A Systematic Review of Optimization Algorithms for Structural Health Monitoring and Optimal Sensor Placement
Abstract
:1. Introduction
- Sensing: Sensors are one of the most critical components of any SHM system, and various sensor types are suitable for SHM, such as accelerometers, strain gauges, optical fiber sensors, tiltmeters, and lasers. SHM sensor systems can detect a system’s condition, such as displacement and stress, and assess the effects of environmental variations, including moisture, wind speed, and temperature. The performance of an SHM system depends highly on the data quality measured by the sensor network. Depending on the system requirements, different monitoring strategies are applied, such as strain monitoring, electromechanical impedance monitoring (EMIM), elastic waves monitoring (EWM), vibration-based damage detection, and comparative vacuum monitoring (CVM). Suitable SHM sensors are also used in other fields, such as construction progress monitoring, structural design, safety risk assessment, maintenance management, and smart operations. A comprehensive review of conventional sensor systems can be found in [6], and of advanced sensor systems in [7,8].
- Data analysis: The recorded sensor data typically undergoes a process of data acquisition, signal conditioning, data transfer, data storage, signal processing, and data interpretation. Many data analysis methods have been developed over the years and are constantly being further advanced. The rapid progress in artificial intelligence (AI) and data mining led to a transformation and renewal of data analysis methodologies for SHM. While data analysis techniques, such as traditional signal processing, are applied to datasets to execute and test models and hypotheses, regardless of the amount of available data, AI methods, such as deep learning, uncover hidden patterns in large volumes of data [9]. A comprehensive review of conventional monitoring strategies can be found in [10], and of advanced monitoring techniques in [11].
1.1. Background on Optimization Algorithms for SHM
- 1.
- Definition of the optimization problem.
- 2.
- Specification of the objectives to be maximized or minimized.
- 3.
- Selection of decision variables.
- 4.
- Consideration of restraints.
- 5.
- Formulation of final models. Here, the desired goal is defined as the objective function, consisting of variables and constraints, which are functional relations of the inequalities and equalities of the variables.
- First-order optimization algorithms [28]: Optimization algorithms minimize or maximize a loss function (or objective function), , using gradient values. Gradient descent is a widely used first-order optimization algorithm. First-order derivatives can determine whether a function increases or decreases at a particular point. First-order derivatives are lines that are tangential to their error surfaces. First-order optimization techniques are generally time-saving and straightforward calculation methods that converge quickly for large datasets.
- Second-order optimization algorithms [29]: In these algorithms, error functions (or objective functions) are maximized or minimized using a second-order derivative, also known as the Hessian. The Hessian of a matrix can be considered the partial derivative of the second order of the same matrix. The second order is rarely used, considering the cost of calculating second derivatives. A function’s curvature, also known as the second-order derivative, can be used to determine whether the first derivative is increasing or decreasing. Second-order derivatives are quadratic surfaces where the error surface’s curvature can be touched. In general, second-order optimization techniques are time-consuming and memory-intensive.
1.2. Selection Process and Organization of Papers
2. Structural Health Monitoring
- Step 1: Define the health monitoring problem. This step includes identifying and defining the system requirements, conditions, and limitations, such as the following: loading environment, damage and failure modes, initial damage conditions, system life cycle, warranty and duty-cycle issues, existing sensors, maintenance history, and diagnostic and prognostic requirements.
- Step 2: Develop the SHM models (analytical, numerical, experimental). In this step, SHM models are developed, specifying the following components and transducers: data-driven and model-based approaches, developing failure and damage models, analyzing the sensitivity of components to damage and loads, developing models based on the effects of EOCs and validating and updating models.
- Step 3: Develop and implement measurement systems. This step includes evaluating the information environment (e.g., bandwidth and amplitudes), encompassing the following: defining variables to identify damage and loads, establishing a measurement infrastructure, adjusting actuators and sensors to the optimal positions to determine fault, and calibrating actuators and sensors continuously.
- Step 4: Interrogate information and develop damage identification algorithms. This step includes filtering and processing measurement data, which entails the following: identifying and minimizing sources of computational variability, extracting damage features using models, identifying and reducing variables that are not measured and detecting and quantifying damage and loads.
- Step 5: Develop damage and performance prediction algorithms. This step includes specifying future loading scenarios: selecting damage and failure models, predicting damage initiation and evolution, defining and reducing uncertainty sources in damage prediction and predicting future performance.
- Types of SHM system
- Types of sensors
- Methods of excitation
- Quantity of sensors and excitation points
- Sensor and excitation locations
- Data transfer type and storage mechanisms
- Types of data acquisition systems
- Information management types
- Types of information interpretation and diagnosis
2.1. Degrees of Freedom
2.2. SHM Assessment Types
- Monitoring time frames:
- .
- Long-term monitoring: This monitoring aims to identify structural faults in a system by monitoring its performance over a long period.
- .
- Short-term monitoring: Assessment methods with a short-term objective, typically involving NDT techniques.
- .
- Early warning: In this type of monitoring, an early warning alarm is issued when a predetermined threshold is exceeded, informing the user to monitor for possible damage.
- .
- Inspection: This type of monitoring aims at assessing the condition of a system or its components on a regularly scheduled basis.
- .
- Collapse warning: This monitoring plan involves the shutdown of the inspected systems when there is a risk of system collapse.
- Monitoring scales:
- .
- Member monitoring: A specific member of a system is monitored.
- .
- Local monitoring: A particular region of a system is assessed.
- .
- Global monitoring: The overall health state of the entire system is monitored.
2.3. Sensor Characteristics
- System objectives: Any SHM strategy must consider the objectives of the system, such as research, condition assessment, validation of design assumptions, or hazard- specific safety.
- Type of structure: Suitable sensor types depend on specific characteristics of the structure to be monitored, such as the type of materials (e.g., concrete or steel), the design life of the structure, or the location of the structure’s site (e.g., underwater or underground).
- Measurable quantities: The type of data that needs to be measured, i.e., the chemical or physical quantity, further dictates the choice of sensors.
- Sensor specifications: The specifications of individual sensor types are crucial properties to be considered and include sensitivity, resolution, bandwidth, and range of senses.
- Physical sensor characteristics: The accuracy of test results can be affected by physical factors of sensors, including size, weight, strength, and interactions with systems.
- EOCs: Sensors designed for laboratory testing may not be suitable for harsh environments. A sensor must be protected from hostile states when operating in harsh conditions, such as at high or low temperatures, in chloride, in humid conditions, or in acid.
- System cost: The total cost of an SHM system is a crucial factor in designing the sensor network. Costs include costs of sensors, acquisition systems, additional hardware, labor, monitoring duration, system maintenance, and expertise in analyzing information and preparing reports.
- Sensor quantity and placements: To determine the sensor numbers and locations, all of the above criteria must be considered. In addition, it is essential to determine how much redundancy the sensing system should have since sensor failure is unavoidable.
2.4. SHM Methodologies
3. Optimal Sensor Placement
- 1.
- Set sensor quantities: In this step, the number of sensors installed on a system is determined. It defines the most cost-effective method by selecting the optimal number of sensors that still enables accurate system representation.
- 2.
- Optimize sensor locations: This step involves deriving the best sensor placements to obtain the most accurate system data.
- 3.
- Evaluate sensor layout: In this step, the performance of various sensor configurations are evaluated, based on optimal system representation.
3.1. Effective Independence
- The vector of the unknown is defined by = [ , , …, ].
- The unknown parameters are and .
- X defines the sampled random variable.
- The likelihood function of is defined by = .
- E defines the expectation.
3.2. Effective Independence Driving-Point Residue (EI–DPR)
3.3. Kinetic Energy (KE)
3.4. Eigenvalue Vector Product (EVP)
3.5. Mutual Information
- and are the measurements from locations A and B, respectively.
- and are the individual probability densities for data A and B, respectively.
- The joint probability density for data A and B is defined by .
3.6. Information Entropy Method
- is the uncertain parameter set (e.g., stiffness parameters, modal parameters, etc.)
- D is defined as the information of the dynamic test.
- is the mathematical expectation concerning .
3.7. Sensitivity-Based Methods
4. Optimization Algorithms
- Optimization describes and predicts the behavior of a process and is implemented with a mathematical model.
- Optimization aims to find decision variables that minimize or maximize one or more objectives while satisfying constraints.
- The choice of the optimization technique and the formulation of the objective functions affect the reliability of optimal solutions.
- Optimization can effectively estimate unknown parameters, especially in complex nonlinear processes.
- Objective function: In an optimization problem, the objective function (or error function) is iteratively minimized or maximized. The objective function is a linear or nonlinear equation that can also be a single numerical quantity. The objective can be various issues, such as the effective return on a stock portfolio, the time of vehicle arrivals at a specified destination, profits or costs of a company’s production, or the vote share of a political candidate.
- Variations: The quantities or variables that optimize the error function are termed variations. They include various parameters, such as the amount of stock to be bought or sold, the advocated policies by a candidate, or the route followed by a vehicle through a traffic network.
- Constraints: The optimization problem constraints limit its variables (limits of variables). A simple example of a constraint in a production process is that it cannot use less than zero resources and cannot use more resources than are available.
- Traditional optimization techniques [177]: These algorithms are deterministic algorithms that follow specific rules to move from one solution to another. Many engineering design problems have been successfully solved using these types of optimization, such as the following: geometric programming, dynamic programming, nonlinear programming, generalized reduced gradient method, and quadratic programming, etc. The two general divisions of these methods are as follows:
- .
- Derivative algorithms: hill-climbing algorithms, including gradient descent and Newton’s method.
- .
- Derivative-free algorithms: trust-region or pattern search methods.
Despite the widespread use of traditional optimization methods for mechanical design optimization, these techniques are ineffective across a broad spectrum of problems. This is primarily due to their tendency to find local optimal solutions, which are not suitable for solving multivariate problems. - Advanced optimization techniques [178]: These algorithms are based on stochastic approaches with probabilistic transition rules. Implementing these methods is relatively new and gaining popularity, since they offer properties that deterministic algorithms do not have. These algorithms are also known as metaheuristic algorithms and include the following: differential evolution (DE), evolutionary algorithm (EA), harmony elements algorithm (HEA), genetic algorithm (GA), Hybrid (Hy) algorithm, biogeography-based optimization (BBO), particle swarm optimization (PSO), swarm intelligence (SI) algorithm, artificial immune algorithm (AIA), artificial bee colony (ABC), simulated annealing (SA), differential evolution (DE), harmony search (HS), cuckoo search (CS), and firefly algorithm (FA), artificial bee colony (ABC), Tabu search (TS) algorithm, genetic programming (GP), monkey algorithm (MA), cooperative–competitive evolutionary algorithm (CoEa), expectation-propagation (EP) algorithm, firefly algorithm (FA), whale optimization algorithm (WOA), mixed-integer linear programming optimization (MILP), hybrid metaheuristic optimization algorithm (HGACS), modified TLBO algorithm (MTLBO), and multi-objective evolutionary algorithm (MOEA).
Type | Refs. | Advantages | Disadvantages |
---|---|---|---|
GA | [186,187] | - Convergence with low probability to local maxima or minima;
- Insensitive to target functions of a specific type; - Possibility of parallel and distributed implementations; - Sensitive to parameters in a string of bits, not values; - Relies on probabilistic transition rules; - Uses objective function information, not derivatives. | - Is complex, especially in multi-objective optimization issues; - Long computation time; - Premature convergence may occur due to fitness function coding. |
PSO | [188,189] | - Fast convergence, especially in improved PSO (IPSO) models; - Simple implementation and supported platforms; - Time efficient compared to GA; - Practicality in solving multimodal and nonlinear functions; - Improved versions can solve high-dimensional problems. | - Effects of high inertial weight on optimal convergence; - Possibility of convergence to a local optimum, especially at large inputs; - Cannot optimize discrete problems; - Inferior to GA in terms of commercialization and maturity. |
SA | [190,191] | - Applicable for large, complex, and highly nonlinear optimization; - Has flexibility and guarantees optimal global convergence; - Known as a versatile programming, and complete, algorithm. | - Inverse relationship between computational time and solution quality; - Not efficient in smooth and minor optimization problems; - Sensitive to the rate of initial temperature change in its initializations; - High computational cost, especially for large data sets. |
MILP | [192,193] | - Simple implementation and supported platforms; - High rate of convergence and low gap percentage compared to heuristic optimization methods; - Guaranteed global optimal convergence; - Ability to formulate, especially for different constraints. | - Sensitive to nonlinear system effects; - Low-quality solutions; - No balance between computing time and accuracy; - Sensitive to a large number of binary variables. |
DE | [194,195] | - Better performance compared to GA; - Uses a combination of the same population chromosome in the formation of a new generation. | - Hardly any chromosomes of the previous generation are carried forward to the next generation. However, better results can be achieved. - Mutation and crossover operations are performed in one process. |
ABC | [196,197] | - Self-organizing; - Collective intelligent data; - Few control parameters; - Fast convergence; - Employs both exploration and exploitation | - Search space limited by initial solution (normal distribution sample should be used in initialization step); - Abandons poor solutions; - Poor local search ability. |
ACO | [198,199] | - Simple implementation; - Derivative free; - Good global convergence properties; - Stable optimal result. | - Uncertain convergence time; - Low computational performance and accuracy of the original ACO. |
MA | [200,201] | - Able to search globally; - Able to efficiently search locally; - Generates optimal solutions with a higher level of stability. | - Originally designed for problems with continuous variables. |
TS | [202,203] | - Quick convergence; - Flexible algorithm; - Good-quality solutions are provided by the algorithm; - Secondary designs are provided by the algorithm. | - Some algorithm parameters need adjustments to find a good solution; - Penalty parameters must be used to satisfy the mathematical model’s constraints; - Re-running the algorithm could change the obtained design. |
1950–1990 | 1990–2000 | 2000–2005 | 2005–2010 | 2010–2015 | 2015–2023 |
---|---|---|---|---|---|
Evolutionary Algorithms | |||||
GA; SA; TS | GP; ES; MA; CA; DE; EP; CoEa | GEA | ICA | TLBO; FPA; | SCA; MCEO; ASA; GSO |
Swarm Intelligence Algorithms | |||||
PSO | AFSA; HBO; TCO | ACO; SFL; MS; DPO; FA; BA | FFO; KH; CS; BMO; GWO; SLCA; ALO; DA; MFO | IAPSO; WOA; SSA; GOA; HHO; FSO; BWO; CSO; HOA; ISSA; FSA | |
Hybrid Algorithms | |||||
CBO-PSO; PSO-CS; GWO-SCA; PSO-GWO; MFO-GSA; PSO-WOA; WOA-SA; SA-MFO; SCA-TLBO; HDPSO; PSO-SCA |
Ref. | Year | Optimization Algorithms | Description |
---|---|---|---|
Wetter and Wright [204] | 2004 | Discrete Armijo gradient algorithm, GA, PSO, and Hooke–Jeeves algorithm, | Based on the results of this study, it was revealed that the biggest cost reduction is achieved by combining particle swarms and Hooke–Jeeves algorithms. Additionally, it was shown that a simple GA is an excellent choice if a user is willing to accept a slight reduction in accuracy for the benefit of fewer simulations. |
Hassan et al. [205] | 2005 | PSO and GA | The results revealed that both PSO and GA produced high-quality solutions, with quality indices of more than 99% confidence levels. However, the computational effort required to reach such high-quality solutions by PSO was lower than the computational effort required by GA. |
Bandyopadhyay et al. [206] | 2008 | AMOSA, NSGA-II, and PAES | In the study, SA-based multi-objective optimization algorithm (AMOSA) performed better in most cases than MOSA or non-dominated sorting GA II (NSGA-II), while Pareto archived evolution strategy (PAES) performed poorly in most cases. In complex cases, AMOSA was less time-consuming than NSGA-II. Further, AMOSA performed much better than NSGA-II regarding problems with multiple objectives. |
Yildiz [207] | 2013 | GA, PSO, Immune algorithm, HTDEA, ABC, and DE algorithm | According to computational results and discussions, the hybrid technique based on DE algorithm (HTDEA) was an effective optimization method for solving structural design problems more efficiently than other algorithms. |
Civicioglu and Besdok [208] | 2013 | CK, PSO, DE
and ABC algorithm | Comparing the CK algorithm with the DE algorithm revealed that the CK algorithm was very successful at solving problems. The DE algorithm acquired a global minimizer with lower run-time complexity and needed fewer function evaluations than the comparison algorithms. PSO and Cuckoo-search (CK) algorithms were statistically more similar to DE than ABC algorithms in performance. CK and DE provided more reliable and precise results than PSO and ABC algorithms. |
Hamdy et al. [209] | 2016 | pNSGA-II, MOPSO, PRGA, ENSES, evMOGA, spMODE-II, and MODA | In the study, the pNSGA-II, MOPSO, Two-phase optimization using the GA (PRGA), Elitist non-dominated sorting evolution strategy (ENSES), Multi-objective evolutionary algorithm, based on the concept of epsilon dominance (evMOGA), Multi-objective DE algorithm (spMODE-II) and Multi-objective dragonfly algorithm (MODA) were run 20 times with a gradually increasing number of evaluations, indicating that the PRGA algorithm explored a large part of the solution space and quickly produced close-to-optimal solutions with good diversity. |
Dogo et al. [210] | 2018 | SGD, vSGD, SGDm, SGDm+n, RMSProp, Adam, AdaGrad, AdaDelta, Adamax and Nadam | The results showed that Nadam performed best across all three datasets, whereas AdaDelta performed worst, compared with Stochastic Gradient Descent (SGD), Root Mean Square Propagation (RMSProp), Adaptive Moment Estimation (Adam), Adaptive Gradient (AdaGrad), Adaptive Delta (AdaDelta), Adaptive moment estimation Extension based on infinity norm (Adamax) and Nesterov-accelerated Adaptive Moment Estimation (Nadam) optimization techniques |
Zaman and Gharehchopogh [211] | 2022 | PSO and PSOBSA | It was shown that IPSO with the backtracking search optimization algorithm (PSOBSA) performed better than other well-known metaheuristic algorithms and PSO variants on almost all of the benchmark problems in terms of global exploration ability and accuracy. |
Tawhid and Ibrahim [212] | 2023 | CS, MBO, and MBOCS algorithm | The study showed that the hybrid swarm intelligence optimization (MBOCS) algorithm could overcome the disadvantages of monarch butterfly optimization (MBO) and CS algorithms. Compared with other algorithms, the MBOCS algorithm outperformed the others and was a competitive and promising technique for solving complex optimization problems. |
4.1. Biology-Based Algorithms
4.1.1. Genetic Algorithm (GA)
- Encoding: The problem’s input parameters, or decision variables, are encoded into a solution series of a finite length. Encoding methods include octal encoding, binary encoding, hexadecimal encoding, value encoding, permutation encoding, and tree encoding.
- Selection: In the selection stage, individuals are selected from a population for later breeding. Selection methods include rank selection, roulette wheel selection, Boltzmann selection, tournament selection, and stochastic universal sampling.
- Mutation: To introduce additional diversity, mutation randomly changes individuals. Mutations include displacement mutation, inversion mutation, scramble mutation, big flipping mutation, and reversing mutation.
- Crossover: During mating, a crossover point is randomly selected between each pair of parents. Crossover methods include K-point crossover, single-point crossover, partially mapped crossover, uniform crossover, order crossover, precedence preserving crossover, shuffle crossover, reduced surrogate crossover, and cycle crossover.
- Step 1: Set up GA parameters.
- Step 2: Create a random population of a specified size.
- Step 3: Calculate the objective function for all population members.
- Step 4: Select the best individuals from a population of candidates.
- Step 5: Perform crossover with two individuals, known as parents, randomly chosen from a mating pool to create two offspring.
- Step 6: Mutate the individuals of a population, based on mutation probabilities.
- Step 7: Perform elitism, where the best individuals in a generation are passed on to the next generation without undergoing any change.
- Step 8: Repeat steps 3 to 7 until the specified number of generations is reached, or the termination criterion is met.
Algorithm 1 Pseudo-code for GA. |
|
4.1.2. Differential Evolution (DE) Algorithm
- stopping criteria that determine the maximum number of generations G (or iterations),
- the dimensions of problem S that scales the difficulty of optimization,
- the boundaries that limit the feasible area and .
- Step 1: Set up the DE parameters that are required for the algorithm.
- Step 2: Create a random population of the specified size.
- Step 3: Calculate the objective function for all solutions.
- Step 4: Select three different target vectors.
- Step 5: Determine the trial vector using the crossover constant.
- Step 6: Choose a vector between the trial and target vectors.
- Step 7: Repeat procedures 3 to 6 until the specified number of generations is reached.
Algorithm 2 Pseudo-code for DE Algorithm. |
|
- (i)
- The initial population of a structure was generated using its damage scenario.
- (ii)
- During the mutation process, a new difference vector was generated, based on the dispersion of individuals through the search space, to automatically balance local and global searching.
- (iii)
- A new exchange operator was designed to avoid the untimely convergence of local optima.
4.1.3. Particle Swarm Optimization (PSO) Algorithm
- 1.
- (best position): the best position of an individual particle.
- 2.
- (global best position [Global-PSO]): the position of each particle is influenced by the best-fit particle in the entire swarm.
- 3.
- (local best position [Local-PSO]): the position of each particle is influenced by the best-fit particle chosen from its immediate neighbors.
- (i)
- Current position
- (ii)
- Best previous position
- (iii)
- Flight velocity .
- Step 1: Set up the PSO parameters needed for the algorithm.
- Step 2: Generate a random population of the specified size.
- Step 3: Calculate the objective function for each member of the population.
- Step 4: Update each particle’s velocity.
- Step 5: Update the particle positions.
- Step 6: Calculate the objective function for all particles.
- Step 7: Using elitism, the best-obtained results are saved.
- Step 8: Repeat steps 4 to 7 until the specified number of generations is met or a termination criterion is reached.
- Modifications of PSO, such as chaotic PSO, quantum-behaved PSO, and fuzzy PSO.
- Extensions of PSO to other optimization fields, such as multi-objective, discrete, constrained, and binary optimization.
- Hybridization of PSO with other metaheuristic methods, such as artificial immune system (AIS), GA, TS, and ACO.
- Parallel implementation of PSO, such as GPU computing, multicore, and cloud computing.
- Theoretical analysis of PSO, such as convergence analysis, and parameter selection.
Algorithm 3 Pseudo-code for PSO Algorithm. |
|
4.1.4. Other Evolutionary Algorithms
4.2. Physics-Based Algorithms
4.3. Geography-Based Algorithms
4.4. Sequential Sensor Placement Algorithms
4.5. Other Optimization Methodologies
4.6. Using Optimization Algorithms in Artificial Intelligence
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Level | Definition |
---|---|
Level I | Detection: Qualitative indication of damage presence |
Level II | Localization: Estimation of damage position |
Level III | Classification: Determination of damage type |
Level IV | Quantification: Assessment of damage extent |
Level V | Prognosis: Estimation of the remaining useful life of the system |
Ref. | Year | Journal | Description |
---|---|---|---|
Hart and Murray [30] | 2010 | Journal of Water Resources Planning and Management | This paper reviewed recently proposed optimization-based sensor placement strategies in SHM systems for water distribution systems. |
Gupta et al. [31] | 2010 | Journal of Intelligent Material Systems and Structures | This article presented various optimization criteria used by researchers for the optimal placement of piezoelectric sensors and actuators on an intelligent structure. |
Yi and Li [32] | 2012 | International Journal of Distributed Sensor Networks | This paper reviewed current developments and research on OSP systems from the viewpoint of both engineers and researchers. |
Noel et al. [33] | 2017 | IEEE Communications Surveys & Tutorials | This paper evaluated SHM strategies using wireless sensor networks (WSNs), providing an overview of current algorithms used for damage detection and localization, as well as outlining challenges associated with network design and future research directions. |
Adedoja et al. [34] | 2018 | Urban Water Journal | An overview of the state-of-the-art of OSP in a water distribution network was presented in this paper, as well as possible solutions and future research directions. |
Ostachowicz et al. [35] | 2019 | Structural Health Monitoring | This article presented a definition of the optimization problem for SHM systems and an overview of optimization strategies for sensor placement. |
Sony et al. [12] | 2019 | Structural Control and Health Monitoring | In this work, next-generation smart sensing technologies, including smartphones, UAVs, cameras, and robotic sensors, were reviewed for their application in vibration-based SHM. |
Tan and Zhang [36] | 2020 | Structural Health Monitoring | This study comprehensively reviewed computational methodologies, such as optimization techniques, to optimize the sensor placement in SHM systems. |
Barthorpe and Worden [37] | 2020 | Journal of Sensor and Actuator Networks | This paper reviewed advancements in the design of SHM systems, from sensor placement optimization (SPO) strategies to system evaluation. |
Hassani et al. [38] | 2022 | Sensors | This study presented an overview of current developments in sensing technologies, sensor placement, and damage detection for composite structures. |
Ghannadi et al. [39] | 2023 | Frattura ed Integrità Strutturale | Simulation annealing algorithms were examined in this work for various SHM applications, including damage detection, optimal sensor placement, and updating of finite element models. |
Optimization Algorithm | OSP Method | Year | Ref. |
---|---|---|---|
GA | Bayesian statistics approach | 2010 | [40] |
PSO algorithm | Fisher information matrix | 2011 | [41] |
Single parenthood GA (SPGA) | Modal assurance criterion | 2012 | [42] |
Improved discrete PSO (IDPSO) | Nearest neighbor index | 2013 | [43] |
Geometrical viewpoint and GA (GVGA) | Modal assurance criterion | 2014 | [44] |
GA-based evolutionary optimization | Modal assurance criterion | 2015 | [45] |
Stochastic optimization | Bayesian experimental design approach | 2016 | [46] |
GA | Effective independence method | 2017 | [47] |
Jaya algorithm | Reduced order model | 2018 | [23] |
Quantum-inspired evolutionary optimization algorithm (DQEA) | Triaxial modal assurance criterion | 2019 | [48] |
PSO algorithm | Multi-objective decision-making strategy | 2020 | [49] |
GA | Iterative updating process | 2021 | [50] |
Multi-objective optimization algorithm | Effective independence method | 2022 | [51] |
GA | Augmented Kalman Filter (AKF) technique | 2023 | [52] |
Optimization Algorithm | Analysis Type | Damage Type | Data Type | Monitored System | Year | Ref. |
---|---|---|---|---|---|---|
Real-coded parallel GA | Model-based method | Crack | Operational modal data | Reinforced concrete beam | 2010 | [53] |
Modified GA (MGA) | Efficient correlation-based index | Stiffness reduction | Natural frequency | Cantilevered beam | 2011 | [54] |
Immunity-enhanced PSO (IEPSO) algorithm | Inverse problem | Stiffness reduction | Natural frequency and mode shape | Beam and truss | 2012 | [55] |
PSO algorithm | Model-based method | Stiffness reduction | Frequency response function (FRF) | Beam and plane frame | 2013 | [56] |
Hybrid algorithm of GA and PSO | Sensitivity-based analysis | Reduction of modulus of elasticity | Natural frequency and mode shape | Laminated composite beam | 2014 | [57] |
Hybrid multi-objective GAs (NS2-IRRGAs) | Inverse problem using modal strain energy (MSE) | Stiffness reduction | Mode shape and stiffness matrix | 3D steel structure | 2015 | [58] |
Democratic PSO (DPSO) algorithm | Modal assurance criterion (MAC) and flexibility matrix | Crack | Modal data | Five-story shear frame | 2016 | [59] |
Modified DE (MDE) algorithm | Flexibility-inverse problem | Delamination | Modal data | Composite plate | 2017 | [60] |
Heuristic optimization (GA) | Model updating problem | Circular hole and delamination | Natural frequency | CFRP plate | 2018 | [61] |
Sunflower optimization (SFO) algorithm | Multi-modal-inverse problem | Crack | Modal data | Composite plate | 2019 | [62] |
Grey wolf (GW) optimization and Harris hawks (HH) optimization | Residual force vector | Crack | Expanded mode shape | Cantilever beam and truss tower | 2020 | [63] |
Hybrid metaheuristic optimization algorithm (HGACS) | ANN-based method | Delamination | Modal data | Laminated composite structure | 2021 | [64] |
PSO algorithm | Sensitivity-based method | Stiffness reduction | Mode shape | 3D truss | 2022 | [65] |
YUKI-ANN algorithm | Modal strain energy | Stiffness reduction | Modal data | Laminated composite plates | 2023 | [66] |
Inclusion Criteria | Exclusion Criteria |
---|---|
Titles, abstracts, or keywords include the following search keywords:
|
|
Journal | Founding Year | Best Quartile | OA | SHM | OSP |
---|---|---|---|---|---|
Ultrasonics | 1963 | Q1 | 721 | 358 | 28 |
Journal of Sound and Vibration | 1964 | Q1 | 2368 | 2812 | 310 |
Meccanica | 1966 | Q2 | 424 | 75 | 22 |
Engineering Structures | 1970 | Q1 | 2059 | 2589 | 190 |
Optical Fiber Technology | 1970 | Q2 | 470 | 190 | 16 |
Computers and Structures | 1971 | Q1 | 2707 | 171 | 78 |
Networks | 1971 | Q1 | 1349 | 36 | 351 |
Mathematical Programming | 1971 | Q1 | 4043 | 2 | 11 |
Computers and Operations Research | 1974 | Q1 | 4861 | 11 | 23 |
Mathematics of Operations Research | 1976 | Q1 | 8928 | 434 | 6672 |
International Journal of Remote Sensing | 1980 | Q1 | 2424 | 211 | 2211 |
Composite structures | 1983 | Q1 | 2148 | 683 | 123 |
Algorithmica | 1986 | Q1 | 1363 | 4 | 21 |
Mechanical Systems and Signal Processing | 1987 | Q1 | 3365 | 1552 | 390 |
Neural Networks | 1988 | Q1 | 2688 | 19 | 28 |
Engineering Applications of Artificial Intelligence | 1988 | Q1 | 3607 | 161 | 85 |
Neurocomputing | 1989 | Q1 | 11,095 | 157 | 106 |
Expert Systems with Applications | 1990 | Q1 | 10,502 | 325 | 141 |
Computational Optimization and Applications | 1992 | Q1 | 1907 | 6 | 12 |
Optimization Methods and Software | 1992 | Q1 | 1648 | 35 | 220 |
Remote Sensing | 1992 | Q1 | 1197 | 400 | 123 |
Mathematical Problems in Engineering | 1992 | Q2 | 1584 | 372 | 758 |
Journal of Combinatorial Optimization | 1997 | Q2 | 1827 | 9 | 20 |
Advances in Structural Engineering | 1999 | Q2 | 343 | 302 | 234 |
Optimization and Engineering | 2000 | Q2 | 847 | 20 | 15 |
Structural and Multidisciplinary Optimization | 2000 | Q1 | 3889 | 69 | 92 |
Structural and Multidisciplinary Optimization | 2000 | Q1 | 3889 | 170 | 92 |
Sensors | 2001 | Q1 | 3178 | 1708 | 100 |
Applied Soft Computing | 2001 | Q1 | 7230 | 166 | 128 |
Structural Health Monitoring | 2002 | Q1 | 633 | 4370 | 550 |
Discrete Optimization | 2004 | Q2 | 605 | 2 | 4 |
Structural Control and Health Monitoring | 2004 | Q1 | 842 | 1385 | 649 |
Cluster Computing | 2005 | Q2 | 2022 | 62 | 102 |
Measurement | 2010 | Q1 | 4000 | 289 | 939 |
Measurement Type | Sensor Type |
---|---|
Velocity | Magnetic induction, Piezoelectric, Optical |
Displacement | Inductive, Capacitive, Gyroscope, Optical, Magnetic, Acoustic emission, Ultrasonic |
Acceleration | Capacitive, Piezoelectric, MEMS, Piezoresistive |
Force | Optical, Piezoresistive |
Strain | Optical, Piezoresistive |
Pressure | Piezoresistive |
Temperature | Acoustic, Thermoresistive, Optical, Thermoelectric |
Ref. | Year | Journal | Description |
---|---|---|---|
Wu et al. [105] | 2020 | Sensors | A comprehensive summary was presented on FOSs used for SHM, including detailed working mechanisms, categories, and principles of FOSs. |
Dutta et al. [15] | 2021 | IEEE Sensors Journal | This paper reviewed recent developments of sensors for high-temperature SHM and advanced fabrication methods, such as fiber Bragg grating (FBG) sensors, eddy current sensors, and low-temperature ceramic technology. |
Rocha et al. [13] | 2021 | Engineering Structures | This work reviewed the most common types of sensors used for laboratory and commercial applications of SHM for aerospace composites. |
Mustapha et al. [106] | 2021 | Vibration | Sensor networks were reviewed for monitoring systems addressing various topics, including optimized sensor networks, force sensors, data transmission, information communication, and data analysis. |
Grabowski et al. [107] | 2021 | Measurement | This paper presented the sensing capabilities of MXene nanomaterials for SHM, including two-dimensional nanomaterials with carbide or nitride layers (X layer) sandwiched between transition metal layers (M-layer). |
Li et al. [108] | 2022 | Construction and Building Materials | This work presented graphene-based nanomaterials (GBNs) used as additives to cementitious materials to form self-sensing composites for SHM systems. |
Glisic [97] | 2022 | Sensors | This paper presented a historical overview of the first hundred years of strain-sensing technology used for civil structure monitoring, outlining transformative milestones and possible future research directions. |
Gao et al. [109] | 2022 | Applied Sciences | This work comprehensively presented recent research advances, challenges, and achievements of flexible piezoresistive strain sensors (FPSs) used for civil SHM. |
Jayawickrema et al. [110] | 2022 | Measurement | Recent publications were reviewed on SHM systems for pipelines, buildings, and bridges, focusing on emerging FOS technology and the application of deep learning (DL) for advanced data analysis. |
Hassani and Dackermann [8] | 2023 | Sensors | A systematic review of conventional and advanced sensor technologies was conducted in this article to provide input parameters for NDT and SHM systems and to determine whether they are suitable for determining the health state of structures. |
Ref. | Year | Journal | Description |
---|---|---|---|
Toh and Park [130] | 2020 | Applied Sciences | This review paper summarized studies applying ML algorithms for fault monitoring. |
Azimi et al. [131] | 2020 | Sensors | This work comprehensively reviewed research on SHM concerning emerging DL-based methods and presented several SHM applications. |
Flah et al. [132] | 2021 | Archives of Computational Methods in Engineering | This review comprehensively reviewed applications of various ML algorithms in SHM systems, including image-based SHM and vibration-based SHM. |
Avci et al. [1] | 2021 | Mechanical Systems and Signal Processing | This paper thoroughly outlined gaps in SHM concerning conventional methods, and presented the most recent applications of DL and ML algorithms in damage detection based on vibration data for civil structures. |
Mishra et al. [133] | 2022 | Journal of Building Engineering | This paper presented a review on SHM of civil engineering infrastructure, focusing on applications of the wireless Internet of Things (IoT)-based real-time wireless sensors technology. |
Gordan et al. [134] | 2022 | Measurement | This work presented functions, models, and categories of data mining (DM) strategies, including GA, fuzzy logic, ANN, and principal element analysis, used for SHM systems. |
Ramalho et al. [135] | 2022 | Structural Control and Health Monitoring | This article comprehensively reviewed testing procedures, equipment, and techniques adopted in NDT and SHM systems. It also presented the basics of Lamb waves and their application to fault identification, ML, statistical analysis, simulation methods, and signal processing. |
Civera and Surace [136] | 2022 | Sensors | This work reviewed recent developments in NDT systems, including acoustic emissions, visual inspection, ultrasonic testing, radiographic testing, infrared thermography, oil monitoring, and electromagnetic testing. |
Hassani et al. [38] | 2022 | Sensors | In this work, the authors comprehensively reviewed the development history of, and research in, different damage detection strategies in composite laminated plates. |
Payawal and Kim [137] | 2023 | Applied Sciences | A review of image-based SHM applications was conducted, which includes discovering and identifying, monitoring and measuring, automating and improving efficiency, and promoting 3D model development. |
Ref. | Year | Analysis Method | Monitored System | Description |
---|---|---|---|---|
Azimi et al. [131] | 2020 | Unsupervised deep neural network | Bridge | This paper proposed a damage detection technique using an unsupervised deep neural network, defined as a deep convolutional denoising autoencoder. In this method, multi-dimensional cross-correlation functions were used as input. |
Choe et al. [138] | 2021 | LSTM | Wind turbine blade | This paper presented a technique concerning sequence-based modeling of DL using gated recurrent unit (GRU) neural networks and an LSTM algorithm to detect structural damage in floating offshore wind turbine (FOWT) blades. |
Movsessian et al. [139] | 2021 | ANN | Wind turbine blade | This study presented a new ANN method that could establish non-linear relationships between particular damage-sensitive features affected by EOCs and new indicators using the Mahalanobis distance (MD). |
Hassani et al. [75] | 2022 | EMD algorithm | Composite plate and spatial truss | This work proposed a new sensitivity-based model concerning the EMD algorithm to detect damage to systems with closely-spaced eigenvalues. |
Corbally and Malekjafarian [140] | 2022 | Data-driven approach | Bridge | This paper presented a new data-driven strategy using ANNs to analyze acceleration records from multiple passes of a traversing vehicle for drive-by monitoring of bridges. |
Hajializadeh [141] | 2022 | DL | Bridge | This paper proposed a novel numerical data-driven damage detection system using a deep convolutional neural network on train-borne signals while moving over a bridge at traffic speed. |
Xu et al. [142] | 2022 | Bayesian method | Wind turbine blade | This paper proposed a time series analysis method, based on Bayesian cointegration, to include more than two damage-sensitive features in the analysis simultaneously. |
Hassani et al. [74] | 2022 | VMD algorithm | Composite plate | In this work, a novel strategy was proposed using VMD algorithm to assemble a new set of input responses captured from condensed frequency response function rows for use in a model updating problem, based on sensitivity. |
Mousavi et al. [143] | 2022 | Signal processing | Steel truss bridge | This work proposed a method based on the complete ensemble EMD algorithm with adaptive noise for identifying damage presence, location, and severity in a steel truss model of a bridge. |
Hassani et al. [65] | 2022 | Model updating method | 3D truss and composite plate | This work proposed a new optimization problem using a modal data-based sensitivity method for reliable and fast damage detection of systems with closely-spaced eigenvalues, such as 3D truss and composite structures. |
Ref. | Year | Method | Description |
---|---|---|---|
Song and Jin [149] | 2008 | Sensitivity-based methods, EI and MAC | This work presented an optimization approach for sensor placement using eigenvector sensitivity, EI, and MAC methods. |
Dinh-Cong et al. [150] | 2019 | MKE | This paper proposed a new two-stage method for sensor optimization and damage detection using symbiotic organisms search algorithm and modal kinetic energy change ratio. |
Blachowski [151] | 2019 | Sensitivity-based methods | This study proposed an approach using a non-negative least square (NNLS) solution and sensitivity and norm minimization for OSP and damage detection in 3D truss structures. |
Yang et al. [152] | 2019 | Redundancy elimination model | This work presented a novel redundancy elimination model that distributed global and local sensors based on the minor enclosing circle method and a sub-clustering algorithm. |
Ariga et al. [153] | 2020 | Mutual information | This paper presented an OSP method, based on mutual information, using a Gaussian process (GP) and the sound-field-interpolation kernel for covariance measurements in a GP model to suitably place sensors. |
Bhattacharyya and Beck [154] | 2020 | Mutual information | This work proposed a strategy based on mutual information maximization for Bayesian OSP, bypassing the necessity for a detailed, and often infeasible, combinatorial search. |
Civera et al. [155] | 2021 | Multi-objective optimization | This paper proposed a novel approach using GAs and multi-objective optimization (MO) for a damage scenario-driven OSP method. |
Sajedi and Liang [156] | 2022 | DGBO | This paper proposed a solution based on deep generative Bayesian optimization (DGBO) for parallel optimization of black-box/expensive error functions for OSP in SHM. |
Mendler et al. [157] | 2022 | Fisher information | This paper presented a method for sensor placement using the Fisher information matrix for optimized sensor design, based on maximum damage detectability in the chosen structural elements. |
Type | Refs. | Advantages | Disadvantages |
---|---|---|---|
Local | [173,174] | - Exact localization of optimal solutions. - High convergence speed. - High efficiency | - No escape from sub-optimal regions of the search space (the starting solution determines the optimization result). |
Global | [175,176] | - Ability to escape from sub-optimal regions of the search space. | - Very low convergence speed, especially in the neighborhood of optimal solutions. - High optimization effort. - Uncertain quality of the optimization results. |
Item | DE | GA | PSO |
---|---|---|---|
Provide a ranking system for solutions | No | Yes | No |
Effect of population size on solution time | Linear | Exponential | Linear |
Effects of best solutions on the population | Less | Medium | Most |
Premature convergence tendency | Low | Medium | High |
Ease of implementation | Medium | Easy | Medium |
Density (continuity) of search area | More | Less | More |
Applications in a variety of fields | Medium | Most | Medium |
Ability to find good solutions without using local search | More | Less | More |
Convergence is improved by homogeneous subgrouping | No | Yes | Yes |
Optimization Algorithm | Objective | Damage Type | Monitored System | Year | Ref. |
---|---|---|---|---|---|
Topology optimization | Damage detection and localization | Stiffness reduction | Composite laminate plate | 2010 | [283] |
BFGS quasi-newton optimization | Damage detection | Variations in the structural variants | Space truss | 2010 | [284] |
Novel multi-objective optimization | Damage detection and identification | Variations in the structural variants | Simple truss | 2010 | [285] |
Modified effective independence distribution vector algorithm | OSP | Crack | High mobility multipurpose wheeled vehicle | 2011 | [286] |
Innovative optimization | OSP | Variations in the structural variants | High-rise building | 2011 | [287] |
Modified evolutionary algorithm based on covariance matrix adaption | Damage detection, localization, and quantification | Crack | Bridge columns | 2011 | [288] |
Information entropy-based algorithm | OSP | Stiffness reduction | Skyscraper | 2011 | [289] |
Improved charged system search algorithm | Damage detection | Stiffness reduction | Truss structures | 2012 | [290] |
Improved evolutionary algorithm | Damage localization and evaluation | Crack | Shear wall and four-fixed supported plate | 2012 | [291] |
Hybrid PSO-Simplex algorithm | Damage identification | Delamination | Composite beam | 2012 | [292] |
Improved swarm intelligence algorithm | Damage detection | Crack | Steel frame | 2012 | [293] |
Big Bang-Big Crunch algorithm | Damage detection | Stiffness reduction | Unbraced frame | 2013 | [294] |
Multi-layer GA | Damage diagnosis | Stiffness reduction | Complex steel truss bridge | 2013 | [295] |
Improved multi-particle swarm co-evolution optimization algorithm | Damage detection | Crack | Seven-story steel frame | 2014 | [296] |
Continuous ant colony optimization algorithm | Damage detection and quantification | Stiffness reduction | Beam type structure | 2014 | [297] |
Novel global artificial fish swarm algorithm | Damage detection | Crack | Building model | 2014 | [298] |
Chaotic artificial bee colony algorithm | Damage identification | Variations in structural variants | Plate | 2015 | [299] |
Improved PSO-NM algorithm | Damage detection and localization | Stiffness reduction | Two-storey frame | 2015 | [300] |
Improved harmony search algorithm | Damage detection | Stiffness reduction | Wind turbine supporting structures | 2015 | [301] |
Artificial bee colony algorithm with hybrid search strategy | Damage detection | Truss and plate | Stiffness reduction | 2016 | [302] |
Improved differential evolution algorithm | Damage detection | Delamination | Composite beam and plate structures | 2016 | [303] |
Modified adaptive harmony search algorithm | Damage detection and localization | Stiffness reduction | Beam-like and complex structures | 2016 | [304] |
Inverse dynamics optimization algorithm | Damage detection | Stiffness reduction | Bridge | 2017 | [305] |
Improved PSO | Damage detection | Stiffness reduction | Beam, truss and plate | 2018 | [306] |
L1-norm optimization algorithm | Damage localization | Stiffness reduction | Metal beam and composite wind turbine | 2018 | [307] |
Enhanced thermal exchange optimization algorithm | Damage identification | Stiffness reduction | Various structures | 2018 | [308] |
Enhanced bat optimization algorithm | Damage detection, localization, and quantification | Variations in structural variants | Large-scale space structures | 2019 | [309] |
Imperialist competitive algorithm | Damage detection, localization, and quantification | Variations in structural variants | Cantilever beam, continuous beam and plane portal frame | 2019 | [310] |
Cuckoo search algorithm | Damage detection | Stiffness reduction | Bridges and beam-like structures | 2019 | [311] |
Hybrid ant lion optimizer with improved Nelder–Mead algorithm | Damage detection, localization, and quantification | Stiffness reduction | Various structures | 2020 | [312] |
Improved artificial bee colony algorithm | Damage detection | Crack | Beam | 2020 | [313] |
Hybrid unified PSO | Damage assessment | Changes in vibration responses | Beam, plane truss and space truss | 2020 | [314] |
Chimp optimization algorithm | Damage detection | Variations in structural variants | Steel truss | 2021 | [315] |
Water strider algorithm | Damage detection | Variations in structural variants | Bridge | 2021 | [316] |
Arithmetic optimization algorithm | Damage detection, localization and quantification | Variations in structural variants | Composite plates | 2021 | [317] |
Gold rush optimization algorithm | Damage detection | Truss structures | Stiffness reduction | 2022 | [318] |
Hybrid Whale-Chimp optimization algorithm | Damage detection | Stiffness reduction | Two-story rigid frame model and simply supported beam | 2022 | [319] |
Hybrid butterfly optimization algorithm | Damage prediction | Crack | Beam | 2022 | [320] |
Artificial Gorilla troops optimization algorithm | Damage detection | Stiffness reduction | Girder bridge | 2023 | [321] |
Hybrid butterfly optimization algorithm | Damage prediction | Crack | Beam | 2022 | [320] |
Artificial Gorilla troops optimization algorithm | Damage detection | Stiffness reduction | Girder bridge | 2023 | [321] |
Hybrid firefly and PSO algorithms | Damage detection | Variations in structural variants | Large-scale truss bridge | 2023 | [322] |
Chaos game optimization algorithm | Damage identification | Variations in structural variants | Steel and aluminum structures | 2023 | [323] |
Ref | Year | Objective Function | Optimization Algorithm |
---|---|---|---|
Zhang et al. [229] | 2014 | IPSO | |
Sun and Büyüköztürk [147] | 2015 | Discrete ABC | |
Yi et al. [324] | 2015 | Adaptive MA | |
Downey et al. [325] | 2018 | Adaptive GA | |
Zan et al. [326] | 2018 | PSO | |
Jaya et al. [327] | 2020 | GA | |
Ponti et al. [328] | 2021 | MOEA | |
Yang et al. [51] | 2022 | Bayesian optimization algorithm | |
Saheb et al. [329] | 2022 | ACO and PSO | |
Goetschi et al. [330] | 2022 | PSO and GA |
Ref. | Year | Stage | Structure | AT | Objective Function | OA | Metric |
---|---|---|---|---|---|---|---|
Hao and Xia [331] | 2002 | One-stage | Cantilever beam | A | GA | Modal data | |
Braun et al. [332] | 2015 | One-stage | Spring-mass system | E and A | ACO | Stiffness | |
Cha and Buyukozturk [58] | 2015 | Multi-stage | 3D steel structures | A | GA | Mode shape and stiffness | |
Vo-Duy et al. [333] | 2016 | Multi-stage | Composite plate | A | DE | Mode shape | |
Gomes et al. [334] | 2016 | Multi-stage | Composite material | A and E | GA | Natural frequency and acceleration | |
Gui et al. [335] | 2017 | One-stage | Frame aluminum structure | E and A | GA and PSO | Measured discrete signal | |
Gomes et al. [61] | 2018 | One-stage | CFRP plate | E and A | GA | Natural frequency | |
Tran-Ngoc et al. [64] | 2021 | One-stage | Composite plate | A | HGACS | Natural frequency and mode shape | |
Ahmadi-Nedushan and Fathnejat [336] | 2022 | Multi-stage | Truss | A | MTLBO | Modal strain energy | |
Hassani et al. [65] | 2022 | Multi-stage | Composite plate | A | PSO | Mode shape |
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Hassani, S.; Dackermann, U. A Systematic Review of Optimization Algorithms for Structural Health Monitoring and Optimal Sensor Placement. Sensors 2023, 23, 3293. https://doi.org/10.3390/s23063293
Hassani S, Dackermann U. A Systematic Review of Optimization Algorithms for Structural Health Monitoring and Optimal Sensor Placement. Sensors. 2023; 23(6):3293. https://doi.org/10.3390/s23063293
Chicago/Turabian StyleHassani, Sahar, and Ulrike Dackermann. 2023. "A Systematic Review of Optimization Algorithms for Structural Health Monitoring and Optimal Sensor Placement" Sensors 23, no. 6: 3293. https://doi.org/10.3390/s23063293