Technical method for performing error evaluation on top-down emission measurement method

Abstract

The invention discloses a technical method for performing error evaluation on a top-down emission measurement method. The method comprises the following steps: 1) carrying out a controlled release experiment, and carrying out emission load inversion by using a top-down emission measurement method to obtain an estimated emission load; 2) forming a structured data set based on the step 1), 3) constructing an adaptive hierarchical error model (ALEM) based on the structured data set, including a structure expression of a system error (mean layer) and a structure expression of a heteroscedasticity model; and 4) according to the structural expression of the system error and the structural expression of the heterovariance model, obtaining conditional probability distribution of the error, and based on the conditional probability distribution, evaluating the system error, the random error and the confidence interval of the emission measurement method.

Description

Technical Field

[0001] This invention relates to the field of environmental measurement technology, and more specifically to a technical method for error assessment of top-down emission measurement methods. Background Technology

[0002] Top-down emissions measurement methods are techniques based on atmospheric observation and inversion of surface emissions. They estimate source emissions by monitoring changes in atmospheric gas concentrations, such as greenhouse gases, and combining this with meteorological fields and inversion techniques. In practical applications, top-down emissions measurement methods (such as those based on satellites, airborne platforms, UAVs, vehicle-mounted systems, and fixed stations) often involve combinations of observation platforms, measurement instruments, and emissions inversion algorithms. Different methods and platforms often exhibit significant differences in error performance under different environmental scenarios, displaying fragmented and non-comparable characteristics. This presents challenges for method selection, applicability analysis, and measurement uncertainty assessment.

[0003] Currently, industry performance evaluation of top-down emission measurement methods mainly relies on controlled release experiments. This involves deploying relevant measurement methods under known emission rates and scenarios, comparing measured emissions with standard releases, and calculating measurement errors and detection capabilities. However, this evaluation method has the following technical limitations:

[0004] (1) Error results are highly dependent on the experimental scenario and are difficult to extrapolate. The error index obtained from the controlled release experiment is obtained under specific source strength, source type, deployment method and meteorological conditions, and only reflects the performance of the evaluated method under the "current experimental scenario". When external conditions change, the error characteristics of the same method may change significantly. Therefore, the error results obtained from a single experiment are difficult to generalize to real complex scenarios and cannot be used to predict measurement errors under other conditions.

[0005] (2) Evaluation results of different methods and different experiments are not comparable. If multiple measurement methods are compared in the same controlled release experiment, the resulting error only applies to that experimental scenario. Once the method evaluation is based on controlled release experiments with different batches, weather and site conditions, the error results are affected by the respective experimental conditions, making it even more difficult to compare the error evaluations of different methods. Therefore, it is difficult to evaluate the performance and applicable boundaries of different measurement methods under a unified benchmark.

[0006] (3) Lack of continuous probability description of conditional error. Existing technologies usually only provide discrete statistics such as mean deviation, standard deviation or detection limit under certain experimental conditions. They cannot characterize the conditional dependence of measurement error on source emission scenarios, instrument performance and environmental factors, let alone form a continuous error probability distribution in a multi-factor space.

[0007] Therefore, under these circumstances, existing technologies cannot quantitatively provide the error probability distribution and uncertainty range for specific measured operating conditions; they cannot systematically compare and analyze the measurement performance of different methods under different conditions within a unified framework; and they also cannot reliably incorporate top-down observation results and their uncertainties into emission inventory calculation and optimization.

[0008] Therefore, there is an urgent need for a new technical solution that combines controlled release experiments with statistical modeling to quantitatively characterize the conditional errors of top-down emission measurement methods under different source characteristics, instrument performance, algorithm assumptions and environmental conditions, so as to provide a basis for error prediction and uncertainty assessment in real scenarios. Summary of the Invention

[0009] To address the aforementioned problems, this invention proposes a conditional error assessment technique for top-down emission measurement methods, aiming to at least partially resolve the shortcomings of existing technologies. This invention constructs a multidimensional dataset containing actual emissions, measurement inversion results, and environmental conditions through controlled release experiments. Based on this dataset, an adaptive hierarchical error model is established to obtain the continuous probabilistic error distribution of the measurement method under different conditions, thereby achieving a unified and generalizable evaluation of the measurement method's performance.

[0010] More specifically, the present invention provides a technical method for error assessment of a top-down emission measurement method, comprising:

[0011] 1) Conduct controlled release experiments and use a top-down emission measurement method to invert emissions and obtain estimated emissions;

[0012] 2) Based on step 1), a structured dataset is formed. Q true It is the experimental standard release amount, It is an estimate of emissions; x is a condition variable.

[0013] 3) Based on structured datasets Construct an adaptive hierarchical error model (ALEM), including: introducing a logarithmic expression for the relative error: Decompose the error into systematic errors. With random error The expression is ;

[0014] The structural expression for systematic error is given by the following equation (1):

[0015]

[0016] in, For constant terms, The coefficient of the linear term; The coefficients of the interaction terms; The coefficient of the power variable; x k x m x l x n p is a variable selected from the condition variable x. n Power;

[0017] random error It follows a heavy-tailed distribution, that is, The structural expression for the heteroscedasticity model is given by equation (2):

[0018] , For constant terms, x is the coefficient of the linear term. j The variable is selected from the condition variable x;

[0019] 4) Based on the structural expression of the systematic error and the structural expression of the heteroscedasticity model, the conditional probability distribution of the error is obtained. Based on this, the systematic error, random error, and confidence interval of the emission measurement method are evaluated.

[0020] According to an embodiment of the present invention, in step 2), the condition variables include environmental factors, source characteristics, instrument performance, and sampling strategy.

[0021] According to an embodiment of the present invention, in step 3), the construction method of the structural expression (1) of the system error and the structural expression (2) of the heteroscedasticity model is as follows:

[0022] 3.1) Based on all the conditional variables in step 1), we set up a mean model (3) and a heteroscedasticity model (4) with all variables being linear terms:

[0023] (3), of which Here, N is the constant term, and N is the total number of condition variables. For condition variable x h The coefficient of the first term;

[0024] (4), of which Here, N is the constant term, and N is the total number of condition variables. For condition variable x h The coefficient of the first term;

[0025] Based on dataset right and Maximum likelihood estimation (MLE) is performed to solve for the coefficients and constants, and the Akaike Information Criterion is calculated. ;

[0026] 3.2) Fixing the variables of the heteroscedasticity model (4), the mean model (3) is optimized, including removing main effects, adding interaction terms, and performing power transformation operations on each variable of the mean model (3) based on maximum likelihood estimation (MLE) and the Akaike Information Criterion (AICc), to obtain the structural expression (1) of the system error; and

[0027] 3.3) Fixing the variables in the structural expression (1) of the system error obtained in step 3.2), optimize the heteroscedasticity model (4), including based on maximum likelihood estimation (MLE) and the Akaike information criterion (…). The main effects of each variable in model (4) were removed to obtain the structural expression (2) of the heteroscedasticity model.

[0028] According to an embodiment of the present invention, in step 3.2), the main effect deletion includes:

[0029] 3.2.1) Construct candidate sets based on the current set of all variables. For each candidate set, remove one variable from the set of all variables. Construct a corresponding linear term model based on each candidate set. For each linear term model, perform MLE and compute the corresponding... , A smaller value indicates a better model. Find the optimal model's AICc, denoted as... Then calculate the AICc difference, that is... AICc cur The AICc value is the mean model (3) from step 3.1).

[0030] 3.2.2) When ∆AICc ≤ threshold δ, select the optimal model as the current model, and repeat the above process of constructing the candidate set and the all-linear model, executing MLE, and so on, based on the variable set of the current model. The calculation yields a new optimal model AICc value, which is then subtracted from the original AICc value. best A new ∆AICc value is obtained;

[0031] 3.2.3) When the new ∆AICc value is less than or equal to the threshold δ (which can be determined empirically, and is generally 2), select the new optimal model as the new current model and repeat step 3.2.2) until the ∆AICc value is greater than the threshold δ, then stop the operation and use the variable set of the final current model as the variable set after main effects are removed.

[0032] According to an embodiment of the present invention, in step 3.2), adding the interaction item includes:

[0033] 3.2.4) Select any two variables from the set of variables after main effects removal to form candidate second-order interaction terms according to the following principles. (1) The contribution of the mean-end variable in the result of step 2) exceeds a predetermined threshold (e.g., 10%); (2) The two variables come from different physical modules, that is, from different types of variables;

[0034] 3.2.5) Pre-add each candidate interaction term to the variable set after main effects removal and build a model for each. Perform MLE on each model and calculate the corresponding... Find the minimum AICc value, and subtract the last AICc value of the current model in step 3.2.3) from the minimum AICc value to obtain the difference ∆AICc;

[0035] 3.2.6) When ∆AICc≤-δ, take the model corresponding to the minimum AICc value as the current model, accept the candidate interaction terms in the current model, add the remaining candidate interaction terms to the variable set of the current model and build models for each model, perform MLE for each model and calculate the corresponding AICc, find the new minimum AICc value, subtract the AICc value of the current model from the new minimum AICc value to obtain the difference ∆AICc;

[0036] 3.2.7) When ∆AICc≤-δ, take the model corresponding to the new minimum AICc value as the new current model, and repeat step 3.2.6) until ∆AICc>-δ, stop the operation, and take the variable set of the final current model as the variable set after adding interaction terms.

[0037] According to an embodiment of the present invention, in step 3.2), the power transformation includes:

[0038] 3.2.8) Select a variable x from the set of variables after adding the interaction term. o Perform a power transformation, i.e. A grid search is performed on p to obtain multiple different values ​​of p, and different values ​​of x are used. o p Replace x respectively o Multiple variable sets are obtained. Modeling is performed based on each variable set, and MLE is executed and AICc is calculated. The minimum AICc value is found, and the minimum AICc value is subtracted from the AICc value of the current model in step 3.2.7) to obtain the difference ∆AICc.

[0039] 3.2.9) When ∆AICc > -δ, do not accept substitution, then select other non-power term variables to perform power transformation, and repeat the operation of step 3.2.8; when ∆AICc ≤ -δ, take the model corresponding to the minimum AICc value as the current model, select non-power term variables in the variable set of the current model to perform power transformation, and repeat the operation of step 3.2.8); until all variables in the variable set after adding interaction terms have undergone power transformation operation, finally obtain the variable set and model after power transformation, that is, the system error model shown in equation (1).

[0040] According to an embodiment of the present invention, in step 3.3), Main effects removal for each variable in the model includes:

[0041] 3.3.1) Construct candidate sets based on the full variable set of the heteroscedasticity model (4), delete one variable from the full variable set in each candidate set, construct the corresponding full linear term model based on each candidate set, perform MLE for each full linear term model and calculate the corresponding MLE. , The smaller the value, the better the model. Find the minimum AICc value and the optimal model, and then use the minimum AICc value to subtract the AICc value of the heteroscedastic model (4) in step 3.3) to obtain the AICc difference, which is also the ∆AICc value.

[0042] 3.3.2) When ∆AICc ≤ threshold δ, select the optimal model as the current model, and repeat the above process of constructing the candidate set and the all-linear model, executing MLE, and so on, based on the variable set of the current model. The calculation yields a new minimum AICc value and a new optimal model. The new minimum AICc value is then subtracted from the minimum AICc value in step 3.3.1) to obtain a new ∆AICc value.

[0043] 3.3.3) When the new ∆AICc value is less than or equal to the threshold δ, select the new optimal model as the new current model and repeat step 3.3.2) until the ∆AICc value is greater than the threshold δ. Stop the operation and use the variable set of the final current model as the variable set after main effects are removed to obtain the heteroscedasticity model shown in equation (2).

[0044] According to an embodiment of the present invention, the Akaike Information Criterion ( The calculation formula is as follows:

[0045]

[0046] Where L is the likelihood value, k is the number of free parameters (including the number of free parameters in the entire model, including systematic error and heteroscedasticity models), and n is the sample size.

[0047] This invention employs a unified logarithmic relative error representation, enabling comparison of errors from different measurement methods on a uniform scale. It constructs a multidimensional dataset of "real emissions - estimated emissions - conditional variables," supporting continuous and conditional error modeling and achieving generalizable error prediction. An adaptive hierarchical error model (mean layer + variance layer) is introduced to systematically characterize the influence of different factors on systematic and random errors. Conditional variance is independently modeled, dynamically adjusting the error distribution based on environmental and observational conditions to improve model robustness and reliability. The model can output a conditional error distribution and perform inverse conditional decomposition at specified error thresholds, assisting in the formulation of measurement strategies and quality control rules. The model outputs a method-specific probability error distribution, which can be used as a likelihood function for inventory correction or multi-source data fusion, achieving statistically consistent fusion applications. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating a technical method for error assessment of a top-down emission measurement method according to an embodiment of the present invention.

[0049] Figure 2 A standardized residual statistical histogram for a technical method of error assessment of a top-down emission measurement method according to an embodiment of the present invention; and

[0050] Figure 3 This is a scatter plot showing the relationship between the measured error and the systematic error of the model estimation in the technical method for error assessment of the top-down emission measurement method according to an embodiment of the present invention. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] It should be understood that the methods and tools involved in the embodiments of the present invention, such as maximum likelihood estimation (MLE), Akaike information criterion (AICc), Student-t distribution, and grid search, are known in themselves. Therefore, the present invention focuses on how to combine and use these methods and tools to achieve the error evaluation technique of the present invention.

[0053] Figure 1 The figure shows a flowchart illustrating a technical method for error assessment of a top-down emission measurement method according to an embodiment of the present invention. As shown, the method for error assessment of a top-down emission measurement method according to the embodiment may include the following steps:

[0054] I. Implementation of Controlled Release Experiment

[0055] Controlled release experiments were conducted under known emission rates and spatial configurations. The top-down emission measurement method under evaluation was used to invert emissions and obtain the corresponding estimated emissions. During the experiments, environmental meteorological factors (wind, temperature, humidity, pressure, etc.), sampling location and geometric parameters, instrument performance indicators, and other conditional variables affecting error were simultaneously collected and recorded. Through controlled release experiments involving multiple scenarios, meteorological conditions, and measurement methods, a structured high-dimensional dataset was generated. ,in This is the standard release rate. It is an estimated emission amount obtained from the measurement method. These are different types of conditional variables, such as environmental factors, source characteristics, instrument performance, and sampling strategies (geometric layout), which are also different physical modules. This dataset forms the physical and statistical basis for the conditional error modeling of this invention.

[0056] More specifically, a traceable mass flow controller (MFC) is used to control the emission of the target gas or alternative tracer. Based on the MFC's range and sensitivity, and considering the actual emission scenario, different emission rates, emission heights, number of emission outlets, and emission geometry can be set. The actual emission volume is denoted as... This value is the baseline emission level in the model.

[0057] A top-down emission measurement method is deployed downwind or in the vicinity of the emission site to perform emission measurement inversion and obtain the estimated emission amount. Simultaneously, the operating conditions are recorded. Weather stations are set up to record the meteorological conditions during the controlled release experiment. Specific content includes, but is not limited to: ① Sampling strategy (geometric layout): sampling distance, sampling crosswind angle, sampling height; ② Instrument performance: signal-to-noise ratio; ③ Source characteristics: emission height, number of emission outlets; ④ Meteorological conditions (environmental factors): wind vector, temperature, humidity, atmospheric pressure, etc. These conditional variables (N) constitute the input vector.

[0058]

[0059] The three types of data obtained from each release experiment are time-aligned to obtain the dataset. Through multiple rounds of experiments, a high-dimensional dataset was generated that spans meteorological conditions, source emission scenarios, and sampling strategies.

[0060] II. Construction of Adaptive Hierarchical Error Model (ALEM)

[0061] This invention proposes an Adaptive Layered Error Model (ALEM) to quantify the systematic and random errors of measurement methods under different conditions. It introduces a logarithmic expression for relative error.

[0062]

[0063] This error, as a response variable, can uniformly describe overestimation and underestimation, and is suitable for continuous statistical modeling. The model decomposes the error into...

[0064]

[0065] in, This represents systematic error (mean layer), reflecting the regular shift of error with respect to condition variables; This represents the random error (variance layer), whose variance varies with the condition variable and exhibits heteroscedasticity. This hierarchical structure can describe different physical driving mechanisms (systematic bias and random instability) separately, overcoming the limitation of a single model that cannot simultaneously express both.

[0066] The structural expression for the systematic error (mean layer) is as follows:

[0067]

[0068] in For constant terms, The coefficient of the linear term of the condition variable; For the interaction term coefficients of conditional variables (such as wind speed × instrument signal-to-noise ratio); The coefficient of the power variable; x k For condition variables, For condition variable x m and x l Second-order interaction terms, x is a power variable. k x m x l as well as It is selected from the original N condition variables x or transformed from the condition variables among them.

[0069] The structural expression for the heteroscedasticity model is as follows:

[0070]

[0071] in, For constant terms, For condition variable x j The coefficient of the first term, x j Selected from the original N condition variables.

[0072] That is, by performing joint likelihood estimation on the mean layer and variance layer, and automatically selecting the main effects, interaction terms, and nonlinear terms based on the data, we obtain: ① conditional mean ① Describes the trend of deviation under specific conditions; ② Conditional variance ③ Describes the magnitude of uncertainty under specific conditions; The model employs a thick-tailed distribution, such as the Student-t distribution, which can adapt to common turbulent disturbances and measurement fluctuations in real-world environments.

[0073] More specifically, the construction process of the above expressions (1) and (2) is as follows:

[0074] First, based on the input vector All condition variables (N) in the model are set as mean model (systematic error model) and heteroscedasticity model (random error model) with all variables (factors) and all being linear terms, as shown in equations (3) and (4) below:

[0075] (3), where β1 is the constant term and N is the total number of condition variables. For condition variable x h The coefficient of the first term;

[0076] (4), of which, Here, N is the constant term, and N is the total number of condition variables. For condition variable x h The coefficient of the first-order term.

[0077] Then, the coefficients and constant term are solved using maximum likelihood estimation (MLE), and the Akaike information criterion is calculated. More specifically, based on the dataset right and Maximum likelihood estimation (MLE) is used to solve for the coefficients. The log-likelihood of a heavy-tailed distribution, such as the Student-t distribution, is expressed as follows:

[0078]

[0079] in, Let be the probability density function of Student-t. For degrees of freedom; Represents the coefficient set , where n is the number of samples.

[0080] An evaluation metric that balances model fit and complexity, such as the Akaike Information Criterion (AICc), is used to adaptively select the optimal model structure. The expression for AICc is:

[0081]

[0082] in, is the likelihood value, k is the number of free parameters (including the number of free parameters in the entire model of the systematic error and heteroscedasticity model, which will change during the modeling process as the systematic error and heteroscedasticity model is constructed), and n is the number of samples.

[0083] Second, fix the variables of the heteroscedasticity model (4), and perform main effect deletion, interaction term addition and power transformation operations on each variable of the mean model (3) to obtain the result expression of the mean model (1).

[0084] Main effect removal involves constructing candidate sets based on the current total variable set, removing one variable from each candidate set (therefore, there are N-1 candidate sets), performing MLE on the constructed linear model for each candidate set, and calculating the corresponding... , The smaller the value, the better the model. The optimal model's AICc is found and denoted as... Then calculate ∆AICc, that is , The optimal model is used as the new current model when ∆AICc ≤ threshold δ (usually 2). The above operation is repeated based on the variable set of the new current model (one variable is deleted) until ∆AICc is greater than the threshold, at which point the operation stops (i.e., no more variables are deleted). This yields the variable set after main effects are removed.

[0085] Adding interaction terms involves selecting any two variables x from the set of variables after removing the main effects, based on the following principles. a x b For example, the second-order interaction terms that constitute candidates The mean-end variable contributes more than a predetermined threshold to the main effect deletion step results (which can be determined empirically, for example, 10%); the two variables come from different physical modules, i.e., different types of condition variables.

[0086] Each candidate interaction term is pre-added to the variable set after main effects removal, and a model (containing constant terms, first-order terms, and interaction terms) is constructed separately. MLE is then performed, and the corresponding values ​​are calculated. Find the optimal model ;like If the candidate interaction terms selected in the optimal model are accepted, then based on the optimal model, the remaining candidate interaction terms are added to the variable set of the optimal model and models are constructed separately. The above process is repeated until the value of ∆AICc is greater than -δ, and finally the variable set after adding interaction terms is obtained.

[0087] Power transformation involves sequentially applying power transformations to each variable in the variable set after adding interaction terms, i.e., selecting a variable xo (which can be a linear variable or an interaction term variable), that is, A grid search is performed on p to obtain multiple different values ​​of p, and different values ​​of x are used. o p Replace x respectively o Multiple variable sets are obtained. Modeling is performed based on each variable set (including constant terms, linear terms, interaction terms, and exponential terms), and Model-Likelihood Exclusion (MLE) and Alternative Integrity Calculation (AICc) are calculated to find the optimal model. ,like If the power transformation is accepted, the optimal model is used as the current model. Then, the above process is repeated for the next variable (non-power term variable) based on the variables of the current model. If ∆AICc is greater than -δ, the power transformation is not accepted, and the above process is repeated for the next non-power term variable. Finally, all variables in the variable set after adding interaction terms are processed to obtain the variable set after power transformation, and then the mean model structure expression (1) is obtained.

[0088] Third, the variables of the obtained mean layer model are fixed, and the heteroscedasticity model (4) is optimized, including based on maximum likelihood estimation (MLE) and the Akaike information criterion (…). Main effects were removed from all variables in the model.

[0089] Main effects removal for each variable in the heteroscedasticity model includes: constructing candidate sets based on the full variable set of the heteroscedasticity model; removing one variable from each candidate set (therefore, there are N-1 candidate sets); and performing MLE on the fully linear model constructed for each candidate set and calculating the corresponding... , The smaller the value, the better the model. The optimal model's AICc is found and denoted as... Then calculate ∆AICc, that is , When ∆AICc ≤ threshold δ (generally 2), the optimal model is taken as the new current model. The above operation is repeated based on the variable set of the new current model (one variable is deleted) until ∆AICc is greater than the threshold, and the operation is stopped (that is, no more variables are deleted). Thus, the variable set after the main effects are deleted is obtained, and the heteroscedasticity model structure expression (2) is obtained.

[0090] III. The final output of the model is the conditional probability distribution of the error:

[0091]

[0092] This allows for the estimation of systematic errors, random errors, and confidence intervals of emission measurement methods. For example, under certain wind speed conditions, atmospheric stability, emission levels, and downwind measurement distances, what is the confidence error range of the target measurement method? It also allows specifying an error threshold to inversely solve for the confidence interval range of the actual emissions under the current conditions. Furthermore, it allows specifying an error threshold to inversely solve for a multi-dimensional conditional constraint domain (what error needs to be achieved, and what conditions need to be met).

[0093] The error assessment method of the present invention will be further described in detail below with reference to specific embodiments.

[0094] To verify the error assessment technology for top-down emission measurements described in this invention, a controlled release experiment was conducted in June 2025 in an open area (114°51′2′′ E, 37°32′11′′ N) in a county in a northern province. In the controlled release experiment, pure N2O gas (purity >99.9999%) was used as the release source, and a calibrated Alicat mass flow controller (0-10SPLM) was used for release flow control. The N2O mass release rate was used as a benchmark to evaluate the measurement error of the ground-based mobile emission monitoring system. During the controlled release experiment and mobile measurement, meteorological parameters such as wind, temperature, humidity, and pressure were simultaneously monitored using a fixed meteorological station.

[0095] The ground-based mobile emission monitoring system tested in this experiment includes an onboard hardware system and an emission inversion algorithm. The onboard platform is equipped with an Aeris Mira Ultra nitrous oxide (N2O) / carbon dioxide (CO2) analyzer (Aeris Technologies, USA) to measure N2O online. In addition, the onboard platform is equipped with a geographic information measurement system and a meteorological measurement system for latitude, longitude, and onboard wind vector measurements. N2O gas is released into the atmosphere via controlled flow for transport and diffusion, while the onboard system simultaneously measures the emissions downwind. Combined with the emission inversion algorithm, the amount of N2O emitted can be estimated. The mobile measurement technology and emission inversion algorithm are implemented using existing methods (CN 119559024 B). A total of 399 sets of valid measurement data were acquired in this experiment, of which 200 sets were used for modeling, and the remaining 199 sets were used for model performance evaluation. Basic information about the controlled release experiment is shown in Table 1.

[0096] Table 1.1 Basic Information on Controlled Release Experiments

[0097]

[0098]

[0099]

[0100] Modeling is based on some measured data.

[0101] A dataset is constructed based on each set of data from controlled release flows, mobile surveys and emission inversion, as well as meteorological monitoring. Mass release rate The formula for calculating (kg / h) is:

[0102]

[0103] in, The volumetric release flow rate (SPLM) of pure N2O gas. The molar mass of N2O is 44 g / mol. The value represents the molar volume of the gas under standard conditions (22.4 L / mol).

[0104] Inversion quantity The estimation is based on the method described in patent CN 119559024 B.

[0105] Error affects variables This includes source characteristics, wind and turbulence factors, instrument measurement signal factors, and geometric factors (initially a total of 9).

[0106] Source characteristics include mass release rate and release source height hs.

[0107] The wind and turbulence factors include the average wind speed u, wind speed fluctuation su, wind direction fluctuation sdir, and turbulence mixing length ML within a single measurement period. These factors are calculated from the meteorological station's measurement parameters.

[0108] In this experiment, the factor related to the instrument measurement signal is the standard signal enhancement En, which is determined by the N2O instrument measurement signal and the background value, representing the intensity of the measurement signal above the background value.

[0109] The geometric factors refer to the geometric layout of the release source and measurement path, including the horizontal angle Alpha of the wind direction measurement path and the plume delivery distance Dp. That is,

[0110]

[0111] The error variable is the log-relative error (i represents the sample in the dataset).

[0112]

[0113] The error is decomposed into systematic error and random error, expressed as follows:

[0114]

[0115] And let:

[0116]

[0117] It is the specific value of the random error of the i-th data set. This means Predicted value of fluctuation intensity. It is the standardized residual.

[0118] Step 1: Initial Model Construction

[0119] The mean model and heteroscedasticity model are defined as having all factor variables, each consisting of linear terms.

[0120]

[0121]

[0122] Therefore, the conditional density of a single sample is:

[0123] in The standard density of the t-distribution: Γ represents the Gamma function.

[0124] Joint log-likelihood of the entire sample:

[0125] The negative log-likelihood is:

[0126] Joint Likelihood Estimation (MLE): Employing the L-BFGS-B constrained optimization algorithm, it estimates the model parameters by minimizing the negative log-likelihood function. This represents the combination of parameters that minimizes the negative log-likelihood function.

[0127]

[0128] Assume the sample size is n (n=200) and the number of free parameters in the model is k (mean-side). 10, variance end 10, t-distribution degrees of freedom 1 out of 21), the Akaike Information Criterion (AICc) is calculated according to the following formula:

[0129] Let the AICc of the current model be

[0130] In this experiment

[0131] Step 2: Main Effect Deletion

[0132] Optimize the mean model by fixing the variables of the variance model. This is based on the current set of all variables. We construct candidate sets, removing one variable from each candidate set, thus creating nine candidate sets. For example:

[0133] ,

[0134] ,

[0135] ,

[0136] … ,

[0137]

[0138] Perform MLE on the total linear term model constructed for each candidate set, and compute the corresponding... . The smaller the value, the better the model. The optimal model's AICc is found and denoted as... ,definition:

[0139]

[0140] like If the threshold is 2, then the item is accepted for deletion and the process proceeds to the next round (currently there are 8 variables left, and this process is repeated to build 8 candidate sets).

[0141] Otherwise, stop the deletion.

[0142] In this experiment, after step 2, sdir and Alpah are deleted. The current variable set is... ,

[0143] Step 3: Add interactive items

[0144] Select from the existing variable pool and Constructing second-order interaction terms The selection criteria are: (1) the contribution of the mean-end variable in the Step 2 result exceeds the threshold (10%); (2) the two variables come from different physical modules (e.g., the two variables come from source features, wind and turbulence variables respectively).

[0145] After adding each candidate interaction item, perform MLE and calculate the corresponding... Find the AICc of the optimal model, denoted as . .

[0146] like If the interaction is successful, the interaction item will be received and the process will proceed to the next round, repeating the above process.

[0147] Otherwise, stop joining.

[0148] Second-order interactions can express most non-additive effects of "coupling of two physical mechanisms", and have better interpretability and engineering feasibility. This optimization of interaction terms does not consider third-order and higher-order terms, because higher-order terms are prone to introducing collinearity and overfitting, which reduces the extrapolation stability of the model.

[0149] In this experiment, interactive items are added after step 3. , , The current variable set is ,

[0150] Step 4: Power Transformation

[0151] Perform power transformations on the existing variables sequentially, that is... Perform a grid search on p, and perform MLE for each value of p to calculate AICc.

[0152] Find the AICc of the optimal model, denoted as ,like If the substitution is not found, the process proceeds to the next round (evaluating the exponential substitution of the next variable).

[0153] Otherwise, stop the replacement.

[0154] In this experiment, after step 4, the result of the power term includes , , , , The current variable set is ,

[0155] Step 5: Optimization of Heteroscedasticity Model

[0156] Optimize the heteroscedasticity model by fixing the variables of the mean model (removing main effects).

[0157] Based on the total variable set of the current heteroscedasticity model We construct candidate sets, removing one variable from each candidate set, thus creating nine candidate sets. For example:

[0158] ,

[0159] ,

[0160] ,

[0161] … ,

[0162]

[0163] Perform MLE on the total linear term model constructed for each candidate set, and compute the corresponding... . The smaller the value, the better the model. The optimal model's AICc is found and denoted as... ,definition:

[0164]

[0165] like If the threshold is 2, then the item is accepted for deletion and the process proceeds to the next round (currently there are 8 variables left, and this process is repeated to build 8 candidate sets).

[0166] Otherwise, stop the deletion.

[0167] In this experiment, after step 5, the current variable set of the heteroscedasticity model is ,

[0168] At this point, both the mean model and the heteroscedasticity model are optimal, and the final expression for solving MLE is:

[0169]

[0170]

[0171]

[0172] The model was validated based on partial observation data.

[0173] Based on the validation dataset and the final error formula described above, calculate... , , , , , where j is a sample in the validation dataset.

[0174] Standardized residuals Create a statistical histogram and determine whether its shape closely resembles a t-distribution to test the rationality of the model assumptions. The statistical histograms and statistical data analysis are as follows: Figure 2 As shown in Table 2.

[0175] Table 2: Standardized Residual Statistical Analysis

[0176]

[0177] The mean and median of the standardized residuals are close to 0, and the skewness is also close to 0, indicating that the residuals are centered at zero and the overall distribution is approximately symmetrical. The kurtosis of the residuals is 0.67, showing that its tails are slightly thicker than those of a normal distribution, indicating that it is reasonable to use the Student-t distribution to model random errors.

[0178] and Scattered relationships such as Figure 3 As shown in the diagram. The 1:1 relationship is defined as follows: the dashed line represents the reference band constructed based on the median of the overall 95% uncertainty.

[0179]

[0180] in, With 𝜈 degrees of freedom The 97.5th percentile of the Student-t distribution, This represents the conditional standard deviation predicted by the heteroscedasticity model.

[0181] The regression results show that right The fitted slope is close to 1, and the coefficient of determination R0 is... 2 =0.799, indicating that the mean model has no significant systematic bias and can explain about 80% of the error variation.

[0182] Coverage probability analysis shows that more than 93% of the sample error values ​​fall within the 95% uncertainty range of the model construction, indicating that the heteroscedastic uncertainty model based on the Student-t distribution has a relatively reasonable and stable coverage performance under both overall and different uncertainty levels.

[0183] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements without departing from the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A technical method for error assessment of top-down emission measurement methods, characterized in that, include: 1) Conduct controlled release experiments and use a top-down emission measurement method to invert emissions and obtain estimated emissions; 2) Based on step 1), a structured dataset is formed. Q true It is the experimental standard release amount, It is an estimate of emissions; x is a condition variable. 3) Based on structured datasets An adaptive hierarchical error model (ALEM) is constructed. Includes: the logarithmic expression for introducing relative error: Decompose the error into systematic errors. With random error The expression is ; The structural expression for systematic error is given by the following equation (1): in, For constant terms, The coefficient of the linear term; The coefficients of the interaction terms; The coefficient of the power variable; x k x m x l x n p is a variable selected from the condition variable x. n Power; random error It follows a heavy-tailed distribution, that is, The structural expression for the heteroscedasticity model is given by equation (2): , For constant terms, x is the coefficient of the linear term. j The variable is selected from the condition variable x; 4) Based on the structural expression of the systematic error and the structural expression of the heteroscedasticity model, the conditional probability distribution of the error is obtained. Based on this, the systematic error, random error, and confidence interval of the emission measurement method are evaluated.

2. The technical method for error assessment of the top-down emission measurement method according to claim 1, characterized in that: In step 2), the condition variables include environmental factors, source characteristics, instrument performance, and sampling strategy.

3. The technical method for error assessment of the top-down emission measurement method according to claim 2, characterized in that: In step 3), the construction methods for the structural expression (1) of the systematic error and the structural expression (2) of the heteroscedasticity model are as follows: 3.1) Based on all the conditional variables in step 1), we set up a mean model (3) and a heteroscedasticity model (4) with all variables being linear terms: (3), of which Here, N is the constant term, and N is the total number of condition variables. For condition variable x h The coefficient of the first term; (4), of which Here, N is the constant term, and N is the total number of condition variables. For condition variable x h The coefficient of the first term; Based on dataset right and Maximum likelihood estimation (MLE) is performed to solve for the coefficients and constants, and the Akaike Information Criterion is calculated. ; 3.2) Fixing the variables of the heteroscedasticity model (4), the mean model (3) is optimized, including removing main effects, adding interaction terms, and performing power transformation operations on each variable of the mean model (3) based on maximum likelihood estimation (MLE) and the Akaike Information Criterion (AICc), to obtain the structural expression (1) of the system error; and 3.3) Fixing the variables in the structural expression (1) of the system error obtained in step 3.2), optimize the heteroscedasticity model (4), including based on maximum likelihood estimation (MLE) and the Akaike information criterion (…). The main effects of each variable in model (4) were removed to obtain the structural expression (2) of the heteroscedasticity model.

4. The technical method for error assessment of the top-down emission measurement method according to claim 3, characterized in that: In step 3.2), main effect deletion includes: 3.2.1) Construct candidate sets based on the current set of all variables. For each candidate set, remove one variable from the set of all variables. Construct a corresponding linear term model based on each candidate set. For each linear term model, perform MLE and compute the corresponding... , A smaller value indicates a better model. Find the optimal model's AICc, denoted as... Then calculate the AICc difference, that is... AICc cur The AICc value is the mean model (3) from step 3.1). 3.2.2) When ∆AICc ≤ threshold δ, select the optimal model as the current model, and repeat the above process of constructing the candidate set and the all-linear model, executing MLE, and so on, based on the variable set of the current model. The calculation yields a new optimal model AICc value, which is then subtracted from the original AICc value. best A new ∆AICc value is obtained; 3.2.3) When the new ∆AICc value is less than or equal to the threshold δ, select the new optimal model as the new current model and repeat step 3.2.2) until the ∆AICc value is greater than the threshold δ. Then stop the operation and use the variable set of the final current model as the variable set after main effects are removed.

5. The technical method for error assessment of the top-down emission measurement method according to claim 4, characterized in that: In step 3.2), the added interactive items include: 3.2.4) Select any two variables from the set of variables after main effects removal to form candidate second-order interaction terms according to the following principles. (1) The contribution of the mean-end variable in the result of step 2) exceeds the predetermined threshold; (2) The two variables come from different physical modules; 3.2.5) Pre-add each candidate interaction term to the variable set after main effects removal and build a model for each. Perform MLE on each model and calculate the corresponding... Find the minimum AICc value, and subtract the last AICc value of the current model in step 3.2.3) from the minimum AICc value to obtain the difference ∆AICc; 3.2.6) When ∆AICc≤-δ, take the model corresponding to the minimum AICc value as the current model, accept the candidate interaction terms in the current model, add the remaining candidate interaction terms to the variable set of the current model and build models for each, perform MLE for each model and calculate the corresponding AICc, find the new minimum AICc value, subtract the AICc value of the current model from the new minimum AICc value to obtain the new difference ∆AICc; 3.2.7) When the new ∆AICc ≤ -δ, take the model corresponding to the new minimum AICc value as the new current model, and repeat step 3.2.6) until ∆AICc > -δ, stop the operation, and take the variable set of the last current model as the variable set after adding interaction terms.

6. The technical method for error assessment of the top-down emission measurement method according to claim 5, characterized in that: In step 3.2), the power transformation includes: 3.2.8) Select a variable x from the set of variables after adding the interaction term. o Perform a power transformation, i.e. A grid search is performed on p to obtain multiple different values ​​of p, and different values ​​of x are used. o p Replace x respectively o Multiple variable sets are obtained. Modeling is performed based on each variable set, and MLE is executed and AICc is calculated. The minimum AICc value is found, and the minimum AICc value is subtracted from the AICc value of the current model in step 3.2.7) to obtain the difference ∆AICc. 3.2.9) When ∆AICc > -δ, do not accept substitution, then select other non-power term variables to perform power transformation, and repeat the operation of step 3.2.8; when ∆AICc ≤ -δ, take the model corresponding to the minimum AICc value as the current model, select non-power term variables in the variable set of the current model to perform power transformation, and repeat the operation of step 3.2.8); until all variables in the variable set after adding interaction terms have undergone power transformation operation, finally obtain the variable set and model after power transformation, that is, the system error model shown in equation (1).

7. The technical method for error assessment of the top-down emission measurement method according to claim 6, characterized in that: In step 3.3), Main effects removal for each variable in the model includes: 3.3.1) Construct candidate sets based on the full variable set of the heteroscedasticity model (4), delete one variable from the full variable set in each candidate set, construct the corresponding full linear term model based on each candidate set, perform MLE for each full linear term model and calculate the corresponding MLE. , The smaller the value, the better the model. Find the minimum AICc value and the optimal model, and then use the minimum AICc value to subtract the AICc value of the heteroscedastic model (4) in step 3.3) to obtain the AICc difference, which is also the ∆AICc value. 3.3.2) When ∆AICc ≤ threshold δ, select the optimal model as the current model, and repeat the above process of constructing the candidate set and the all-linear model, executing MLE, and so on, based on the variable set of the current model. The calculation yields a new minimum AICc value and a new optimal model. The new minimum AICc value is then subtracted from the minimum AICc value in step 3.3.1) to obtain a new ∆AICc value. 3.3.3) When the new ∆AICc value is less than or equal to the threshold δ, select the new optimal model as the new current model and repeat step 3.3.2) until the ∆AICc value is greater than the threshold δ. Stop the operation and use the variable set of the final current model as the variable set after main effects are removed to obtain the heteroscedasticity model shown in equation (2).

8. The technical method for error assessment of the top-down emission measurement method according to claim 3, characterized in that: Akaike Information Guidelines ( The calculation formula is as follows: Where L is the likelihood value, k is the number of free parameters, and n is the sample size.

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