An Ensemble Hybrid forecasting Model for Annual Runoff Based on Sample Entropy, Secondary Decomposition, and Long Short-Term Memory Neural Network

doi:10.21203/rs.3.rs-269127/v1

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An Ensemble Hybrid forecasting Model for Annual Runoff Based on Sample Entropy, Secondary Decomposition, and Long Short-Term Memory Neural Network

https://doi.org/10.21203/rs.3.rs-269127/v1

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Accurate and consistent annual runoff prediction in regions is a hot topic in the management, optimization, and monitoring of water resources. A novel prediction model (ESMD-SE-WPD-LSTM) is presented in this study. Firstly, the extreme-point symmetric mode decomposition (ESMD) is used to produce several intrinsic mode functions (IMF) and a residual (Res) by decomposing the original runoff series. Secondly, the sample entropy (SE) method is employed to measure the complexity of each IMF. Thirdly, we adopt wavelet packet decomposition (WPD) to further decompose the IMF with the maximum SE into several appropriate components and detailed components. Then the LSTM model, a deep learning algorithm based recurrent approach, is employed to predict all components obtained in the previous step. Finally, the forecasting results of all components are aggregated to generate the final prediction. The proposed model, which is applied to five annual series from different areas in China, is evaluated based on four quantitative indexes (R, NSEC, MAPE and RMSE). The results indicate that the ESMD-SE-WPD-LSTM outperforms other benchmark models in terms of four quantitative indexes. Hence the proposed model can provide higher accuracy and consistency for annual runoff prediction, making it an efficient instrument for scientific management and planning of water resources.

Environmental Policy

annual runoff prediction

two-phase decomposition

Long Short-Term Memory

extreme-point symmetric mode decomposition

wavelet packet decomposition

sample entropy

Table 1 Statistical description of runoff series at five stations.

Data	Station	Size	Max	Min	Mean	Std	Skewness	SE
Site1	Mopanshan	53	903.00	281.00	558.70	143.40	7.50	2.53
Site2	Hongjiadu	55	2831.00	1052.00	1778.00	402.10	-7.63	Inf
Site3	Changshui	56	37.62	1.32	8.17	6.25	-7.70	1.48
Site4	Dahuofang	56	4043.00	536.30	1501.00	793.90	-7.70	1.72
Site5	Biliuhe	57	1466.00	100.50	607.90	328.00	-7.76	Inf

where Std is the standard deviation, SE is the sample entropy.

Table 2 Input variables for Site 1.

Number	Series		LSTM	ANFIS	ANN
1		Original	r_(t-1)~r_(t-3)	r_(t-1)~r_(t-6)	r_(t-1)~r_(t-3)
2	ESMD	IMF1	r_(t-1)~r_(t-10)	/	/
3		IMF2	r_(t-1)~r_(t-4)	/	/
4		IMF3	r_(t-1)~r_(t-6)	/	/
5		R	r_(t-1)~r_(t-6)	/	/
6	WPD	WPD₁	r_(t-1)~r_(t-3)	/	/
7		WPD₂	r_(t-1)~r_(t-10)	/	/
8		WPD₃	r_(t-1)~r_(t-7)	/	/
9		WPD₄	r_(t-1)~r_(t-3)	/	/
10		WPD₅	r_(t-1)~r_(t-6)	/	/
11		WPD₆	r_(t-1)~r_(t-6)	/	/
12		WPD₇	r_(t-1)~r_(t-4)	/	/
13		WPD₈	r_(t-1)~r_(t-5)	/	/
14	SSA	Y	r_(t-1)~r_(t-4)	/	/
15	SSA	Res	r_(t-1)~r_(t-7)	/	/
16	CEEMDAN	IMF1	r_(t-1)~r_(t-10)	/	/
17		IMF2	r_(t-1)~r_(t-6)	/	/
18		IMF3	r_(t-1)~r_(t-6)	/	/
19		IMF4	r_(t-1)~r_(t-6)	/	/
20		IMF5	r_(t-1)~r_(t-6)	/	/
21		Res	r_(t-1)~r_(t-6)	/	/

where represents the estimated value of runoff and r _(t-p) is the runoff at time t-p.

Table 3 Parameters of ANFIS.

Parameter	Value	Parameter	Value
Number of clusters	10	Maximum epochs	100
Partition matrix index	2	Expected error	0
Maximum iteration	500	Initial Step Size	default
Minimum improvement	1.00E-05	Step decrease rate	default
		Step increase rate	default

Table 4 Errors of different models at Site 1.

Model	Training				Testing
	RMSE	MAPE	NSEC	R	RMSE	MAPE	NSEC	R
ANN	145.0215	23.6669	0.0685	0.3721	194.6033	34.7285	-9.5937	0.6722
ANFIS	0.0043	6.61E-04	0.9999	0.9999	250.1728	43.8852	-16.5076	0.4622
LSTM	3.3901	0.5691	0.9994	0.9997	115.7743	18.1835	-2.7495	0.7046
ESMD-LSTM	1.7438	0.2405	0.9998	0.9999	45.1321	5.8335	0.4302	0.8465
ESMD-SE-SSA-LSTM	1.9972	0.2845	0.9998	0.9999	34.1646	4.7031	0.6735	0.8521
ESMD-SE-CEEMDAN-LSTM	3.3099	0.5435	0.9995	0.9997	48.0671	6.36	0.3537	0.8796
ESMD-SE-WPD-LSTM	3.2342	0.4926	0.9995	0.9997	28.102	3.8847	0.7791	0.9163

Table 5 Errors of different models at Site 2.

Model	Training				Testing
	RMSE	MAPE	NSEC	R	RMSE	MAPE	NSEC	R
ANN	346.4129	16.474	0.2215	0.4738	526.9013	36.4785	-0.6134	0.4062
ANFIS	10.5946	0.3151	0.9991	0.9996	838.9304	44.8574	-3.0901	0.4369
LSTM	10.1828	0.449	0.9992	0.9996	318.7191	18.0374	0.4097	0.7515
ESMD-LSTM	6.6829	0.3167	0.9997	0.9999	177.0237	12.4764	0.8179	0.9166
ESMD-SE-SSA-LSTM	6.0601	0.291	0.9997	0.9999	152.5725	7.4409	0.8647	0.9386
ESMD-SE-CEEMDAN-LSTM	6.0175	0.2762	0.9997	0.9999	173.1621	10.345	0.8257	0.9397
ESMD-SE-WPD-LSTM	13.8734	0.6764	0.9985	0.9993	100.1278	4.6052	0.9417	0.9817

Table 6 Errors of different models at Site 3.

Model	Training				Testing
	RMSE	MAPE	NSEC	R	RMSE	MAPE	NSEC	R
ANN	3.4587	56.1092	0.4387	0.6659	2.4828	76.9781	-3.6987	0.3065
ANFIS	0.0028	0.0506	0.9999	0.9999	2.7558	70.2027	-4.7884	-0.3839
LSTM	0.0628	1.0024	0.9998	0.9999	2.851	72.5634	-5.1958	0.4509
ESMD-LSTM	0.1396	2.3601	0.9991	0.9995	1.3811	41.8609	-0.4539	0.922
ESMD-SE-SSA-LSTM	0.0565	0.9792	0.9998	0.9999	1.9175	62.4839	-1.8027	0.4123
ESMD-SE-CEEMDAN-LSTM	0.0607	1.0825	0.9998	0.9999	2.3784	53.6268	-3.312	0.7577
ESMD-SE-WPD-LSTM	0.145	2.6589	0.999	0.9995	0.5059	15.2434	0.8049	0.9618

Table 7 Errors of different models at Site 4.

Model	Training				Testing
	RMSE	MAPE	NSEC	R	RMSE	MAPE	NSEC	R
ANN	723.0598	43.6156	0.1321	0.4400	783.1462	25.9669	-0.079	0.2764
ANFIS	472.6449	26.5543	0.6358	0.7977	1.41E+03	67.2697	-2.5172	0.2394
LSTM	1.8759	0.1285	0.9999	0.9999	833.9399	39.0403	-0.2235	0.3178
ESMD-LSTM	13.9342	0.9872	0.9997	0.9998	697.4458	45.4508	0.1442	0.6198
ESMD-SE-SSA-LSTM	27.0888	1.9613	0.9988	0.9994	450.488	29.8515	0.643	0.8541
ESMD-SE-CEEMDAN-LSTM	34.3317	2.2771	0.9981	0.9992	433.6346	24.7855	0.6692	0.8334
ESMD-SE-WPD-LSTM	23.0008	1.6829	0.9992	0.9996	380.0629	25.6718	0.7459	0.9478

Table 8 Errors of different models at Site 5.

Model	Training				Testing
	RMSE	MAPE	NSEC	R	RMSE	MAPE	NSEC	R
ANN	319.4179	55.5948	0.0611	0.4038	337.2026	107.0206	-3.899	0.5656
ANFIS	0.0222	0.0037	0.9999	0.9999	487.9529	89.148	-9.2585	0.6683
LSTM	1.0043	0.1556	0.9999	0.9999	327.0245	55.9468	-3.6077	0.6221
ESMD-LSTM	8.3861	1.2453	0.9994	0.9997	165.4607	50.4692	-0.1796	0.7105
ESMD-SE-SSA-LSTM	9.881	1.8414	0.9991	0.9996	102.616	26.2473	0.5463	0.7953
ESMD-SE-CEEMDAN-LSTM	10.5398	1.803	0.9989	0.9995	127.2091	42.5835	0.3028	0.7543
ESMD-SE-WPD-LSTM	9.7325	1.8012	0.9991	0.9996	99.0973	23.5913	0.5769	0.8975

Table 9. Errors of ESMD-LSTM at different sites.

Station	Subseries	Training				Testing
		RMSE	MAPE	NSEC	R	RMSE	MAPE	NSEC	R
Site 1	IMF1	0.1781	0.3634	0.9999	0.9999	49.9027	39.5243	0.6357	0.8718
	IMF2	1.468	15.2196	0.9993	0.9996	5.2289	13.3999	0.9424	0.9864
	IMF3	0.8486	2.588	0.9997	0.9999	4.5101	40.5524	0.9266	0.986
	Res	0.7363	0.1133	0.9999	0.9999	2.1791	0.347	0.9964	0.9995
Site 2	IMF1	2.7151	1.6453	0.9999	0.9999	154.651	226.7093	0.5346	0.9175
	IMF2	4.5865	8.4604	0.9994	0.9997	66.7728	26.3457	0.7362	0.8732
	IMF3	4.7047	11.0664	0.9979	0.9989	16.7141	20.1374	0.9796	0.9996
	IMF4	0.935	2.1518	0.9998	0.9999	4.1435	4.5707	0.9928	0.9997
	Res	1.0575	0.0491	0.9997	0.9999	0.3623	0.0219	0.9585	0.9999
Site 3	IMF1	0.0338	2.1861	0.9999	0.9999	1.6716	225.4832	-0.4806	0.5734
	IMF2	0.0773	8.7615	0.999	0.9995	0.2749	223.1044	0.4037	0.8098
	IMF3	0.1126	13.1545	0.9915	0.9957	0.1576	17.1221	0.9399	0.9996
	Res	0.0354	0.3416	0.9999	0.9999	0.0945	2.3463	0.888	0.9999
Site 4	IMF1	7.3214	10.8294	3.1682	0.9996	0.9998	64.0341	-0.3026	0.5044
	IMF2	2.2703	3.2761	9.4609	0.9999	1.0000	249.4696	-1.0744	0.9602
	IMF3	5.1216	7.7177	20.136	0.9997	0.9999	14.0539	0.6048	0.8565
	IMF4	0.3379	0.4301	2.2856	0.9999	0.9999	17.6623	0.9795	0.9979
	Res	0.5936	0.7293	0.0389	0.9998	0.9999	0.2036	0.9837	0.9999
Site 5	IMF1	0.571	0.3493	0.9999	0.9999	160.4688	106.7409	-0.6215	0.8488
	IMF2	0.7339	0.8001	0.9999	0.9999	33.2195	177.8473	-1.4824	0.8428
	IMF3	8.3574	8.8112	0.9963	0.9981	14.2533	23.0252	0.9181	0.9599
	IMF4	1.2021	6.666	0.9995	0.9998	10.183	14.9286	0.9749	0.9994
	IMF5	0.6124	2.9234	0.9998	0.9999	3.6636	10.3663	0.9822	0.9994
	Res	1.2012	0.1602	0.9999	0.9999	3.8196	0.9587	0.9474	0.9999

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Editorial decision: Major revisions
26 May, 2021
Editor assigned by journal
22 Feb, 2021
First submitted to journal
22 Feb, 2021

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An Ensemble Hybrid forecasting Model for Annual Runoff Based on Sample Entropy, Secondary Decomposition, and Long Short-Term Memory Neural Network

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