Regional lake and reservoir water quality uncertainty simulation method based on Bayesian transfer learning

Abstract

The present invention discloses a method for simulating the uncertainty of regional lake and reservoir water quality based on Bayesian transfer learning, which includes the following steps: S1, collecting automatic water quality monitoring data of multiple lakes and reservoirs in the region, and preprocessing the monitoring data; S2, numbering multiple lakes and reservoirs respectively, dividing the lakes and reservoirs into target domains and source domains, and selecting water quality indicators to be simulated as target indicators; S3, using a Bayesian additive regression tree to construct a target indicator simulation model in the source domain, and adopting a cross-validation strategy to train the model; S4, using the data of the target domain to update the parameters of the target indicator simulation model in the source domain, constructing a Bayesian transfer model of the target domain target indicator, and performing uncertainty simulation of the target domain water quality target indicator; S5, according to the output results of the Bayesian transfer model, identifying the key factors affecting the mean and uncertainty of the target domain water quality target indicator, and analyzing the driving mechanism of the key factors on the fluctuation of the target domain water quality indicator.

Description

Technical Field

[0001] The present invention belongs to the technical field of water quality monitoring and water body management, and specifically relates to a method for simulating regional lake and reservoir water quality uncertainty based on Bayesian transfer learning. Background Art

[0002] With the rapid development of industrialization and urbanization, the water quality of lakes and reservoirs is receiving increasing attention. The accuracy and completeness of water quality monitoring data are crucial for water quality assessment and management, as these data form the foundation for developing scientific and rational remediation measures. However, water quality monitoring data is often affected by factors such as instrument failure and environmental interference, resulting in missing or anomalies. In such cases, transfer learning can be an effective solution. Through transfer learning, existing relevant domain knowledge can be leveraged to fill in the gaps in the data, thereby improving the model's generalization and prediction accuracy.

[0003] Furthermore, the simulation and prediction of lake and reservoir water quality indicators often require considering the combined impact of multiple related factors, but traditional methods often struggle to effectively handle the uncertainty and complexity of the data. To address this challenge, it is necessary to develop a method that can quantify model uncertainty. By quantifying uncertainty, we can more accurately assess the reliability of model predictions and provide more scientific decision-making support for water quality management. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a regional lake and reservoir water quality uncertainty simulation method based on Bayesian transfer learning. This method combines transfer learning and uncertainty quantification methods, which can not only effectively deal with the problem of missing data, but also realize accurate simulation and uncertainty analysis of lake and reservoir water quality indicators, and identify key factors affecting water quality. It can improve the accuracy and reliability of water quality simulation and prediction, thereby providing strong support for the sustainable management of lake and reservoir water quality.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] The regional lake and reservoir water quality uncertainty simulation method based on Bayesian transfer learning includes the following steps:

[0007] S1. Collect automatic water quality monitoring data from multiple lakes and reservoirs in the region and pre-process the monitoring data;

[0008] S2. Number multiple lakes and reservoirs respectively, divide them into target domains and source domains, and select water quality indicators to be simulated as target indicators;

[0009] S3. Use Bayesian additive regression tree to build a target indicator simulation model in the source domain and use cross-validation strategy to train the model;

[0010] S4. Select variable parameters of the target indicator simulation model in the source domain, use the data of the target domain to update the parameters of the target indicator simulation model in the source domain, construct a Bayesian migration model of the target indicator in the target domain, and perform uncertainty simulation of the water quality target indicator in the target domain;

[0011] S5. Based on the output results of the Bayesian migration model, the mean and confidence interval of the predicted value are given, the key factors affecting the mean and uncertainty of the target water quality indicators in the target domain are identified, and the driving mechanism of the key factors on the fluctuation of the target water quality indicators is analyzed.

[0012] Preferably, the monitoring data in step S1 include water temperature, pH, dissolved oxygen, ammonia nitrogen, and total nitrogen, total phosphorus and chlorophyll a concentrations.

[0013] Preferably, the specific process of step S1 is:

[0014] S11. Collect automatic water quality monitoring data from multiple lakes and reservoirs in the region to obtain time series data for each monitoring indicator; then use the STL method to decompose the time series data into long-term trend terms, seasonal cycle terms, and residual terms;

[0015] S12. For the residual items obtained by decomposition, the generalized extreme studentized residual method is used to perform outlier test, identify abnormal data, and mark the abnormal data as missing values;

[0016] S13. Use the Kalman filter method to fill in the missing values. By continuously fusing the measured values ​​and state estimates, the accuracy of the state estimation is gradually improved to complete the missing value filling.

[0017] Preferably, in step S13, the Kalman filtering method includes establishing a state space model to describe the concentration change process, setting the covariance matrix of process noise and observation noise, and realizing dynamic interpolation of missing values ​​through a prediction-update cycle.

[0018] Preferably, the specific process of step S2 is:

[0019] S21. Assign unique numbers from 1 to N to each lake in the region, use some of the lakes as target domains for individual water quality simulations, and use the remaining lakes as source domains for the source datasets used for model training.

[0020] S22. Select the water quality indicators to be simulated and ensure that the selected water quality indicators are recorded in the monitoring data of all lakes and reservoirs.

[0021] Preferably, the specific process of step S3 is:

[0022] S31. Using the data from source lakes and reservoirs, construct a simulated data set of target indicators, where the target indicator serves as the response variable and other water quality indicators serve as predictor variables.

[0023] S32. Using a Bayesian additive regression tree to construct a target indicator simulation model for predicting the target indicator; wherein the Bayesian additive regression tree can capture complex nonlinear relationships and provide stable prediction results by constructing a Bayesian model of multiple additive regression trees;

[0024] The specific process of step S32 is:

[0025] S321. The mathematical form of the target indicator simulation model is: ,in, The target indicator for prediction; For the The index of the regression tree; is the number of regression trees; are the characteristics or explanatory variables used to predict the target indicator; For the The prediction function of a binary regression tree; is the error term, which represents the difference between the model prediction value and the actual observation value; Represents the error term The mean is 0 and the variance is Normal distribution; is the standard deviation of the error term, which is used to measure the degree of dispersion between the model prediction value and the actual observation value;

[0026] S322. Each tree contains internal node splitting rules and leaf node parameters , each tree is made a weak learner by regularizing the prior constraint: ,in, To control the tree depth The probability that a node becomes a terminal node when ; To control the tree depth; and Both control tree depth Hyperparameters of

[0027] S323, Bayesian additive regression tree uses Markov chain Monte Carlo for posterior inference, which is used to iteratively update each tree while performing conditional updates based on other trees and allowing samples to be generated from the posterior distribution; regression function In a specific The posterior mean at the value is estimated by averaging all Markov Chain Monte Carlo samples and is calculated as: ,in, is the regression function In a specific The posterior mean estimate at the value; is the total number of Markov Chain Monte Carlo samples; For the The index of the Markov Chain Monte Carlo samples; For the Markov chain Monte Carlo samples in The value of the additive tree model evaluated at the value;

[0028] S324, regression function The confidence interval for is constructed from the quantiles of the posterior sample and is calculated as: ,in, is the regression function In a specific Confidence interval at the value; Indicates interval; is the regression function The quantile function of the posterior sample;

[0029] S33. K-fold cross validation is used to train and evaluate the Bayesian additive regression tree to improve the generalization ability of the target indicator simulation model.

[0030] Preferably, in step S33, the K-fold cross-validation includes dividing the source domain data into K parts, of which K-1 parts are used for training and the remaining 1 part is used for validation, and the cycle is repeated for K rounds, and the prediction error of the target indicator simulation model on different data subsets is calculated to improve the prediction stability and reliability of the target indicator simulation model for unseen data.

[0031] Preferably, the specific process of step S4 is:

[0032] S41. Analyze the target indicator simulation model constructed in the source domain and determine variable parameters; wherein the variable parameters include the depth of the decision tree and the node splitting rule;

[0033] S42. Using the data of the target domain, the variable parameters of the target indicator simulation model in the selected source domain are adjusted and optimized by a Bayesian inference method, so that the target indicator simulation model in the source domain can adapt to the actual situation of the target domain;

[0034] S43. After the parameters are updated, a Bayesian migration model suitable for the target domain is obtained; wherein the Bayesian migration model integrates the prior knowledge of the target indicator simulation model in the source domain and the data information of the target domain.

[0035] Preferably, the specific process of step S5 is:

[0036] S51. Calculate the predicted mean and confidence interval of the target water quality indicator in the target area based on the output results of the Bayesian migration model;

[0037] S52. Use the feature importance index output by the Bayesian migration model to identify the variables that have the greatest impact on the mean and uncertainty of the target water quality indicators in the target domain, and select the variables with the greatest impact on uncertainty as key factors;

[0038] S53. For the selected key factors, quantify the response relationship between the key factors and the target indicators, and analyze the driving mechanism of the fluctuation of the target water quality indicators in the target domain.

[0039] Preferably, the specific process of step S52 is:

[0040] S521. Calculate the initial root mean square error of the Bayesian migration model on the original test set, and use the initial root mean square error as a benchmark indicator;

[0041] S522. Randomly disrupt the value of each feature, use the disturbed data to re-predict and calculate the disturbance root mean square error, and use the disturbance root mean square error as the post-disturbance indicator;

[0042] S523. Use the difference between the baseline index and the perturbation index to measure the importance of the feature. The larger the difference, the more critical the feature is to the model prediction.

[0043] After adopting the above technical solution, the present invention has the following beneficial effects: the present invention combines transfer learning and uncertainty quantification methods to not only effectively deal with the problem of missing data, but also achieve accurate simulation and uncertainty analysis of lake and reservoir water quality indicators, and identify key factors affecting water quality, which can improve the accuracy and reliability of water quality simulation and prediction, thereby providing strong support for the sustainable management of lake and reservoir water quality. Specifically, the regional lake and reservoir water quality uncertainty simulation method based on Bayesian transfer learning of the present invention is direct and easy to use. In the data preprocessing stage, through time series decomposition, outlier identification and missing value interpolation, it effectively solves data quality problems, reduces the interference of abnormal data on model construction and accuracy assessment, and ensures data integrity and reliability. In terms of model construction, the Bayesian additive regression tree (BART) combined with a cross-validation strategy can accurately capture the complex nonlinear relationships of water quality indicators and provide stable prediction results, which are significantly better than traditional statistical models and empirical methods. The introduction of Bayesian transfer learning realizes knowledge transfer and model optimization across lakes and reservoirs, breaks through the traditional method's reliance on a single data set, and improves the model's generalization ability and adaptability. Furthermore, this method can identify key factors and analyze their driving mechanisms, providing a scientific basis for water quality management. Therefore, this invention has significant advantages in quantifying the commonalities and differences among regional lakes and reservoirs. It can accurately and scientifically simulate water quality uncertainty, providing solid theoretical and technical support for regional lake and reservoir water environment management and regulation, and has important theoretical significance and broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0046] like Figure 1 As shown in Figure 1, the regional lake water quality uncertainty simulation method based on Bayesian transfer learning includes the following steps:

[0047] S1. Collect automatic water quality monitoring data from multiple lakes and reservoirs in the region and pre-process the monitoring data;

[0048] The monitoring data in step S1 include water temperature, pH, dissolved oxygen, ammonia nitrogen, and total nitrogen, total phosphorus and chlorophyll a concentration;

[0049] The specific process of step S1 is:

[0050] S11. Collect automatic water quality monitoring data from multiple lakes and reservoirs in the region to obtain time series data for each monitoring indicator; then use the STL method to decompose the time series data into long-term trend terms, seasonal cycle terms, and residual terms;

[0051] S12. For the residual items obtained by decomposition, the generalized extreme studentized residual method is used to perform outlier test, identify abnormal data, and mark the abnormal data as missing values;

[0052] S13. Use Kalman filtering to fill missing values. By continuously fusing measurement values ​​and state estimates, the accuracy of state estimates is gradually improved to complete the missing value filling.

[0053] In step S13, the Kalman filter method includes establishing a state space model to describe the concentration change process, setting the covariance matrix of process noise and observation noise, and realizing dynamic interpolation of missing values ​​through a prediction-update cycle;

[0054] S2. Number multiple lakes and reservoirs respectively, divide them into target domains and source domains, and select water quality indicators to be simulated as target indicators;

[0055] The specific process of step S2 is:

[0056] S21. Assign unique numbers from 1 to N to each lake in the region, use some of the lakes as target domains for individual water quality simulations, and use the remaining lakes as source domains for the source datasets used for model training.

[0057] S22. Select the water quality indicators to be simulated and ensure that the selected water quality indicators are recorded in the monitoring data of all lakes and reservoirs;

[0058] S3. Use Bayesian additive regression tree to build a target indicator simulation model in the source domain and use cross-validation strategy to train the model;

[0059] The specific process of step S3 is:

[0060] S31. Using the data from source lakes and reservoirs, construct a simulated data set of target indicators, where the target indicator serves as the response variable and other water quality indicators serve as predictor variables.

[0061] S32. Using a Bayesian additive regression tree to construct a target indicator simulation model for predicting the target indicator; wherein the Bayesian additive regression tree can capture complex nonlinear relationships and provide stable prediction results by constructing a Bayesian model of multiple additive regression trees;

[0062] The specific process of step S32 is:

[0063] S321. The mathematical form of the target indicator simulation model is: ,in, The target indicator for prediction; For the The index of the regression tree; is the number of regression trees; are the characteristics or explanatory variables used to predict the target indicator; For the The prediction function of a binary regression tree is constructed as follows: for each tree, a binary decision tree is constructed by fitting it on the training data set, specifically selecting feature dimensions and their partitioning thresholds as the splitting rules for internal nodes, and fitting the local target value at each leaf node. is the error term, which represents the difference between the model prediction value and the actual observation value; Represents the error term The mean is 0 and the variance is Normal distribution; is the standard deviation of the error term, which is used to measure the degree of dispersion between the model prediction value and the actual observation value;

[0064] S322. Each tree contains internal node splitting rules and leaf node parameters , each tree is made a weak learner by regularizing the prior constraint: ,in, To control the tree depth The probability that a node becomes a terminal node when ; To control the tree depth; and Both control tree depth Hyperparameters of

[0065] S323, Bayesian additive regression tree uses Markov chain Monte Carlo for posterior inference, which is used to iteratively update each tree while performing conditional updates based on other trees and allowing samples to be generated from the posterior distribution; regression function In a specific The posterior mean at the value is estimated by averaging all Markov Chain Monte Carlo samples and is calculated as: ,in, is the regression function In a specific The posterior mean estimate at the value ; is the total number of Markov Chain Monte Carlo samples; For the The index of the Markov Chain Monte Carlo samples; For the Markov chain Monte Carlo samples in The value of the additive tree model evaluated at the value; wherein the specific process of obtaining the value of the additive tree model is: The value is input into each tree of the sample, and reaches the leaf node along the split path. The leaf node value is taken, and the output values ​​of all trees are summed up to obtain the overall prediction value under this iteration, which is the value of the additive tree model.

[0066] S324, regression function The confidence interval for is constructed from the quantiles of the posterior sample and is calculated as: ,in, is the regression function In a specific Confidence interval at the value; Indicates interval; is the regression function The quantile function of the posterior sample;

[0067] S33. K-fold cross validation is used to train and evaluate the Bayesian additive regression tree to improve the generalization ability of the target indicator simulation model;

[0068] In step S33, the K-fold cross-validation includes dividing the source domain data into K parts, of which K-1 parts are used for training and the remaining part is used for validation, and repeating K rounds, and calculating the prediction error of the target indicator simulation model on different data subsets to improve the prediction stability and reliability of the target indicator simulation model for unseen data;

[0069] S4. Select variable parameters of the target indicator simulation model in the source domain, use the data of the target domain to update the parameters of the target indicator simulation model in the source domain, construct a Bayesian migration model of the target indicator in the target domain, and perform uncertainty simulation of the water quality target indicator in the target domain;

[0070] The specific process of step S4 is:

[0071] S41. Analyze the target indicator simulation model constructed in the source domain and determine variable parameters; wherein the variable parameters include the depth of the decision tree and the node splitting rule;

[0072] S42. Using the data of the target domain, the variable parameters of the target indicator simulation model in the selected source domain are adjusted and optimized by a Bayesian inference method, so that the target indicator simulation model in the source domain can adapt to the actual situation of the target domain;

[0073] S43. After the parameters are updated, a Bayesian transfer model suitable for the target domain is obtained; wherein the Bayesian transfer model integrates the prior knowledge of the target indicator simulation model in the source domain and the data information of the target domain;

[0074] S5. Based on the output of the Bayesian migration model, provide the mean and confidence interval of the predicted value, identify the key factors that affect the mean and uncertainty of the target water quality indicators in the target area, and analyze the driving mechanism of the key factors on the fluctuation of the target water quality indicators;

[0075] The specific process of step S5 is:

[0076] S51. Calculate the predicted mean and confidence interval of the target water quality indicator in the target area based on the output results of the Bayesian migration model;

[0077] S52. Use the feature importance index output by the Bayesian migration model to identify the variables that have the greatest impact on the mean and uncertainty of the target water quality indicators in the target domain, and select the variables with the greatest impact on uncertainty as key factors;

[0078] The specific process of step S52 is:

[0079] S521. Calculate the initial root mean square error of the Bayesian migration model on the original test set, and use the initial root mean square error as a benchmark indicator;

[0080] S522. Randomly disrupt the value of each feature, use the disturbed data to re-predict and calculate the disturbance root mean square error, and use the disturbance root mean square error as the post-disturbance indicator;

[0081] S523. Use the difference between the baseline index and the perturbed index to measure the feature importance. The larger the difference, the more critical the feature is to the model prediction.

[0082] S53. For the selected key factors, quantify the response relationship between the key factors and the target indicators, and analyze the driving mechanism of the fluctuation of the target water quality indicators in the target domain.

[0083] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A regional lake and reservoir water quality uncertainty simulation method based on Bayesian transfer learning, characterized by: The following steps are involved: S1. Collect automatic water quality monitoring data from multiple lakes and reservoirs in the region and pre-process the monitoring data; S2. Number multiple lakes and reservoirs respectively, divide them into target domains and source domains, and select water quality indicators to be simulated as target indicators; S3. Use Bayesian additive regression tree to build a target indicator simulation model in the source domain and use cross-validation strategy to train the model; Step S3 includes: The Bayesian additive regression tree uses Markov chain Monte Carlo for posterior inference, which is used to iteratively update each tree while performing conditional updates based on other trees and allowing samples to be generated from the posterior distribution; regression function In a specific The posterior mean at the value is estimated by averaging all Markov Chain Monte Carlo samples and is calculated as: ,in, is the regression function In a specific The posterior mean estimate at the value; is the total number of Markov Chain Monte Carlo samples; For the The index of the Markov Chain Monte Carlo samples; For the Markov chain Monte Carlo samples in The value of the additive tree model evaluated at the value; Regression function The confidence interval for is constructed from the quantiles of the posterior sample and is calculated as: ,in, is the regression function In a specific Confidence interval at the value; Indicates interval; is the regression function The quantile function of the posterior sample; S4. Select variable parameters of the target indicator simulation model in the source domain, use the data of the target domain to update the parameters of the target indicator simulation model in the source domain, construct a Bayesian migration model of the target indicator in the target domain, and perform uncertainty simulation of the water quality target indicator in the target domain; S5. Based on the output of the Bayesian migration model, provide the mean and confidence interval of the predicted value, identify the key factors that affect the mean and uncertainty of the target water quality indicators in the target area, and analyze the driving mechanism of the key factors on the fluctuation of the target water quality indicators; Step S5 includes: Calculate the initial root mean square error of the Bayesian transfer model on the original test set and use the initial root mean square error as the benchmark indicator; Randomly shuffle the values ​​of each feature, use the perturbed data to re-predict and calculate the perturbation root mean square error, and use the perturbation root mean square error as the perturbation indicator; The importance of a feature is measured by the difference between the baseline indicator and the perturbation indicator. The larger the difference, the more critical the feature is to the model prediction.

2. The regional lake and reservoir water quality uncertainty simulation method based on Bayesian transfer learning according to claim 1, characterized in that: The monitoring data in step S1 include water temperature, pH, dissolved oxygen, ammonia nitrogen, total nitrogen, total phosphorus and chlorophyll a concentration.

3. The regional lake water quality uncertainty simulation method based on Bayesian transfer learning according to claim 1 is characterized in that: The specific process of step S1 is: S11. Collect automatic water quality monitoring data from multiple lakes and reservoirs in the region to obtain time series data for each monitoring indicator; then use the STL method to decompose the time series data into long-term trend terms, seasonal cycle terms, and residual terms; S12. For the residual items obtained by decomposition, the generalized extreme studentized residual method is used to perform outlier test, identify abnormal data, and mark the abnormal data as missing values; S13. Use the Kalman filter method to fill in the missing values. By continuously fusing the measured values ​​and state estimates, the accuracy of the state estimation is gradually improved to complete the missing value filling.

4. The method for simulating regional lake and reservoir water quality uncertainty based on Bayesian transfer learning according to claim 3, characterized in that: In step S13, the Kalman filter method includes establishing a state space model to describe the concentration change process, setting the covariance matrix of process noise and observation noise, and realizing dynamic interpolation of missing values ​​through a prediction-update cycle.

5. The regional lake and reservoir water quality uncertainty simulation method based on Bayesian transfer learning according to claim 1 is characterized in that: The specific process of step S2 is: S21. Assign unique numbers from 1 to N to each lake in the region, use some of the lakes as target domains for individual water quality simulations, and use the remaining lakes as source domains for the source datasets used for model training. S22. Select the water quality indicators to be simulated and ensure that the selected water quality indicators are recorded in the monitoring data of all lakes and reservoirs.

6. The regional lake and reservoir water quality uncertainty simulation method based on Bayesian transfer learning according to claim 1, characterized in that: The specific process of step S3 is: S31. Using the data from source lakes and reservoirs, construct a simulated data set of target indicators, where the target indicator serves as the response variable and other water quality indicators serve as predictor variables. S32. Using a Bayesian additive regression tree to construct a target indicator simulation model for predicting the target indicator; wherein the Bayesian additive regression tree can capture complex nonlinear relationships and provide stable prediction results by constructing a Bayesian model of multiple additive regression trees; S33. K-fold cross validation is used to train and evaluate the Bayesian additive regression tree to improve the generalization ability of the target indicator simulation model.

7. The method for simulating regional lake and reservoir water quality uncertainty based on Bayesian transfer learning according to claim 6, characterized in that: In step S33, the K-fold cross-validation includes dividing the source domain data into K parts, of which K-1 parts are used for training and the remaining 1 part is used for validation, and the cycle is repeated for K rounds, and the prediction error of the target indicator simulation model on different data subsets is calculated to improve the prediction stability and reliability of the target indicator simulation model for unseen data.

8. The regional lake and reservoir water quality uncertainty simulation method based on Bayesian transfer learning according to claim 1 is characterized in that: The specific process of step S4 is: S41. Analyze the target indicator simulation model constructed in the source domain and determine variable parameters; wherein the variable parameters include the depth of the decision tree and the node splitting rule; S42. Using the data of the target domain, the variable parameters of the target indicator simulation model in the selected source domain are adjusted and optimized by a Bayesian inference method, so that the target indicator simulation model in the source domain can adapt to the actual situation of the target domain; S43. After the parameters are updated, a Bayesian migration model suitable for the target domain is obtained; wherein the Bayesian migration model integrates the prior knowledge of the target indicator simulation model in the source domain and the data information of the target domain.

9. The regional lake and reservoir water quality uncertainty simulation method based on Bayesian transfer learning according to claim 1, characterized in that: The specific process of step S5 is: S51. Calculate the predicted mean and confidence interval of the target water quality indicator in the target area based on the output results of the Bayesian migration model; S52. Use the feature importance index output by the Bayesian migration model to identify the variables that have the greatest impact on the mean and uncertainty of the target water quality indicators in the target domain, and select the variables with the greatest impact on uncertainty as key factors; S53. For the selected key factors, quantify the response relationship between the key factors and the target indicators, and analyze the driving mechanism of the fluctuation of the target water quality indicators in the target domain.

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