760.3691.1480.487RMSE23.24324.285582.8901.0710.698R20.9750.9970.9510.9930.986MAE13.14816.369314.2020.7190.492MAPE2.061%0.017%——1.397%6.474%SMAPE2.065%0.017%——1.408%5.948%CEEMDAN-InformerMSE358.043242.237100222.7670.6970.249RMSE18.92215.564316.5800.8350.499R20.9840.9980.9860.9960.991MAE11.87411.098203.0450.6170.346MAPE1.795%0.011%——1.180%4.250%SMAPE1.795%0.011%——1.185%4.108%Compared with those of the RNN, CNN, LSTM, BiLSTM, and Informer models, CO2 concentration prediction using the CEEMDAN-Informer model reduced the RMSE by 24.5%, 22.2%, 23.2%, 21.5%, and 18.5%, respectively (Table 1); in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the RMSEs by 50.2%, 49.7%, 49.3%, 41.0%, and 35.9%, respectively; in light intensity prediction, the CEEMDAN-Informer model reduced the RMSEs by 54.6%, 55.1%, 53.8%, 50.8%, and 45.6%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the RMSEs by 38.7%, 37.5%, 35.3%, 28.9%, and 22.1%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the RMSEs by 49.6%, 44.1%, 35.1%, 27.0%, and 28.5%, respectively.Compared with those of the RNN, CNN, LSTM, BiLSTM, and Informer models (Table1), CO2 prediction using the CEEMDAN-Informer model reduced the MAEs by 26.3%, 14.8%, 16.6%, 13.2%, and 9.6%, respectively; in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the MAEs by 49.5%, 49.0%, 48.6%, 37.8%, and 32.2%, respectively; in light intensity prediction, the CEEMDAN-Informer model reduced the MAEs by 38.1%, 38.5%, 37.6%, 33.4%, and 35.3%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the MAEs by 31.8%, 30.5%, 27.1%, 16.4%, and 14.2%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the MAEs by 55.9%, 50.3%, 38.7%, 26.9%, and 29.6%, respectively.Compared with those of the RNN, CNN, LSTM, BiLSTM, and Informer models (Table1), the CEEMDAN-Informer model reduced the MAPEs of CO2 prediction by 20.3%, 14.7%, 17.1%, 13.5%, and 13.0%, respectively; in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the MAPEs by 52.3%, 51.6%, 48.7%, 38.0%, and 37.3%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the MAPEs by 34.8%, 34.3%, 33.7%, 19.1%, and 15.5%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the MAPEs by 52.5%, 50.5%, 46.74%, 32.0%, and 34.3%, respectively.We also compared the performance of the CEEMDAN-Informer model with those of the combined EMD models. Compared with the EMD-RNN, EMD-CNN, EMD-LSTM, and EMD-BiLSTM models (Table2), in CO2 prediction, the CEEMDAN-Informer model reduced the RMSEs by 20.7%, 20.1%, 19.5%, and 18.0%, respectively; in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the RMSEs by 44.7%, 43.3%, 44.5%, and 31.6%, respectively; in light intensity prediction, the CEEMDAN-Informer model reduced the RMSEs by 49.6%, 45.5%, 46.3%, and 44.1%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the RMSEs by 33.2%, 31.6%, 28.8%, and 22.0%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the other RMSEs by 40.4%, 31.6%, 28.1%, and 21.5%, respectively.Table 2
Prediction errors of combined EMD models.
MethodMetricCO2 concentrationAtmospheric pressureLight intensityHumidityTemperatureEMD-RNNMSE569.583792.121395241.8521.5620.703RMSE23.86628.145628.6831.2500.838R20.9740.9960.9580.9910.970MAE13.62420.050305.8220.8710.644MAPE2.108%0.021%——1.735%8.158%SMAPE2.147%0.021%——1.721%7.978%EMD-CNNMSE561.451753.845338558.2421.4900.533RMSE23.69527.456581.8581.2200.730R20.9740.9960.9590.9910.976MAE13.19319.215294.8580.8180.542MAPE2.087%0.020%——1.719%7.853%SMAPE2.072%0.020%——1.687%7.414%EMD-LSTMMSE553.256786.858347852.1491.3750.482RMSE23.52128.051589.7901.1730.694R20.9760.9960.9600.9920.978MAE13.18819.790298.1250.7710.509MAPE2.013%0.019%——1.694%7.104%SMAPE2.021%0.019%——1.657%6.916%EMD-BiLSTMMSE532.458518.857321129.8601.1450.405RMSE23.07522.778566.6831.0700.636R20.9760.9970.9640.9930.986MAE13.10316.154277.8540.7080.448MAPE1.988%0.017%——1.417%5.548%SMAPE1.995%0.017%——1.410%5.124%CEEMDAN-InformerMSE358.043242.237100222.7670.6970.249RMSE18.92215.564316.5800.8350.499R20.9840.9980.9860.9960.991MAE11.87411.098203.0450.6170.346MAPE1.795%0.011%——1.180%4.250%SMAPE1.795%0.011%——1.185%4.108%Compared with those of the EMD-RNN, EMD-CNN, EMD-LSTM, and EMD-BiLSTM models (Table2), the CEEMDAN-Informer model reduced the MAEs of CO2 prediction by 12.8%, 10.0%, 9.8%, and 9.3%, respectively; in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the MAEs by 44.6%, 42.2%, 43.9%, and 31.3%, respectively; in light intensity prediction, the CEEMDAN-Informer model reduced the MAEs by 33.6%, 31.1%, 31.8%, and 26.9%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced MAEs by 29.2%, 24.5%, 20.0%, and 12.9%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the MAEs by 46.2%, 36.2%, 32.0%, and 22.8%, respectively.Compared with the EMD-RNN, EMD-CNN, EMD-LSTM, and EMD-BiLSTM models (Table2), the CEEMDAN-Informer model reduced the MAPEs of CO2 prediction between the predicted and real data by 14.8%, 14.0%, 10.8%, and 9.6%, respectively; in the atmospheric pressure prediction, the CEEMDAN-Informer model reduced the MAPEs by 48.8%, 46.9%, 43.5%, and 35.5%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the MAPEs by 32.0%, 31.3%, 30.3%, and 16.7%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the model MAPEs by 47.9%, 45.8%, 40.1%, and 23.3%, respectively.In the cases of the combined CEEMDAN models, when compared with the CEEMDAN-RNN, CEEMDAN-CNN, CEEMDAN-LSTM, and CEEMDAN-BiLSTM models (Table3), in CO2 prediction, the CEEMDAN-Informer model reduced the RMSEs by 17.5%, 15.5%, 16.5%, and 14.6%, respectively; in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the RMSEs by 41.5%, 40.0%, 39.7%, and 24.9%, respectively; in light intensity prediction, the CEEMDAN-Informer model reduced the RMSEs by 43.7%, 41.5%, 36.1%, and 40.0%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the RMSEs by 32.0%, 31.3%, 23.2%, and 18.0%, respectively; in temperature prediction, the CEEMDAN-Informer model reduced the RMSEs by 36.5%, 27.4%, 23.1%, and 19.0%, respectively.Table 3
Prediction errors of combined CEEMDAN models.
MethodMetricCO2 concentrationAtmospheric pressureLight intensityHumidityTemperatureCEEMDAN-RNNMSE526.682708.483317257.4961.5060.618RMSE22.95026.617563.2561.2270.786R20.9750.9960.9610.9910.974MAE12.98719.175283.9620.8530.597MAPE2.077%0.020%——1.718%7.483%SMAPE2.094%0.020%——1.685%7.249%CEEMDAN-CNNMSE501.896674.359293723.3871.4790.473RMSE22.40325.968541.9631.2160.688R20.9760.9960.9640.9910.978MAE12.73118.046271.8950.8070.491MAPE1.896%0.019%——1.687%7.175%SMAPE1.893%0.019%——1.680%6.874%CEEMDAN-LSTMMSE514.781667.048246108.6391.1840.422RMSE22.68925.827496.0931.0880.649R20.9770.9970.9690.9920.981MAE12.89017.337247.9830.7430.468MAPE1.976%0.017%——1.581%6.755%SMAPE1.967%0.017%——1.593%6.431%CEEMDAN-BiLSTMMSE491.188429.587278586.6241.0380.380RMSE22.16320.726527.8131.0190.616R20.9790.9970.9700.9940.986MAE12.53114.986258.6150.6870.423MAPE1.890%0.015%——1.378%5.132%SMAPE1.918%0.015%——1.364%4.897%CNN-LSTMMSE334.845294.584182547.5520.8670.314RMSE18.29917.163427.2560.9310.560R20.9860.9970.9780.9950.988MAE11.81612.783227.2530.6460.391MAPE1.791%0.013%——1.252%4.876%SMAPE1.792%0.013%——1.258%4.624%CEEMDAN-InformerMSE358.043242.237100222.7670.6970.249RMSE18.92215.564316.5800.8350.499R20.9840.9980.9860.9960.991MAE11.87411.098203.0450.6170.346MAPE1.795%0.011%——1.180%4.250%SMAPE1.795%0.011%——1.185%4.108%Compared with the CEEMDAN-RNN, CEEMDAN-CNN, CEEMDAN-LSTM, and CEEMDAN-BiLSTM models (Table3), in CO2 prediction the CEEMDAN-Informer model reduced the MAEs between the predicted and real data by 8.5%, 6.7%, 7.8%, and 5.2%, respectively; in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the model MAEs by 42.1%, 38.5%, 35.9%, and 25.9%, respectively; in light intensity prediction, the CEEMDAN-Informer model reduced the MAEs by 28.5%, 25.3%, 18.1%, and 21.4%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the MAEs by 27.6%, 23.6%, 16.9%, and 10.2%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the model MAEs by 42.0%, 29.5%, 26.0%, and 18.1%, respectively.Compared with the CEEMDAN-RNN, CEEMDAN-CNN, CEEMDAN-LSTM, and CEEMDAN-BiLSTM models (Table3), in CO2 prediction, the CEEMDAN-Informer model reduced the MAPEs between the predicted and real data by 13.5%, 5.3%, 9.1%, and 5.0%, respectively; in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the MAPEs by 46.2%, 40.9%, 36.6%, and 29.0%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the MAPEs by 31.3%, 30.0%, 25.3%, and 14.3%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the MAPEs by 43.2%, 40.7%, 37.0%, and 17.1%, respectively.Compared with the CNN-LSTM model (Table3), the CEEMDAN-Informer model exhibited a poor predictive ability for the CO2 dataset but exhibited better predictive abilities for the other four datasets.In atmospheric pressure prediction, the RMSE of the CEEMDAN-Informer was 9.3% less than that of the CNN-LSTM model. In light intensity prediction, the CEEMDAN-Informer model RMSE was 25.9% less than that of the CNN-LSTM model. In humidity prediction, the CEEMDAN-Informer model RMSE was 10.3% less than that the CNN-LSTM model. In temperature prediction, the CEEMDAN-Informer model RMSE was 10.9% less than that of the CNN-LSTM model.In atmospheric pressure prediction, the MAE of the CEEMDAN-Informer was 13.2% less than that of the CNN-LSTM model. In light intensity prediction, the CEEMDAN-Informer model MAE was 10.6% less than that of the CNN-LSTM model. In humidity prediction, the CEEMDAN-Informer model MAE was 4.5% less than that of the CNN-LSTM model. In temperature prediction, the CEEMDAN-Informer model MAE was 11.5% less than that of the CNN-LSTM model.In atmospheric pressure prediction, the MAPE of the CEEMDAN-Informer model was 15.4% less than that of the CNN-LSTM model. In humidity prediction, the CEEMDAN-Informer model MAPE was 5.8% less than that of the CNN-LSTM model. In temperature prediction, the CEEMDAN-Informer model MAPE was 12.8% less than that of the CNN-LSTM model.


### 3.3. Model Complexity and Running Time

The temporal complexity of the EMD algorithm is defined asOL2, and the spatial complexity is defined as OL2. The ProbSparse self-attention mechanism achieves OLlnL temporal complexity and OLlnL memory usage.The IMFs are independent of one another. After decomposition, all IMFs and the residual can be predicted in parallel; therefore, the total complexity of the hybrid model is the sum of the complexities of the EMD method and the Informer network, that isOL2+LlnL.In terms of actual running overhead, the CEEMDAN decomposition procedure is run only once and takes about a third of the time of one Informer method prediction. When the components and residuals are predicted sequentially step by step, the overhead becomes the time spent on one prediction multiplied by the number of components and residuals.There were approximately 20000 CO2 concentration, atmospheric pressure, temperature, and humidity data points in each dataset. Taking the training time for the CO2 dataset as an example, the running times for the comparison models are presented in Table 4.Table 4
Training times for the CO2 dataset.
MethodTraining time (s)CEEMDAN-BiLSTM3485CNN-LSTM3107CEEMDAN-Informer2762CEEMDAN-CNN2914


## 3.1. CEEMDAN Decomposition Results

Figure9 shows the decomposition results for CO2 concentrations by CEEMDAN. The results are divided into 13 IMFs and one residual. CEEMDAN’s decomposition results for atmospheric pressure are shown in Figure 10, which include 10 IMFs and one residual. CEEMDAN’s light intensity decomposition results are shown in Figure 11, which include 12 IMFs and one residual. The CEEMDAN humidity decomposition results are shown in Figure 12, which include 12 IMFs and one residual. The CEEMDAN temperature decomposition results are shown in Figure 13, which include 12 IMFs and one residual.Figure 9
CEEMDAN-based decomposition of the CO2 concentration dataset.Figure 10
CEEMDAN-based decomposition of the atmospheric pressure dataset.Figure 11
CEEMDAN-based decomposition of the light intensity dataset.Figure 12
CEEMDAN-based decomposition of the humidity dataset.Figure 13
CEEMDAN-based decomposition of the temperature dataset.


## 3.2. Simulation Results

Figures14–18 show the predicted CO2 concentration, atmospheric pressure, light intensity, humidity, and temperature, respectively, compared with actual data in the test phase.Figure 14
CO2 prediction results and actual data in the test phase.Figure 15
Atmospheric pressure prediction results and actual data in the test phase.Figure 16
Light intensity prediction results and actual data in the test phase.Figure 17
Humidity prediction results and actual data in the test phase.Figure 18
Temperature prediction results and actual data in the test phase.Figures19–23 show the RMSE prediction errors between the actual data and the predicted values for CO2 concentration, atmospheric pressure, light intensity, humidity, and temperature, respectively, in the test phase. Figure 24 shows the single IMF training loss function for the CO2 dataset decomposed by CEEMDAN. We also compared many of the time series forecasting algorithms, including RNN [28], CNN [28], LSTM [28], BiLSTM, and the Informer model, with the model proposed herein. In addition, a model combining the above models with EMD and CEEMDAN was compared with the proposed CEEMDAN-Informer model. This study also used the CNN-LSTM method [29]. The predictive performances of the different models are presented in Table 1.Figure 19
CO2 prediction error in the test phase.Figure 20
Atmospheric pressure prediction error in the test phase.Figure 21
Light intensity prediction error in the test phase.Figure 22
Humidity prediction error in the test phase.Figure 23
Temperature prediction error in the test phase.Figure 24
Single IMF training loss function for the CO2 dataset decomposed by CEEMDAN.Table 1
Prediction errors of the different models.
MethodMetricCO2 concentrationAtmospheric pressureLight intensityHumidityTemperatureRNNMSE628.711978.899487481.8971.8580.982RMSE25.07431.287698.1991.3630.991R20.9730.9950.9510.9910.961MAE16.12522.015328.4860.9050.785MAPE2.253%0.023%——1.811%8.955%SMAPE2.216%0.023%——1.800%8.710%CNNMSE592.845957.548498524.8861.7840.799RMSE24.34830.944706.0631.3360.894R20.9740.9960.9500.9910.970MAE13.95321.783330.1530.8880.697MAPE2.107%0.022%——1.799%8.588%SMAPE2.098%0.022%——1.782%8.220%LSTMMSE607.908945.915471187.0781.6670.592RMSE24.65630.756686.4311.2910.769R20.9750.9960.9520.9900.975MAE14.24221.589325.5140.8460.565MAPE2.167%0.021%——1.780%7.979%SMAPE2.180%0.021%——1.743%7.444%BiLSTMMSE579.833696.083414738.0121.3790.468RMSE24.07926.383644.0021.1750.684R20.9740.9970.9530.9920.986MAE13.69617.867304.9430.7400.474MAPE2.077%0.018%——1.459%6.259%SMAPE2.056%0.018%——1.460%5.861%InformerMSE540.253589.742339760.3691.1480.487RMSE23.24324.285582.8901.0710.698R20.9750.9970.9510.9930.986MAE13.14816.369314.2020.7190.492MAPE2.061%0.017%——1.397%6.474%SMAPE2.065%0.017%——1.408%5.948%CEEMDAN-InformerMSE358.043242.237100222.7670.6970.249RMSE18.92215.564316.5800.8350.499R20.9840.9980.9860.9960.991MAE11.87411.098203.0450.6170.346MAPE1.795%0.011%——1.180%4.250%SMAPE1.795%0.011%——1.185%4.108%Compared with those of the RNN, CNN, LSTM, BiLSTM, and Informer models, CO2 concentration prediction using the CEEMDAN-Informer model reduced the RMSE by 24.5%, 22.2%, 23.2%, 21.5%, and 18.5%, respectively (Table 1); in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the RMSEs by 50.2%, 49.7%, 49.3%, 41.0%, and 35.9%, respectively; in light intensity prediction, the CEEMDAN-Informer model reduced the RMSEs by 54.6%, 55.1%, 53.8%, 50.8%, and 45.6%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the RMSEs by 38.7%, 37.5%, 35.3%, 28.9%, and 22.1%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the RMSEs by 49.6%, 44.1%, 35.1%, 27.0%, and 28.5%, respectively.Compared with those of the RNN, CNN, LSTM, BiLSTM, and Informer models (Table1), CO2 prediction using the CEEMDAN-Informer model reduced the MAEs by 26.3%, 14.8%, 16.6%, 13.2%, and 9.6%, respectively; in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the MAEs by 49.5%, 49.0%, 48.6%, 37.8%, and 32.2%, respectively; in light intensity prediction, the CEEMDAN-Informer model reduced the MAEs by 38.1%, 38.5%, 37.6%, 33.4%, and 35.3%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the MAEs by 31.8%, 30.5%, 27.1%, 16.4%, and 14.2%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the MAEs by 55.9%, 50.3%, 38.7%, 26.9%, and 29.6%, respectively.Compared with those of the RNN, CNN, LSTM, BiLSTM, and Informer models (Table1), the CEEMDAN-Informer model reduced the MAPEs of CO2 prediction by 20.3%, 14.7%, 17.1%, 13.5%, and 13.0%, respectively; in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the MAPEs by 52.3%, 51.6%, 48.7%, 38.0%, and 37.3%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the MAPEs by 34.8%, 34.3%, 33.7%, 19.1%, and 15.5%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the MAPEs by 52.5%, 50.5%, 46.74%, 32.0%, and 34.3%, respectively.We also compared the performance of the CEEMDAN-Informer model with those of the combined EMD models. Compared with the EMD-RNN, EMD-CNN, EMD-LSTM, and EMD-BiLSTM models (Table2), in CO2 prediction, the CEEMDAN-Informer model reduced the RMSEs by 20.7%, 20.1%, 19.5%, and 18.0%, respectively; in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the RMSEs by 44.7%, 43.3%, 44.5%, and 31.6%, respectively; in light intensity prediction, the CEEMDAN-Informer model reduced the RMSEs by 49.6%, 45.5%, 46.3%, and 44.1%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the RMSEs by 33.2%, 31.6%, 28.8%, and 22.0%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the other RMSEs by 40.4%, 31.6%, 28.1%, and 21.5%, respectively.Table 2
Prediction errors of combined EMD models.
MethodMetricCO2 concentrationAtmospheric pressureLight intensityHumidityTemperatureEMD-RNNMSE569.583792.121395241.8521.5620.703RMSE23.86628.145628.6831.2500.838R20.9740.9960.9580.9910.970MAE13.62420.050305.8220.8710.644MAPE2.108%0.021%——1.735%8.158%SMAPE2.147%0.021%——1.721%7.978%EMD-CNNMSE561.451753.845338558.2421.4900.533RMSE23.69527.456581.8581.2200.730R20.9740.9960.9590.9910.976MAE13.19319.215294.8580.8180.542MAPE2.087%0.020%——1.719%7.853%SMAPE2.072%0.020%——1.687%7.414%EMD-LSTMMSE553.256786.858347852.1491.3750.482RMSE23.52128.051589.7901.1730.694R20.9760.9960.9600.9920.978MAE13.18819.790298.1250.7710.509MAPE2.013%0.019%——1.694%7.104%SMAPE2.021%0.019%——1.657%6.916%EMD-BiLSTMMSE532.458518.857321129.8601.1450.405RMSE23.07522.778566.6831.0700.636R20.9760.9970.9640.9930.986MAE13.10316.154277.8540.7080.448MAPE1.988%0.017%——1.417%5.548%SMAPE1.995%0.017%——1.410%5.124%CEEMDAN-InformerMSE358.043242.237100222.7670.6970.249RMSE18.92215.564316.5800.8350.499R20.9840.9980.9860.9960.991MAE11.87411.098203.0450.6170.346MAPE1.795%0.011%——1.180%4.250%SMAPE1.795%0.011%——1.185%4.108%Compared with those of the EMD-RNN, EMD-CNN, EMD-LSTM, and EMD-BiLSTM models (Table2), the CEEMDAN-Informer model reduced the MAEs of CO2 prediction by 12.8%, 10.0%, 9.8%, and 9.3%, respectively; in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the MAEs by 44.6%, 42.2%, 43.9%, and 31.3%, respectively; in light intensity prediction, the CEEMDAN-Informer model reduced the MAEs by 33.6%, 31.1%, 31.8%, and 26.9%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced MAEs by 29.2%, 24.5%, 20.0%, and 12.9%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the MAEs by 46.2%, 36.2%, 32.0%, and 22.8%, respectively.Compared with the EMD-RNN, EMD-CNN, EMD-LSTM, and EMD-BiLSTM models (Table2), the CEEMDAN-Informer model reduced the MAPEs of CO2 prediction between the predicted and real data by 14.8%, 14.0%, 10.8%, and 9.6%, respectively; in the atmospheric pressure prediction, the CEEMDAN-Informer model reduced the MAPEs by 48.8%, 46.9%, 43.5%, and 35.5%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the MAPEs by 32.0%, 31.3%, 30.3%, and 16.7%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the model MAPEs by 47.9%, 45.8%, 40.1%, and 23.3%, respectively.In the cases of the combined CEEMDAN models, when compared with the CEEMDAN-RNN, CEEMDAN-CNN, CEEMDAN-LSTM, and CEEMDAN-BiLSTM models (Table3), in CO2 prediction, the CEEMDAN-Informer model reduced the RMSEs by 17.5%, 15.5%, 16.5%, and 14.6%, respectively; in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the RMSEs by 41.5%, 40.0%, 39.7%, and 24.9%, respectively; in light intensity prediction, the CEEMDAN-Informer model reduced the RMSEs by 43.7%, 41.5%, 36.1%, and 40.0%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the RMSEs by 32.0%, 31.3%, 23.2%, and 18.0%, respectively; in temperature prediction, the CEEMDAN-Informer model reduced the RMSEs by 36.5%, 27.4%, 23.1%, and 19.0%, respectively.Table 3
Prediction errors of combined CEEMDAN models.
MethodMetricCO2 concentrationAtmospheric pressureLight intensityHumidityTemperatureCEEMDAN-RNNMSE526.682708.483317257.4961.5060.618RMSE22.95026.617563.2561.2270.786R20.9750.9960.9610.9910.974MAE12.98719.175283.9620.8530.597MAPE2.077%0.020%——1.718%7.483%SMAPE2.094%0.020%——1.685%7.249%CEEMDAN-CNNMSE501.896674.359293723.3871.4790.473RMSE22.40325.968541.9631.2160.688R20.9760.9960.9640.9910.978MAE12.73118.046271.8950.8070.491MAPE1.896%0.019%——1.687%7.175%SMAPE1.893%0.019%——1.680%6.874%CEEMDAN-LSTMMSE514.781667.048246108.6391.1840.422RMSE22.68925.827496.0931.0880.649R20.9770.9970.9690.9920.981MAE12.89017.337247.9830.7430.468MAPE1.976%0.017%——1.581%6.755%SMAPE1.967%0.017%——1.593%6.431%CEEMDAN-BiLSTMMSE491.188429.587278586.6241.0380.380RMSE22.16320.726527.8131.0190.616R20.9790.9970.9700.9940.986MAE12.53114.986258.6150.6870.423MAPE1.890%0.015%——1.378%5.132%SMAPE1.918%0.015%——1.364%4.897%CNN-LSTMMSE334.845294.584182547.5520.8670.314RMSE18.29917.163427.2560.9310.560R20.9860.9970.9780.9950.988MAE11.81612.783227.2530.6460.391MAPE1.791%0.013%——1.252%4.876%SMAPE1.792%0.013%——1.258%4.624%CEEMDAN-InformerMSE358.043242.237100222.7670.6970.249RMSE18.92215.564316.5800.8350.499R20.9840.9980.9860.9960.991MAE11.87411.098203.0450.6170.346MAPE1.795%0.011%——1.180%4.250%SMAPE1.795%0.011%——1.185%4.108%Compared with the CEEMDAN-RNN, CEEMDAN-CNN, CEEMDAN-LSTM, and CEEMDAN-BiLSTM models (Table3), in CO2 prediction the CEEMDAN-Informer model reduced the MAEs between the predicted and real data by 8.5%, 6.7%, 7.8%, and 5.2%, respectively; in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the model MAEs by 42.1%, 38.5%, 35.9%, and 25.9%, respectively; in light intensity prediction, the CEEMDAN-Informer model reduced the MAEs by 28.5%, 25.3%, 18.1%, and 21.4%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the MAEs by 27.6%, 23.6%, 16.9%, and 10.2%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the model MAEs by 42.0%, 29.5%, 26.0%, and 18.1%, respectively.Compared with the CEEMDAN-RNN, CEEMDAN-CNN, CEEMDAN-LSTM, and CEEMDAN-BiLSTM models (Table3), in CO2 prediction, the CEEMDAN-Informer model reduced the MAPEs between the predicted and real data by 13.5%, 5.3%, 9.1%, and 5.0%, respectively; in atmospheric pressure prediction, the CEEMDAN-Informer model reduced the MAPEs by 46.2%, 40.9%, 36.6%, and 29.0%, respectively; in humidity prediction, the CEEMDAN-Informer model reduced the MAPEs by 31.3%, 30.0%, 25.3%, and 14.3%, respectively; and in temperature prediction, the CEEMDAN-Informer model reduced the MAPEs by 43.2%, 40.7%, 37.0%, and 17.1%, respectively.Compared with the CNN-LSTM model (Table3), the CEEMDAN-Informer model exhibited a poor predictive ability for the CO2 dataset but exhibited better predictive abilities for the other four datasets.In atmospheric pressure prediction, the RMSE of the CEEMDAN-Informer was 9.3% less than that of the CNN-LSTM model. In light intensity prediction, the CEEMDAN-Informer model RMSE was 25.9% less than that of the CNN-LSTM model. In humidity prediction, the CEEMDAN-Informer model RMSE was 10.3% less than that the CNN-LSTM model. In temperature prediction, the CEEMDAN-Informer model RMSE was 10.9% less than that of the CNN-LSTM model.In atmospheric pressure prediction, the MAE of the CEEMDAN-Informer was 13.2% less than that of the CNN-LSTM model. In light intensity prediction, the CEEMDAN-Informer model MAE was 10.6% less than that of the CNN-LSTM model. In humidity prediction, the CEEMDAN-Informer model MAE was 4.5% less than that of the CNN-LSTM model. In temperature prediction, the CEEMDAN-Informer model MAE was 11.5% less than that of the CNN-LSTM model.In atmospheric pressure prediction, the MAPE of the CEEMDAN-Informer model was 15.4% less than that of the CNN-LSTM model. In humidity prediction, the CEEMDAN-Informer model MAPE was 5.8% less than that of the CNN-LSTM model. In temperature prediction, the CEEMDAN-Informer model MAPE was 12.8% less than that of the CNN-LSTM model.


## 3.3. Model Complexity and Running Time

The temporal complexity of the EMD algorithm is defined asOL2, and the spatial complexity is defined as OL2. The ProbSparse self-attention mechanism achieves OLlnL temporal complexity and OLlnL memory usage.The IMFs are independent of one another. After decomposition, all IMFs and the residual can be predicted in parallel; therefore, the total complexity of the hybrid model is the sum of the complexities of the EMD method and the Informer network, that isOL2+LlnL.In terms of actual running overhead, the CEEMDAN decomposition procedure is run only once and takes about a third of the time of one Informer method prediction. When the components and residuals are predicted sequentially step by step, the overhead becomes the time spent on one prediction multiplied by the number of components and residuals.There were approximately 20000 CO2 concentration, atmospheric pressure, temperature, and humidity data points in each dataset. Taking the training time for the CO2 dataset as an example, the running times for the comparison models are presented in Table 4.Table 4
Training times for the CO2 dataset.
MethodTraining time (s)CEEMDAN-BiLSTM3485CNN-LSTM3107CEEMDAN-Informer2762CEEMDAN-CNN2914


## 4. Discussion

We established a combined method for predicting the trends in multiple greenhouse microclimate indicators using an improved EMD decomposition method and an Informer neural network. This method was then applied to forecast five types of greenhouse microclimates using data with different characteristics. The method had high accuracies for all five datasets, with the highest accuracy for atmospheric pressure (R2 of 0.998).Figures9–13 show the original data, IMF components, and residuals of five types of datasets decomposed using the CEEMDAN method. The number of IMFs generated after decomposition of the CO2 dataset was the highest (13), while the number of IMFs generated after atmospheric pressure decomposition was the lowest (10). The results of the CEEMDAN decompositions indicate that greenhouse microclimate data have complex time series characteristics and that the CEEMDAN method can clearly separate the differences in the complex features while reducing modal mixing to a large extent. Figures 14–18 show comparisons between the predicted and actual values of the greenhouse microclimate data in the test set range. Figures 19–23 show the errors between the predicted and actual values of the greenhouse microclimate data. The trends of change in the predicted values were extremely similar to the changes in the actual values in most ranges, and the error of each dataset was generally in a small range, which indicates that the proposed method is stable.The combined CEEMDAN-Informer model exhibited large MSE differences among the predicted result errors for the various datasets, among which the MSE of light intensity was the largest. In addition to the large original MSE value of the dataset, the trend of changes in the light intensity dataset was relatively special, and the data changed widely within a short period of time. This had an impact on the predictive performance of the combined model. However, compared with the other models, the predictive accuracy of the model proposed in this study is still higher. This experimental result indicates that the combined CEEMDAN-Informer model has good performance for predicting climate change trends in greenhouses. The proposed method is sensitive to the data and has high requirements for long-term error-free greenhouse sensors in practical application. Figure25 shows the predictive results for the CO2 dataset compared with other models.Figure 25
CO2 prediction MSE errors.There were 13 IMFs obtained after CO2 decomposition, which was the largest of all datasets. Eight of the IMFs were high-frequency IMFs, which indicates that the CO2 dataset is extremely complex. In addition, according to the decomposition results, the amplitudes of the high-frequency CO2 IMFs were also extremely irregular. After a high amplitude, a long period of low amplitude occurred, which was followed by a sudden high amplitude. This type of data trend is a major challenge for the Informer model; therefore, prediction accuracy may be reduced. Table 5 shows the predictive accuracies of the above datasets forecasted using the CEEMDAN-Informer model at different time scales.Table 5
Data accuracy at different time intervals.
Time intervalMinuteHourDailyWeeklyCO2 concentrationMSE358.042837334.7307828259.6403317589.7595585RMSE18.922019918.2956492916.113358824.28496569Atmospheric pressureMSE242.2370179234.5481332166.648611425.1759523RMSE15.5639653715.3149643512.9092451820.61979516Light intensityMSE100222.7668120290.116128512.1308561340.67966RMSE316.5797954346.8286553168.8553548247.6705062HumidityMSE0.696585810.6244832840.6022013160.130442565RMSE0.8346171640.7902425470.7760163110.361168334TemperatureMSE0.2494294370.2634082210.3342142250.227481595RMSE0.4994291110.5132331060.578112640.476950307Table5 shows that most of the datasets yielded high predictive accuracies on three different time scales (minutes, hours, and days). The datasets with low predictive accuracies were the result of large amplitude fluctuations. As the time period increased, the amount of data in the test set decreased. With a smaller data volume, the influence of the error size for a single data point on the error of the entire test set increased. Specifically, as the time span increased, a gap formed between the error of the test set and the error of the original time interval that changed with changes in the data point error. As shown in Table 5, the error of the light intensity dataset varied widely between each time interval, while the error of the temperature dataset varied little between each time interval.The advantage of the approach proposed herein is that the combination of the CEEMDAN method and the Informer network improved the predictive accuracies of long-term CO2 concentration, atmospheric pressure, light intensity, temperature, and humidity time series data in a greenhouse environment. In addition, the model requires simple original datasets. However, the proposed method has disadvantages related to the fact that the Informer model has many parameters that must be set and require a relatively long time for adjustment. After CEEMDAN decomposition, the amount of data processed increases, thereby increasing the processing time. The dataset components need to be entered into the prediction model separately, making the operation rather cumbersome. This study was limited by the fact that some environmental factors (e.g., soil trace element contents) were not predicted using the proposed method. In addition, the present study did not examine greenhouse environments in different regions or with different external climates. Therefore, comprehensive environmental factor prediction should be improved in future research.


## 5. Conclusions

Greenhouse agriculture is an important component of modern agriculture. Greenhouse microclimates are crucial for the healthy growth of greenhouse crops and increasing yields. However, greenhouse microclimates are affected by many aspects both outside and inside the greenhouse and change frequently; thus, prediction using a single model is difficult. Predicting the changes in greenhouse microclimate can allow farmers to better stabilize the internal environment of a greenhouse, promote crop growth, and increase crop yields. The composite CEEMDAN-Informer model was proposed to anticipate trends in greenhouse microclimatic changes. The model described herein was used to forecast climatic changes in a greenhouse every 15 minutes for 14–21 days. The CEEMDAN-Informer model performed better than other single and combined models. The CEEMDAN-Informer model had RMSEs for CO2 concentration, atmospheric pressure, light intensity, temperature, and humidity data in greenhouse microclimates that were less than 18.93, 15.57, 316.59, 0.84, and 0.50, respectively. In future research, we can test the long-term prediction ability of the model over a longer time span of dataset prediction; in addition, we should include other environmental factors of the greenhouse into the prediction scope of the model to test the universality of the model. Furthermore, whether the climate and seasonal factors in different locations would affect the prediction of the model remains a point of concern. The findings of this study can be used to improve the model by establishing an adaptive system that controls the changes in different parameters and deals with noise and losses in the different datasets. The findings can also be used to build an automatic prediction system for greenhouse climate using the Internet of Things. Applications such as agricultural IoT systems or agricultural information systems are able to predict trends in multiple greenhouse microclimate factors using the method proposed in this paper. Therefore, greenhouse managers can better prepare for extreme environmental changes and minimize crop losses.



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*Source: 6486940-2023-02-09.xml*