Rapid Correction of Turbidity Interference on Chemical Oxygen Demand Measurements by Using Ultraviolet-Visible Spectrometry

Abstract

We developed a simple, rapid, and high-precision method to compensate for the turbidity interference in the measurement of water parameters using ultraviolet-visible spectrometry. By combining direct orthogonal signal correction (DOSC) with partial least squares (PLS), we corrected the full spectra (220 nm to 600 nm), significantly enhancing the accuracy of the water parameter calculations. First, DOSC was applied to filter out turbidity-related components, retaining only the spectral elements most closely associated with the target substance, without requiring a standard baseline for the turbidity effect. Then, 13 wavelengths were selected from the corrected full spectra to construct the discrete absorption spectra. Further, a PLS regression model was established based on the corrected discrete absorption spectra and their corresponding concentrations. In our experiment, this method effectively eliminated the blue shift and peak height reduction caused by turbidity, especially in shorter wavelengths, which are more sensitive to interference. Moreover, when applied to new samples, the correlation coefficients (R²) between the predicted and actual values improved from 0.5455 to 0.9997, and the root mean square error (RMSE) decreased from 12.3604 to 0.2295 after correction. Overall, the DOSC-PLS method, together with ultraviolet-visible spectrometry, posed a great potential for the precise monitoring of target water parameters in field studies.

1. Introduction

In recent years, rapid economic development has led to increasingly severe environmental pollution, particularly water contamination [1,2,3]. Chemical oxygen demand (COD) serves as a key composite indicator for monitoring organic pollution in water bodies [4]. The real-time detection of COD values provides valuable insights into water quality and pollution levels, which is crucial for preventing and controlling water pollution and ensuring hydrosphere security [5,6].

Ultraviolet-visible (UV-Vis) absorption spectroscopy is widely employed for measuring water parameters including the COD, turbidity, nitrates, etc. Compared to other water quality analytical technologies, such as fluorescence spectroscopy and infrared (IR) absorption spectroscopy [7,8], UV-Vis absorption spectroscopy offers advantages, including simpler setups, faster and more straightforward measurements, reduced instrumental complexities, and the ability to conduct quantitative analyses based on the Lambert–Beer law. UV-Vis absorption spectroscopy has evolved from a single-wavelength [9] to a dual-wavelength [10] and, ultimately, to a multidimensional spectral analysis [11]. Due to the complex composition of substances in aquatic environments, single- or dual-wavelength methods are often inadequate for detection. Furthermore, single wavelengths are highly susceptible to interference from other non-target substances in the water, resulting in wavelength shifts or fluctuations, which, in turn, lead to inaccurate quantification. Thus, full spectrum analysis, which offers richer information across various wavelengths, has emerged as a superior method for water quality monitoring [12].

Although full-spectrum technology significantly enhances detection accuracy compared with single-wavelength technology, environmental factors such as turbidity still limit measurement precision. Therefore, it is necessary to correct the interference caused by turbidity before establishing a concentration prediction model for the target substance [13]. In many situations, particularly when sensors are used for real-time monitoring, direct subtraction is often employed by directly subtracting the baseline of turbidity effects, based on the superposition of the Lambert−Beer law [14,15]. However, the scattering intensity of turbidity varies with wavelength, affecting shorter wavelengths more significantly than longer ones, leading to inaccuracies. Additionally, a blue shift phenomenon occurs [16], where the peak of the sample shifts to a lower wavelength as turbidity increases. To address this issue, Hu et al. [17] introduced an impact index, K_N(λ), to refine the results of direct subtraction, allowing for correction across different interference levels. Furthermore, they used a numerical fitting curve to correct the blue shift in the spectra of mixtures of standard turbidity and standard COD solutions. However, the method of subtraction relies on a normalized absorption spectrum of standard turbidity, as well as the turbidity level, potentially impacting the calibration’s effectiveness.

Several chemometric methods have been applied to reduce or eliminate the interference caused by suspended particles, such as Multiplicative Scatter Correction (MSC), derivative operations, and orthogonal signal correction (OSC), which apply mathematical formulas to compensate for disturbances in spectral data. For instance, Chen et al. [18] used the MSC method to effectively eliminate shifts caused by inter-species scattering, enhancing the accuracy of predicted concentrations of nitrate and COD. Hu et al. [19] applied a fourth-order derivative to effectively remove deviations in spectral data caused by turbidity particles. Wang et al. [20] introduced OSC to compensate for additional absorption due to turbidity; however, the irreversibility of the spectral arrays in OSC was not discussed. Additionally, linear regression-based partial least squares (PLS) is often employed to construct COD concentration prediction models due to the linear relationship between absorbance and concentration [14,21,22].

With the rises of machine learning and deep learning, researchers have developed correction methods for the automatic compensation for interference and to further improve the accuracy of water quality parameters’ detection. Alavi et al. [23] utilized algorithms such as particle swarm optimization and extreme learning machines to process complex spectra data, identify features related to COD concentration, and establish prediction models for various water samples. Jeong et al. [24] employed neural networks to assess wastewater quality, based on spectral data measured between 200 nm and 400 nm. Zhang et al. [25] proposed a 1D U-Net deep learning approach to eliminate turbidity interference and restore pure absorbance spectra for water quality analyses. However, large datasets are often required for deep learning model training, and processing speeds may not meet the demands of rapid detection.

In this paper, we proposed a correction model for UV-Vis absorption spectra, termed DOSC-PLS, which combines the direct orthogonal signal correction (DOSC) algorithm and partial least squares (PLS) to address turbidity interference in full-spectrum detection. We focused on the water parameter COD and examined the accuracy of predicted COD values before and after correction. In this correction method, DOSC was used to remove information that was orthogonal (unrelated) to the concentration array from the spectral array and to form the correction coefficient. To address the irreversibility issues in the spectral arrays, especially with small sample size, the Moore–Penrose inverse was introduced, enhancing the overall applicability of this method. For an unknown sample, corrected spectra were obtained by multiplying the correction coefficient with the corresponding absorbance. Subsequently, PLS regression was applied to predict the COD concentration using absorbance at selected feature wavelengths. The performance of the DOSC-PLS method was compared with MSC-PLS and DOSC-Back Propagation neural network (DOSC-BP) using new experimental testing samples to verify its effectiveness. Additionally, actual water samples were prepared to further assess its generalization.

2. Materials and Methods

2.1. Measurement Principle

According to the Lambert–Beer law, the absorbance, A, of a solution is proportional to the product of its concentration, c, and the path length, b [26]. This relationship can be expressed as follows:

$$A=\log ({\displaystyle \frac{I_0}{I_t}})=kbc$$

(1)

$${\displaystyle \frac{I_0}{I_t}}=e^{kbc}$$

(2)

where I₀ is the intensity of the incident light, I_t is the intensity of the transmitted light, and k is a proportionality factor related to the wavelength of the incident light, the temperature, and the light-absorbing substance. As the Lambert–Beer law follows the principle of superposition, the absorbance of a mixture is equal to the sum of the absorbances of its individual components. Consequently, the ideal absorbance of a mixture of target substance and turbidity can be described as follows:

$$\begin{array}{ll}{A}_{mix\_ideal}& =\log ({\displaystyle \frac{I_0}{I_t}})\\ & =\log ({\displaystyle \frac{I_0}{I_{t\_tur}}})+\log ({\displaystyle \frac{I_{t\_tur}}{I_t}})\\ & =A_{tur}+A_{sub}\end{array}$$

(3)

In an ideal situation (Figure 1a), we assumed that the incident light was uniformly absorbed by the turbid solution and that the light transmitted though the turbidity, I_{t_tur}, completely served as the incident light for the target substance. However, in actuality, the turbidity effect arises from suspended particles in water that obstruct light propagation. These particles not only absorb light but also scatter it, as shown in Figure 1b, leading to deviations in the acquisition and the processing of spectral signals. This scattering, I_{0_sca}, reduces the amount of light, I_{t_tur}, that reaches the target substance, making it less than expected. The actual incident light reaching the target substance is $I_{t\_tur}^{\prime }$, where $I_{t\_tur}^{\prime }=I_{t\_tur}-I_{0\_sca}$. Therefore, the actual absorbance of the mixture should be updated as follows:

$$\begin{array}{ll}{A}_{mix\_actual}& =\log ({\displaystyle \frac{I_0}{I_{t\_tur}}})+\log ({\displaystyle \frac{I_{t\_tur}^{\prime }}{I_t}})\\ & =\log ({\displaystyle \frac{I_0}{I_{t\_tur}}})+\log ({\displaystyle \frac{I_{t\_tur}-I_{0\_sca}}{I_t}})\\ & <\log ({\displaystyle \frac{I_0}{I_{t\_tur}}})+\log ({\displaystyle \frac{I_{t\_tur}}{I_t}})\end{array}$$

(4)

Based on this, the actual absorbance of a mixture is lower than the sum of the individual absorbances of the turbidity and the target substance. Hence, the interference caused by turbidity on the target substance is a consequence of their combined absorption and scattering properties.

2.2. Sample Preparation and Spectrum Measurement

The NTU (nephelometric turbidity unit) standard (ISO 7027-1984) with formazine is widely used to measure water turbidity due to its optical stability and homogeneous particle size. In this study, a series of turbidity solutions was prepared by diluting a 400 NTU standard formazine solution (purchased from Shanghai Macklin Biochemical Technology Co., Ltd, Shanghai 201206, China) with ultrapure water. Additionally, the COD standard solution was obtained by dissolving potassium hydrogen phthalate in deionized water. Then, a series of secondary COD standard solutions were prepared by diluting a 100 mg/L COD standard solution to concentrations ranging from 5 mg/L to 50 mg/L.

The standard turbidity and standard COD solutions were then sequentially mixed to obtain 70 different solutions with known turbidity and COD concentrations. These solutions were used as the training set to develop the correction method, while the remaining samples were reserved for testing. Detailed information about the mixed samples is listed in

Table 1. Mixed samples used for training and testing the correction method.

Samples	COD (mg/L)	Turbidity (NTU)
1~7	5	0, 5, 10, 20, 30, 40, 50
8~14	10
15~21	15
22~28	20
29~35	25
36~42	30
43~49	35
50~56	40
57~63	45
64~70	50

.

The UV-Vis absorption spectra of all the samples were measured using a UV spectrophotometer (AGILENT Cary 100, Santa Clara, CA, USA). The absorption wavelengths were scanned from 220 nm to 600 nm at intervals of 1 nm (with a bandwidth of 2 nm). To minimize the impact of machine noise, each sample was measured three times in parallel, and the averages of these measurements were recorded as the final spectral data for further processing using MATLAB.

2.3. The Method for Turbidity Correction Based on DOSC-PLS

The direct orthogonal signal correction (DOSC) method, derived from the orthogonal signal correction (OSC) algorithm, was employed to mitigate the interference caused by turbidity. OSC is widely used as a pre-treatment for NIR spectra; its core principle involves orthogonalizing the spectrum’s array X and the concentration’s array Y, thereby eliminating concentration-independent information from X [27,28]. Turbidity is irrelevant to the dissolved-target-substance concentrations in UV-vis absorption spectra; thus, this method can be used to effectively eliminate the turbidity’s interference.

However, the OSC method has limitations, as it ignores measurement errors in Y and requires strict orthogonality for the OSC components in X. This constraint can result in incomplete orthogonality or cause the final OSC component to fall outside the X-space. To address these problems, DOSC was developed [29], which uses only least squares steps, consistently identifying components that are orthogonal to Y while capturing the largest variation in X. DOSC avoids the need for component selection by iteratively removing irrelevant parts, thus reducing the model’s complexity and enhancing its robustness and predictive ability. In this study, we employed DOSC to correct turbidity interference. The main steps of the method are as follows:

Given the training set, the absorption spectra matrix is marked as X_train (I × J), and the concentration matrix is marked as Y_train (J × K), where I is the number of spectral points, J is the number of samples, and K is the number of DOSC components to be subtracted. First, the projection of Y_train onto the space of X_train is calculated using the as following equation:

$$M=X_{train}^{{\rm T}}{(X_{train}^{+})}^{{\rm T}}{Y}_{train}$$

(5)

Considering that X_train is a singular matrix (I > J), its Moore–Penrose inverse is computed, denoted as $X_{train}^{+}$. The projection of X_train onto the orthogonal complementary space of Y_train is represented as Z, expressed as follows:

$$Z=X_{train}^{{\rm T}}-M{M}^{+}{X}_{train}^{{\rm T}}$$

(6)

A principal component analysis (PCA) or singular value decomposition (SVD) is then applied to $Z{Z}^{{\rm T}}$ to extract the first n principal components of T (corresponding to the number of DOSC components to be subtracted). T serves as a basis for the low-dimensional subspace that captures the maximum variance of $Z{Z}^{{\rm T}}$, which is the part of X_train unrelated to Y_train.

The DOSC-corrected spectra, X_DOSC, of the calibration data, X, can be written as:

$$X_{DOSC}={(X-T{P}^{{\rm T}})}^{{\rm T}}$$

(7)

$$P=X_{train}T{(T^{{\rm T}}T)}^{-1}$$

(8)

where P is the loadings matrix and $T{P}^{{\rm T}}$ is the orthogonal part removed from the original spectra X. The new vectors, T, can be expressed as linear combinations of X:

$$T=X^{{\rm T}}R$$

(9)

where R is the weights matrix of the original spectra in the principal orthogonal directions, which can be obtained as follows:

$$R={(X^{{\rm T}})}^{+}T$$

(10)

After getting the weights, R, and the loadings, P, the correction coefficient is obtained and the corrected spectra for the new data, X_new, can be directly computed as follows:

$$X_{new\_DOSC}={(X_{new}(1-R{P}^{{\rm T}}))}^{{\rm T}}$$

(11)

After correction, the PLS regression algorithm is used to model the relationship between the corrected spectra and concentrations of target substance. In the PLS algorithm, PCA decomposition is simultaneously applied to both the spectral matrix X_DOSC and concentration matrix Y, extracting new variables, F and G, that effectively summarize the original data [30]. A linear regression relationship is then established between F and G, and regression coefficients are calculated to predict the concentrations for the unknown samples.

The selection of the number of principal components in PLS is crucial for the model’s predictive ability. Too few components may fail to capture the characteristics of the data, while too many can lead to overfitting. Therefore, the leave-one-out cross-validation method is employed to determine the optimal number of principal components. By calculating the sum of the squared prediction errors (PRESS) and the root mean square error of the cross-validation (RMSECV), we effectively determine the optimal number of PLS components. The expression of PRESS and RMSECV are as follows,

$$PRESS={\displaystyle \sum _{i=1}^N{(y_i-{\widehat{y}}_i)}^2}$$

(12)

$$RMSECV=\sqrt{{\displaystyle \frac{PRES{S}_k}{N}}}$$

(13)

where N is the number of samples, k is the number of components, y_i is the true value for sample i, and ${\widehat{y}}_i$ is the model-predicted value of sample i. A lower RMSECV value indicates more accurate prediction results.

Overall, the DOSC-PLS model process consists of two parts: training and testing, as illustrated in Figure 2. During the training phase, the training set is processed through the DOSC method to calculate two key parameters: the weights, R, and the loadings, P, which are used to obtain the correction coefficient. After the spectra have been corrected for turbidity, a PLS regression model is established to predict concentration. This is done by constructing the PLS regression function, based on the relationship between the turbidity-corrected spectra and the actual concentrations in the training data. In the testing phase, the previously calculated weights, R, and loadings, P, were applied to the new spectral data to calculate the turbidity-corrected spectra, according to function 11. These corrected spectra are then sent into the PLS regression function, developed during the training phase, to predict the concentration of the unknown samples.

3. Results

3.1. Spectral Characteristics of Turbidity

Turbidity in water reflects the optical features of light scattering, with the formazine particle sizes generally following a normal distribution, centered at 1.2 μm. As a result, most formazine particles conform to the Mie scattering theory. As shown in Figure 3a, the loss of the light intensity increases with rising turbidity. To compensate for the light attenuation during transmission, the turbidity level is typically measured. Given that the characteristic region of organic matter lies within the ultraviolet band, the turbidity detection method entails the establishment of a linear regression between the absorbance values in the visible light range and the corresponding turbidity values.

To correct for turbidity interference, normalizing the spectral curve is essential. The absorption spectrum of turbidity can be derived by multiplying the normalized spectrum by the specific turbidity level, which enables subtracting the turbidity component from the mixed spectra. The normalized spectrum is obtained by dividing each individual absorption spectrum by its corresponding turbidity level, and subsequently averaging the results. As shown in Figure 3b, the normalized spectral curves closely overlap. For the samples requiring correction, the turbidity level was measured first, and then the absorption spectrum of the turbidity was calculated by multiplying the turbidity value by the normalized spectra. These steps form the basis for the direct subtraction method.

3.2. Influence of Turbidity on COD Measurement

Figure 4a presents the absorption spectra of a series of standard COD solutions, with peaks appearing consistently around 280 nm. A strong linear relationship was observed between the absorbance at 280 nm and the varying COD concentration, with the R² being over 0.999 (Figure 4b). However, after adding the standard turbidity solutions, a blue shift occurred, causing the peaks of solutions with standard COD to move toward shorter wavelengths as the turbidity increased. For example, the spectra of a mixture with a COD concentration of 40 mg/L are shown in Figure 4c, clearly highlighting this shift.

We further compared the absorbance of the peak at 280 nm across different concentrations (Figure 4d). The total absorbance generally increased uniformly with turbidity. Furthermore, we applied the direct subtraction method, described in Section 3.1, to remove the turbidity absorbance from the mixed solution. The blue shift became more pronounced with the increase of turbidity, as shown in Figure 4e. Additionally, the absorbance at 280 nm was found to decrease in comparison to the COD standard solutions without turbidity, and this reduction became more pronounced at higher concentrations, as illustrated in Figure 4f. This demonstrates that simply subtracting the turbidity spectra from the mixture is ineffective for correction, aligning with the conclusion in Equation (4).

3.3. Turbidity Correction Results Based on DOSC-PLS

The experimental data in Table 1 were divided into training and testing sets for evaluating the performance of the DOSC-PLS model. The training set consisted of 42 mixed samples with turbidity concentrations of 0 NTU, 5 NTU, 10 NTU, 20 NTU, 30 NTU, 40 NTU, and 50 NTU and COD concentrations of 5 mg/L, 10 mg/L, 20 mg/L, 30 mg/L, 40 mg/L, and 50 mg/L. This set was used to construct the turbidity correction method, based on the DOSC algorithm, and to establish the COD concentration prediction model using PLS. The testing set comprised 28 samples with turbidity concentrations identical to the training set and COD concentrations of 15 mg/L, 25 mg/L, 35 mg/L, and 45 mg/L, designed to evaluate the turbidity correction effects on untrained spectra.

First, we used the training set to determine the correction parameters in the DOSC method. We constructed the spectra array X(I × J) and the concentration array Y(J × K), where I represents the spectral range from 220 nm to 600 nm at 1 nm intervals (totally 381), J is 42 (the number of samples), and K is 1. Considering turbidity interference and the presence of additional ultrapure water solvents in the mixed solutions, the number of components, n, was set to 2 in the DOSC. This allowed for the extraction of the first two score matrices, T, requiring orthogonal treatment. The weight matrix, R, was subsequently calculated by regression, enabling the calculation of a new score matrix, T. Following this, the loading matrix, P, was calculated. With these matrices, the correction coefficient was obtained and the corrected spectra, X_DOSC, were further calculated.

The corrected absorption spectra of the training set are shown in Figure 5a. Regardless of the COD concentration, the spectra affected by varying levels of turbidity interferences were effectively corrected, aligning with the undisturbed spectra (0 NTU turbidity). Considering that the features of the turbidity-corrected absorption spectra were concentrated in the range of 230 nm to 290 nm, we further selected 230 nm, 235 nm, 240 nm, 245 nm, 250 nm, 255 nm, 260 nm, 265 nm, 270 nm, 275 nm, 280 nm, 285 nm, and 290 nm to construct the discrete spectra (Figure 5b). It is clear that the peaks of these corrected spectra at all the COD concentrations were realigned around 280 nm, effectively addressing the blue shift issue.

The COD prediction model was further constructed using the corrected spectra, based on PLS. To reduce the computational complexity, the discrete spectra were set as independent variables, while the actual COD concentrations were set as dependent variables. The principal components of the independent variables, obtained by cross-validation, were set to two in the PLS model. By integrating the DOSC and PLS, the DOSC-PLS method was established.

To validate the real performance of the DOSC-PLS model, the testing set was employed. The corrected absorption spectra for the testing samples are illustrated in Figure 6a, demonstrating that even untrained data can be effectively corrected for turbidity interference. The absorption spectra were restored to their original characteristics, facilitating accurate COD concentration measurements.

The PLS regression model was then used to predict the concentrations of the turbidity-corrected samples. For samples without correction, the COD value was predicted using the PLS calibration model, established with the standard COD solutions. The COD prediction results, both without turbidity correction and after applying the DOSC method, are shown in Figure 6b. Without correction, the values of R² and the root mean square error (RMSE) were 0.47768 and 12.7257, respectively. After correction, they improved to 0.9991 and 0.43698. These results indicate that the DOSC effectively enhances turbidity correction, restoring spectral shapes and improving the accuracy of the COD measurements. Moreover, even the untrained spectral data yielded satisfying corrected results and prediction accuracy, demonstrating the strong generalization ability of this model, which contributes to enhance COD measurement precision.

3.4. Comparison of Different Turbidity Correction Methods

To validate the effectiveness of the DOSC-PLS method for compensating COD measurements on new samples, we prepared 40 new mixed samples with turbidity concentrations of 15 NTU, 25 NTU, 35 NTU, and 45 NTU and COD concentrations of 5 mg/L, 10 mg/L, 15 mg/L, 20 mg/L, 25 mg/L, 30 mg/L, 35 mg/L, 40 mg/L, and 45 mg/L. The results were compared against those obtained without turbidity correction, as well as those corrected using the MSC-PLS and DOSC-PLS models. Additionally, a BP neural network was applied to predict the COD concentration combined with the DOSC.

As shown in Figure 7a, the MSC method largely improved the blue shift caused by turbidity scattering. However, deviations still existed when compared to the standard spectrum of 0 NTU, particularly in the range of 250–350 nm. In Figure 7b, the spectra corrected by the DOSC closely approximated the standard spectrum of 0 NTU, effectively eliminating both the blue shift and the peak height reduction caused by turbid substances.

In Figure 8a, the predicted COD values obtained using different methods are compared. The turbidity compensation algorithms significantly improved the measurement accuracy. Among them, the predicted concentrations of methods from both the DOSC-PLS and the DOSC-BP methods aligned well with the actual concentrations. However, the MSC-PLS results showed noticeable deviations, particularly at lower concentrations. We further compared the results of DOSC-PLS and DOSC-BP individually. The fitting curves demonstrate that both methods exhibit a strong linear relationship with the actual concentrations, with an R² of over 0.99 (Figure 8b,c), emphasizing the significance of the correction and the efficiency of the DOSC.

The corresponding R² and root mean square error (RMSE) values for all of the methods were calculated, as shown in

Table 2. Comparison of results using different spectral processing methods.

Methods	R2	RMSE
Without correction	0.5455	12.3604
MSC-PLS	0.9994	3.2771
DOSC-PLS	0.9997	0.2295
DOSC-BP	0.9970	0.8639

. The MSC-PLS method showed good consistency with the actual concentrations, achieving an R² of 0.9994. Also, the RMSE decreased from 12.3604 to 3.2771. Nevertheless, the RMSE remained higher than those of the DOSC-PLS and the DOSC-BP, which were 0.2295 and 0.8639, respectively. Although the DOSC-BP performed well, discrepancies still existed at low concentrations, particularly at 5 mg/L (Figure 8c). Furthermore, compared to the BP prediction model, the PLS model was less dependent on large training sets and performed effectively, even with smaller sample sizes, making it easier to apply to diverse water bodies for rapid predictions.

3.5. Experiments of Actual Water Samples

We verified the accuracy of COD measurements using the DOSC-PLS with experimental water samples. In this section, we further validate the accuracy of the DOSC-PLS combined with UV-Vis spectroscopy by measuring actual wastewater samples. These samples were provided by a printing factory and comprised two types: untreated and treated samples. The untreated samples represent raw wastewater directly collected, while the treated samples were collected after undergoing the standard sewage treatment protocol in the factory, which primarily includes coagulation, sedimentation, and filtration.

The initial samples were diluted with deionized water and a total of 13 samples were obtained. The actual COD values of the wastewater samples were determined in the laboratory using the standard potassium dichromate method (GB11914-89) [31]. The turbidity levels were measured using a portable turbidimeter (Hach 2100Q). The actual COD values and turbidity levels of the samples are listed in

Table 3. The actual COD values and turbidity levels of the wastewater samples, before and after treatment.

Sample	Type	COD (mg/L)	Turbidity
1	Untreated	347.3	98.95
2		277.8	79.16
3		231.5	65.97
4		173.6	49.48
5		138.9	39.58
6		86.81	24.74
7		57.88	12.37
8		23.15	7.916
9	Treated	45.7	4.45
10		30.47	2.967
11		22.85	2.225
12		15.23	1.483
13		11.43	0.7417

.

The full absorption spectra of all the samples were measured using a UV-vis spectrometer across the same range of wavelengths (220–600 nm). The DOSC was then applied for spectral correction and the PLS was used to calculate the COD values. The fitting result between the actual COD values obtained by the potassium dichromate method and the COD values obtained by the DOSC-PLS methodology is shown in Figure 9. The overall R² exceeded 0.9, and the RMSE was 35.61. The values obtained using the DOSC-PLS methodology did not align well with those obtained by classical chemical methodology in the untreated samples, particularly at higher COD concentrations (above ~50 mg/L). This discrepancy may result from high levels of turbidity and the presence of numerous organic compounds. The untreated samples contain suspended particles with complex compositions and diverse particle size distributions, which reduces the effectiveness of the turbidity compensation method.

In contrast, for the samples obtained after sewage treatment, during which, large suspended particles are filtrated, the composition of turbidity particles becomes simpler, and turbidity levels decrease to below 5 NTU. Under these conditions, the predicted values matched well with the actual values, where the R² reached 0.9998 and the RMSE was 2.0946.

In general, the testing results verified the high precision and robustness of our proposed methods, emphasizing their potential for consistent and reliable online COD monitoring. However, it should be noted that the correction coefficient obtained in this study was based on the prepared water samples using COD and turbidity chemical standard solutions. These solutions may not fully represent the diverse chemical and physical properties of dissolved organic matter and suspended particles in actual water. As a result, the methodology was not effective for testing untreated wastewater samples with high levels of COD and turbidity. However, it demonstrates a high precision in testing sewage-treated water samples with comparatively lower turbidity, where the predicted COD values align well with those obtained by the standard chemical method. This highlights its advantage in enabling the rapid and accurate monitoring of the COD values in treated wastewater.

Furthermore, since the spectra of water samples from different sources can vary, to enhance the effectiveness of this method across various water bodies, local calibrations should be performed to construct the turbidity correction model based on local water samples, rather than relying on a uniform correction coefficient.

4. Conclusions

In this study, we proposed the direct orthogonal signal correction combined with partial least squares (DOSC-PLS) method to correct turbidity interference in UV-vis spectra, significantly increasing the accuracy of COD prediction. The introduction of the concentration array in the DOSC algorithm preserved more COD-related information, while the analysis of full-spectra features allowed the selection of a discrete spectrum with 13 wavelengths. This method required only a small dataset for training to determine the correction coefficient, making it both efficient and practical. A major advantage of the DOSC-PLS method is its simplicity and generalization, making it adaptable across various aquatic environments. Unlike traditional methods, it eliminates the need to measure turbidity levels or establish standard curves when predicting unknown samples, reducing potential calculation errors. Our results showed that the DOSC-PLS significantly improved COD prediction, with the R² value increasing from 0.5455 to 0.9997 and the RMSE decreasing from 12.3604 to 0.2295 after turbidity correction. When testing wastewater samples, the DOSC-PLS methodology exhibited limitations in handling samples with high COD and turbidity levels. However, it was demonstrated to be effective for sewage-treated samples, particularly when the COD and the turbidity levels were lower than 50 mg/L and 5 NTU, respectively. Under these conditions, the predicted COD values aligned well with those obtained through the classical chemical methodology, highlighting its potential for practical applications in monitoring treated wastewater.

In summary, this study focused on the correction of UV-Vis spectra to account for turbidity, not only enhancing the accuracy of COD measuring but also extending its application to various spectrophotometric tasks. The application of this correction method can enhance the precision of the detection of different water parameters. However, it is necessary to adjust the characteristic wavelengths in accordance with the specific substance under investigation.