Time series forecasting for uni- variant data using hybrid GA-OLSTM model and performance evaluations

Abstract

Time series forecasting of uni-variant rainfall data is done using a hybrid genetic algorithm integrated with optimized long-short term memory (GA-OLSTM) model. The parameters included for the valuation of the efficiency of the considered model, were mean square error (MSE), root mean square error (RMSE), cosine similarity (CS) and correlation coefficient (r). With various epochs like 5, 10, 15 and 20, the optimal window size and the number of units were observed using the GA search algorithm which was found to be (49, 9), (12, 8), (40, 8), and (36, 2) respectively. The computed MSE, RMSE, CS and r for 10 epochs were found to be 0.006, 0.078, 0.910 and 0.858 respectively for the LSTM model, whereas the same parameters were computed using the Hybrid GA-OLSTM model was 0.004, 0.063, 0.947 and 0.917 respectively. The experimental results expressed that the Hybrid GA-OLSTM model gave significantly better results comparing the LSTM model for 10 epochs has been discussed in this research article.

Introduction

Forecasting rainfall using a uni-variant dataset is almost impossible due to its internal variability and chaotic nature, however, some approaches have provided prominent results [1, 2]. Nowadays various approaches have been used for prediction, based on statistical and soft computing techniques [3]. Accordingly, various techniques based on machine learning, including artificial neural network (ANN) [4–7], support vector machine (SVM) [8], adaptive basis function (ABF) [9], multiple layer perceptron(MLP) [10], multiple nonlinear regression (MNLR) [11], adaptive neuro-fuzzy inference system (ANFIS) [12] have been used extensively. Deep learning, which has the superior ability to reflect nonlinearity and complex characteristics of rainfall time series, is also being used nowadays for the prediction of rainfall. The dynamical and the empirical approach are the fundamental approaches in deep learning. In the dynamical approaches, physically built models were used for predictions that are entirely dependent on the system’s equation that predicts the rainfall, whereas the other method i.e. the empirical scheme is dependent on the analysis of historical weather data and their correspondence with various atmospheric variables over multifarious regions. Regression, fuzzy logic and deep learning techniques are the most widely employed within the empirical scheme [13–21].

However, with LSTM, poorly selected initial weights could sometimes lead to inaccurate performance. The inspiration behind this study was to consider a method such that LSTM could start with a set of properly selected initial weightings to reduce forecasting error. Specifically, the considered hybrid approach (GA-OLSTM) is responsible for both the learning and memorization intelligence using the LSTM Network along with the searching ability of the genetic algorithm [22]. Factors to judge the quality of prediction with their significance were MSE, RMSE, CS and r.

Salman et al., proposed a merged-LSTM model and a comparison, was made with the LSTM model. The author reported the merged LSTM model worked well in predicting visibility by 4.8% higher accuracy [14]. Poornima and Pushpalatha informed an LSTM (intensified) based recurrent neural network (RNN) to predict rainfall. The results obtained by them were compared with various models to evaluate the improvement to forecast rainfall [23]. Crivellari and Beinat proposed another deep learning approach based on a problem related to trajectory prediction. The author reported that the LSTM model outperformed in comparison with global Markov model (GMM) and variable-order Markov model (VGMM) [24]. Ding and Qin proposed a multi-value associated network model of LSTM-based on a deep recurrent neural network (Associated Net). Experimental results proved that the average accuracy of the Associated Net model was better than that of the other two models discussed and it has the ability to predict the multiple values together. They reported an accuracy of more than 95% in each of the predictions [25]. Qiu et al. compared the results obtained using their proposed model with three other models including the LSTM model, the LSTM with wavelet denoising and the gated recurrent unit (GRU) neural network model for prediction of stock and they also reported that LSTM with attention model performs outstandingly in comparison with other models [26]. Chimmula and Zhang presented LSTM networks, to forecast the future COVID-19 cases [27].Ouma et al. compared the result between LSTM and wavelet neural network for rainfall prediction and runoff trend analysis [28].

Dataset and algorithm used

In this work, we required to collect time series monthly rainfall historical data of Chhattisgarh region in order to predict the rainfall in coming months. Forecasting of monthly rainfall was planned using the hybrid approach (GA-OLSTM). This algorithm was implemented using Keras and Tensor flow libraries of Python 3.9.7 software.

Collection of time series monthly dataset

A time-series uni-variant monthly rainfall data of Chhattisgarh State, India from January 1901 to December 2017 was collected. In all, monthly rainfall data of 1404 months were used and has been collected from the Indian Metrological Department (IMD). The geographical location of Chhattisgarh, India is 17°46′, north to 24°5′ north latitude and from 80°15′ east to 54°20′ east longitude [29].

LSTM model

LSTM is considered a technique to remove the problem of long-term dependency. LSTM networks can have historical information of more than thousand-time steps. LSTM is possible to be scaled to a lot longer sequences than a traditional RNN, removing the inbuilt drawbacks of a traditional RNN, i.e., exploding and vanishing gradients. Nowadays, LSTM is highly used in many sequential modelling operations, like speech recognition, natural language processing and motion detection [19, 30]. The LSTM is a deep recurrent neural network-based model consisting of a memory cell and incorporating, three multiplicative gating units input gate, output gate and a forget gate. A recurrent connection is being established between the cells. Every gate does continuous operations for the cells like write, read and reset. The cell is for conveying “state” values over arbitrary time intervals [30–32]. The calculation procedure for the Block of LSTM block is been discussed earlier [19, 30–33, 36, 37].

Hybrid GA-OLSTM model

The considered work consists of an LSTM network integrated with a GA search algorithm. As previously elaborated, the initial values of the weighting matrices may make the difference in the results obtained by LSTM [19]. GA has been used to assist in searching the appropriate initial values for the weighting matrices of the LSTM. GA is a searching algorithm based on population that utilizes a chromosomes population in the process of searching. Every chromosome speaks for a suitable solution. Figure 1 exhibits the flow diagram of the method used.

Fig. 1.

Shows the flow diagram of the hybrid (GA-OLSTM) method used [15, 33, 34]

In this study, a hybrid approach of LSTM network combined with GA for finding the appropriate time window and number of LSTM units for rainfall time series forecasting. Since the past information is used in the learning process in the LSTM network, an appropriate window size becomes an important factor to be considered. It is to note that, for the window a very small window size, important information will be neglected by the model whereas, for very large window size, the model will be over-fitted on the training data.

The evolutionary search algorithm, GA was used, to identify the optimal size of time windows and the number of LSTM units. The GA can be split into various stages such as initialization stage, fitness calculation stage; termination criteria check stage, selection stage, crossover stage, mutation stage, evaluation and replacement etc. [21, 33, 35]. In this study, binary arrays are used as chromosomes and the MSE of the prediction model was functioning like the fitness value.

In the second stage of the algorithm, to evaluate the fitness of GA various sizes of time windows along with different numbers of LSTM units are applied. The populations are initialized with random values that consist of possible solutions, before the start of exploring the search space by the genetic operators. The chromosomes taken in this study were converted into binary digits that specify the size of the time window and the number of LSTM units. The selection and recombination operators start to search for a better solution with the help of the genetic operators. A predefined fitness function is used to evaluate the solutions, and strings with excellent results opted for the reproduction. An important part of GA is the fitness function and is required to be selected with attention. In this study, RMSE was chosen to calculate the fitness of each chromosome, and various architectural factors that return the shortest RMSE was selected as the optimal solution. If the result of the reproduction process fulfils the termination criteria, derived optimal or near-optimal solution is applied to the forecasting model. The whole process is repeated, if the result does not satisfactory. To find an excellent solution for the problem, genetic parameters, such as crossover rate, mutation rate, and population size, can affect the parameter. In this work, population size, number of generations, probability of mutating an individual and probability of mating two individuals were taken as 4, 4, 0.1 and 0.4 respectively.

Results and discussion

A time series uni-variant dataset was used to predict monthly rainfall using LSTM model. Then GA-OLSTM model which is a hybrid model was also used in efforts to improve the prediction accuracy. The comparative analysis was done to conclude the best combination of windows size and number of LSTM units.

Experimental outcomes

In the experimental results, we started experimenting with the time series Uni-Variant data by applying the LSTM model. With 10 epochs various factors such as MSE, RMSE, CS, and r were calculated to investigate the accuracy of forecasting data and found as 0.006, 0.078, 0.910 and 0.858 respectively which is illustrated in Table 1. A deep learning tool was utilized to find these parameters. These values were an indicator of poor resemblance between observed (actual) and forecast data; therefore, the Hybrid GA-OLSTM model was taken into consideration for further experimental work. The graph obtained for window size and number of units (20, 16) is shown in Fig. 2a.

Table 1.

LSTM network-based analysis of uni-variant time-series data

LSTM input parameter	Window size = 20, Number of units = 16
Accuracy parameters	10 epochs
MSE	0.006
RMSE	0.078
CS	0.910
r	0.858

Fig. 2.

a Comparison between actual and forecast rainfall (10 epoch (s), optimal window size = 20, number of LSTM units = 16) using LSTM algorithm. b Comparison between actual and forecast rainfall (10 epoch (s), optimal window size = 12, number of LSTM units = 8) using hybrid (GA-OLSTM) algorithm

A prediction is recommended to use a hybrid (GA-OLSTM) approach of LSTM network integrated with GA to find the optimized window size and the number of LSTM units for rainfall forecasting using uni- variant time series data. The whole study was carried out in two sections. The first section of the analysis involved designing the appropriate LSTM network. An LSTM network was used with a sequential input layer followed by two hidden layers, incorporating the optimal parameters investigated by GA for 5, 10, 15 and 20 epochs respectively. As a result of GA search for 5, 10, 15 and 20 epochs, the optimal window size and number of units were observed to be (49,9), (12,8), (40,8), and (36,2) respectively. Subsequently, in the second section forecasting of time series uni-variant data was done using the LSTM model with the optimal parameters obtained from the results of the first section.

To examine the efficiency of the results obtained using the Hybrid GA-OLSTM model, the above used statistical-based various parameters were estimated. We went for the various window size and the number of units attained from GA search to observe the quality of prediction for various epoch(s) such as 5, 10, 15 and 20 respectively (Table 2). The factors MSE and RMSE are expected to be less for obtaining optimum prediction quality. On the other hand, the values of CS and r must be close to one. When these values are closed to 1, we consider the actual and predicted data are very similar and when the said values are closed to 1, we may conclude about the usefulness of the prediction made. If we observe Table 2, it was found that the value of RMSE and MSE is 0.063 and 0.004 for 10 epochs, which is the smallest in comparison to that of prediction result obtained for the rest of the epochs. We also got the value of CS and r as 0.947, and 0.917 respectively which is again highest for 10 epochs. The graph obtained for window size and number of units (12, 8) which gave the best possible result is shown in Fig. 2b. In this figure, a great resemblance between the actual and forecast data can be observed.

Table 2.

Hybrid (GA-OLSTM) Model-based analysis of uni-variant time-series data

LSTM input parameter	Window size = 49, number of units = 9	Window size = 12, number of units = 8	Window size = 40, number of units = 8	Window size = 36, number of units = 2
Accuracy parameters	5 epochs	10 epochs	15 epochs	20 epochs
MSE	0.006	0.004	0.004	0.005
RMSE	0.079	0.063	0.063	0.075
CS	0.89	0.947	0.936	0.905
r	0.821	0.917	0.899	0.849

Comparison of performance between LSTM and hybrid GA-OLSTM model

A comparison is being done with the performance of the Hybrid GA-OLSTM with the LSTM Model. As depicted in Table 3 LSTM was less stable and has large errors. On the other hand, Hybrid GA-OLSTM presented better performance. The predicted MSE and RMSE of the LSTM model is 0.006 and 0.078, while the predicted MSE and RMSE of the GA-OLSTM model is 0.004 and 0.063 respectively. Lastly, the predicted CS and r of the LSTM model is 0.91 and 0.858, while the same for the GA-OLSTM model is 0.947 and 0.917 respectively, which express great accuracy resemblance between the actual and predicted data.

Table 3.

Comparative evaluation table between the models used

Model	Optimal parameters	MSE	RMSE	CS	R
LSTM	Window size = 20, number of units = 16	0.006	0.078	0.91	0.858
Hybrid GA-OLSTM	Window size = 12, number of units = 8	0.004	0.063	0.947	0.917

Conclusion

In the present research paper, LSTM model and hybrid (GA-OLSTM) model for rainfall forecasting based on the uni-variant time series analysis using PYTHON v 3.9. An attempt had been made to forecast the monthly rainfall of 1404 months applying the LSTM algorithm using 10 epochs. The experimental factors like MSE, RMSE, CS, and r were calculated to judge the quality of forecasting. These parameters were found as 0.006, 0.078, 0.910 and 0.858 respectively. The values of CS and r were not close to 1. It was an indicator that the actual data and predicted data do not have a significant resemblance. Therefore we applied a rainfall prediction hybrid model (GA-OLSTM), which is one of the typical methodologies of deep learning. For better rainfall prediction GA search algorithm was integrated with LSTM network and a comparison is done between the hybrid (GA-OLSTM) model and the LSTM model. Therefore the hybrid (GA-OLSTM) model was used to predict the rainfall for 10 epochs. The same parameters were calculated and found 0.004, 0.063, 0.947 and 0.917 respectively which preserved the high accuracy of resemblance and exhibited reduced loss too. The values of CS and r were close to 1. It was indicative that the actual data and predicted data have a significant resemblance and exhibited reduced loss too. These overall results demonstrate that a hybrid (GA-OLSTM) approach in comparison with an LSTM model can be an effective method for rainfall forecasting to reflect temporal patterns.

Future scope

The work carried out in this article may be extended by using the reported GA-OLSTM model for the multivariate data. In this work, univariate time series data was used for analysis whereas, in the future, multivariate data may be processed for obtaining better prediction results. It is planned to access the desired multivariate data from Google Earth Interface "CRU TS Version 4.04". The interface discussed is available on the website of the Climate Research Unit (CRU).

Author contributions

NT rest of article. SK supervision. SS supervision.

Funding

No funding support was received.

Availability of data and material

Data is collected from the website of the Indian Metrological Department Pune (https://www.springernature.com/gp/authors/research-data-policy/data-availability-statements/12330880).

Code availability

Coded by ourselves in python.

Declarations

Conflict of interest

There is no conflict of interest.

Ethics approval

The work submitted is the original work of our team and the contents submitted above are not submitted elsewhere for publication.

Consent to participate

Both the authors have contributed to the article.

Consent for publication

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