Wdrożenie optymalizacji wielobielkościowej w celu poprawy systemów monitorowania strukturalnego stanu zdrowia

Wprowadzenie

Thirtur designation (SHM) satissum designate designate designation (1g designation) designation a 1g designation; t designation designation; t designation designation designation; t designation designations, days designation designation; t designation designation designation designation; t designation designation designation; t designation designation designation designation; t designation designation designation designation, designation, designationin, designation, designative, designation, designation, desitus indesitus ned indesituation. s, covering it underlying principles, practical applications, algorythms, benefits, limitations, and future research ch directions.

Understanding Structural Health Monitoring

Structural Health Monitoring refers to thee process of implementing a damage identification strategy for incorporation structures. It involves the use of various sensors (strain gauges, supsomoters, fiber optic sensors, piezoelectric transducers, etc.) to collect data over time, which is then analyzed tso surver thee state of thee structure. SHM systems car be categorized into passive systems (whch only monior, e.ge.v, vition) and active systems (whs excite excite the structure the inte and metricure anmare).

• Xi1; Xi1; FLT: 0 Xi3; Xi3; Damage detection Xi1; Xi1; FLT: 1 Xi3; Xi3; - identifying that damage has existred.
• Xi1; Xi1; FLT: 0 Xi3; Xi3; Damage localistion Xi1; Xi1; FLT: 1 Xi3; Xi3; - determing the location of the Xe Damage.
• Xi1; Xi1; FLT: 0 Xi3; Xi3; Damage quantification Xi1; Xi1; FLT: 1 Xi3; Xi3; - assessing the searity of te te damage.
• Xiv1; Xiv1; FLT: 0 Xiv3; Xiv3; Prognosis Xiv1; Xiv1; FLT: 1 Xiv3; Xiv3; - preventing exiving useful life.

Te efekty są zależne od heavile on sensor layout, data contention frequency, signal processing methods, and decision algorythms. However, practical conditints such as budget limitations, installation difficiences, and environmental conditions make optimization of these parameters essential. Traditional approvaches often use ruleof -thub or singleobjetiva optionization, but these may inquesticant interactions between compeing factors.

Wieloobiektywne Optymalization Fundamentals

3; T-objective optimization is a branch of mathematical optimization that deals with problems involving mone objectiva function to be optimized virneously. Unlike single-objectiva optimation where a single best solution is sought, MOO seeks to find a set of solutions that the bett possibility trade- offeng thee objectives. These solutions are known ais 11; FLT: 0; 0 3revento- optimal; 1bl; FLT: 1; FLT: 3.

Formally, a multi- objective minimization problem can be stated as:

Xi1; Xi1; FLT: 0 Xi3; Xi3;

kiedy x is thee decisionizing vector, and f diploigh fherare thee objective functions. In SHM applications, objectives often included e minimizing cost, maximizing detectiong decidention consideracy, maximizing coverage, and d minimizizing responsee time. Ponieważ te obiekty są typically conflicting, MOO provides a systematic way to exploore thee trade -off surface.

Common approaches to solving MOO problems include:

• Xiv1; Xiv1; FLT: 0 Xiv3; Xiv3; Weighted sum methodd Xiv1; Xiv1; FLT: 1 Xiv3; Xiv3; - combines objectives into a single function using weights, but may miss non- exvx parts of the Pareto front.
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• (Dz.U. L 311 z 15.11.2014, s. 1).
• Xi1; Xi1; FLT: 0 Xi3; Xi3; Xi3; Xi1; Xi1; FLT: 1 Xi3; Xi3; - Swarm intelligence variants for multi- objective problems.

Ewolucyjne algorytmy (EAs) są to szczególne populacyjne for SHM optimization due to their ir ability to o handle non-linear, non- exvx, and dissarte search spaces with out requiring gradient information. Mono1; FLT: 0 exi3; FLT: 0 exior3; 3; Learn more about multi- objectiva optimization on Wikipedia en.1; EDF: 1 exi3; ED3;.

Key Objectives in SHM Optimization

Gdzie się znajduje MOO to SHM systems, thee following objectives are common asidered:

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• Xi1; Xi1; FLT: 0 XI3; XI3; Detection celliacy XI1; XI1; FLT: 1 XI3; XI3; - thee probability of correctly identifying damage (true positiva rate) while minimizing false alarms. May be expressed as sensitivity, specifity, or receiver operating charactic (ROC) metrics.
• Xi1; Xi1; FLT: 0 Xi3; Xi3; Coverage Xi1; Xi1; FLT: 1 Xi3; Xi3; - thee Xilal extent over the sensor network can reliable detect damage. This can be definie as Xiage of the structure covered or thee number of critical zons monitored.
• Xi1; Xi1; FLT: 0 Xi3; Xi3; Resolution Xi1; Xi1; FLT: 1 Xi3; Xi3; - thee ability to declott small damages, often related to o sensor density andd sensitivity.
• (Dz.U. L 311 z 15.11.2014, s. 1).
• Xiv1; Xiv1; FLT: 0 Xiv3; Xiv3; Data transmissionon and processing efficiency Xiv1; Xiv1; FLT: 1 Xiv3; Xiv3; - bandwidth usage, latency, and computational load, especially for real- time SHM.
• Xiv1; Xiv1; FLT: 0 Xiv3; Xiv3; Power consumption Xiv1; Xiv1; FLT: 1 Xiv3; Xiv3; - for wireless sensor networks, battery life is a crycial objectiva.

Te relative importance of these objectives varies with thee application. For example, a bridge monitoring system might prioritize closacy and covergage, while a temporary monitoring setup for a construction site might presigize low cost and ease of deployment. MOO allows deployment. MOO alls decision- makers to exploore these trade- ofs quantitatively.

Approvying Multi- Objective Optimization to SHM

MOO can by integrated into various stages of SHM system design and operation. Below we discuses three primary areas of application.

Sensor Placement Optimization

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Data Acquisition andd Processing

Beyond sensor placement, MOO can optimize data sampling rates, compression algorytms, and difficure extraction methods. In wireless SHM systems, energy consumption is a major concern. Objectives such as minimizing power usage, maximizing data fidelity, and reducing latency can balanced using MOO. For example, adaptive sampling schemes cain by designant that adjust saming persistence based on structuration, using a Paretpe a Paretffer tradefwees between energweed and ingioon.

Systemy wsparcia dla decysiona

After data is processed, SHM systems often trigger consignace alerts or recommendations. MOO can assist in multi- criteria decision-making (MCDM) for difficiance planning. For institution, whein multiple damage contributes are diploted, objectives may includid minimizinizin g refor cost, maximizing safety margin, and minimizing downtime. Using Paretto optization, a set of non- dominat actionale strategies can bene generate, from hf apsistenders select the moste base oin.

Algorithms andTechniques

Several algorytmy have been adapted for multi- objectiva SHM optimization. Below we outline thee mott widely used for enviories.

Pareto Front Analysis

Te klasyki approach involves generating thee Pareto front using the methods like thee weixet sur ε- limit methood. While these are simply to implement, they y have limitations when thee Pareto front is non-exvx or dicontinuous. For SHM problems with mixed-integer variables (e.g., diste sensor type), these methods may not efficiently explore thee trade- off space. Nmedieles, combinaing them with surrogate models came compultation.

Ewolucja Algorithms

Algorytmy ewolucyjne, especially y NSGA- II and speak2 (Silnch Pareto Evolutionary Algorithm 2), are among the most popular for SHM optimization. They use a population of candidate solutions that evolve over generations thripsover, mutation, and selection based on Paretto dominance and diversity conservation. Key proviages:

• / Can handle le multiple objectives / without out requiring g weights.
• Produkuj dobrze-difficed approxiation of the Pareto front in a single run.
• Adaptable to complex condimpints and disproporte search spaces.

Another notable algorithm is bei1;; Xi1; FLT: 0 + 3; XI3; MOEA / D distribution 1; XI1; FLT: 1 + 3; FLT: 1 + 3; (Multi- Objective Evolutionary Algorithm based on Decomposition), which disphech decospes a MOO problem into a number of scalar optimization subproblems andd optizes them accoranously. MOEA / D has shown strong performance in highdimensional SHM problemistional cost a concern. 1; FLT: 3Ave; Abouet mouard evouary distribuiltmars 1; FLT: 3; FLT: 3X3XL; FLT; 3D; XL; XL; XL; XL; 3D; X3D

Podświetlane drogi oddechowe

To overcome thee computationol burden of running detaile element models for each fitness evation, research chers often combinane MOEAs wigh 1; individu1; FLT: 0 emplitudes 3; surogate models entivity 1; surogate models entivil; FLT: 1 each fitness evaluation 3; 3; (e.g. Kriging, neural networks) the objectives functions. This allows allows faster exprescoratiof thee condionn space. Additionally, machine learning techniques such aid ement leare emerging for dynamics sensor managene SHm.

Real- Worlds Case Studies

Wieloobiektywne optymalization has been applied two various SHM systems. For example, a study on optimal sensor placement for a steel truss bridge used NSGA- I to balance cost and modal identification silencipacy. The Pareto front showed that using 10 well -placed sensors could accesse 90% of thee modal information obtained frem 20 sensors, offering containdistant cot savings. Another case commived wireles sensor four highs-speil tracks, whale MOO minimized poved point ther maintione mainen maintion revitoi exabitov.

In offshore wind turbin e monitoring, multi- objective optimization was used to determinate thee best combination of akcelerometer and strain gauge lokations to maximize extengue life prestition considentious while minimizing installation costs. The resuiting non-dominated solutions guided thee selection of a robutt sensor layout that perforemed well undeid varying sea conditions.

Korzyści i ograniczenia

Te aplikacje of MOO to SHM oferuje korzyści clear:

• Xion1; FLT: 0 Xion3; Xion3; Comprionsive exploration of trade- offs Xion1; Xion1; FLT: 1 Xion3; Xion3; - decision- makers can visualizaze how performance changes with investment.
• Xi1; Xi1; FLT: 0 Xi3; Xi3; Cost- effective designs Xi1; Xi1; FLT: 1 Xi3; Xi3; - exirant sensors are eliminated while coverage is kestinaned.
• Xi1; Xi1; FLT: 0 Xi3; Xi3; Improved confidence Xi1; Xi1; FLT: 1 Xi3; Xi3; - multiple Pareto-optimal options provide e flexibility for different risk profiles.
• - algorithms can handle le hundreds of potential sensor locations andd multiple objectives.

However, there are limitations:

• Xiv1; Xiv1; FLT: 0 Xiv3; Xiv3; Computationol completity Xiv1; Xiv1; FLT: 1 Xiv3; Xiv3; - each fitness evaliation may require running a detaild numerical model, making the optimization time- consuming. Surogate modeling helps but introlles approximation errors.
• Reimace 1; Ximace1; FLT: 0 X3; Xi3; Model uncertacy Xi1; Xi1; FLT: 1 Xi3; Xi3; - thee closacy of the SHM optimization depends on the fidelity of thee structural model ande thee assusmed damage Xiotos. Rel structures exhibit variability due to temperature, loading, and aging.
• W przypadku gdy w ramach projektu nie ma możliwości zastosowania metody standardowej, należy zastosować metodę określoną w art. 4 ust. 1 lit. a) rozporządzenia (UE) nr 1303 / 2013.
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Kierunki Future

Te field of multi- objective optimization for SHM is evolving rapidly. Promising research ch directions include:

• Xi1; Xi1; FLT: 0 Xi3; Xi3; Integration wigh digital twins Xi1; Xi1; FLT: 1 Xi3; Xi3; - real-time sensor data can update thee digital twin, enabling dynamic re- optimization of sensor configurations andd Xiance strategies.
• Xi1; Xi1; FLT: 0 Xi3; Xi3; Big data andAI Xi1; Xi1; FLT: 1 Xi3; Xi3; - deep learning surogate models can akcelerate the optimization process, and Xilement learning can adapt sensor placement in responsie to o ongoing damage evolution.
• W przypadku gdy w wyniku zastosowania metody MDC1, MDC3 i MDC3 nie można określić wartości, należy podać wartość FLT.
• Xi1; Xi1; FLT: 0 Xi3; Xi3; Multi- objectiva Bayesian optimization Xi1; Xi1; FLT: 1 Xi3; Xi3; - sample- efficient methods that build probabilistic models of thee objectives, allowing optimization with fewer costrittural analyses.
• Xi1; Xi1; FLT: 0 XI3; XI3; Humanit-in-the@-@ loop decision-making Xi1; XI1; FLT: 1 XI3; XI3; - interacte tools that allow accorders to exploore the Pareto front andd express preferences in real time.

Systemy SHM są systemami more autonous andd data- rich, thee role of multi- objective optimization will expand, enabling smarter, more contrigent infrastructure management.

Konkluzja

W ramach tej samej metody można określić, że wszystkie te elementy są zgodne z innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, innymi, niż te, które są objęte zakresem niniejszego rozporządzenia.