IWOA-Elman Neural Network and Its Application to Backfill Strength Prediction

doi:10.12068/j.issn.1005-3026.2025.20240105

Abstract

Abstract:

Uniaxial compressive strength of mine backfill is critical for stope stability. In response to the problem of low efficiency and long time consumption in traditional testing methods， an improved whale optimization algorithm （IWOA） incorporating chaotic mapping， adaptive weighting， and Levy flight was proposed. IWOA was used to optimize the weights and thresholds of an Elman neural network， and an IWOA-Elman prediction model was constructed. Based on backfill proportioning data from a mine， the model was trained and tested with mass fractions of cement， fly ash， and tailings as inputs and compressive strength as output. Comparative analysis with Elman， PSO-Elman， and WOA-Elman models demonstrates superior convergence of IWOA. The root mean square error （RMSE） and mean absolute percentage error （MAPE） of the IWOA-Elman model are 0.050 7 and 3.326 9， respectively， indicating higher accuracy. The model provides a valuable reference for backfill strength prediction and intelligent backfill design.

Key words: intelligent backfill, improved whale optimization algorithm, Elman neural network, IWOA-Elman prediction model, backfill strength prediction

CLC Number:

TD 35

Hao-ran GAO, Hong-lei LIU, De-fu CHE, Tian-xing LAN. IWOA-Elman Neural Network and Its Application to Backfill Strength Prediction[J]. Journal of Northeastern University(Natural Science), 2025, 46(11): 125-133.

Figures/Tables 11

Fig.1 Structure of Elman neural network

Fig.2 Effect diagram of the Cubic chaotic mapping

Fig.3 Nonlinear improved curve of convergence coefficienta

Fig.4 Technology roadmap

Fig.5 Results of optimal number of nodes in hidden layer

Table 1 Comparison of optimization performance of five algorithms

测试函数	评价标准	GA	PSO	GWO	WOA	IWOA
F1	平均值	96 196.995 2	26.193 0	1.44E-17	1.44E-71	4.53E-233
	标准差	15 688.467 3	7.782 6	1.26E-17	7.24E-71	0
	运行时间/s	0.046 7	0.094 9	0.088 5	0.032 4	0.035 9
	最优解	63 125.415 2	14.353 6	1.37E-18	7.35E-90	0
F2	平均值	40.763 2	4.841 5	8.74E-17	5.61E-51	4.09E-123
	标准差	6.721 5	1.821 6	4.864E-17	1.59E-50	2.09E-122
	运行时间/s	0.045 9	0.084 1	0.052 1	0.026 4	0.028 5
	最优解	27.947 0	2.367 2	2.20E-17	1.37E-58	0
F3	平均值	37 988.551 5	689.380 3	1.72E-05	40 759.439 9	3.99E-173
	标准差	9 551.639 6	1 559.514 7	3.51E-05	13 734.184 9	0
	运行时间/s	0.128 4	0.170 7	0.134 5	0.106 0	0.109 8
	最优解	22 527.125 2	43.465 7	1.35E-08	12 273.764 9	0
F4	平均值	69.545 0	3.742 7	1.04E-06	48.771 9	2.38E-100
	标准差	7.971 9	0.961 3	1.18E-06	28.136 3	1.30E-99
	运行时间/s	0.045 0	0.085 9	0.048 8	0.024 7	0.027 9
	最优解	42.183 1	1.881 9	4.90E-08	0.430 6	0
F5	平均值	10 136.241 4	0.627 5	0.684 0	0.430 2	0.130 6
	标准差	5 161.029 3	0.157 9	0.339 9	0.240 5	0.039 9
	运行时间/s	0.044 8	0.085 2	0.048 9	0.024 5	0.026 9
	最优解	1 385.651 2	0.329 5	0.158 4	0.099 5	0.051 2

Fig. 6 Comparison of test function operation

Table 2 Comparative results of algorithm tests and evaluation indicators of prediction models

预测模型	$δ M A E$		$δ R M S E$		$R 2$		$δ M A P E$ /%
预测模型	训练集	测试集	训练集	测试集	训练集	测试集	训练集	测试集
Elman	0.126 4	0.163 0	0.186 5	0.182 2	0.965 1	0.921 5	12.640 0	16.300 0
PSO-Elman	0.114 6	0.155 8	0.135 0	0.175 4	0.981 8	0.927 3	9.997 7	13.866 6
WOA-Elman	0.092 4	0.139 9	0.133 0	0.154 3	0.982 3	0.943 7	7.164 2	10.403 6
IWOA-Elman	0.093 3	0.046 6	0.130 4	0.050 7	0.983 0	0.993 9	6.774 9	3.326 9

Table 2 Comparative results of algorithm tests and evaluation indicators of prediction models

预测模型	$δ M A E$		$δ R M S E$		$R 2$		$δ M A P E$ /%
预测模型	训练集	测试集	训练集	测试集	训练集	测试集	训练集	测试集
Elman	0.126 4	0.163 0	0.186 5	0.182 2	0.965 1	0.921 5	12.640 0	16.300 0
PSO-Elman	0.114 6	0.155 8	0.135 0	0.175 4	0.981 8	0.927 3	9.997 7	13.866 6
WOA-Elman	0.092 4	0.139 9	0.133 0	0.154 3	0.982 3	0.943 7	7.164 2	10.403 6
IWOA-Elman	0.093 3	0.046 6	0.130 4	0.050 7	0.983 0	0.993 9	6.774 9	3.326 9

Fig.7 Comparison of model training set and test set performance

Table 3 Model prediction error and accuracy

样本序号	抗压强度实际值/MPa	Elman		PSO-Elman		WOA-Elman		IWOA-Elman
		抗压强度预测值	相对误差/%	抗压强度预测值	相对误差/%	抗压强度预测值	相对误差/%	抗压强度预测值	相对误差/%
		MPa	相对误差/%	MPa	相对误差/%	MPa	相对误差/%	MPa	相对误差/%
预测准确率 / %		83.702 5		86.135 0		89.597 5		96.597 5
1	1.85	1.670 3	9.71	1.578 0	14.70	2.058 4	11.26	1.794 0	3.03
2	0.43	0.576 6	34.09	0.557 3	29.60	0.361 0	16.05	0.412 5	4.07
3	1.67	1.450 9	13.12	1.620 2	2.98	1.750 8	4.84	1.598 4	4.29
4	2.13	1.953 9	8.27	1.955 7	8.18	2.331 4	9.46	2.177 2	2.22

Fig.8 Error comparison curves of prediction models

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