Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Municipal solid waste incineration (MSWI) technology is a key technology for promoting the recycling of renewable energy, sustainable development, and environmental protection. Furnace temperature (FT) is of great significance for the stable efficient operation and pollution emission of such process. Particle swarm rolling optimization (PSRO) strategy is proposed for FT based on model predictive control. The experiments show the effectiveness of the proposed method by using the actual operation data in a MSWI plant of Beijing. This is an interesting study, and the following issues should be addressed in the new version.

1. PSRO should use its full name instead of its abbreviation when it first appears in the Abstract section. Please check the entire article.

2. What is the disadvantages of IT2FBLS? How to improve it in the further researches?

3. In Fig. 1, it is not “solid waste combustion”. That is to say, the description in the figure is inconsistent with that in the text

4. What is DXN in Fig.1.

5. A brief introduction to PSO should be provided in the form of subsection 2.3.

6. Reference 39 should be a more authoritative journal reference.

7. What is the input of IT2FBLS prediction model? Please check if the symbol representation in the text is appropriate

8. What’s useless rate? Where define it for the first time?

9. Why use simple PSO? A remark should be given.

Comments on the Quality of English Language

Minor editing of English language required.

Author Response

Response to Reviewer 1 Comments

Municipal solid waste incineration (MSWI) technology is a key technology for promoting the recycling of renewable energy, sustainable development, and environmental protection. Furnace temperature (FT) is of great significance for the stable efficient operation and pollution emission of such process. Particle swarm rolling optimization (PSRO) strategy is proposed for FT based on model predictive control. The experiments show the effectiveness of the proposed method by using the actual operation data in a MSWI plant of Beijing. This is an interesting study, and the following issues should be addressed in the new version.

Response:

We appreciate your recognition of the merits of our work, and we are committed to making the necessary improvements to improve the clarity, rigor, and overall quality of our papers to meet the standards of the journal. Thank you and other reviewers for taking the time and expertise to review our work, and for the opportunity to refine our contributions under your guidance. We have highlighted the modified parts in red in the article for annotation.

 

Comments 1: PSRO should use its full name instead of its abbreviation when it first appears in the Abstract section. Please check the entire article.

Response 1:

Thank you for pointing this out.

We have revised in the new version.

The revised content is as follows：

“…Next, particle swarm rolling optimization (PSRO) is used to solve the optimal control law se-quence to ensure optimization efficiency…”

 

Comments 2: What is the disadvantages of IT2FBLS? How to improve it in the further researches?

Response 2:

The primary disadvantage of the Interval Type-2 Fuzzy Broad Learning System (IT2FBLS) is its computational complexity, which can be a bottleneck in real-time applications with limited hardware computation resource. Future research could focus on developing more efficient algorithms to reduce computational load and improve real-time performance.

 

Comments 3: In Fig. 1, it is not “solid waste combustion”. That is to say, the description in the figure is inconsistent with that in the text

Response 3:

We apologize for this inconsistency.

We have changed the "solid waste incineration" to "solid waste combustion" in Fig. 1.

 

Comments 4: What is DXN in Fig.1.

Response 4:

The DXN in Fig. 1 refers to dioxins, which, as a type of incineration product, have strong biological toxicity.

We have added a brief explanation in Figure 1 for better understanding. The modified Figure 1 is as follows.

Figure 1. Process flow of an MSWI plant in Beijing.

 

Comments 5: A brief introduction to PSO should be provided in the form of subsection 2.3.

Response 5:

Thank you for the suggestion.

We have included a brief introduction to PSO in subsection 2.3, explaining its fundamental principles and relevance to our research. The revised content is as follows：

"2.3. Particle Swarm Optimization (PSO)

PSO is a widely used computational method for solving optimization problems by mimicking the social behavior of birds [44]. Its simplicity and effectiveness make it a popular choice for finding optimal solutions in complex scenarios.

In PSO, a swarm of particles represents potential solutions to the optimization problem [45]. These particles traverse the solution space, adjusting their positions based on their own experiences and those of neighboring particles. Each particle is characterized by a position and velocity, which are updated using following formulas [46]:

          

where ,  is the number of particle; ,  is the dimension of particle;  is the inertia coefficient;  is the d-dimensional velocity of the nth particle at the current time;  and  are acceleration coefficients;  and  are uniformly distributed random numbers in the interval [0,1];  is the individual optimal position of the nth particle at the current time;  is the global optimal position of the population;  is the position of the particle."

 

[44] Zuo, Z., Yang, X., Li, Z., Wang, Y., Han, Q., Wang, L., & Luo, X. (2020). MPC-based cooperative control strategy of path planning and trajectory tracking for intelligent vehicles. IEEE Transactions on Intelligent Vehicles, 6(3), 513-522.

[45] Taieb, A., Salhi, H., & Chaari, A. (2022). Adaptive TS fuzzy MPC based on particle swarm optimization-cuckoo search algorithm. ISA transactions, 131, 598-609.

[46] He, H., Wang, Y., Han, R., Han, M., Bai, Y., & Liu, Q. (2021). An improved MPC-based energy management strategy for hybrid vehicles using V2V and V2I communications. Energy, 225, 120273.

 

Comments 6: Reference 39 should be a more authoritative journal reference.

Response 6:

We have replaced Reference 39 in the old version with a citation from a more authoritative journal to enhance the credibility of our work. The revised content is as follows：

"…where  and  represent the prediction horizon and control horizon of the system (i.e., the step size of the predicted values and control law set in each iteration, satisfying[43]) …"

 

[43] Sasfi, A., Zeilinger, M. N., & Köhler, J. (2023). Robust adaptive MPC using control contraction metrics. Automatica, 155, 111169.

 

Comments 7: What is the input of IT2FBLS prediction model? Please check if the symbol representation in the text is appropriate

Response 7:

The input to the IT2FBLS prediction model is the historical furnace temperature and MV. We have modified Figure 3 to make its input more prominent and added a description of "the input of IT2FBLS prediction model" in the text. The revised content is as follows：

Figure 3. Diagram of PSRO-MPC control strategy.

"…The inputs are the historical MV and furnace temperature, defined as , and the output is the predicted output  for the next 1 to  moments …"

 

Comments 8: What’s useless rate? Where define it for the first time?

Response 8:

Regarding your two questions, we reply separately as follows.

(1) The "useless rate" in IT2FBLS refers to the proportion of enhancement nodes that are inactive or have minimal impact on the output during computations. This metric evaluates how efficiently the network utilizes its enhancement nodes and connections during training and inference. A high useless rate may suggest that the network is over-parameterized, leading to inefficient use of resources. This information can be used to reduce the network size through pruning or to apply regularization techniques.

(2) This definition was initially introduced in reference [R1] to assess the activity level of neurons in fuzzy neural networks (FNN). In this context, it is applied to determine the activity level of enhancement nodes in IT2FBLS.

[R1] Qiao, J., Zhang, W., & Han, H. (2016). Self-organizing fuzzy control for dissolved oxygen concentration using fuzzy neural network 1. Journal of Intelligent & Fuzzy Systems, 30(6), 3411-3422.

 

Comments 9: Why use simple PSO? A remark should be given.

Response 9:

Given the dynamic unknowns, strong disturbances, and uncertainties in furnace temperature (FT) control, applying optimization algorithms in MSWI must prioritize safety. As this is the first application of the PSO algorithm for FT control, starting with a simple PSO aids in convergence analysis, establishing a theoretical foundation for understanding the algorithm's convergence (see Section 3.2.3) and ensuring consistent performance. This approach meets the safety and performance requirements for furnace temperature control. In future work, we will explore improved PSO algorithms to further enhance FT control performance while maintaining safety.

A remark is added as the end of sub-section 3.2.2. It is as follows.

Remark: Given the dynamic unknowns, strong disturbances, and uncertainties in FT control of MSWI process, applying intelligent optimization algorithms for MPC must prioritize safety. As this is the first application of the PSO algorithm for FT control, starting with a simple PSO aids in convergence analysis and establishes a theoretical foundation for understanding the algorithm's convergence. This meets the safety and performance requirements for FT control. In future work, we will explore improved PSO algorithms to further enhance control performance while maintaining safety.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript proposes a method of intelligent control of furnace temperature (FT) in the municipal solid waste incineration (MSWI) process. It fits well the scope of MDPI Sustainability and could be published after major revision. My detailed comments are provided below.

(1) English must be thoroughly checked, e.g. in Lines 11, 39, 220, 275, 584, etc.

(2) The authors must provide the list of multiple Abbreviations.

(3) Among five selected variables of the MSWI process, the authors have chosen the secondary air volumetric flow rate as the manipulated variable. Clearly, this variable does not affect much the FT as compared to other four variables. Could the authors provide some more information on the effect of the primary air flow rate or other variables on the FT? Otherwise, this analysis looks like a trivial linear analysis for small disturbances. 

(4) The text in Lines 155-163 is insufficient for the clear description of Figure 1. The authors must add some more information both to the text and to the figure to clarify the MSWI process.

(5) Figures 2 and 3 are lacking a clear explanation of the procedure.

(6) The mathematical part is too long. It contains many indefinite parameters and lacks clarity. The authors must thoroughly reformulate the mathematical approach.

(7) The authors must provide a simple validation example for the proposed approach.

(8) I wonder about the value of the "regularization parameter" of 2^-30 (Line 461), which looks unrealistic. 

(9) Figure 4 must be replotted as the curves are indistinguishable. 

(10) Numbers in Tables 1 to 3 must be shown in a common format.

 

(11) Some figures are could be readily removed, like Figs. 7, 8, 11, 12.

 

Comments on the Quality of English Language

Moderate editing of English is required

Author Response

Response to Reviewer 2 Comments

This manuscript proposes a method of intelligent control of furnace temperature (FT) in the municipal solid waste incineration (MSWI) process. It fits well the scope of MDPI Sustainability and could be published after major revision. My detailed comments are provided below.

Response:

Thank you for your recognition of our work and your review of our manuscript. We have revised the new version according to your feedback to improve the quality of the manuscript.

Comments 1: English must be thoroughly checked, e.g. in Lines 11, 39, 220, 275, 584, etc.

Response 1:

We appreciate the reviewer's attention to detail.

“(Lines 11)

To address the inherent nonlinearity and uncertainty of the incineration process, a FT control strategy is proposed. Firstly, by analyzing the process characteristics of the MSWI process and FT control, the secondary air volume is selected as the manipulated variable to control FT.”

“(Lines 39)

However, due to the variability in MSW composition in developing countries like China, which introduces uncertainty into the incineration process, on-site control technology in MSWI plants still largely relies on manual control by field experts, despite long-term industrial application and localization of automatic combustion control systems imported from developed countries.”

“(Lines 220)

The input is the system error, and its output is the corrected secondary air volume prediction to achieve FT tracking. The input of the interval type-2 fuzzy broad prediction module consists of the current and historical MV and FT, and its output is the FT prediction. This module includes an IT2FBLS prediction model, parameter learning, structure learning, and feedback correction sub-modules.”

“(Lines 275)

 Finally, the output of the IT2FNN layer composed of K subsystems is denoted as…”

“(Lines 584)

However, unconstrained exploration may cause the FT to deviate from the setpoint value range, leading to untraceable results, which is a clear limitation of existing methods.”

In addition to the mentioned lines, we also conduct a thorough review and revision of the English language throughout the manuscript, particularly, to improve clarity, grammar, and readability.

 

Comments 2: The authors must provide the list of multiple Abbreviations.

Response 2:

Thank you for the suggestion.

We have included a comprehensive list of abbreviations used in the manuscript to ensure that all abbreviations are clearly defined and easily understood by the readers. They are as follows,

Appendix 1. Corresponding meanings of abbreviations.

Number	Abbreviations	Meanings
1.	FT	Furnace temperature
2.	MSWI	Municipal solid waste incineration
3.	IT2FBLS	Interval Type-2 Fuzzy Broad Learning System
4.	MPC	Model Predictive Control
5.	PSRO	Particle Swarm Rolling Optimization
6.	MSW	Municipal solid waste
7.	FNN	Fuzzy neural network
8.	IT2FNN	Interval Type-2 FNN
9.	RBFNN	Radial Basis Function Neural Network
10.	PSO	Particle swarm optimization
11.	BLS	Broad learning system
12.	FBLS	Fuzzy BLS
13.	PCC	Pearson correlation coefficient
14.	MV	Manipulated variable
15.	NARX	Nonlinear autoregressive exogenous
16.	PSROM	Particle Swarm Rolling Optimization Module
17.	IT2FBPM	Interval Type-2 Fuzzy Broad Prediction Module
18.	BMM	Begian-Melek-Mendel
19.	RMSE	Root Mean Square Error
20.	R2	R-squared
21.	ISE	Integral of Squared Error
22.	IAE	Integral of Absolute Error
23.	Devmax	Maximal Deviation from setpoint
24.	BPNN	Backpropagation NN
25.	GD-MPC	Gradient descent-based MPC

 

Comments 3: Among five selected variables of the MSWI process, the authors have chosen the secondary air volumetric flow rate as the manipulated variable. Clearly, this variable does not affect much the FT as compared to other four variables. Could the authors provide some more information on the effect of the primary air flow rate or other variables on the FT? Otherwise, this analysis looks like a trivial linear analysis for small disturbances. 

Response 3:

We acknowledge the reviewer's concern.

We have provided a more detailed analysis of the impact of the primary air flow rate and other variables on furnace temperature (FT).

" FT is directly influenced by the solid waste combustion process. During this process, MSW is mechanically fed onto the grate, where it undergoes drying, combustion, and burnout as it moves along the grate, eventually transforming into ash and high-temperature flue gas. Primary air is introduced from beneath the grate to supply oxygen for combustion, while secondary air is injected above the flame to provide oxygen for redox reactions in the flue gas and to enhance turbulence within the furnace. This makes the MSWI process an "air and material distribution" system, with key manipulated variables being primary air flow, secondary air flow, and grate speed.

Through analysis and insights from operational engineers at the MSWI plant [42], five key variables were identified as critical to influencing FT: primary air flow, secondary air flow, the average speed of the feeder, the average speed of the drying grate, and urea injection flow—the latter being used to lower pollutant concentrations within the incinerator. These five inputs formed the basis of the controlled object model for FT, from which the manipulated variable (MV) was chosen. Pearson correlation coefficient (PCC) values between these variables and FT were calculated using specific operational data from the plant, with detailed results available in [14].

Among the variables considered, aqueous ammonia showed the highest PCC value with FT, followed by secondary air flow. However, the reliance on aqueous ammonia stems from differences in control technologies between Chinese MSWI plants and those in developed countries, leading to its excessive use in some plants to meet emission standards. As a result, aqueous ammonia was not selected as the manipulated variable for FT. Instead, since stable combustion is the central goal of MSWI control through the "air and material distribution" process, secondary air flow was chosen as the manipulated variable for FT in this study.

This study specifically examines data from a single day of operation, where FT ranged between 880°C and 988°C. Future research will explore FT fluctuations across different ranges and conduct multi-condition studies over extended periods.

 

Comments 4: The text in Lines 155-163 is insufficient for the clear description of Figure 1. The authors must add some more information both to the text and to the figure to clarify the MSWI process.

Response 4:

We appreciate the reviewer's observation.

We have revised the text in Lines 155-163 of old version to provide a clearer and more detailed description of Figure 1. The revised content is as follows：

“In the grate furnace used in the MSWI process, MSW is fed into the incinerator by a grab and undergoes drying, combustion, and burnout stages. These processes are supported by combustion air, high-temperature radiation, and heating. During incineration, the organic matter in the MSW is gasified and pyrolyzed, releasing heat and destroying pathogenic organisms such as viruses and bacteria. The entire process is divided into six subsystems: solid waste fermentation, solid waste combustion, waste heat exchange, steam power generation, flue gas cleaning, and flue gas emission, as shown in Figure 1…”

“…As shown in Figure.1, the MSWI process flow is as follows:

MSW is delivered to the plant by compactor collection vehicles, weighed at a weighbridge, and unloaded into the deposit pool from the platform. In the pool, the MSW is thoroughly crushed, mixed, and stacked using a crane grab, allowing microorganisms to ferment and naturally dehydrate the waste [38]. This fermentation process, which usually takes 5-7 days, increases the calorific value of the solid portion by about 30%. The grab then lifts the fermented MSW and transfers it to the hopper [39], where it slides into the chute and is fed into the incinerator. The MSW is dried by the furnace's heat radiation and the preheated primary air before entering the combustion stage. During combustion, air is added to provide the necessary oxygen, and in some cases, other media may assist. After several hours of high-temperature combustion, the combustible components are fully burned, generating heat, while the non-combustible ash is pushed out of the furnace by the burnout grate. The high-temperature flue gas produced from MSW combustion passes through various boiler heating surfaces, where it is absorbed and cooled. Toxic substances and heavy metals in the flue gas are treated through denitrification [40], desulfurization, dust removal, and ash collection, converting them into non-toxic, harmless gases that meet environmental standards and are released into the atmosphere through a chimney by an induced draft fan [41]. Meanwhile, deionized water in the waste heat boiler absorbs the heat generated by incineration, converting it into high-temperature steam. This steam expands to generate power, driving the turbine and generator to produce electricity.

The primary objective of the MSWI process is to safely treat MSW, with power generation or heat production serving as secondary goals. Typically, the power output of the steam turbine generator in an MSWI plant is synchronized with the incinerator's operation, and the external power grid does not impose restrictions on power dispatching. Consequently, the main goal of the MSWI process's automatic control system is to ensure stable MSW combustion, maintain consistent boiler steam production, minimize the loss on ignition of slag, and reduce pollutant emissions as much as possible.”

 

Comments 5: Figures 2 and 3 are lacking a clear explanation of the procedure.

Response 5:

We have enhanced the explanation of the procedures depicted in Figures 2 and 3. They are shown as follows.

Figure 2:

Figure 2 illustrates the edge verification platform, which includes a safety isolation acquisition device, OPC server, and data acquisition and storage platform. The safety isolation device ensures unidirectional data flow, safeguarding the system from external signal interference and malicious attacks. Using hardware isolation technology, data is securely transmitted from the plant's DCS net to the OPC server via high-speed Ethernet and TCP/IP protocols and stored according to predefined intervals or trigger conditions. The OPC server uniformly manages and distributes various types of data and communicates with both upper-level computers and the lower-level data storage platform. The data acquisition and storage platform collect, processes, and stores data received from the OPC server.

 

Figure 3:

The PSRO-MPC control process operates as follows: First, the particle swarm rolling optimization module adjusts the secondary air flow based on system error. Next, the IT2FBLS prediction submodule calculates the model's predicted output using current and historical MV and FT as inputs. Concurrently, the parameter learning submodule and structural learning submodule update the IT2FBLS parameters and the number of enhancement nodes in real-time to enhance prediction accuracy and reduce model redundancy. Finally, the feedback correction submodule corrects the predicted output based on the prediction error, producing the final predicted output.

 

Comments 6: The mathematical part is too long. It contains many indefinite parameters and lacks clarity. The authors must thoroughly reformulate the mathematical approach.

Response 6:

We recognize that the mathematical section might be overly intricate and challenging to comprehend. To address this, we've thoroughly revised the section, simplifying it where feasible and clearly defining all parameters to enhance clarity without compromising the approach's rigor.

 

Comments 7: The authors must provide a simple validation example for the proposed approach.

Response 7:

The real-world MSWI process prohibits the direct implementation of advanced algorithms like MPC based on offline research and strictly limits access to external systems. Consequently, the authors utilized the edge verification platform depicted in Figure 2 for data collection. Presently, most of the researches is focused on advanced control algorithms using offline historical data. In future studies, we plan to validate these algorithms on experimental platforms that mirror industrial sites; and then, with domain experts' permission, we can conduct validations on actual industrial sites.

 

Comments 8: I wonder about the value of the "regularization parameter" of 2^-30 (Line 461), which looks unrealistic.

Response 8:

We apologize for the mistake in writing 2 ^ -3 as 2 ^ -30. In fact, the regularization coefficient is used to prevent overfitting, and when its value is 2 ^ -30, it loses its function as a penalty term. We have made revisions in the main text.

"…The initial number of enhancement layer nodes was 9, with 1 neuron in the prediction output layer, and a regularization parameter of 2^-3…"

"…The hyperparameters for FBLS were set as follows: 9 fuzzy subsystems, 3 fuzzy rules, 10 enhancement nodes, and a regularization parameter of 2^-3…"

 

Comments 9: Figure 4 must be replotted as the curves are indistinguishable.

Response 9:

We have replotted Figure 4 and added marks on the curves of each different method with improved contrast and line differentiation to ensure that all curves are clearly distinguishable. The revised figure is as follows：

Figure 4. Output curve of prediction model.

 

Comments 10: Numbers in Tables 1 to 3 must be shown in a common format.

Response 10:

We have revised Tables 1 to 3 to ensure that all numbers are presented in a consistent format. The revised version  is as follows：

 

Table 1. Performance indicators of predictive models.

Model	Dataset	RMSE	R2
IT2FBLS	Training	3.2470E+00	9.7098E-01
	Validation	3.2974E+00	9.7013E-01
	Testing	3.4554E+00	9.6730E-01
FBLS	Training	3.3715E+00	9.6871E-01
	Validation	3.3774E+00	9.6867E-01
	Testing	3.6378E+00	9.6376E-01
BPNN	Training	4.0779E+00	9.5422E-01
	Validation	3.9428E+00	9.5729E-01
	Testing	4.0666E+00	9.5472E-01

 

Table 2. Comparison of Constant Value Tracking Performance Indicators.

	Performance index
	ISE	IAE	DEVmax
PSRO-MPC	1.165E-01	1.173E-01	2.2429E+00
GD-MPC	4.6300E-02	1.3970E-01	1.6269E+00
IT2FBLS	5.8105E-02	1.3652E-01	1.6915E+00
PID	6.7040E-01	7.0620E-01	1.7428E+00

 

Table 3. Comparison of constant setpoint tracking performance indicators.

	Performance index
	ISE	IAE	DEVmax
PSRO-MPC	2.6051E+00	2.0791E-01	3.2747E+00
GD-MPC	4.2040E-01	3.7190E-01	3.3937E+00
IT2FBLS	4.8357E-01	3.3440E-01	5.1309E+00
PID	3.2857E+00	1.5120E+00	4.3929E+00

 

Comments 11: Some figures are could be readily removed, like Figs. 7, 8, 11, 12.

Response 11:

We appreciate your feedback.

Upon careful review, we determined that Figures 7, 8, 11, and 12 are integral to the article. Figures 7 and 11 display the declining curves of the MPC's objective function, illustrating the effectiveness of our proposed PSRO algorithm. Figures 8 and 12 showcase the online structural updates of the IT2FBLS prediction model during the control process, reflecting the efficacy of our Structural Learning Submodule. These figures validate our method and facilitate the analysis of experimental results. Thus, we believe they should remain in the main text.

 

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Authors,

In the course of reading and analysing your article, I have formulated the following comments and questions.

1. The conclusions lack a scientific component and require correction. Emphasis should be placed on the creation of the model and its relevance to the field of research.

2. Figures 1-3 are cluttered and may benefit from separation or simplification.

3. The fundamental principles governing the creation of models include testing for adequacy and adaptation. In the conclusion, the author should indicate how these principles have been followed in the work presented.

Author Response

Response to Reviewer 3 Comments

In the course of reading and analysing your article, I have formulated the following comments and questions.

Response:

Thank you for your recognition of our work and your review of our manuscript. We have revised each article according to your feedback to improve the quality of the manuscript.

 

Comments 1: The conclusions lack a scientific component and require correction. Emphasis should be placed on the creation of the model and its relevance to the field of research.

Response 1:

We appreciate the reviewer’s feedback.

We have revised the conclusions section to emphasize the scientific contributions of our work, particularly the creation of the proposed model and its relevance to the field of research.

The revised version is as follows：

“It's worth noting that the proposed IT2FBLS prediction model significantly advances the control of FT in the MSWI process. By effectively modeling the complex, nonlinear dynamics of FT, the IT2FBLS model enhances the predictive accuracy of MPC strategies. This advancement ensures more stable and efficient FT operations, leading to reduced emissions and improved energy recovery. The model’s adaptability to the intricate data in MSWI processes underscores its relevance and potential impact, making a valuable contribution to the broader field of sustainable waste management technologies.”

 

Comments 2: Figures 1-3 are cluttered and may benefit from separation or simplification.

Response 2:

We agree with the reviewer that Figures 1-3 could be clearer.

In order to show the contents of the figure more clearly and facilitate readers' understanding, we have added text descriptions to the three figures in the new version.

 

Comments 3: The fundamental principles governing the creation of models include testing for adequacy and adaptation. In the conclusion, the author should indicate how these principles have been followed in the work presented.

Response 3:

We acknowledge the importance of adhering to fundamental modeling principles.

In the revised conclusion, we have explicitly stated how we have tested the adequacy and adaptability of our proposed model.

The new version is shown as follows,

“We developed an IT2FBLS prediction model using operational data from an MSWI plant in Beijing, China. The model’s adequacy and adaptability were rigorously evaluated by comparing its predictions to actual furnace temperature values and benchmarking its performance against alternative methods. The results confirmed the model's superior accuracy in capturing the complex dynamics of the MSWI process and its robustness under varying operational conditions. Moreover, the IT2FBLS model was successfully integrated into the MPC framework for FT control, leading to improved stability and efficiency in temperature regulation. This outcome underscores the model’s practical applicability and its potential to enhance control strategies in the MSWI field.”

 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have properly addressed all my comments. The manuscript could be now considered for publication.