Fig. 1

BPNN structure diagram"

Fig. 2

The trained BPNN structure"

Fig. 3

Validation of BPNN battery model (a) Comparison of BPNN output voltage with reference voltage (b) Error of BPNN battery model (Ut, Reference-Ut, BPNN )"

Fig. 4

The SOC estimation framework based on BPNN-AUKF"

Fig. 5

The effect of temperature on the relationship between Ut and SOC"

Fig. 6

Utvs. SOC fitting curve based on temperature compensation strategy"

Table 1

Temperature compensation coefficient"

Fig. 7

Ut prediction results of BPNN, ECMFFRLS and ECMEKF (a) Ut Compare (b) Error between predicted and reference values"

Table 2

The terminal voltage MAE and RMSE predicted by BPNN, ECMFFRLS and ECMEKF are compared"

Fig. 8

The SOC estimation results of BPNN-AUKF, ECMFFRLS-UKF and ECMEKF-UKF"

Table 3

The MAE and RMSE of SOC estimated by BPNN-AUKF, ECMFFRLS-UKF and ECMEKF-UKF are compared"

Fig. 9

Current curves of UDDS, LA92 and HWFET"

Fig. 10

The BPNN battery model predicts the terminal voltage of three driving cycles"

Table 4

The MAE and RMSE of SOC estimation for three driving cycles of BPNN-AUKF"

Fig. 11

The SOC estimation results of UDDS, LA92 and HWFTE are obtained by BPNN-AUKF method"

Table 5

The MAE and RMSE of the terminal voltage values of the three driving cycles predicted by the BPNN battery model"

Fig. 12

The terminal voltage prediction results of BPNN, ECMFFRLS and ECMEKF at different temperatures (a) 10 ℃; (b) 0 ℃; (c) -10 ℃; (d) -20 ℃"

Table 6

The MAE and RMSE of the terminal voltage values calculated by the three battery models at different temperatures are calculated"

Fig. 13

The SOC estimation results of BPNN-AUKF, ECMFFRLS-UKF and ECMEKF-UKF at different temperatures (a) 10 ℃; (b) 0 ℃; (c) -10 ℃; (d) -20 ℃"

Table 7

The MAE and RMSE of SOC estimated by BPNN-AUKF, ECMFFRLS-UKF and ECMEKF-UKF at different temperatures were compared"