Optimization of Sensor Positions and Orientations for Multiple Load Case Scenarios

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents a methodology for optimizing sensor positions and orientations in structural health monitoring under multiple load cases. The authors introduce a modified genetic algorithm to minimize the difference between maximal structural responses and sensor-detected responses. The following are the comments:

1. How were the weights for different load cases determined? Were they normalized based on load severity or empirical significance?
2. The strain model uses α and β for perpendicular sensitivity. Are these values experimentally calibrated, or assumed? Could their variability affect optimization robustness?
3. Several related studies should be mentioned: Partial-model-based damage identification of long-span steel truss bridge based on stiffness separation method. Stiffness separation method for reducing calculation time of truss structure damage identification.
4. Thermal loads induce thermal strain. Why were strain and temperature optimizations treated separately? Could coupled physics improve accuracy?
5. Please consider acknowledging limitations and suggest constraint integration.
6. Please consider to define α, β Suggest providing references to state values and justifying assumptions.

Author Response

Thank you for your constructive comments in this review. Your comments provided valuable insights to refine the contents of the paper. Below we try to address the raised issues as best as possible.

1. “How were the weights for different load cases determined? Were they normalized based on load severity or empirical significance?”

Answer: The weights were determined to ensure that every load case is equally important. The weight for load case i is the inversed maximal response of the structure to the applied load as illustrated in Equation (8).

2. “The strain model uses α and β for perpendicular sensitivity. Are these values experimentally calibrated, or assumed? Could their variability affect optimization robustness?”

Answer: The sensitivity coefficients α and β, used in the strain model to take into account perpendicular strain components are based on literature data. According to engineering practice outlined in [28,29], in the numerical example we considered α = β = 0.01.

The above information were added to Section 4 of the manuscript.

3. “Several related studies should be mentioned: Partial-model-based damage identification of long-span steel truss bridge based on stiffness separation method. Stiffness separation method for reducing calculation time of truss structure damage identification.”

Answer: The mentioned studies are very relevant to our work. These papers support the core idea, that critical structural responses can be captured effectively using simplified or localized models. This idea aligns with the way we optimize sensor placement to capture maximal field values under multiple load cases. These papers illustrated both theoretical and practical value of stiffness separation and partial modelling in designing efficient sensor networks under limited measurement conditions.

4. “Thermal loads induce thermal strain. Why were strain and temperature optimizations treated separately? Could coupled physics improve accuracy?”

Answer: The main goal was to define a method for optimal sensor placement, taking into account any physical quantity under measurement. Temperatures and strains were taken as examples of simple scalar and tensor quantities. This method could be also used to determine e.g. optimal accelerometers positions. In the coupled thermomechanical problem, the proposed method and algorithms could be utilized to determine optimal positions of a given number of temperature sensors and a given number of strain sensors, separately. Different combinations of numbers of temperature and strain sensors could be then used to train required prediction model and this way a minimal number of each sensor type could be determined that ensures required prediction accuracy. Defining and solving an optimization problem that allows to find minimal number of temperature and strain sensors and their optimal mutual position is a very interesting direction for future research and the authors are grateful to the Reviewer for this idea.

The above information were added to the manuscript.

5. “Please consider acknowledging limitations and suggest constraint integration.”

Answer: The constraints for the optimization are presented in formulas (2)-(4). There are physical constraints related to sensor installation (limited surface access or curvature). Also, whole point of the optimization is that the number of sensors is lower than the number of load cases.

Even though the proposed optimization method improves prediction accuracy, it has some limitations. First, it uses computationally generated data (from FEM model in the numerical example). This means that all load cases must be identified and known, as well as an accurate numerical model is required. The sensor noise in real-life situations can be overcome by adding artificial white gaussian noise to the numerically generated data. This will make the prediction model more immune to noisy input data. Uncertainties like sensor installation errors or structural degradation over time may also occur, that will affect the measurements.

Another limitation is that the proposed method does not optimize the number of sensors, so the user needs to try different variants.

The manuscript was expanded with discussion about the abovementioned limitations and the Conclusion section was expanded with future research directions.

6. “Please consider to define α, β Suggest providing references to state values and justifying assumptions”

Answer: The values depend on sensor type, size, material and are defined by sensors producers. Nowadays foil strain gauges are characterized by a very low sensitivity for the transverse strain, less or equal to 1% for the sensitivity in the axial direction, as explained in [27]. The grid geometry and manufacturing for such gauges lead to a nearly identical response in orthogonal directions (α ≈ β). For FBG sensors the sensitivity can be negative or positive up to few percent [34].

 

Once again, thank you for the time you put in reviewing the paper and we look forward to meeting your expectations.

Reviewer 2 Report

Comments and Suggestions for Authors

Comments on “Optimization of sensors positions and orientations for multiple load case scenarios”

The research presented an optimization model aimed at determining the optimal number, placement, and orientation of sensors for structural load monitoring across multiple load cases and measurement types. The objective is to maximize monitoring accuracy by minimizing the discrepancy between the structure’s maximum response and the sensor-detected responses under various loading scenarios. The proposed model was validated through a case study involving a composite structure, using 1 to 3 sensors across seven different load cases.

Below are detailed comments for the authors to address:

• The number of keywords should be reduced, as there are currently 11, which is excessive.
• The literature review is currently incomplete. The authors are encouraged to include a dedicated “Related Works” section that critically reviews prior research in the field of sensor placement optimisation. A brief overview of relevant machine learning (ML) methods would also benefit readers and provide important context.
• The novelty of the proposed method needs to be better articulated and expanded. While the authors state that the novelty lies in their objective function, they do not clearly explain how this function differs from existing approaches, nor do they justify its significance or originality.
• Section 2 should be shortened, as it is currently too lengthy. Well-established concepts can be briefly mentioned and cited rather than described in full. The finite element (FE) modelling component could be expanded and presented as a separate section. Additionally, the current presentation of FE results is shallow and requires further detail.
• While the results are presented, the paper lacks in-depth discussion. The validation using a feedforward artificial neural network (ANN) model is only briefly described. The rationale for selecting this algorithm, the process for designing its architecture, and how it compares to existing ANN models should be discussed. Furthermore, the authors should compare the ANN's performance with other ML models to justify their choice.
• The discussion section should be strengthened by addressing the limitations of the proposed model and offering insights into its practical applicability.

Author Response

Thank you for your constructive comments in this review. Your comments provided valuable insights to refine the contents of the paper. Below we try to address the raised issues as best as possible.

1. “The number of keywords should be reduced, as there are currently 11, which is excessive.”

Answer: The number of keywords was reduced

2. “The literature review is currently incomplete. The authors are encouraged to include a dedicated “Related Works” section that critically reviews prior research in the field of sensor placement optimisation. A brief overview of relevant machine learning (ML) methods would also benefit readers and provide important context.”

Answer: The literature review was significantly expanded according to the Reviewer’s suggestions.  We included ‘Related Works’ section and reviewed previous work on sensor placement optimisation. This section now describes key approaches, identified existing gaps and situates our contribution in the current literature. Moreover, we included a summary of relevant machine learning techniques to help put the work in context for readers who are not so familiar with this area of study.

3. “The novelty of the proposed method needs to be better articulated and expanded. While the authors state that the novelty lies in their objective function, they do not clearly explain how this function differs from existing approaches, nor do they justify its significance or originality.”

Answer: The novelty is in the application— the paper concerns load or stress monitoring for different load cases while most literature focuses on damage detection, modal identification, or mode shape reconstruction. Previous approaches (e.g., EFI, FIM, or hybrid methods) are aimed at improving observability or detect damage, not to track varying operational loads or stresses under different scenarios without knowing the load location.

Our objective function also differs significantly. Instead of maximizing information content (as in FIM-based methods) or targeting dynamic modes, it minimizes the difference between true maximum structural response (e.g. strain or temperature) and sensor-detected response under all load cases. It includes positions and orientations of the sensors and is therefore well suitable for direction dependent measurements such as 3D strain measurements. This function directly targets the performance of load/stress prediction models, making it better suited for machine-learning-driven monitoring systems under real conditions.

4. “Section 2 should be shortened, as it is currently too lengthy. Well-established concepts can be briefly mentioned and cited rather than described in full. The finite element (FE) modelling component could be expanded and presented as a separate section. Additionally, the current presentation of FE results is shallow and requires further detail.”

Answer: Section 2 was shorten. New Section 3 was created where information about FEM model were moved. More discussions were provided for fig. 12 and 13.

5. “While the results are presented, the paper lacks in-depth discussion. The validation using a feedforward artificial neural network (ANN) model is only briefly described. The rationale for selecting this algorithm, the process for designing its architecture, and how it compares to existing ANN models should be discussed. Furthermore, the authors should compare the ANN's performance with other ML models to justify their choice.”

Answer: One of the authors, in his previous research has already compared accuracy and computational time of different ML models in the presented specific application (operational load monitoring), please see reference [35]. Four different types of ML models were considered: Artificial neural networks (ANNs), Adaptive neuro-fuzzy inference systems (ANFIS), support-vector machines (SVM) and Gaussian processes for machine learning (GPML). For each type, hyperparameter optimization was performed using grid-search approach, to find an architecture of the highest accuracy. Then, the four optimal prediction models were compared. The accuracy of predictions was measured and was of the same order of magnitude for each model. GPML and ANFIS were eliminated because they both turned out to be less accurate and more computationally demanding than SVM model. ANN was about 3.4 times faster than SVM. For this reason, ANN was selected as the prediction model in the considered paper. The architecture was also chosen based on the previous research where the feed forward model with one hidden layer turned out to be sufficient for similar application. The number of neurons in the hidden layer was chosen arbitrarily because the main goal in the presented research was to compare the accuracy of predictions from sensor measurements of optimized and random placement. To achieve this, utilizing a prediction model of identical architecture for each case is crucial.

This previous work was cited as [35] and explanation about choosing the specific ML method and ANN architecture was added to the paper.

6. The discussion section should be strengthened by addressing the limitations of the proposed model and offering insights into its practical applicability.

Answer: Even though the proposed optimization method improves prediction accuracy, it has some limitations. First, it uses computationally generated data (from FEM model in the numerical example). This means that all load cases must be identified and known, as well as an accurate numerical model is required. The sensor noise in real-life situations can be overcome by adding artificial white gaussian noise to the numerically generated data. This will make the prediction model more immune to noisy input data. Uncertainties like sensor installation errors or structural degradation over time may also occur, that will affect the measurements.

Another limitation is that this method does not optimize the number of sensors, so the user needs to try different variants. Temperatures and strains were taken as examples of simple scalar and tensor quantities. This method could be also used to determine e.g. optimal accelerometers positions. In the coupled thermomechanical problem, the proposed method and algorithms could be utilized to determine optimal positions of a given number of temperature sensors and a given number of strain sensors, separately. Different combinations of numbers of temperature and strain sensors could be then used to train required prediction model and this way a minimal number of each sensor type could be determined that ensures required prediction accuracy. Defining and solving an optimization problem that allows to find minimal number of temperature and strain sensors and their optimal mutual position is a very interesting direction for future research.

The practical applicability is where OLM is implemented: airplanes, bridges, pipelines, wind turbines, underground vehicles for mining industry [21,22,23].

The manuscript was expanded with discussion about the abovementioned limitations and the Conclusion section was expanded with future research directions. Introduction section was expanded with references to practical applications of OLM.

 

Once again, thank you for the time you put in reviewing the paper and we look forward to meeting your expectations.

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript “Optimization of Sensors Positions and Orientations for Multiple Load Case Scenarios” delivers the objective stated in its title and adds a sound contribution to previous work.

Its impact falls under the Structural Health Monitoring broader field, not as an advance, but as a tool.

Modelling and optimisation are done to the current state-of-the-art and no sceintific shortcomings were found.

On the other hand, the manuscript is poorly prepared, showing a lack of depth on the field broader view. This is particularly obvious in the introduction and shalow literature review.

Analysis could, and should, be taken to another level, investigating the outcomes and future prospects and, above all, framing and discussiong the research limitations.

The bottom line is that this is not an advance in the field, nor something worth refering to as novel, but it is an hones contribution, that will be instrumental for others.

Hence, the manuscript should be improved and published.

Author Response

Thank you for your constructive comments in the review. Your comments provided valuable insights to refine the contents of the paper. Below please find the summary of modifications made to the manuscript.

1. Strengthening of the Manuscript and Expansion of the State-of-the-Art

The revised version is improved by the addition of the literature review and the focus in the context of the problem as well as a more detailed explanation of the proposed solution. In the introduction, the discussion of the existing sensor placement techniques is extended and deepened. This extended overview places the proposed method more clearly in a state of the art. Moreover, an overview of machine learning methods and their applications in SHM techniques was added.

2. Novelty Compared to Existing Publications

The novelty of the presented work is in the application— the paper concerns load or stress monitoring for different load cases while most literature focuses on damage detection, modal identification, or mode shape reconstruction. Previous approaches (e.g., EFI, FIM, or hybrid methods) are aimed at improving observability or detect damage, not to track varying operational loads or stresses under different scenarios without knowing the load location.

Our objective function also differs significantly. Instead of maximizing information content (as in FIM-based methods) or targeting dynamic modes, it minimizes the difference between true maximum structural response (e.g. strain or temperature) and sensor-detected response under all load cases. It includes positions and orientations of the sensors and is therefore well suitable for direction dependent measurements such as 3D strain measurements. This function directly targets the performance of load/stress prediction models, making it better suited for machine-learning-driven monitoring systems under real conditions.

This work also considers sensors of different physical quantities within the same framework. Temperatures and strains were taken into account as examples of scalar and tensor quantities. However, the same optimization methodology and algorithms could be used e.g. for finding optimal accelerometers positions.

3. Expansion of Methodology description

More detailed explanation on how are the weights w_i for different load cases calculated is provided. Also, description about the sensitivity coefficients to perpendicular strain, α and β, was extended. References to literature values were provided and justification of assumed values in the numerical example was added. Also, validation section is improved. Now, comparison of some machine learning models is added, and why an artificial neural network (ANN) was chosen, based on preliminary investigation on their performances.

4. Results Discussion

More discussions were provided for obtained FEM results. Conclusion section was expanded with future research directions formulated based on the obtained results.

 

Once again, thank you for the time you put in reviewing the paper and we look forward to meeting your expectations.

 

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript has been revised.

Author Response

thank you for your comments

Reviewer 2 Report

Comments and Suggestions for Authors

The paper can be accepted

Author Response

thank you for your comments