The absorbance spectra were measured by a Purkinje T9 dual beam spectrophotometer (Beijing Purkinje General Instrument Ltd., China). The T9 spectrophotometer is a high-sensitivity scientific grade UV-Vis spectrophotometer, equipped with a high-performance PMT receiver and a special grating, mixed C-T dual monochromator and dual beam, so it has a high dynamic range and good SNR. The hexadecyl trimethyl ammonium bromide was used as stabilizer solution, nitroso R salt solution (0.4%) was chosen as chromogenic reagent, acetic acid-sodium acetate buffer (pH = 5.5) was prepared as buffer solution, and standard stock solutions of copper (12.5 mg/L) and nickel (12.5 mg/L) were prepared.

First, transfer the appropriate amount of copper and nickel standard solutions to a 25 ml volumetric flask. Then, add 2 ml nitroso R salt, 3 ml hexadecyl trimethyl ammonium bromide and 5 ml acetic acid-sodium acetate buffer. Finally, dilute and mix the solution with distilled water to ensure uniformity. The ultraviolet visible absorption spectra of the solution is measured with a reagent blank in the wavelength range of 350–600 nm. The prepared copper and nickel concentration ranges are both 0.3–3 mg/L 60 groups of copper and nickel mixed solutions in different proportions were prepared for spectral modeling analysis.

The spectral signal of copper and nickel single ion solution and the mixed solution are shown in Figure 2, where the copper concentration is 1.2 mg/L, the nickel concentration is 1.2 mg/L, and the wavelength detection range is 350–600 nm.

According to Figure 2, at the same concentration of 1.2 mg/L, the sensitivity of copper is higher than that of nickel. The peak of copper is at 405 and 488 nm, the peak of nickel is at 452 nm, copper and nickel overlap severely in the entire wavelength range. The reason is that copper and nickel ions are close neighbors in the periodic table, and their electrochemical characteristics are very similar, which makes the detection spectral signals overlap seriously, resulting in low spectral signal resolution and few characteristic wavelength variables. It is difficult to simultaneously detect the concentration of copper and nickel in zinc wastewater solution. Therefore, it is very important to select the characteristic wavelength to improve the resolution of copper and nickel absorption spectra.

Figure 3 shows a group of absorption spectra of Cu in zinc wastewater solution, in which the concentration range of Cu is 0.3–3 mg/L. Figure 4 shows a group of absorption spectra of Ni in zinc wastewater solution, in which the concentration range of Ni is 0.3–3 mg/L.

To evaluate the linearity of copper and nickel in the zinc wastewater solution, multiple wavelengths were randomly selected to perform linear fitting of absorbance and concentration. The linear regression equation and correlation coefficient (R ²) are shown in Table 1.

The correlation coefficient (R ²) is used to characterize the linear correlation of ions. The larger the value of R ², the better the linearity. It can be seen from Table 1 that copper ion have no linearity at wavelengths of 375 nm. They are generally linear at 417 and 535 nm, and have good linearity at 450, 496 and 517 nm. The nickel ion has a small correlation coefficient (R ²) at wavelengths of 375 nm, so the linearity is very poor; it has good linearity at 417, 450 and 496 nm. Because the effective information of copper and nickel at different wavelength points is different, when modeling and detecting the concentration of copper and nickel by the partial least squares method, it is necessary to select the characteristic wavelength variables, and select the wavelength variables with high spectral signal sensitivity, large amount of information and strong linear correlation, so as to improve the accuracy of simultaneous detection of copper and nickel.

According to the steps of characteristic interval wavelength selection method described in section 2, the 30 sets of correction sets are modeled for the full-band wavelength variables of 350–600 nm, and the global RMSECV and R ² values of copper are 0.9851 and 0.0674, and the global RMSECV and R ² values of nickel are 0.9836 and 0.0712, which are used as the threshold for the subsequent screening of the characteristic interval. The whole band is divided into P sub intervals, PLS modeling is carried out respectively, and the RMSECV and R ² values of P sub intervals are obtained. All sub intervals greater than RMSECV threshold and less than R ² threshold are eliminated, and t (1 < t < Q) characteristic intervals are combined in turn in the remaining Q sub intervals to establish a joint interval PLS model. The combined modeling of the optimal characteristic intervals of copper and nickel after each interval division is shown in Table 2.

It can be seen from Table 2 that the optimal characteristic interval combination of copper is to divide the whole band into 10 intervals, and when the second, fifth and seventh intervals are combined in sequence, the minimum value of RMSECV is 0.0403 and the maximum value of R ² is 0.9978. The optimal feature interval combination of nickel is to divide the whole band into 12 intervals, and when the fourth, sixth and seventh intervals are combined in sequence, the minimum value of RMSECV is 0.0459 and the maximum value of R ² is 0.9965. The results of the combined wavelength screening of characteristic intervals are shown in Figures 5, 6. The wavelength ranges corresponding to the optimal characteristic intervals of copper are 375–400 nm, 450–475 nm, and 500–525 nm. The wavelength range corresponding to the optimal characteristic intervals of nickel is 410–430 nm, 450–470 nm, and 470–490 nm.

The proposed characteristic interval modeling method (CIM) is used to detect the concentration of copper and nickel mixed solutions in 30 groups of prediction sets, and the performance is compared with full band partial least squares method (FBPLS), competitive adaptive weighting method (CARS) and Monte Carlo uninformative variable elimination method (MC_UVE). Table 3 shows the modeling comparison of four feature extraction methods. Using the calibration model by CIM, the predicted and actual values of Cu and Ni in mixture solution are shown in Figure 7.

It can be seen from Table 3 that there are a large number of blank, overlapping and suppressed wavelengths in the full band wavelength, which interfere with the accurate and efficient modeling of ions, so the accuracy is very low and the real-time performance is poor. The CARS method selects fewer wavelengths, which is not ideal for measuring copper and nickel in zinc wastewater solution. The MC_UVE method still retains many redundant wavelength points when selecting variables, which makes the accuracy of the model worse. The proposed characteristic interval modeling method selects the region with higher sensitivity and reduces the masking and suppression differences of other ions to be measured. The predicted root mean square error (RMSEP) is lower, and the correlation coefficients (R ²) is higher. The average relative errors of Cu and Ni in the 30 validation sets are 3.27% and 4.12%. The maximum error of Cu is 7.16%, and the maximum error of Ni is 8.33%. The relative error is within 5%, which meets the requirements of industrial detection. As can be seen from Figure 7 that the predicted value is almost consistent with the actual value. The predicted root mean square errors (RMSEP) for Cu and Ni are 0.0413 and 0.0457, and the correlation coefficients (R ²) of Cu and Ni are 0.9974 and 0.9966, respectively. The results indicate that the proposed characteristic interval modeling method can effectively realize the simultaneous detection of copper and nickel in zinc industrial wastewater.