Method For Optimal Placement Research Articles

Data-driven parallel optimization method for sensor placement and state estimation based on generative adversarial principle in unobservable systems

Abstract Data-Driven State Estimation (DDSE) is characterized by low measurement requirements and high estimation accuracy, which provides the possibility of stable and efficient estimation for unobservable distribution systems with low measurement quantities. However, the lack of an efficient and flexible sensor placement method with DDSE at this stage hinders the development and application of DDSE in distribution networks. To address this issue, a data-driven parallel optimization method for sensor placement and state estimation based on the generative adversarial principle in unobservable systems is proposed in this paper. This method transforms sensor placement and state estimation into an adversarial learning model, solvable through gradient descent. The sensor placement optimization strategy generates a cost-effective placement scheme, while DDSE evaluates the sensor scheme, provides improvement suggestions, and enhances its estimation accuracy. Through adversarial training, the proposed scheme yields a significantly reduced number of sensor placement schemes compared to traditional methods, while maintaining high precision of DDSE. Simulation results on the IEEE-33 node system validate the effectiveness of the proposed approach.

Joint optimal PMU and DULR placement in distribution network considering fault reconstruction and state estimation accuracy

Due to the rapid development of the distribution network, there is an urgent need for high-precision state estimation and safe and stable operation, this paper proposes a joint optimal placement method for Phasor Measurement Unit (PMU) and Dual Use Line Relay (DULR) in distribution networks considering fault reconstruction and state estimation accuracy. The proposed method aims to minimize the cost of PMU and DULR configuration. Based on the known pseudo-measurements and Supervisory Control and Data Acquisition (SCADA) measurements, we use the E-optimal standard design of the state estimation error covariance matrix to form the state estimation accuracy index and take the relay protection function of Feeder Terminal Unit (FTU) device and DULR device into consideration of the fault reconstruction. By solving the mixed integer semidefinite programming (MISDP) model, the optimal placement result is obtained, so that the network under normal condition and the network after multiple fault reconstruction can meet the constraints of state estimation accuracy and load loss rate respectively. The proposed method is tested on IEEE 33-node, 123-node systems as an example. The experimental results show that the proposed method is effective and practical.Note to Practitioners—This study is stimulated by the need for optimizing the placement of Micro-PMU (µPMU) in distribution network. Since the new µPMU device DULR has the same relay protection function as FTU, and distributed generation can supply power to the island after failure, this paper adds the load loss rate to the constraint conditions to study the influence of fault reconstruction on the placement scheme. A new two-step SE method considering mixed measurements was used in this paper to improve the computational efficiency of real-time SE of large-scale system while ensuring the accuracy of the calculation results. We have conducted tests in IEEE-33 and IEEE-123 systems. After preliminary verification, compared with the single fault scenario, we find that the placement scheme considering multiple fault scenarios can effectively improve the accuracy of state estimation and reduce the load loss rate of each fault scenario and only increase the cost a little. The increase in the number of DG and contact lines in the network will also effectively improve the feasibility of the placement scheme. The increase of the number of FTU configurations can effectively reduce the configuration of DULR by adding a small amount of µPMU, reduce the total cost as a result. In future studies, we will further consider the integrated configuration of µPMU, DULR and FTU, to meet more failure scenarios while reducing costs.

A Novel FBG Placement Optimization Method for Tunnel Monitoring Based on WOA and Deep Q-Network

By employing the whale optimization algorithm’s (WOA) capability to reduce the probability of being stuck in a locally optimal solution, this study proposed an improved WOA-DQN algorithm based on the Deep Q-Network algorithm (DQN). Firstly, the mathematical model of Fiber Bragg Grating (FBG) sensor placement was established to calculate the reward of DQN. Secondly, the effectiveness and applicability of WOA-DQN were validated through experiments in nine cases. It indicated that the algorithm is far superior to other methods (Noisy DQN, Prioritized DQN, DQN, WOA), especially with the learning rate of 0.001, the initial noise 0.4, the hidden layer 3–512, and the updated frequency of 20. Finally, the FBG sensors were placed at [0°, 27°, 30°, 47°, 51°, 111°, 126°, 219°, 221°, 289°] to detect the accurate deformation of the tunnel with the maximum error 8.66 mm, which is better than the traditional placement. In conclusion, the algorithm provides a theoretical foundation for sensor placement and improves monitoring accuracy. It further shows great promise for deformation monitoring in tunnels.

A physics-driven sensor placement optimization methodology for temperature field reconstruction

Perceiving the global field from sparse sensors has been a grand challenge in the monitoring, analysis, and design of physical systems. In this context, sensor placement optimization is a crucial issue. Most existing works require large and sufficient data to construct data-based criteria, which are intractable in data-free scenarios without numerical and experimental data. To this end, we propose a novel physics-driven sensor placement optimization (PSPO) method for temperature field reconstruction using a physics-based criterion to optimize sensor locations. In our methodological framework, we firstly derive the theoretical upper and lower bounds of the reconstruction error under noise scenarios by analyzing the optimal solution, proving that error bounds correlate with the condition number determined by sensor locations. Furthermore, the condition number, as the physics-based criterion, is used to optimize sensor locations by the genetic algorithm. Finally, the best sensors are validated by reconstruction models, including non-invasive end-to-end models, non-invasive reduced-order models, and physics-informed models. Experimental results, both on a numerical and an application case, demonstrate that the PSPO method significantly outperforms random and uniform selection methods, improving the reconstruction accuracy by nearly an order of magnitude. Moreover, the PSPO method can achieve comparable reconstruction accuracy to the existing data-driven placement optimization methods.

Sparse regularized graph pooling network optimal sensor placement method for diesel engine vibration fault perception system

Vibration sensor network optimization increases monitoring effectiveness and reduces sensor quantity and transmission burden. However, the traditional model-driven methods depend on precise finite element models, challenging for complex machinery. This paper presents a data-driven approach using the Sparse Regularized Graph Pooling Network (SRGPN), which conceptualizes sensor networks as graphs and uses graph pooling to identify optimal sensor combinations. A sparsity regularization term related to the number of sensors is included in the loss function, aiming for the minimal yet effective sensor combination. Additionally, a monitoring capability metric suited for diesel engines with multi-source impulse signals is proposed, reflecting the sensors’ monitoring capacity. Validated through simulations and tests on a diesel engine test bench, the results show that SRGPN optimally places sensors near excitation sources, balancing sensor count and monitoring needs. This approach shows potential for optimizing sensor placements in condition monitoring.

Optimal sensor placement and structural health monitoring methods of ancient stone bridges based on an improved genetic algorithm: Taking Lugou Bridge as an example

In this paper, a modified genetic algorithm (GA), Meta-GA, was developed to determine the optimal sensor placement (OSP). Then, the proposed OSP method was compared with the other two GA-based methods. Finally, a 15-month-long structural health monitoring was conducted for Lugou Bridge using the best sensor layout. The deformation monitoring results were compared with point cloud using a four-step method. The damage detection capability of the obtained sensor layout was also verified. The results show that Meta-GA has good computational efficiency and it can save 9.16 %∼28.24 % of optimization time compared to GA. Moreover, the damage sensitivity index obtained from Meta-GA is 12 %∼64 % higher than those of GA-based methods. Furthermore, the error between the monitoring deformation and the point cloud results is almost within 15 %. 90 % of apparent damage locations can be identified based on current sensor data. The research results can support for the structural health monitoring of masonry bridge.

GCP Placement Methods for Improving the Accuracy of Shoreline Extraction in Coastal Video Monitoring

In coastal video monitoring, the direct linear transform (DLT) method with ground control points (GCPs) is commonly used for geo-rectification. However, current practices often overlook the impact of GCP quantity, arrangement, and the geographical characteristics of beaches. To address this, we designed scenarios at Chuam Beach to evaluate how factors such as the distance from the camera to GCPs, the number of GCPs, and the height of each point affect the DLT method. Accuracy was assessed by calculating the root mean square error of the distance errors between the actual GCP coordinates and the image coordinates for each setting. This analysis aims to propose an optimal GCP placement method. Our results show that placing GCPs within 200 m of the camera ensures high accuracy with few points, whereas positioning them at strategic heights enhances shoreline extraction. However, since only fixed cameras were used in this study, factors like varying heights, orientations, and resolutions could not be considered. Based on data from a single location, we propose an optimal method for GCP placement that takes into account distance, number, and height using the DLT method.

An all-purpose method for optimal pressure sensor placement in water distribution networks based on graph signal analysis

Many researchers have addressed the challenge of optimal pressure sensor placement for different purposes, such as leakage detection, model calibration, state estimation, etc. However, pressure data often need to serve multiple purposes, and a method to optimize sensor locations with versatility for various objectives is still lacking. In this paper, a graph-based optimal sensor placement (GOSP) framework is proposed, which aims to provide a robust and all-purpose approach to identify critical points for pressure monitoring. By analysing the spatial variation frequencies of WDN pressures, the relationship between measurements and the global variation of original pressures is established. On this basis, the D-optimality criterion is adopted to formulate the objective of GOSP, which aims to maximize the information on the spatial distribution of pressures that can be obtained from measurements. The new-proposed objective ensures that the sensor locations are compatible with various application scenarios. The proposed method was applied to a real-life distribution network, and was compared with other optimal sensor placement methods oriented towards burst detection and pipe roughness calibration. Based on comparative studies in different scenarios including unknown pressure estimation, burst detection, and model calibration, the effectiveness and robustness of the proposed method have been proved.

Novel optimal sensor placement method towards the high-precision digital twin for complex curved structures

The complex shape of the structure and the new needs for high-precision in digital twin modeling pose challenges for sensor placement optimization. A novel optimal sensor placement towards the high-precision digital twin (OSP-HDT) method is proposed for complex curved structures. It comprises three key aspects. Firstly, leveraging the spatial dimensionality reduction method, the complex curved surface is simplified into a planar representation. Subsequently, candidate sensor placement points can be easily identified by dividing the background mesh in the plane and screening them within the curved surface. These candidate points are then binary encoded to facilitate the subsequent optimization. Secondly, the method collects result data from the finite element model, treating it as virtual sensor data. Using this data, a surrogate model is constructed and then the objective function is formulated based on both the global and local critical areas precision of the surrogate model. Thirdly, the sensor placement optimization model is constructed, followed by optimization design using the efficient multi-objective covariance matrix adaptive evolutionary strategy. Through the steps above, the optimal sensor placement can be identified. To validate the proposed OSP-HDT method, an experiment is conducted on an S-shaped variable cross-section stiffened shell, with the construction of the corresponding digital twin. Compared to the uniform placement with an equivalent number of sensors, the OSP-HDT method demonstrated a significant 9.0% improvement in global precision and a remarkable 62.1% enhancement in local precision of critical areas. Furthermore, when compared to the random sensor placement strategies, the OSP-HDT method exhibited a 20.5% increase in global precision, together with a 44.2% increase in the local precision. Notably, even when compared to the full sensor placement, the OSP-HDT method can maintain comparable local precision, while significantly reducing the number of sensors by 77.6%. The above comparison indicates that the proposed OSP-HDT method can build a digital twin model with higher global and local precision for complex structures.

Assessment of different optimal sensor placement methods for dynamic monitoring of civil structures and infrastructures

The optimal sensor placement is a critical aspect in the structural health monitoring of structures, as the number and layout of sensors directly impact the quality and usefulness of collected data. When developing a monitoring system, it is of paramount importance to use the minimum number of sensors to gain the maximum amount and quality of information. However, in the case of a limited number of sensors, their location on the structure becomes crucial. This study aims to assess the potential of several optimal sensor placement methods for the development of cost-efficient and well-dimensioned dynamic structural health monitoring systems to be implemented in a wide range of civil engineering structures and infrastructures. Indeed, the construction stock consists of a great variety of civil engineering structures and infrastructures that significantly differ from each other in terms of typology, historical period, construction techniques, materials, etc. Some of the most widely used optimal sensor placement methods are selected and applied in real case studies, and the obtained sensor configurations are discussed and compared. The results illustrated in this paper will contribute to defining good practice in the optimal sensor placement procedure for typical civil engineering structures and infrastructures.

Optimal placement of light sensor for improving energy efficiency and visual comfort in smart buildings

The energy consumed by artificial lighting accounts for a significant part of the energy consumption in buildings. Thus, energy consumption can be significantly decreased using optimization techniques, such as the optimum placement of the lighting sensors. In this paper, an optimal placement method of the light sensors is presented to minimize the lighting system's equipment costs and energy consumption and also meet visual comfort under the requirements of the European standard EN12464–1 regarding illuminance-based criteria. In the beginning, based on the illumination measurement grid's mathematical model, the potential location of the sensors is determined. As an average of the dimming levels of the LED lights, the objective function has been introduced. Then, the illuminance and uniformity levels are defined as constraints for the optimization problem. The Battle Royale Optimization (BRO) algorithm is used to solve the optimization problem. Ultimately, based on the results of the BRO algorithm and the calculation of the illuminance deviation, the optimal location of the light sensors is determined. The proposed method is tested in an office room. A fuzzy logic controller is developed to regulate the lighting control system's dimming levels to evaluate the proposed method's performance with other approaches. The comparison results have shown that the proposed method is superior as regards the number of sensors and the optimal sensor position, significant savings in energy consumption of up to 30.8%, and satisfactory visual comfort per the requirements of the European standard EN12464–1.

Optimal sensor placement for ensemble-based data assimilation using gradient-weighted class activation mapping

We introduce an optimal sensor placement method using convolutional neural networks for ensemble-based data assimilation. The proposed method utilizes the gradient-weighted class activation mapping of the convolutional neural networks to identify important regions for assimilation processes. It is achieved by using the initial ensemble of samples for data assimilation as training data to construct a convolutional neural network-based surrogate model. In doing so, the method can estimate optimal sensor locations in an a priori manner, allowing for sensor placement before conducting data assimilation processing. Moreover, the gradient-weighted class activation mapping is used to alleviate the effect of error accumulation during the backpropagation process through global averaging. Further, these observation sensors are incorporated to reconstruct mean turbulent flow fields based on the ensemble Kalman method. The proposed optimal sensor placement method is applied to two flow applications with complex geometries, i.e., flows around periodic hills and an axisymmetric body of revolution. Both cases demonstrate that the proposed method can significantly reduce the number of sensors without sacrificing the accuracy of the reconstructed flow field.

A maximum entropy deep reinforcement learning method for sequential well placement optimization using multi-discrete action spaces

Well placement optimization is a crucial method to solve the planar conflicts in reservoir development, mainly to determine the optimal well locations and drilling sequence to maximize the economic benefits of reservoir development. However, the current well placement optimization methods face the problems of high-dimensional discretization of optimization variables and lack of effective incentives for policy exploration, which make it challenging to improve the global optimization ability (the ability to jump out of locally optimal solutions in time and continuously search for better solutions in the whole optimization process) and real-time adjustability of the well placement optimization methods under limited numerical simulation times. In this paper, we propose a new sequential well placement optimization method, based on the Discrete Soft Actor-Critic Algorithm (DSAC), which incorporates the maximum entropy mechanism to formulate well placement and drilling sequencing schemes more efficiently and maximize the net present value (NPV) over the entire life cycle of reservoir development. Specifically, the method models the well placement optimization problem as a Markov Decision Process (MDP) and achieves sequential well placement optimization by training a Deep Reinforcement Learning (DRL) agent that maps reservoir states to a stochastic policy of well placement variables as well as evaluates the value function of the current policy. The DRL agent can determine the optimal infill well location in real-time based on the reservoir state at different times during the development process, thus obtaining the optimal drilling sequence. The proposed method in this paper has two innovations. First, by reconstructing the large-scale discrete action space of well placement optimization variables into multi-discrete action spaces, and with the maximum entropy mechanism, policy exploration is encouraged to improve the global optimization capability. Second, the trained policy can swiftly adapt the subsequent well placement scheme for a specific state of the target reservoir without the requirement to initiate training from scratch, which can realize the offline application of the trained policy and has better real-time adjustability. To verify the effectiveness of the proposed method, it is tested in 2D and 3D reservoir models. The results show that DSAC not only outperforms the gradient-based optimization method, classical evolutionary algorithms, and existing reinforcement learning proximal policy optimization (PPO) method in terms of global optimization ability but also shows better real-time adjustability of the trained policy when applied offline.

Presenting a new method for optimal placement of reliability-based distributed generation units in the transmission system considering the demand response schedule

Presenting a new method for optimal placement of reliability-based distributed generation units in the transmission system considering the demand response schedule

Study of Reducing Transmission Losses in Java-Bali System with the Addition of Capacitors along with Optimal Capacitor Placement Methods Using Quasi-Dynamic Simulation

The Java-Bali electricity system is the largest electricity system in Indonesia which consists of 5 areas including Jakarta-Banten area, West Java area, Central Java area, East Java area and Bali area. This system is operated to meet the economic, reliability, quality, and green principles. In the case of reliability, one of the essential aims is minimization of transmission losses due to importance in system improvement to increase system operational efficiency to the possible extent. Transmission losses are an inevitable part of the electric power transfer process from generation stations to consumers. The power losses in a transmission line are inversely proportional to the square of the line voltage. This implies that lower line voltages result in higher power losses. Therefore, it is crucial to maintain optimal voltage levels to minimize transmission losses and ensure efficient energy delivery across the power system. One effective way to achieve this is by integrating capacitors into the system. In this study, we have explored two methods that aim to pinpoint the most advantageous locations for the integration of new capacitors. The goal is to optimize capacitor planning, with an emphasis not only on improving voltage levels but also on minimizing transmission losses within the Java-Bali system. The research results indicate that implementing two proposed methods can significantly reduce transmission losses in The Java-Bali system. Method-1 involves identifying the lowest voltage over the course of a year, while Method-2 focuses on the lowest voltage value within the first quartile (Q1/25%) during the same period

A Novel Optimal Sensor Placement Method for Optimizing the Diagnosability of Liquid Rocket Engine

There are hundreds of various sensors used for online Prognosis and Health Management (PHM) of LREs. Inspired by the fact that a limited number of key sensors are selected for inflight control purposes in LRE, it is practical to optimal placement of redundant sensors for improving the diagnosability and economics of PHM systems. To strike a balance between sensor cost, real-time performance and diagnosability of the fault diagnosis algorithm in LRE, this paper proposes a novel Optimal Sensor Placement (OSP) method. Firstly, a Kernel Extreme Learning Machine-based (KELM) two-stage diagnosis algorithm is developed based on a system-level failure simulation model of LRE. Secondly, hierarchical diagnosability metrics are constructed to formulate the OSP problem in this paper. Thirdly, a Hierarchy Ranking Evolutionary Algorithm-based (HREA) two-stage OSP method is developed, achieving further optimization of Pareto solutions by the improved hypervolume indicator. Finally, the proposed method is validated using failure simulation datasets and hot-fire test-run experiment datasets. Additionally, four classical binary multi-objective optimization algorithms are introduced for comparison. The testing results demonstrate that the HREA-based OSP method outperforms other classical methods in effectively balancing the sensor cost, real-time performance and diagnosability of the diagnosis algorithm. The proposed method in this paper implements system-level OSP for LRE fault diagnosis and exhibits the potential for application in the development of reusable LREs.

Scenario modeling-aided AP placement optimization method for indoor localization and network access

Scenario modeling-aided AP placement optimization method for indoor localization and network access

A Sensor Placement Approach Using Multi-Objective Hypergraph Particle Swarm Optimization to Improve Effectiveness of Structural Health Monitoring Systems.

In this paper, a novel Multi-Objective Hypergraph Particle Swarm Optimization (MOHGPSO) algorithm for structural health monitoring (SHM) systems is considered. This algorithm autonomously identifies the most relevant sensor placements in a combined fitness function without artificial intervention. The approach utilizes six established Optimal Sensor Placement (OSP) methods to generate a Pareto front, which is systematically analyzed and archived through Grey Relational Analysis (GRA) and Fuzzy Decision Making (FDM). This comprehensive analysis demonstrates the proposed approach's superior performance in determining sensor placements, showcasing its adaptability to structural changes, enhancement of durability, and effective management of the life cycle of structures. Overall, this paper makes a significant contribution to engineering by leveraging advancements in sensor and information technologies to ensure essential infrastructure safety through SHM systems.

Sensor Placement Optimization of Visual Sensor Networks for Target Tracking Based on Multi-Objective Constraints

With the advancement of sensor technology, distributed processing technology, and wireless communication, Visual Sensor Networks (VSNs) are widely used. However, VSNs also have flaws such as poor data synchronization, limited node resources, and complicated node management. Thus, this paper proposes a sensor placement optimization method to save network resources and facilitate management. First, some necessary models are established, including the sensor model, the space model, the coverage model, and the reconstruction error model, and a dimensionality reduction search method is proposed. Next, following the creation of a multi-objective optimization function to balance reconstruction error and coverage, a clever optimization algorithm that combines the benefits of Genetic Algorithms (GA) and Particle Swarm Optimization (PSO) is applied. Finally, comparison studies validate the methodology presented in this paper, and the combined algorithm can enhance optimization effect while relatively reducing running time. In addition, a sensor coverage method for large-range target space with obstacles is discussed.

Способ построения двухэлементной цифровой антенной решетки для оценки угловых координат радиосигналов со сверхразрешением с повышенной точностью на основе нижней границы Крамер-Рао

In the paper an effective method for optimal placement of directional antenna elements for digital spatial signal estimation is discussed. The digital antenna array evaluates spatial coordinates with the subsequent beamforming. However, as it is well known, the relative position of antenna elements, their number and the shape of the radiation pattern have a significant impact on the quality of the spatial pseudospectrum. The paper uses the previously obtained expression for estimating the Cramer-Rao lower bound to reduce the number of antenna elements without losing the accuracy of direction-of-arrival estimation of the signals. For example, a two-element array is obtained. The elements have a flat-top radiation pattern. It is shown that the accuracy of the MUSIC method in the obtained array is higher or comparable to the array composed of three elements.