A Surrogate-Assisted Intelligent Adaptive Generation Framework for Cost-Effective Coal Blending Strategy in Thermal Power Units

Abstract

The coal cost of coal-fired units accounts for more than 70% of the total power generation cost. In addition to determining coal costs, coal blending strategies (CBS) significantly impact various types of costs, such as pollutant removal and emissions. To address these issues, we propose a framework for generating cost-effective CBS. The framework includes a unit output condition recognition module (UOCR) that enables the adaptive classification of output conditions based on historical operation datasets, performing intelligent condition recognition with Imitator and pre-trained image classification models using blending strategies and unit parameters as inputs. The cost-effective strategy generation module (CESG) employs a surrogate model to evaluate the economic viability of strategies in terms of coal and environmental costs, among other factors. It also employs UOCR as another surrogate model to validate strategy feasibility. Cost-effective strategies are generated via a population-based metaheuristic algorithm. In the case study, the UOCR achieved an average training accuracy of 96.64%, and the generated cost-effective strategies reduced costs by an average of 3.37% compared to currently implemented strategies.

1. Introduction

Thermal power generation, predominantly coal-fired, plays a crucial role as the “ballast” in China’s electricity supply structure, accounting for 66.3% of the nation’s total power generation as of 2023 [1]. Amid increasing grid dispatch volatility and pressures from electricity market bidding, cost control in coal-fired power units faces new challenges. Within the cost composition of coal-fired units, coal expenses alone account for over 70% of total production costs. Coal blending is a technique widely applied in coal-fired units to optimize combustion efficiency, reduce power generation costs, and meet environmental standards by mixing coals with varying prices and qualities in specific ratios. This technique directly determines coal production costs and significantly impacts pollutant removal and emissions-related processes. Therefore, improving the coal blending strategy remains a core priority in controlling production costs for coal-fired units.

Research on cost control in coal-fired units is primarily divided into internal cost control and external cost control [2]. Internal costs include fuel costs, equipment and maintenance costs, labor costs, and financial investment costs, among others, among which fuel costs are the most significant component, typically accounting for over 70% of power generation costs. External costs encompass environmental costs and resource consumption costs. With increasingly stringent environmental regulations on thermal power in countries and regions such as China, the optimization of environmental costs for coal-fired units has become a key issue of focus [3,4,5,6].

Coal blending decisions not only determine coal costs but also define coal quality indicators such as sulfur and ash content. Using numerical simulations and combustion experiments, the basic chemical characteristics of blended coal have been relatively well studied [7,8]. Sulfur, ash, and other coal quality factors in blended coal are key contributors to pollutants generated during combustion, which constitute a major source of environmental costs [9,10,11]. Therefore, ensuring the adoption of rational coal blending strategies (CBS) during operation is of great practical significance for the overall cost control of coal-fired units [12].

A multi-constraint optimization model was proven to be an effective approach for optimizing CBS. Yan et al. proposed a hybrid dynamic coal blending method, employing a multi-stage dynamic decision model to balance economic benefits with environmental protection, optimizing coal procurement, blending, and distribution plans to achieve the dual goals of reducing carbon and PM10 emissions [13]. Lv et al. introduced a two-layer coal blending optimization method based on an equilibrium strategy to achieve coordinated reductions in carbon and PM10 emissions under uncertain conditions [14]. Amini et al. developed a coal blending optimization strategy based on a robust optimization model, aiming to maximize economic profit and reduce blending risk while addressing uncertainties in coal quality, sampling, and measurement [15]. This model leverages fuzzy expectations and possibility measures to optimize the blending scheme, balancing the conflict between environmental protection and economic benefits. Yuan et al. proposed a coal blending optimization method based on petrographic characteristics, using Xgboost and support vector regression to construct a coke quality prediction model and employing a multi-constraint optimization model to minimize coal costs while meeting quality requirements [16]. Nawaz et al. examined coal blending strategies from a supply chain perspective, aiming to reduce emissions while maintaining generation efficiency. They simulated co-combustion patterns of various coal types and biomass to assess the technical and economic feasibility of coal blending strategies across different scenarios [17].

However, in the study of CBS optimization models, the approach to ensuring that coal blending strategies meet power generation requirements is often overly simplified. The use of thermoelectric conversion parameters [13,14] or simple calorific value estimates of coal [15,16,17] clearly falls short of accurately reflecting the complex and dynamic thermoelectric conversion processes of power units. During the operation of coal-fired units, ensuring that power generation meets dispatch requirements remains the most critical technical metric. These factors necessitate adjusting coal blending strategies in practical operations based on human experience rather than optimization models, resulting in inefficiencies in the decision-making process and economic losses.

On the other hand, coal-fired power units, as a mature type of generation technology, benefit from advanced digital control systems such as distributed control systems and safety instrumented systems, enabling the effective collection and storage of extensive operational data. Moreover, with the rapid advancement of parameter control research [18], output condition recognition with high accuracy was already achieved using unit operation data as an input [19,20]. Consequently, it becomes feasible to leverage data-driven models to more accurately reflect the power generation corresponding to CBS.

To address the aforementioned issues, we developed a data-driven intelligent adaptive generation framework for cost-effective CBS, comprising two main components: a unit output recognition module (UOCR) and a cost-effective strategy generation module (CESG). The primary contributions are as follows:

• The framework can intelligently and adaptively recognize the output conditions of units with reasonable accuracy based on CBS and supplementary feature parameters.
• Building on the first component, we designed a surrogate-assisted optimization model to generate cost-effective CBS.
• The framework provides extensibility in terms of algorithm selection, such as recognition and optimization algorithms.

The following sections first introduce the current experience-based coal blending decision-making process and its limitations. Then, the composition and technical details of the proposed framework are described in detail, including a novel dedicated neural network called ’Imitator.’ Subsequently, a case study and analysis of the framework were conducted using real operational data from a coal-fired unit. Next, the main contributions of this work are discussed, and directions for future research are suggested. Finally, the paper concludes with a summary and key findings.

2. Coal Blending Decision-Making for Thermal Power Units

As shown in Figure 1, the CBS has substantial influence on various types of generation costs. Among these, coal cost is directly determined by the CBS and typically accounts for over 70% of the total operating costs in thermal power units, making it a central concern in generation cost management.

Other cost types related to CBS can be collectively referred to as auxiliary costs, which are significantly impacted by coal quality indicators such as sulfur and ash content in the blended coal. These costs are highly beneficial for a comprehensive evaluation of the economic efficiency of CBS and specifically include desulfurization and denitrification costs, emission tax costs, and equipment electricity costs. Desulfurization and denitrification costs refer to the expenses incurred from treating raw flue gas to meet environmental regulatory requirements. Emission tax costs are taxes paid by thermal power plants on pollutants ultimately emitted by the units. Equipment electricity costs refer to the expenses associated with electricity purchased from the external grid for operating equipment such as coal crushers, feeders, and coal conveyor belts.

Currently, the formulation of CBS in most coal-fired power plants is primarily based on human experience. Figure 2 illustrates the typical decision-making process for developing CBS. Upon receiving an output dispatch requirement, fuel or operations managers refer to the CBS menu to establish the blending ratio for each coal type and set the total coal feed rate, forming an initial blending strategy. This strategy is then continuously adjusted based on feedback from the unit’s actual output until the output reaches the required range, resulting in the final CBS. The CBS menu is structured with fixed unit conditions, segmented by output ranges based on theoretical upper and lower output limits. It provides reference values for blending strategies, which, based on past experience, are feasible in terms of coal quality (e.g., calorific value) and coal cost efficiency.

This experience-based decision-making process for generating CBS focuses on meeting dispatch conditions while considering some economic factors. However, as grid dispatch becomes increasingly complex and pressures from electricity market bidding intensify, this approach has begun to reveal two key limitations:

• The output condition classification that serves as a reference for initial CBS may not adapt well to actual circumstances. This decision-making process provides fixed condition classifications based on theoretical output limits and derives an initial CBS from past experience. However, during operation, the grid’s dispatch of unit output adjusts according to the actual power load, with outputs often concentrated within a specific range of the theoretical limits. This range may be covered by only a minimal number of reference condition classifications, resulting in an initial CBS with insufficient granularity that lacks the adaptability to adjust dynamically to real production needs, thus differing significantly from the final feasible CBS. Additionally, the initial CBS primarily focuses on coal cost, to some extent overlooking other cost types.
• The method of adjusting the initial CBS to form the final CBS is inefficient and fails to ensure economic viability. The process of fine-tuning the initial CBS to a final CBS relies entirely on continuous adjustments based on actual output feedback and manual judgment. This process may lead to fuel wastage and has a high probability of compromising the economic efficiency of the initial blending strategy.

3. Framework for Generating Cost-Effective Coal Blending Strategy

To address the limitations of the experience-based CBS decision-making process, this paper proposes a cost-effective CBS generation framework. This framework allows fuel and operations managers to quickly generate a current cost-effective CBS by specifying output conditions along with a few past blending strategies and unit parameters. Figure 3 illustrates the framework’s components and the connection between the UOCR and the cost-effective strategy generation module.

The UOCR enables the adaptive classification of unit output conditions and can intelligently identify these conditions using CBS and other unit parameters as inputs. This module first performs adaptive classification based on the actual operational dataset. Then, by using the imitator, it transforms CBS and other inputs into dimensions compatible with image classification models, allowing fine-tuned pre-trained models to perform output condition recognition.

The cost-effective strategy generation module is designed with a surrogate-assisted CBS model to generate strategies that account for costs related to coal, environmental factors, and equipment power consumption under specified output conditions. This module first applies the UOCR as a surrogate model to impose output condition constraints in the strategy generation process. Then, it uses a regression surrogate model to evaluate additional costs within the objective function. Finally, a population-based optimization algorithm is employed to solve the strategy generation model, producing a cost-effective CBS.

Figure 4 further summarizes the workflows of the framework. The workflows are divided into two stages. Stage 1 is based on offline historical datasets. Firstly, the labeled output condition dataset was obtained through the adaptive unit output classification of UOCR. Secondly, the historical unit output condition dataset, CBS dataset, and supplementary features dataset were used to fine-tune the Imitator and pre-trained image classification models in UOCR. Finally, based on the historical CBS dataset and auxiliary costs dataset, Auto-ML was used to construct the surrogate model of auxiliary cost in CESG.

Stage 2 is the process of achieving cost-effective CBS generation using the trained-out framework. After inputting real-time CBS data, supplemental features data, and dispatch requirements, CESG generates CBS, updates CBS with the goal of reducing the total cost (including coal cost and auxiliary costs), and finally generates a cost-effective CBS. During this process, UOCR continuously provides CESG with information about the output conditions corresponding to the generated CBS.

3.1. Unit Output Condition Recognition Module

3.1.1. Adaptive Unit Output Condition Classification

Unit output condition classification involves dividing output into different ranges based on magnitude while simultaneously categorizing CBS and relevant unit parameters. This paper proposes an adaptive condition classification method that determines output probability distributions and completes interval division based on past operational data. The set of output data $O$ in the operational dataset is expressed as:

$$O=\{o_i\mid i=1,2,\dots ,L\},$$

(1)

where $o_i$ represents any output data point and $L$ is the dataset length. We employed Kernel Density Estimation (KDE) to model the probability density of output data. KDE is a non-parametric method that does not require any assumptions about the data’s distribution, making it particularly suitable for handling complex, irregular, or unknown distributions. This characteristic aligns well with the practical scenario where the output data distribution is often multimodal. Consequently, the process of modeling the probability density of output data can be expressed as

$$p(o_j)={\displaystyle \frac{1}{Lh}}{\displaystyle \sum _{i=1}^{L}Kernel}\left({\displaystyle \frac{o_j-o_i}{h}}\right),$$

(2)

where $o_j\in O$, $h$ is the smoothing parameter, and $Kernel(\cdot )$ typically uses a Gaussian kernel function. Based on the size of the output dataset and ensuring sufficient training samples for each condition classification, the total number of unit output conditions is set to $n$. The set of conditions is then defined as

$$Conditions=\{Conditionk|k=1,2,\dots ,n\}.$$

(3)

When the output dataset is sufficiently large, the number of conditions will significantly increase compared to the fixed value used in experience-based decision-making models. The upper limit $o_k$ for each condition satisfies:

$${\displaystyle {\int }_{o_{k-1}}^{o_k}p}(t)dt={\displaystyle \frac{1}{n}},k=0,1,\dots ,n,$$

(4)

where $o_0$ represents the minimum output value in the actual dataset and $o_n$ represents the maximum output value in the actual dataset. Any unit output condition classification can be expressed as:

$$Conditionk=\left\{\begin{array}{l}\{o_i|o_{k-1}\le o_i<o_k\},if1\le k<n\hfill \\ \{o_i|o_{k-1}\le o_i\le o_k\},ifk=n\hfill \end{array}\right.,k=1,2,\dots ,n,$$

(5)

where k is the label for unit condition classification.

Figure 5 illustrates the process of unit output condition classification based on probability distribution for past operational data. By setting the total number of conditions as $n$, adaptive classification results can be obtained.

3.1.2. Imitator

According to state-space theory, the operating condition of a unit can be described by a state vector composed of several unit parameters, where the features of the state vector are determined by the magnitude of the unit parameters. This bears a strong resemblance to the features formed by pixels of varying values in an image. Therefore, we designed the imitator to expand the unit condition recognition input matrix—comprising CBS and supplementary unit parameters, resembling a grayscale image—into a three-channel input matrix commonly used in image classification models, enabling initial feature extraction and transformation of the unit parameter matrix. Firstly, for inputs, to ensure the comprehensiveness of unit condition recognition, additional unit parameters—such as boiler feedwater temperature, pressure, and flow rate—can be selected as supplementary features alongside CBS. The CBS ${x_{CBS}}^t\in {ℝ}^c$ and supplementary features ${x_{SF}}^t\in {ℝ}^s$ at time $t$ can be expressed as:

$${x_{CBS}}^t=[x_1^t,x_2^t,\dots ,x_c^t],$$

(6)

$${x_{SF}}^t=[x_1^t,x_2^t,\dots ,x_s^t],$$

(7)

where $x_1^t$ represents the total coal flow rate, $c$ denotes the total number of coal types involved in blending, $x_2^t,\dots ,x_c$ represents the blending ratio of the $c-1$ type coal, the omitted blending ratios can be calculated using $1-{\displaystyle \sum _{i=2}^c{x}_i^t}$, $s$ indicates the total number of supplementary features, and ${x_{SF}}^t$ composes of scalar values for each supplementary feature at time $t$. After unifying the subscripts, the combined unit parameter features at time $t$ can be defined as:

$$x^t={[{x_{CBS}}^t,{x_{SF}}^t]}^T={[{x_1}^t,{x_2}^t,\dots ,x_m^t]}^T,$$

(8)

where $m=c+s$ represents the total number of input features. Secondly, since adjustments to certain parameters in thermal power units have significant delays in affecting output, the Imitator’s input can incorporate unit parameter combinations by backtracking $\tau -1$ time steps from time $t$. Thus, the Imitator input $X^t\in {ℝ}^{\tau \times m}$ at time $t$ can be expressed as:

$$X^t=[x^{t-\tau +1},\dots ,x^t].$$

(9)

To simplify calculations and facilitate subsequent feature dimension transformations, $\tau =m$ is typically set such that $X^t$ forms a square matrix. Additionally, $x_i^t$ represents the normalized values of the features:

$$x_i^t={\displaystyle \frac{{\widehat{x}}_i^t-\min (\{{\widehat{x}}_i^j|j=1,2,\dots ,L\})}{\max (\{{\widehat{x}}_i^j|j=1,2,\dots ,L\})-\min (\{{\widehat{x}}_i^j|j=1,2,\dots ,L\})}},i=1,2,\dots ,m,$$

(10)

where ${\widehat{x}}_i^t$ is the original value of the feature, and $\max (\{{\widehat{x}}_i^j|j=1,2,\dots ,L\})$ and $\min (\{{\widehat{x}}_i^j|j=1,2,\dots ,L\})$ are the maximum and minimum values of the corresponding feature in the dataset, respectively. Figure 6 illustrates the structure of the input $X^t$. Horizontally, it consists of $x^t$ arranged in chronological order, while vertically, each $x^t$ is composed of CBS and supplementary unit parameters. After normalization, $X^t$ can be viewed as a grayscale image with an equal width and height of $m$.

In the design of Imitator, as shown in Figure 7, a simple combination of attention mechanisms and transposed convolution matrices is used for feature extraction and transformation of the input. The final output matches the common input dimensions required by pre-trained image classification models.

Firstly, broadcast $x^t$ to form $X_{1,Q}^t\in {ℝ}^{m\times m}$ as the input for the query, using $X^t$ as the input for the key and value, and perform the forward propagation calculation for multi-head attention, with the number of heads set as $r$:

$$Q_{1,i}=X_{1,Q}^t{W}_{1,i}^Q,$$

(11)

$$K_{1,i}=X^t{W}_{1,i}^K,$$

(12)

$$V_{1,i}=X^t{W}_{1,i}^V,$$

(13)

$$hea{d}_i^t=\mathrm{softmax}\left({\displaystyle \frac{Q_{1,i}^t{(K_{1,i}^t)}^T}{\sqrt{d_k}}}\right)V_{1,i},$$

(14)

$${\widehat{h}}_1^t=[hea{d}_1^t,\dots ,hea{d}_r^t]W_1^O,$$

(15)

where $i=1,2,\dots ,r$, $W_{1,i}^Q\in {ℝ}^{m\times d_1^q}$, $W_{1,i}^V\in {ℝ}^{m\times d_1^v}$, and $W_{1,i}^K\in {ℝ}^{m\times d_1^k}$ are the weight matrices for the head $i$ and $Q_{1,i}$, $K_{1,i}$, and $V_{1,i}$ are the query, key, and value for the head $i$, respectively; $d_1^q=d_1^k$; and $hea{d}_i^t\in {ℝ}^{m\times d_1^v}$ is the attention score for the head $i$, calculated using the dot-product attention mechanism. $W^O\in {ℝ}^{(d_1^{v}r)\times m}$ is the output weight matrix of the multi-head attention mechanism, and ${\widehat{h}}_1\in {ℝ}^{m\times m}$ is the output of the multi-head attention mechanism. The multi-head attention extracts the similarity information between $x^t$ and each unit parameter combination across supplementary time steps. The sum of $X_{Q_1}^t$ and ${\widehat{h}}_1^t$ yields the first hidden state, $h_1^t\in {ℝ}^{m\times m}$:

$$h_1^t=X_{Q_1}^t+{\widehat{h}}_1^t.$$

(16)

Secondly, three consecutive transposed convolution layers are used to progressively expand the feature dimensions and the number of channels of $h_1$:

$$U_1^t〈i,j,l〉={\displaystyle \sum _{a=0}^{w_1-1}{\displaystyle \sum _{b=0}^{w_1-1}{h}_1^t}}〈i-a,j-b〉K_1〈a,b,l〉,$$

(17)

$$U_2^t〈i,j,g〉={\displaystyle \sum _{a=0}^{w_2-1}{\displaystyle \sum _{b=0}^{w_2-1}{\displaystyle \sum _{l=0}^2{U}_2^t}}}〈i-a,j-b,l〉K_2〈a,b,l,g〉,$$

(18)

$$h_2^t〈i,j,g〉={\displaystyle \sum _{a=0}^{w_3-1}{\displaystyle \sum _{b=0}^{w_3-1}{\displaystyle \sum _{l=0}^2{U}_2^t}}}〈i-a,j-b,l〉K_3〈a,b,l,g〉$$

(19)

where $K_1\in {ℝ}^{w_1\times w_1\times 3}$, $K_2\in {ℝ}^{w_2\times w_2\times 3\times 3}$, $K_3\in {ℝ}^{w_3\times w_3\times 3\times 3}$ are the weight matrices of the three transposed convolutions, $〈•〉$ represents the matrix indexing operation, $U_1^t\in {ℝ}^{u_1\times u_1\times 3}$, $U_2^t\in {ℝ}^{u_2\times u_2\times 3}$ represent the outputs of the first and second convolutional kernels, and $h_2^t\in {ℝ}^{u\times u\times 3}$ is the output of the third convolutional kernel, which serves as the second hidden state. The stride for all three convolutional kernels is set to 1, with zero padding. The width and height $h_2^t$ for each channel can be calculated as follows:

$$u=m+w_1+w_2+w_3-3.$$

(20)

where $u$ is the required width and height for fine-tuning inputs in pre-trained image classification models, typically set to 224 or 384, and the specific values of $w_1$, $w_2$, $w_3$ can be adjusted based on $m$. Using multiple consecutive transposed convolution layers instead of a single transposed convolution layer is beneficial because, in most cases, $m\ll u$ and multiple layers help control the size of the convolutional kernel.

Finally, $X_{1,Q}^t$ is scaled and broadcast along the channel dimension to form $X_{2,Q}^t\in {ℝ}^{u\times u\times 3}$, with scaling performed using bilinear interpolation:

$$X_{2,Q}^t〈i,j,g〉={\displaystyle \sum _{i=0}^1{\displaystyle \sum _{j=0}^1{\varpi }_{p_i}}}{\varpi }_{q_j}{X}_{1,Q}^t〈p_i,q_j〉,$$

(21)

where ${\varpi }_{p_i}$, ${\varpi }_{q_j}$ represent the interpolation weights in the row and column directions, which depend on the distances between $p_i$ and $p$ as well as $q_i$ and $q$. The closer the distance is, the higher the weight is, and $p=i{\displaystyle \frac{m}{u}}$, $q=j{\displaystyle \frac{m}{u}}$. Using $X_{2,Q}^t$ as the query input, attention is computed for each channel:

$$Q_{2,g}=X_{2,Q}^t〈:,:,g〉W_{2,g}^Q,$$

(22)

$$K_{2,g}=h_2^t〈:,:,g〉W_{2,g}^K,$$

(23)

$$V_{2,g}=h_2^t〈:,:,g〉W_{2,g}^V,$$

(24)

$$channe{l}_g^t=\mathrm{softmax}\left({\displaystyle \frac{Q_{2,g}^t{(K_{2,g}^t)}^T}{\sqrt{d_k}}}\right)V_{2,g},$$

(25)

$${\widehat{h}}_3^t=[channe{l}_1^t{W}_{2,1}^O,\dots ,channe{l}_g^t{W}_{2,g}^O],$$

(26)

where $g=1,2,3$, $W_{2,i}^Q\in {ℝ}^{u\times d_2^q}$, $W_{2,i}^K\in {ℝ}^{u\times d_2^k}$, and $W_{1,i}^V\in {ℝ}^{u\times d_2^v}$ are the weight matrices for the channel $g$, and $Q_{2,g}$, $K_{2,g}$, and $V_{2,g}$ are the query, key, and value for the channel $g$, respectively. The $channe{l}_g^t\in {ℝ}^{u\times d_2^v}$ is the attention score for the channel $g$, calculated using the dot-product attention mechanism. $W_{2,g}^O\in {ℝ}^{(d_2^{v}r)\times u}$ is the output weight matrix of the attention mechanism, and ${\widehat{h}}_3^t\in {ℝ}^{u\times u\times 3}$ is the output of the attention mechanism. The attention mechanism further explores the similarity information between $x^t$ and $h_2^t$ after dimension transformation. By summing $X_{2,Q}^t$ and ${\widehat{h}}_3^t$, the Imitator’s output $h^t\in {ℝ}^{u\times u\times 3}$ is obtained:

$$h^t=X_{2,Q}^t+{\widehat{h}}_3^t.$$

(27)

In both attention mechanisms used by the Imitator, the results obtained by broadcasting $x^t$ are used as input for the query, essentially extracting the similarity information between $x^t$ and each unit parameter combination across supplementary time steps. The three consecutive transposed convolutions expand the dimensions and channels of $X^t$ to facilitate transforming $X^t$ into data input formats commonly used by pre-trained image classification models, such as 224 × 224@3 or 384 × 384@3. Through two addition operations, the feature representation of $x^t$ is gradually enhanced in the dimension transformation process, simplifying the complexity of the unit output condition recognition task. In summary, the design of the Imitator’s working mechanism enables the unit output condition recognition task—with the unit parameter matrix as input and classification labels as output—to leverage mature and robust image classification models, such as ResNet [21], ResNeXt [22], and Vision Transformers [23], which are pre-trained on large-scale image classification datasets and widely validated in both academia and industry. This setup allows for selecting different model architectures based on the data characteristics and variations in different unit operation datasets, ensuring the foundational performance of the UOCR.

3.1.3. Intelligent Condition Recognition Based on Pre-Trained Image Classification Models

The Imitator output h^t transforms the unit parameter input matrix into the commonly used input data dimensions for fine-tuning pre-trained image classification models. The forward process of the pre-trained image classification model can be expressed as:

$$Z^t=PTIC(h^t),$$

(28)

where $Z^t\in {ℝ}^{d_Z}$ denotes the feature vector before entering the classifier and $PTIC(•)$ represents the forward propagation of the pre-trained image classification model. Next, $H^t$ is fed into the classifier:

$${\tilde{z}}^t=W_{clf}{Z}_t+\beta ,$$

(29)

where ${\tilde{z}}^t\in {ℝ}^n$ is the output of the classifier, $W_{clf}\in {ℝ}^{d_Z\times n}$ is the classifier’s weight, and $\beta$ is the classifier’s bias. The recognition result $\tilde{k}$ of the UOCR can be obtained by:

$$\tilde{k}=\mathrm{Softmax}({\tilde{z}}^t).$$

(30)

The loss function of the UOCR is defined by the cross-entropy function:

$$\mathcal{L}=-{\displaystyle \sum _{i=1}^C{z}_i}\log (p_i),$$

(31)

where $z_i\in {ℝ}^n$ is the one-hot encoding of the true class, with the $k$-th component as 1 and the others as 0. The $k$ is the classification label for the unit condition. The $p_i$ is calculated as follows:

$$p_i={\displaystyle \frac{e^{{\tilde{z}}_i}}{{\displaystyle \sum _{j=1}^n{e}^{{\tilde{z}}_j}}}}.$$

(32)

Through fine-tuning the pre-trained image classification model, the Imitator, and the classifier, a trained UOCR is obtained. This module achieves intelligent recognition of output conditions by using a unit parameter matrix composed of multi-step CBS and supplementary features as input.

3.2. Cost-Effective Strategy Generation Module

3.2.1. Calculation of Power Generation Costs and Coal Quality Indicators

The evaluation of a CBS can be determined through its corresponding power generation cost. To provide a comprehensive measure of CBS generation costs, auxiliary costs such as desulfurization and denitrification costs, emission tax costs, and equipment electricity consumption are included in addition to coal costs. Furthermore, this paper adopts a cost-per-unit-generation approach for cost accounting, with the conversion between unit output and generation given by:

$$E={\displaystyle {\int }_{t-\mathsf{\Delta }t}^{t}o(t)dt}.$$

(33)

where $E$ represents the power generation of $\mathsf{\Delta }t$, measured in $kW·h$, and $o(t)$ is the function of output over time, measured in $kW$. Based on actual production practices in thermal power plants, when $\mathsf{\Delta }t$ is small, $o(t)$ remains relatively constant, and $o^t$ within $\mathsf{\Delta }t$ can be considered as an average value. Thus,

$$E=o^t\mathsf{\Delta }t.$$

(34)

In the cost calculation of CBS, we use the lower limit obtained from adaptive classification as the unified $o^t$, and the power generated in Condition $k$ within $\mathsf{\Delta }t$ is:

$$E_k=o_{k-1}\mathsf{\Delta }t,$$

(35)

enabling a uniform power unit cost within the same condition. This simplified calculation method, which considers a single-point value over a short period as an average value of $\mathsf{\Delta }t$, is extended to the entire cost accounting process.

The coal cost $C_{coal}$ can be calculated from the CBS as follows:

$$C_{coal}={\displaystyle \frac{x_1^t({\displaystyle \sum _{i=2}^c{p}_i}{x}_i^t+p_1(1-{\displaystyle \sum _{i=2}^c{x}_i^t}))}{o_{k-1}\mathsf{\Delta }t}},$$

(36)

where $p_i, i=2,3,\dots ,c$ correspond to the prices of each type of coal in the blending strategy and $p_1$ is the price of the last type of coal that was omitted.

Auxiliary costs $C_{auxiliary}$ include desulfurization and denitrification costs, emission tax costs, and equipment electricity costs. Desulfurization and denitrification costs are mainly calculated based on the consumption of desulfurization materials such as limestone and urea within $\mathsf{\Delta }t$. Emission tax costs are calculated based on the net flue gas flow and the concentrations of nitrogen oxides, sulfur oxides, and dust within $\mathsf{\Delta }t$. Equipment electricity costs are calculated based on the electricity consumed by equipment involved in the CBS process within $\mathsf{\Delta }t$. The full mathematical formulas for calculating auxiliary costs $C_{auxiliary}$ are detailed in Figure 3. Here, we use nitrogen oxide emission tax costs as an example:

$$C_{N{O}_x}={\displaystyle \frac{{\varsigma }_{N{O}_x}{V}_{clean}{p}_{N{O}_x}}{{\tau }_{N{O}_x}{o}_{k-1}\mathsf{\Delta }t}},$$

(37)

where ${\varsigma }_{N{O}_x}$ represents the concentration of nitrogen oxides in the net flue gas, measured in ${\mathrm{kg}/\mathrm{Nm}}^3$, $p_{N{O}_x}$ represents the unit price of nitrogen oxides in the emission tax, measured in $\mathrm{CNY}/\mathrm{kg}$, ${\tau }_{N{O}_x}$ is the nitrogen oxide equivalent factor, and $V_{clean}$ represents the total volume of net flue gas in standard atmospheric cubic meters, measured in ${\mathrm{Nm}}^3$. This calculation depends on the original flue gas flow rate, pressure, temperature, humidity, and environmental atmospheric pressure. It is evident that the CBS cannot directly calculate $C_{auxiliary}$ through explicit computation. Therefore, we express the power generation cost of CBS as:

$$C={\displaystyle \frac{x_1^t({\displaystyle \sum _{i=2}^c{p}_i}{x}_i^t+p_1(1-{\displaystyle \sum _{i=2}^c{x}_i^t}))}{o_{k-1}\mathsf{\Delta }t}}+C_{auxiliary}(x_{CBF}^t).$$

(38)

The CBS requires calculating coal quality indicators such as ash content, sulfur content, calorific value, and volatile matter. These coal qualities of CBS can be calculated using a weighted average as follows:

$${\phi }_{quality}={\displaystyle \sum _{i=2}^c{x}_i^t{\phi }_{i,quality}}+(1-{\displaystyle \sum _{i=2}^c{x}_i^t}){\phi }_{1,quality},$$

(39)

where ${\phi }_{quality}$ represents the coal quality to be calculated, ${\phi }_{i,quality}$ represents the coal quality of type $i$ coal, and ${\phi }_{1,quality}$ represents the coal quality of the omitted type.

3.2.2. Surrogate-Assisted Generation Model

Based on CBS generation cost accounting, coal quality calculations, and the UOCR, this paper demonstrates a surrogate-assisted cost-effective CBS generation model:

$$\begin{array}{c}\min (C)=\min \left({\displaystyle \frac{x_1^t({\displaystyle \sum _{i=2}^c{p}_i}{x}_i^t+p_1(1-{\displaystyle \sum _{i=2}^c{x}_i^t}))}{o_{k-1}\mathsf{\Delta }t}}+C_{auxiliary}(x_{CBS}^t)\right)\\ \mathrm{s}.\mathrm{t}.\left\{\begin{array}{l}UOCR(x_{CBS}^t)=k_{dispatch}\\ {\phi }_s\le {\phi }_s^{\max }\\ {\phi }_{ash}\le {\phi }_{ash}^{\max }\\ {\phi }_v\le {\phi }_v^{\max }\\ {\phi }_{cal}\ge {\phi }_{cal}^{\min }\\ {\displaystyle \sum _{i=2}^c{x}_i^t}\le 1\end{array}\right.\end{array}.$$

(40)

Firstly, the constraints in generating the CBS need to account for coal quality and output conditions. Here, $UOCR(•)$ refers to the surrogate model using the trained UOCR, with real-time values used for the previous $m-1$ steps of CBS and all supplementary features, combined with the generated CBS as input, to output the recognized unit condition label. The $k_{dispatch}$ denotes the required unit condition label, and ${\phi }_s^{\max }$, ${\phi }_{ash}^{\max }$, and ${\phi }_v^{\max }$ are the upper limits for sulfur content, ash content, and volatile matter, respectively. The ${\phi }_{cal}^{\min }$ represents the minimum calorific value required to ensure normal unit operation.

Secondly, the objective function for strategy evaluation uses a surrogate model, specifically $C_{auxiliary}(•)$, which is a regression surrogate model for CBS and auxiliary costs. Auto-ML technology can be employed to identify the most suitable surrogate model from classic regression models such as LightGBM-XT, LightGBM, KNN, RandomForest, and other similar models, along with their weighted ensemble models. By adopting a data-driven surrogated model for auxiliary costs, the strategy generation model ensures scalability. Beyond the auxiliary costs covered in this study, costs associated with carbon footprints and carbon tax could also be incorporated into the objective function under certain scenarios, thereby enabling different types of CBS generation control. The weighted ensemble model of multiple regression models fitting $C_{auxiliary}(•)$ can be expressed as:

$$C_{auxiliary}(x_{CBS}^t)={\displaystyle \sum _{i=1}^M{\alpha }_i}{C}_{auxiliary}^i(x_{CBS}^t),$$

(41)

where $M$ is the total number of models in the weighted ensemble, $C_{auxiliary}^i(•)$ represents the surrogate model for calculating the $i$ type of auxiliary cost, and ${\alpha }_i$ is the weight of the $i$ surrogate model in the final auxiliary cost calculation.

3.2.3. Cost-Effective CBS Generation

In designing the generation model, we employed data-driven surrogate models for both the evaluation function and constraints, resulting in a mathematically implicit expression. Therefore, the generation of CBS can be achieved using population-based metaheuristic algorithms such as genetic algorithms, differential evolution algorithms, and particle swarm optimization. These algorithms generate a certain number of individuals as candidate CBS, using a fitness function composed of the inverse of the objective function and penalty terms as the evaluation standard for the population. The population is iteratively refined based on fitness scores. After all iterations, the individual with the highest fitness in the population is the generated cost-effective CBS. The mathematical expression of the fitness function is as follows:

$$Fittness({\tilde{x}}_{CBS,i}^t)=\left\{\begin{array}{ll}{\displaystyle \frac{1}{C}},& ifconstraint({\tilde{x}}_{CBS,i}^t)\\ Penalty,& ifnotconstraint({\tilde{x}}_{CBS,i}^t)\end{array}\right.,$$

(42)

where ${\tilde{x}}_{CBS,i}^t$ represents an individual in the population, i.e., a generated candidate CBS; $Penalty$ is a penalty term, typically much smaller than the inverse of the objective function; and $constraint(•)$ represents the constraint check calculation. The iteration strategy of swarm intelligence algorithms generally focuses on individuals with higher fitness in the population, gradually eliminating those that do not meet the constraints. This ensures the effectiveness of the cost-reducing CBS generated under constraint conditions. The pseudocode for the CBS generation process of CESG is shown in Algorithm 1. In Algorithm 1, $pop$ represents the set population size, $\Im$ denotes the total number of constraints in the generation model, and $Iteration(•)$ refers to the population update process of the selected population-based metaheuristic algorithm, such as selection, crossover, and mutation in genetic algorithms.

Algorithm 1. The Pseudocode for the CBS Generation Process of CESG

Input $pop$, $c$, $X^t$

Output $bestfitness$, $best{x}_{CBS}^t$

Initialize ${\tilde{X}}_{CBF}^t=rand(pop,c)$, $bestfitness=-\infty$, $best{x}_{CBS}^t=0\in {ℝ}^c$

return $bestfitness$, $best{x}_{CBS}^t$

4. Case Study and Analysis

4.1. Overview of the Sample Coal-Fired Unit and Experimental Environment

This work used a 350 MW coal-fired power unit produced by BABCOCK & WILCOX BEIJING COMPANY LTD, located in a coastal province in southeastern China, as the subject of the case study. During the significant coal price fluctuations caused by international conditions in 2021–2022, the performance of this unit was notably impacted, with a marked increase in power generation costs. As shown in Figure 8, this unit initially classified operating conditions into four types based on theoretical output limits and used reference values from manually derived initial CBS strategies, which were then adjusted according to feedback from actual output to obtain the final CBS. With increasing grid dispatch volatility and pressure from electricity market bidding, this unit urgently required an accurate and cost-effective CBS decision-making process to control power generation costs.

This unit primarily stored raw coal in six coal storage silos: silos 1 and 2 stored Coal Type A, silos 3 and 4 stored Coal Type B, and silos 5 and 6 stored Coal Type C. The three types of coal varied sequentially in price and calorific value and exhibited significant differences in coal quality indicators, such as sulfur content, ash content, and volatile matter. The CBS for this unit can be expressed as:

$${x_{CBS}}^t=[x_1^t,x_2^t,x_3^t],$$

(43)

where $x_1^t$ represents the total coal flow, $x_2^t$ denotes the blending ratio of Coal Type A, and $x_3^t$ denotes the blending ratio of Coal Type B. The blending ratio of Coal Type C can be calculated from the equation.

The experimental environment was equipped with an Intel(R) Xeon(R) Platinum 8369B CPU (2.90 GHz), an Nvidia A10 GPU (24 GB VRAM), and 32 GB RAM, running on the Ubuntu 18.04 operating system. The framework in the case study was implemented primarily using Python 3.9.18, PyTorch 1.12.0, Transformers 4.44.1, and Autogluon 1.0.0.

4.2. Sample Dataset

Let $\mathsf{\Delta }t$ be set to 1 minute; we selected a continuous dataset of length 5008 from the normal operating data of the sample unit.

Table 1. Description of input parameter data in the dataset.

	Mean	Min	Max
Total Coal Flow Rate (t/h)	145.38	72.03	240.85
A Coal Percentage (%)	0.41	0.21	0.75
B Coal Percentage (%)	0.27	0.07	0.61
Main Steam Pressure (MPa)	2.70	1.92	3.47
Main Steam Flow Rate (t/h)	785.83	534.33	1038.70
Main Steam Temperature (°C)	567.21	547.52	581.52
Feedwater Pressure (MPa)	22.09	16.00	26.38
Feedwater Temperature (°C)	269.27	251.43	283.59
Feedwater Flow Rate (t/h)	772.52	540.43	1042.08

describes the data used as input for intelligent condition recognition, including the original CBS and the six supplementary unit parameters we selected, with a dataset length of 5008.

The total number of adaptive condition classifications $n$ in the unit output recognition module was 6, with a backtracking step length $m$ of 9. The dataset could form 5000 condition recognition samples. Figure 9 illustrates the unit output within the dataset, along with the division of the training and test sets for intelligent condition recognition in a 4:1 ratio. The training and test set division for the auxiliary cost surrogate model was the same as that for intelligent condition recognition.

The coal quality and price data for the three types of coal required by the CBS generation module within the dataset are shown in

Table 2. Coal quality and price data in the dataset.

Quality Indicators	Coal Type
	A	B	C
Sulfur Content (%)	1.17	1.22	1.26
Ash Content (%)	29.26	28.63	30.79
Volatile Matter (%)	17.42	15.90	16.33
Calorific Value (Kcal/kg)	5200.00	4576.81	3205.24
Price (CNY/t)	843.31	725.77	650.28

.

4.3. Hyperparameter Settings for Proposed Framework

The hyperparameter settings for the UOCR are shown in

Table 3. Hyperparameter settings for the unit output recognition module.

Power Output Situation Label Number	Input Steps length	Train Hyperparameter
		Epoch	Initial Learning Rate of Imitator	Initial Learning Rate of Pre-Trained Model	Initial Learning Rate of Classifier
6	9	25	1 × 10−4	1 × 10−5	1 × 10−4

. During training, to ensure stable updates, a hyperparameter reduction strategy was applied, reducing the learning rate to 70% of the initial rate at the 15th epoch.

The input $X^t\in {ℝ}^{9\times 9}$ of the unit condition recognition module, after normalizing the parameters, yielded the grayscale image shown in Figure 10.

The number of heads in the multi-head attention mechanism within the Imitator was $r=3$, and the transposed convolution kernel weight matrices were $K_1\in {ℝ}^{56\times 56\times 3}$, $K_2\in {ℝ}^{65\times 65\times 3\times 3}$, $K_3\in {ℝ}^{97\times 97\times 3\times 3}$, with a training dropout set to 30%. The output of the Imitator was $h^t\in {ℝ}^{224\times 224\times 3}$. To evaluate the effectiveness of the UOCR, we conducted comparative experiments by pairing the Imitator with various pre-trained image classification models of differing architectures and parameter sizes. As shown in

Table 4. Parameter counts, sources of pre-trained weights, and batch size settings for different pre-trained image classification models.

	Number of Parameters	Source of Pre-Trained Weights	Batch Size
ResNet18	11.7M	[24]	256
ResNet34	21.8M		256
ResNet50	25.6M		200
ResNet101	44.5M		100
ResNeXt50-32X4D	25.0M		128
ResNeXt101-32X4D	88.8M		64
Vit-Base	86.4M	[25]	64

, these models included ResNet18, ResNet34, ResNet50, ResNet101, ResNeXt50-32X4D, ResNeXt101-32X4D, and Vision Transformer Base (ViT-Base). All image classification models, except ViT-Base, which was pre-trained on Image-21K, were pre-trained on Image-1K, with fine-tuning inputs formatted as 224 × 224@3 images, using the latest pre-trained weights from PyTorch or Transformers. Due to GPU memory limitations in the experimental environment, batch sizes varied depending on the pre-trained model applied within the unit output recognition module. For models with larger parameter sets, batch size was maximized within the available GPU memory.

In the CESG example, constraint thresholds for sulfur content, ash content, volatile matter, and calorific value were set based on the coal quality management requirements and actual conditions of the reference unit, as shown in

Table 5. Coal quality constraint indicator settings.

	Minimum	Maximum
Sulfur Content (%)	-	1.5
Ash Content (%)	-	30
Volatile Matter (%)	-	20
Calorific Value (Kcal/kg)	4200

.

The models used for the auxiliary cost surrogate experiments included LightGBM [26], LightGBMLarge [26], LightGBMXT [26], CatBoost [27], ExtraTrees [28], KneighborsDist [29], KneighborsUnif [29], NeuralNetTorch [30], RandomForest [31], XGBoost [32], NeuralNetFastAI [33], and their weighted ensemble model, WeightedEnsemble [34]. We let the unit output condition label obtained through adaptive classification in the dataset be equal to the dispatch label $k=k_{dispatch}$. The CBS generation model in the case framework can be expressed as:

$$\begin{array}{c}\min (C)=\min \left({\displaystyle \frac{x_1^t({\displaystyle \sum _{i=2}^3{p}_i}{x}_i^t+p_1(1-{\displaystyle \sum _{i=2}^3{x}_i^t}))}{o_{k-1}\mathsf{\Delta }t}}+C_{auxiliary}(x_{CBS}^t)\right)\\ \mathrm{s}.\mathrm{t}.\left\{\begin{array}{l}UOCR(x_{CBS}^t)=k\\ x_2^t+x_3^t\le 1\\ {\phi }_s\le 1.5\%\\ {\phi }_{ash}\le 30\%\\ {\phi }_v\le 20\%\\ {\phi }_{cal}\ge 4200\end{array}\right.\end{array}.$$

(44)

We employed a roulette-based genetic algorithm as the population-based optimization algorithm [35,36,37], with candidate solutions initialized randomly and iteration strategies including crossover and mutation. The individuals in the genetic algorithm were composed of ${x_{CBS}}^t$. The penalty term was 1 × 10⁻², and the fitness function can be expressed as:

$$Fittness({\tilde{x}}_{CBs,i}^t)=\left\{\begin{array}{ll}{\displaystyle \frac{1}{C}},& \hfill ifconstraint({\tilde{x}}_{CBS,i}^t)\hfill \\ 1\times {10}^{-2},& \hfill ifnotconstraint({\tilde{x}}_{CBS,i}^t)\hfill \end{array}\right.$$

(45)

The additional hyperparameter settings for the genetic algorithm are shown in

Table 6. Genetic algorithm hyperparameter settings.

Population Size	Crossover Rate	Mutation Rate	Max Generations
100	0.80	0.01	20

.

4.4. Experimental Results and Analysis of UOCR

The experimental results for the adaptive output condition classification are shown in Figure 11. In the actual dataset, the output was concentrated between 180.0 and 307.1 MW. Figure 11a illustrates the distribution of output points across each classification, where adaptive output condition classification ensured that the total number of output points in each category was approximately the same. This resulted in similar label counts for each type in subsequent intelligent condition recognition training. Figure 11b compares unit output condition classification based on human experience with adaptive condition classification. The adaptive method significantly enhanced the granularity of conditions, supporting a higher level of refinement in CBS.

Figure 12 and

Table 7. Comparison of training error, training accuracy, and test accuracy for UOCRs using different pre-trained models.

	Training Loss	Training Accuracy	Test Accuracy
ResNet18	1.164 × 10−1	95.94%	80.21%
ResNet34	1.024 × 10−1	95.94%	79.95%
ResNet50	7.723 × 10−2	96.95%	85.20%
ResNet101	4.925 × 10−2	98.08%	85.20%
ResNeXt50-32X4D	6.914 × 10−2	97.20%	81.25%
ResNeXt101-32X4D	1.129 × 10−1	95.46%	76.46%
ViT-Base	2.914 × 10−1	89.94%	75.11%

present the training error, training accuracy, and test accuracy of UOCRs using different pre-trained models. Without adjusting hyperparameters for different pre-trained models and with only 25 epochs of training, all models except ViT-Base achieved over 95% training accuracy and over 80% test accuracy. Among them, the UOCRs using ResNet50 and ResNet101 achieved the highest test accuracy.

As shown in Figure 13, we selected data points from six different unit conditions and input them into the unit condition recognition module using ResNet50 to observe the effect of the Imitator. The first column shows the input in the form of a 9 × 9 grayscale image, where higher pixel values appear closer to white. Columns 2–4 display the 224 × 224 three-channel images processed by the Imitator, where higher pixel values appear darker. In the first column, it is evident that the original inputs from the six different conditions already showed significant differences. In columns 2–4, the outputs processed by the Imitator clearly retained these original input features as the 9 × 9 grayscale image was expanded to a 224 × 224 three-channel image.

Specifically, along the height of the image, areas close to white in the original input resulted in very dark or very light horizontal stripes in the output, reflecting differences in the magnitude of different unit parameters in the input. Along the width of the image, the output showed vertical stripes with varying intensities, corresponding to temporal changes in the same unit parameter in the input. This effect was particularly pronounced in unit conditions 3 to 6, as illustrated in Figure 14. The structural design of the Imitator expanded the input dimensions to 224 × 224@3 and, through its learnable parameters, preserved distinct feature differences among different conditions in the output.

UOCR first divided the output conditions into more granular categories compared to human experience, based on the total set classifications and the actual production dataset. Next, the Imitator, pre-trained image classification model, and classifier were used to achieve intelligent condition recognition based on CBS. The Imitator’s output features, which exhibited distinct differences across various conditions, enabled the pre-trained image classification model—trained on three-channel image datasets and fine-tuned with prior knowledge from pre-trained weights—to achieve higher accuracy in the unit condition recognition task.

4.5. Experimental Results and Analysis of CESG

Using the ResNet50 UOCR, which achieved the highest test accuracy, we selected data points from six conditions to conduct an experimental analysis on CESG. Figure 15 illustrates the selected data points and their preceding eight steps of output conditions used as input for the optimization strategy generation module.

Table 8. Experimental results of the auxiliary cost surrogate model.

	Train RMSE	Test RMSE	Test MAPE
WeightedEnsemble	1.625 × 10−3	3.706 × 10−3	4.312%
LightGBMXT	1.694 × 10−3	3.800 × 10−3	4.428%
CatBoost	1.706 × 10−3	3.728 × 10−3	4.386%
LightGBM	1.708 × 10−3	3.776 × 10−3	4.356%
LightGBMLarge	1.780 × 10−3	3.678 × 10−3	4.277%
ExtraTrees	1.812 × 10−3	3.416 × 10−3	3.990%
KneighborsDist	1.857 × 10−3	4.080 × 10−3	4.683%
NeuralNetTorch	1.927 × 10−3	3.855 × 10−3	4.324%
RandomForest	1.937 × 10−3	3.643 × 10−3	4.246%
KneighborsUnif	1.970 × 10−3	4.066 × 10−3	4.663%
XGBoost	2.006 × 10−3	3.563 × 10−3	4.173%
NeuralNetFastAI	2.348 × 10−3	3.338 × 10−3	3.831%

presents the experimental results for the auxiliary cost surrogate model. In CESG, we used the weighted ensemble model with the lowest training error as the surrogate model for auxiliary costs.

Figure 16 shows the iteration process of the genetic algorithm in the experimental phase of the CESG. After the fourth generation, all condition experiments yielded over 70 constraint-compliant individuals. In the experiments for Conditions 1, 3, and 5, the total number of compliant individuals stabilized close to the total population size until the end of iterations, while in Conditions 2, 4, and 6, the number fluctuated but generally was maintained above 70% of the total population. Even though the generation model included implicit surrogate models in both the objective function and constraints, using a population-based optimization algorithm proved feasible and efficient in generating candidate solutions for CBS optimization. The abundance of candidate solutions ensured a continuous reduction in total costs, with the final CBS generated in all six conditions showing a significant decrease in total costs compared to the initially generated strategies.

In designing the generation model, we imposed constraints on the generated strategy for output condition, calorific value, ash content, sulfur content, and volatile matter. Figure 17 compares the generated cost-effective CBS, the original strategy, and the constraint thresholds. Across all conditions, the generated cost-effective CBS met the output condition and four coal quality constraints and showed minimal differences from the original strategy in most indicators, ensuring practical applicability.

Figure 18 shows the rate of change in total coal flow; proportions of A coal, B coal, and C coal; total cost; coal cost; and other costs between the generated cost-effective CBS and the original strategy across six unit conditions.

Table 9. Comparison between the generated cost-effective CBS and the original strategy across six unit conditions in terms of total coal flow, proportion of A coal, proportion of B coal, proportion of C coal, total cost, coal cost, and other costs.

	Total Coal Flow Rate (t/h)	A Coal Percentage	B Coal Percentage	Total Cost (CNY/ (kW·h))	Coal Cost (CNY/ (kW·h))	Other Cost (CNY/ (kW·h))
Cond. 1 Orig.	88.803	59.53%	12.82%	0.457	0.382	0.075
Cond. 1 Gen.	89.620	46.41%	12.23%	0.431	0.356	0.075
Cond. 2 Orig.	122.521	44.47%	13.43%	0.520	0.440	0.080
Cond. 2 Gen.	118.318	49.01%	7.83%	0.501	0.426	0.075
Cond. 3 Orig.	147.906	35.48%	19.04%	0.562	0.487	0.075
Cond. 3 Gen.	135.080	46.05%	11.57%	0.526	0.452	0.074
Cond. 4 Orig.	164.573	44.22%	19.42%	0.579	0.509	0.070
Cond. 4 Gen.	168.005	40.64%	17.60%	0.561	0.493	0.069
Cond. 5 Orig.	174.444	43.09%	37.92%	0.581	0.512	0.069
Cond. 5 Gen.	186.077	48.02%	8.71%	0.578	0.511	0.067
Cond. 6 Orig.	200.385	43.91%	38.05%	0.597	0.527	0.070
Cond. 6 Gen.	197.129	45.76%	37.75%	0.592	0.521	0.071

provides the specific values for these indicators. In the six unit conditions, the generated cost-effective CBS achieved an average total cost reduction of 3.37% and an average coal cost reduction of 3.62% compared to the original strategy. The generated strategies exhibited significant variation across different unit conditions. For instance, in Conditions 1 and 5, the proportion of C coal and total coal flow were notably increased, while in Conditions 2 and 3, the proportion of A coal rose and total coal flow was reduced. Conditions 4 and 6 were obtained by fine-tuning the original strategy. Additionally, the auxiliary costs included in the strategy evaluation often differed substantially from changes in coal costs, which enhanced the global cost-effectiveness of the generated strategy in unit operation.

Overall, CESG can produce differentiated cost-effective CBS tailored to various conditions. These strategies comply with practical production constraints on output conditions and coal quality, significantly reducing total costs compared to the original strategy, and demonstrate strong robustness and applicability.

5. Discussion

In this study, we improved coal blending decision-making for thermal power units through the design and implementation of a cost-effective CBS strategy generation framework. This framework includes a UOCR and a cost-effective strategy generation module. Once the UOCR is trained, the CESG only requires inputting the specified unit conditions and a few unit parameters to generate the cost-effective CBS strategy. Our research shows that the cost-effective CBS strategies generated by this framework comply with practical production constraints and have a significant economic advantage in power generation costs compared to conventional experience-based blending strategies.

The UOCR first achieves adaptive classification of unit output conditions by forming output condition categories that are practical for production based on a set number of classifications and actual operational data. It then uses real blending strategies and selected supplementary unit parameters as inputs; with our Imitator architecture, the pre-trained image classification model, when fine-tuned, can intelligently recognize unit output conditions. Case study results indicate that, with a set classification count of six, the UOCRs using ResNet, ResNeXt, and Vision Transformer architectures achieved an average training accuracy of 96.64%, with a maximum test accuracy of 85.20%.

The CESG employs a surrogate-assisted model to evaluate not only coal costs but also auxiliary costs, such as emission taxes and desulfurization/denitrification costs. For strategy generation constraints, in addition to coal quality limitations, the module generates strategies that produce the desired unit output conditions use UOCR as a constraint. Case study results demonstrate broad applicability across six conditions; the generated strategies meet practical production constraints and, compared to the original strategy, reduce the total costs by an average of 3.37% and the coal cost by 3.62%. In some output conditions, the reduction in total cost and coal cost reached 8.7% and 6.3%, respectively.

Given that coal costs and auxiliary costs, which serve as evaluation targets in this framework, account for at least 70% of actual power generation costs in coal-fired power units—and coal-fired power continues to supply over 60% of electricity in China—the cost-effective CBS decision-making process enabled by this framework holds significant value for reducing costs and enhancing efficiency in power generation.

The proposed surrogate-assisted intelligent adaptive cost-effective CBS strategy generation framework opens avenues for future research and development. The following three points are recommended as references:

• The design concept of combining the Imitator with pre-trained image classification models in the UOCR module offers promising opportunities for applying larger-scale deep learning models to the thermal power sector. This approach provides a potential pathway for leveraging advanced model architectures with greater parameter capacity in industrial applications.
• Conducting more extensive case studies is necessary to comprehensively evaluate the framework’s design. Different types of thermal power units, such as ultra-supercritical units or those combined with renewable energy generation, operate under distinct mechanisms, which may pose new challenges to the framework’s stability. Additionally, thermal power units in different regions face varying cost structures, requiring adjustments to auxiliary cost design based on case studies. For instance, European thermal power plants may need to incorporate carbon footprint considerations into cost calculations.
• The framework’s performance in engineering environments requires further experimentation. In the current case study, the trained framework took 50–70 seconds from initialization to generating a cost-effective CBS (detailed timing information is provided in the Figure 3), leaving room for improvement. However, the experimental environment in this study may not represent the operational conditions available in most engineering applications. The framework needs to be tested in a wider range of operating environments to comprehensively validate its performance.

6. Conclusions

This study proposes a surrogate-assisted intelligent adaptive cost-effective CBS strategy generation framework that reduces reliance on human experience in CBS decision-making and significantly enhances the economic efficiency of coal blending strategies. The framework consists of a UOCR and a cost-effective strategy generation module. The UOCR achieves adaptive classification of unit output conditions based on real data, utilizing CBS and supplementary unit parameters as inputs to intelligently recognize unit output conditions using the Imitator and pre-trained image classification models. Across architectures such as ResNet, ResNeXt, and Vision Transformer, the UOCRs achieved an average training accuracy of 96.64%. The CESG is designed with a surrogate-assisted model to comprehensively evaluate strategy cost-effectiveness and to impose constraints on the generated output conditions and coal quality requirements based on UOCR, producing cost-effective CBS using population-based metaheuristic algorithms that, on average, reduce the total costs by an average of 3.37% and the coal cost by 3.62% compared to the original strategy. In some output conditions, the reduction in total cost and coal cost reached 8.7% and 6.3%, respectively.