The increasing vulnerability of communities to natural hazards motivates n ovel design and assessment methods to ensure that the built environment performs optimally during its lifetime. The current design methodologies do not account for life -cycle impacts across multiple performance domains such as economy and environment. Therefore, low-effort and designer -centric computational methods are needed to support a multi -objective performance -based design , from the conceptual stage to design development. This study presents a framework for a holistic performance -based seismic design of buildings. The proposed framework leverages machine learning techniques to extract the implicit , and highly complex, r elationship between design parameters , geometric configuration , and performa nce measures . At early design, data- driven surrogate models (trained on performance inventories) are used to identify candidate structural systems and their approximate des ign parameters . At the detailed design stage , a deep learning -based engine generates seismic risk estimates based on simpler nonlinear static analysis on the candidate systems or their equivalent low -order dynamic models . A case study i llustrates the framework ’s application for performance -based seismic design of multistory commercial bui ldings in Charleston, SC. Keywords: Machine learning, performance -based earthquake engineering, seismic design, deep learning 1. Introduction Performance -based earthquake engineering (PBEE) [1,2] is a modular framework to quantify the impact of earthquakes on the built environment through global performance measures. The framework consists of four independent modules of seismic hazard, structural response, damage, and loss analyses. Each m odule is represented as a conditional probability, where analysis data are used to characterize the probability distribution of the module’s random variable (s). This modularity facilitates a rigorous and interdisciplinary approach to account for different factors that shape seismic performance , enabling a pathway toward a more holistic seismic design. A holistic design (Figure 1) directly account s for performance across different domains over the entire design stages, from early design concepts to design de velopment and post -construction operation. Despite the promising features of PBEE , this framework is still not widely used after nearly two decades since its inception , except for special buildings that justify the additional time and effort needed. Most PBEE efforts are limited to seismic evaluation of novel structural systems such as buildings supplemented with dissipative devices (e.g., structural fuses [3,4] , hysteretic devices [5,6] ), fiber reinforced polymer - or shape memory alloy -based components [7–10], special braces (e.g., gap inclined [11], crescent -shaped [12], knee bracing [13]) or strongback assemblies [14,15] . 2 Perhaps t he most notable effort in using PBEE for design was directed at tall building s as part of the PEER/ATC project in 2006 [16]. A critical barrier in using PBEE is the simulation challenges and modeling complexities of developing sophisticated nonlinear finite element models, selecting appropriat e ground motion s, and performing time -consuming time history analysis . Such complexities substantially increase when ap plying PBEE to generate design alternatives ( i.e., at the early design stage ), or considering different performance objectives simultaneously (particularly if a different type of analysis is needed for each objective). Therefore, different studies aimed to simplify performing PBEE by introducing approximate analysis methods or developing efficient computational platforms . Machine learning (ML) -based methods have been recently introduced to alleviate PBEE computational challenges , such as predicting structural response and developing models based on experimental, health monitoring , or field reconnaissance data [17,18] . ML methods can aid with both achieving computationally inexpensive models and design automation. Nevertheless, most studies on structural response estimation focused on predicting nonlinear responses ( or fragility functions) based on ground motion -related and detailed design parameters [17]. Section 2 reviews the current literature on ML application s for seismic design and performance evaluation . This study proposes an ML-assisted modular framework to implement PBEE for a holistic seismic design, encompassing both the early stage and design development . To this end , the framework provides risk -informed guidance a t the early design on system select ion and initial ranges for design and configuration parameters , and ensures that the desired performance (e.g., total repair cost) is achieved at the design development stage. The proposed framework relies on the hypothesis that th ere is a complex relationship between building performance , configuration , and design. This relationship allows shifting the time and effort needed to perform such assessments from designers into ML models , hence sidestepping performing PBEE assessments over a large design space. In addition, the ML models facilitate rigorous sensitivity assessment Sustainability performanceResiliency performanceInitial ConstructionOperational PhaseHazards OccurrenceConceptual designSchematic designDesign developmentDesign Performance criteriaEarly design Detailed design Design Documents Aging & deteriorationFigure 1. A holistic design approach: the relationship between design and performance is accounted at every stage. 3 and optimization to identify the most critical design decisions. Lastly, t he framework considers earthquakes’ economic and environ mental impacts and their interaction. The organization of this chapter is as follows: Section 2 reviews the literature on using ML for seismic design and assessment, Section 3 provides an overview of the framework and each module, and Section 4 presents a case study that illustrates different modules ’ application s. 2. Background The appl ication of ML in PBEE has mainly focused on its predictive capabilities to serve as surrogate s for computationally -expensive finite element simulations. The majority of pr evious studies have addressed component -level predictions such as RC columns [19,20] , concrete -filled steel columns [21,22] , masonry walls [23], or RC walls [24,25] . Several authors aimed to predict seismic responses of archetypal buildings based on desig n- and hazard -related parameters, as shown in Table 1 . Furthermore, i nstead of developing ML -based mapping functions, a few studi es focused on creating novel ML architectures to directly estimate time-history responses based on ground motion (GM) sequences. For example, Ahmed et al. showed that stacked long short -term memory (LSTM) accurately predicts damage states for ductile and n on-ductile frames [26]. On the other hand, Luo and Pa al developed an ML -based solver to estimate structure response by construc ting the stiffness matrix of RC frames using experimental data of RC components [27]. In a quest to generalize ML models, effort s have been made to predict the seismic performance of building inventories with varying configuration s and design s. For example, Nguyen et al. applied 8 ML models to a database of 468 steel moment -resisting frames and showed that random forest c ould predict building damage states with an accuracy level of 98% [28]. In addition, they concluded that spectral acceleration at 1 s is the most important predictor. Guan et al. examined data-driven and hybrid ML models to predict the drift demand o f 621 steel frames, and showed that random forests c ould accurately predict the seismic demands for both low - and high -rise buildings, although hybrid ML models provide higher accuracy than purely data -driven ones . Moreover, they found that the ratio of fl oor height to the building height and spectral acceleration and displacement at the fundamental period are the most influential for hybrid ML models, whereas spectral acceleration at the first mode dominated the purely data -driven models [29]. Table 1. Literature review of recent studies using ML to predict the seismic performance of buildings Study Year Structure type ML method description Predictors Target Selected algorithm(s) Hwang et al.[30] 2021 RC frame (2)a Plastic hinge properties, damping, period, S a(T1) MIDR, Collapse Boosting (6)b Demirtzis et al. [31] 2022 RC buildings (30) Height, eccentricity, ratio of walls base shear , and 14 GM parameters MIDR LightGBM (15) Kazemi et al. [32] 2023 Steel frames (8) Weight, period, Sa(T1), soil type, record number MIDR XGboost,Breg, HistGBR, ERTReg (11) Dabiri et al. [33] 2022 fragility database (214) Footprint, height, period Fragility parameters Decision trees (5) Kiani et al. a number in parenthesis shows the number of studied buildings b number in parenthesis shows the number of studied algorithms 4 Recently, ML -based approaches have been applied to regional -scale and community -level seismic assessments of buildings. Kourehpaz and Molina Mutt applied ML algorithms on a database of 36 RC frames, and used the trained model for portfolio assessment of RC wall -building across the Metro Seattle region [34]. Instead of using an ML model trained on small datasets, Lu et al. [35] developed an open -source scientific framework that can perform city -scale nonlinear time history analysis and applied this f ramework to 1.8 million buildings in San Francisco Bay Area using SimCenter [36] workflow. Nevertheless, t he reviewed literature suggest s that despite the significant existing literature on using ML at different scales , an ML -assisted framework is still needed to achieve performance -consistent design throughout the entire design process. 3. ML-assisted holistic seismic design This section presents the motivation and overview of the developed framework . Next, the application of the methodology for each design stage is dis cussed. Lastly, suitable databases to supplement the framework are introduced. 3.1. Objectives & Motivation A conventional design often follows the designer’s intuition and judgment from a precedent -based perspective [37]. These cognitive biases [38] can lead to missing more resilient and sustainable structural systems. In addition, the conventional seismic design aims to satisfy the safety requirements ( such as required strength and stabilit y) of building code under severe earthquakes. However, this approach cannot explicitly consider other performance objectives (e.g., minimizing repair costs or downtime) over the building life cycle , or even guarantee that the life safety objectives will be met. Computational tools integrate simulation and quantitative measures to supplement the design procedure and lesse n the role of intuition and precedence . PBEE can be a practica l computational approach to quantify the seismic -related consequences of different design decision s. PBEE also offers a systematic approach to treat different sources of uncertainties (due to hazard and structural modeling) using global performance measures that are easily understandable by the entire design team. Furthermore, due to PBEE’s modular nature, the assessment results can be seamlessly combined with other quantitative risk measures to provide a comprehensive evaluation. Several challenges need to be addressed to increase the application of PBEE in the design . First, PBEE requires ample data and particular skills (e.g., hazard modeling and simulation) that are not common in large design firms, and non -existent in small ones. These sequential analyses span different disciplines ranging from engineering seismology to str uctural engineering. Second, PBEE assessment is time -consuming and computationally expensive, and the needed effort and time significantly increase as the number of candidate design alternatives grows . For example, for each new design alternative, new stru ctural models should be developed, and based on the assessment type, a new ground motion selection needs to be performed if the decision notably changes the structure’s stiffness and mass. 5 The main objective of this study is to combine PBEE and data -drive n modeling, where data - driven models overcome the computational challenges and offer a fast means to extend and scale PBEE over the design space. As shown in Figure 2, this data -driven perfo rmance -based seismic design framework provides the following advantages over traditional heuristics: 1. Compilation of a broad design space : A successful design should consider many design alternatives (i.e., design space exploration) so that no high-perform ing candidate system is excluded . Here, statistical sampling -based approaches are used to populate the design space efficiently . Sampling -based approaches also allow space reduction to reduce the sheer effort needed for the high cardinality of real -world design problems. 2. Consideration of holistic life -cycle performance : A holistic design should consider multiple performance objectives such as environmental, economic , and hazard -related performance. Most previous efforts are aimed at the combined economic a nd environmental impacts of the design decisions, primari ly for shape optimization of structural components. In addition, these studies overlook the interaction of different performance measures. The framework uses multiple performance measures, where the interaction is considered through refined assessments that generate data needed for ML algorithms. 3. Characterization of seismic performance range : Commonly , PBEE is not applied for designing ordinary buildings (such as multistory concrete or steel frames) , or is reserved Figure 2. Motivation and objectives of the proposed framework Performance -based AssessmentData -driven ModelingExtract hidden relationships Modeling interdependenciesExplicit treatment of uncertainty Global performance measuresFast-changing natureImprecise and uncertain Interdisciplinary problemDesign Effort -intensiveDesign space exploration Characterized by Addressed byLegend Compilation of a broad design spaceCharacterizing hazard performanceHolistic life- cycle performanceA data -driven performance -based design framework Optimization & identifying critical decisionsUncertainty treatment 6 for later stages of design or assessment. This framework extends PBEE application from early stages (to characterize seismic performance range over the approximate description of different candidate systems) to detailed design and optimiza tion. 4. Treatment of uncertainties : Both PBEE and data -driven introduces different sources of uncertainties into the design. PBEE assessments are characterized by uncertainties related to hazard characterization, structural response analysis, and loss esti mation, whereas data - driven models introduce uncertainties into the input variables ( e.g., inherent randomness, insufficient training data), algorithm hyperparameters, and mapping algorithms. The proposed framework leverages the uncertainty quantification methods native to both methodologies to treat the most governing sources of uncertainties comprehensively . 5. Optimization and sensitivity analysis of design decisions : The data -driven surrogate models facilitates performing a larger number of PBEE analysis at low computational costs, hence allowing to identify the most critical design decisions through sensitivity assessments (such as variance -based sensitivity), or dete rmining the optimum range of these parameters to achieve the intended performance range. 3.2. Framework Overview The proposed framework consists of two modules: early design and detailed design. At early design, the framework uses imprecise information provided by the designer in a pipeline of different simplified models to aid with select ing suitable structural system s, and providing preliminary insights on possible sizing. At detailed design, the framework uses a deep learning (DL) model to provide precise loss estimates based on more detailed des ign descriptors for the selected systems , where the DL can readily map seismic fragility to changes in structural properties. 3.2.1. Early design module Early design defines the design problem and explore s the solution space to identify candidate systems. The proposed framework provides risk -informed insights on the best possible structural systems and preliminary estimates on system design and configuration (e.g., weight, footprints) . Figure 3 shows the schematics of the early design module. This module relies on surrogate models to estimate the performance range based on crude design and topology information. The word “surrogate” here refers to different lower -order models, such as knowledge -based or data -driven models, that are computationally inexpensive and conform to the limited data availability of earlier design stages . For example, approximating performance based on assessments of similar buildings from literature ( i.e., knowledge -based), or using decision trees that can predict performance based on a set of assumed building characteristics ( i.e., data-driven). As shown in Figure 3, the primary workflow in the proposed data -driven framework uses supervised -learning ML algorithms to build surrogate models from PBEE assessment data . This data can be generated by alternate pathways and is supported through a knowledge -based module. As a result, the framework provides a fast means to explore design space, where the designer only needs to chang e the statistical surrogate model input accordingly to get instant assessment results. At the same time, the designer does not need to perform detailed performance -based assessments, but rather utilize a performance data inventory. The latter could be acco mplished by exploiting 7 available open databases, prior assessments, or performing simplified PBEE assessments . The first module requires performance databases to support the surrogate models. Currently, few open databases provide adequate data granularity over different building taxonomies and performance measures. Section 3.3 discusses several available databases for seismic and environmental performance. The framework provides designers with a sequential approach to leverage three different surrogate modeling techniques for performing convergence -divergence cycles , as shown in Figure 4. In a typical early design procedure, the designer performs a series of convergence (i.e., removing unfavorable design alternatives) a nd divergence (i.e., introducing new design alternatives) cycles to arrive at the final alternativ es. This sequential approach uses surrogate models with lower fidelity at the earlier stage to remove redundant alternatives from the large and highly variab le (both intra - and inter -system variabilities) initial design space. Next, data -driven surrogate models are implemented to estimate hazard performance ranges and compare alternatives in the second convergence cycle. Lastly, low -order dynamic models , such a s simplified single -degree -of- freedom (SDOF) systems , are developed for the few selected candidates, and parametric studies are performed to explore those design alternatives as a divergence cycle. Define design parametersSample design parameterPerformance - based assessment Prior knowledgeData -driven Surrogate Models Performance inventory Knowledge -based surrogate modelsOntology & Data typeSchema Collect dataKnowledge - based surrogate Data -driven surrogate Physics -based surrogateSequential D-space explorationHazard DataStructural DataConsequence DataHazard AnalysisHazard open data/toolsStructural analysisSimplified structural analysisDetailed loss assessmentSimplified loss assessment Sensitivity assessment Statistical testsEarly design guidanceUncertainty quantificationOptimization Primary steps Secondary steps Required tools/ methods outputLegendFigure 3. Early design module 8 3.2.2. Detailed Design Module After selecting the final candidate structural system (s) and initializing their parameter range, t he second module provides a more detailed seismic design . Here, t he designer needs to provide a more detailed description of the structural system through simplified nonlinear static (i.e., pushover) analysis. A deep learning -based engine then translate s the resulting force -deformation relationship (i.e., pushover cur ves) into probabilistic seismic demand models (PSDMs) , which can be readily mapped to seismic loss through pre -defined damage states and vulnerability functions. As shown in Figure 5, the deep learning model (i.e., P2M ) comprises an encoder to encode pushover curves and a decoder to construct the PSDM S through the encoded values. The loss function couples the changes in estimated intercept and slope values, avoiding separate training and overfitting [39]. PSDM’s error characterizes fragility variance and impact loss prediction. Therefore, P2M explicitly estimate s PSDM erro r using a separate network to track and update error estimation as a moving target. Different network types can be implemented for each network ; however , preliminary results indicate that long short -term memory (LSTM) could be slightly more efficient in ca pturing PSDM slope and intercept [39]. The P2M mapping also pro vides an efficient means to incorporate structural modeling uncertainties into the assessment through the “stochastic pushover” [39] method. This method changes the structural model properties, such as plastic hinges properties, and repeats pushover analysis for each set of new paramet ers. Next, P2M estimates the variation in PSDMs due to structural models change , creating a direct mapping between resultant fragility curves and structural models through pushover analysis. Therefore, the designer can perform a new pushover analysis for a ny given design decision and instantly calculates the changes in the structure’s fragility . The designer can also perform a few pushover analys es to estimate upper and lower -bond pushover curves and characterize the seismic performance range in terms of fr agility or loss variances . In addition, since this approach directly measure d the impact of different design Unacceptable design Acceptable designReduced Space Feasible SpaceAlternative SpaceInitial Space X1: Hazard -related Repair cost X2: Initial cost X3: Embodied CarbonX1X2X3 X1X2X3 X1X2X3 X1X2X3Knowledge - based SurrogateData -driven SurrogatePhysics -based SurrogateInformation Information Information InformationDerivativesFigure 4. Sequential workflow to use surrogate models for early design 9 decisions on the fragility curves (and consequently loss estimates) without performing a nonlinear dynamic analysis, it is suitable for the dynamic and fast -paced nature of the design. 3.3. Performance Data Inventories Preparing data, including acquisition and preprocessing, is the first and perhaps the most critical step of any ML -based framework. T he proposed methodology requires extensive open data on the seismic and environmental performance of different building systems . Future hazard performance databases can be presented as relational databases (RDBs) to promote easier data sharing and collaboration . RDBs organize interrelated data tables using shared fields (i.e., keys), facilitat ing more efficient data storage and integration. T hese databases can be hosted on Design -Safe CI, which allows user s to extract data by defining a search criterion through web -based SQL quer ies. The criterion is defined by using database keys to combine tables (i.e., performing a join), and filtering the results to meet user conditions. Adopting RDBs and open data practices scale the individual efforts in PBEE to community -driven scientific workflows necessary for addressing seismic resiliency challenges . 3.5.1. Vulnerability data The global synergies on vulnerability modeling resulted in several databases that can be used to quickly characterize seismic performance in terms of loss or probability of experiencing a given damage state. Such data (particularly fragility curves) can also be used as the input to calculate higher -level performance measures. Among these databases, the Global Earthquake Model (GEM) provide s fragility curves, damage -to-loss models, or capacity curves for different structures [40]. Figure 5. Detailed design module C(copy weights and biases) Net IEncoder Net II -A Net II -BSlope A DPushover curve DecoderB B C DATraining schedule Net II -C Net IError -estimator ) + ⋅ Sigmoid Sigmoid Tanh ⋅ ⋅TanhSigmoid : cell state | h: hidden state | x: input data ReLU+BNNet-I output PSDM parametersStructural ParametersStructural ModelPushover Analysis Demand ModelLoss EstimateFEM LiteratureP2M 10 Curated published literature on PBEE for different structural systems can also be used as a resource to provide such data. Therefo re, Esteghamati et al. compiled an open relational database, denoted as “INventory of Seismic Structural Evaluation, Performance functions, and Taxonomies (INSSEPT )” [41,42] , to aggregate 222 PBEE case studies from 39 papers . The current version of INNSEPT provides simulation -based data on building topology, design, location, and seismic performance in terms of fragility and PSDM parameters for 144 moment -resisting frame s, 30 braced frame s, and 24 wall -building system s. 3.5.2. Environmental performance data Life cycle assessments (LCAs) provide a systematic approach to evaluat ing environmental impacts. Different LCA approaches exist with different level s of complexity , such as process - based and economic input -out method s. Unli ke PBEE assessments, several guidelines establish standardized approach es to perform ing LCA. However, standardized LCA studies require the definition of scope and system boundary, which vary between different studies and prevent t heir reuse for other proje cts. A few studies performed comparative LCAs between different structural systems, where their published impact data can be used as an approximate value, useful for the early design stage. For example, Esteghamati et al. compared six commercial buildings with varying foundation, structural, and envelope systems [42], provided impact data, and LCA and energy models on a public repository [43]. 3.5.3. Seismic recovery data The current PBEE assessments mainly focus on seismic risk in terms of monetary metrics such as repair cost. However, the recovery of building s after an earthquake event is an essential predictor of community resilience . Post-earthquake recovery models rely on empirical data, such as duration -based parameters that define recovery activities. Omoya et al. developed a relational database to compile the recovery efforts of 3695 buildings after the 2014 Napa earthquake [44]. The relational database provides empirical data on building general topology, site, observed damage, and dura tion-based recovery measures ( such as timestamps for initiation and compl etion of permitting or repair. Such data can then be integrated in to recovery models through analytical approaches [45,46] 4. Case study This section discusses the prelimin ary application of the proposed framework for the seismic design of mid -rise commercial buildings for a site in Charleston, SC. 4.1. Design problem definition A structural engineer is assumed to be consulted on identifying high-performing design alterna tives for a multistory commercial building project in Charleston, SC. This site is subjected to high wind and earthquake hazards , although only earthquake hazard is considered . For the sake of this illustration, several assumptions are made . First, building footprints are commonly determined based on zoning and ordinance requirements and thus have a fixed value. However, it is assumed that the designer can find the best general topology that meets certain limitations ( e.g., mid-rise, building dimensio n in each direction between 42 ft to 180 ft) . Second, although the framework can consider multiple performance objectives, this illustration only focuses on seismic - 11 related repair costs and embodied carbon during the building’s service life of 50 years . Third, while the framework aims to guide structural system selection, t he illustration scope is limited to o nly multistory concrete frames due to the unavailability of adequate data for the considered site. 4.2. Building inventory description Curre ntly, a comprehensive performance inventory does not exist for the considered site. Therefore , an inventory of 720 RC moment frames was developed through an automated workflow as a proof -of-concept to provide data for the framework . Figure 6.a shows the sc hematics of the workflow to generate this inventory . The geometric configuration of a multistory symmetric concrete frame can be defined through four parameters of dimensions in two perpendicular directions, the number of stories , and bay length (Figure 6.b). A Latin Hypercube Sampling was then used to generate 60 samples of these topology parameters based on their practical ranges. For each set of sampled topology parameter s, 12 different sets of section sizes are generated for frame beams and columns through a pseudo -directional sampling . Additional information on frame and section sampling can be found in [47]. The paired topology and designed sections are then used to create finite element models suitable for performance -based seismic assessments. 4.2.1. Finite element modeling A two -dimensional finite element model was developed in OpenSees [48] for each sampled pair of topology and design parameters . As shown in Figure 6.c, the finite el ement model uses a concentrated plasticity approach, representing frame members as elastic elements with two nonlinear plastic hinges at both ends. The hinge properties were determined based on Ibarra - Medina -Krawinkler (IMK) model [49]. The parameters of the IMK model ’s backbone curve (such Figure 6. Compiling concrete frame inventory: (a) the workflow to generat e performance data, (b) a typical plan of a symmetric concrete frame building, (c) general configuration of the nonlinear models, (d) generated synthetic GMs for the site of this study (a) Geometry DataSection SamplingSection DatabaseSection parameters Geometry parametersStructural modelPerformance Data GM database Cost data EI dataLHS samplingFEMLCA + Loss (b) (c) (d) LY LBay Gravity frame Moment framePlastic hingePanel zoneTruss element Leaning ColumnElastic elementLx Period (s)Sa(T1) (g) 12 as pre -and post -capping deformation) and the cycle deterioration were obtained from a set of regression equations proposed by Haselton for symmetric RC sections [50]. The stiffness of plastic hinges and elastic elements were adjusted to remo ve the unrealistic damping forces due to plastic hinge formulation [51]. The leaning column concept accounted for the P -delta effects of gravity frames [52]. 4.2.2. GM selection & time -history analysis Due to Charleston’s special seismicity, conventional GM selection methods based on generic GM suites are inefficient. Therefore, a careful geologically -realistic seismic hazard analysis [53] was used to generate synthetic GM s. Four hazard levels were selected corresponding to 2%, 5%, 7%, and 10% exceedance probabilities in 50 years. Earthquake magnitude (M) and distance (R) pairs were generated based on an inverse transform sampling from the hazard deaggregation at each considered hazard level, where the number of M -R pairs in each bin was proportional to the bin’s contribution to the hazard [54]. A synthetic GM record is generated for each M -R pair using a stochast ic method described in [55]. Two GM sets were developed to perform the nonlinear time - history analysis : (a) 20 records scaled to maximum considered earthquake levels, (b) 80 unscaled records (20 records for each considered hazard level). The scaled record set was used to check the structu ral models based on code requirements for drift and collapse, whereas the second set was used to perform a cloud analysis considering different response levels [56,57] . In cloud analysis, the spectral acceleration at the first mode (i.e., Sa(T1)) was used as the GM intensity measure (IM) . Floor peak accelerati on and maximum interstory drift responses were recorded as the engineering demand parameters (EDPs) . 4.2.3. Seismic l oss assessment An assembly -based approach [58] was used to derive life -cycle repair cost s based on considered EDPs . This approach aggregates building component losses to assembly categories, reducing the required data and computation, which is suitable for portfolio assessments. In this approach , collapse and non -collapse losses are separated. The collapse losses were taken as building replacement and demolishing costs multiplied by collapse probability , where collapse was defined as the building reaching a maximum inter -story drift of 10% [59]. Logistic distribution was used to derive collapse probability. The average collapse probability for the compile d building inventor y was 0.52% , with a standard deviation of 0.19%. Out of 720 buildings, only 1.5% did not collapse under any given record, whereas 2.4% had a collapse probability over 1% with a maximum value of 2.4%. For non -collapse losses, t he repair c ost for three assemblies (structural, non-structural drift -sensitive, and non -structural acceleration sensitive) and their corresponding damage states were derived from the HAZUS manual [60]. A lognormal distribution was fit ted to EDP -IM pairs from cloud analysis to calculate damage distributions. Since HAZUS repair costs are in terms of building construction costs, the RSMeans database was used to calculate the monetary values. Lastly, t he expected total loss values were integrated over the IM intensities to estimate the expected annual loss (EAL) values for each assembly. Figure 7 compares the variation of different EAL values (normalized by building replacement cost) with respect to the structure’s fund amental period, floor area, and average beam section size. While structures with a higher fundamental period show a larger structural loss, they have a smaller 13 non-structural acceleration -sensitive loss. Similarly, a positive correlation between floor area and structural losses (and a negative correlation to non -structural acceleration -sensitive losses) is observed. However, increasing average beam section sizes reduces structural loss and slightly increases non -structural acceleration -sensitive losses for the considered inventory . Nevertheless, the impact of all these parameters on collapse loss is small. The ML models must capture thes e underlying relationships to predict the total loss due to different topology and design parameters. 4.2.4. Environmental impact assessment Whole -building life cycle assessments (WLCA) were performed on the developed building inventory following a proces s-based approach described in ISO14 044. The WLCA boundary included the structural frames, floors, envelope s, and partitions [61]. The frame topology and design information were obtained from the automated workflow output, whereas partition material was calculated based on FEMA P -58 normative tool [47]. A brick -veneered concrete masonry block was assumed for the envelope system with a window -to-wall ratio of 0.31 . The environmental impact assessment was carried out for embodied global warming poten tial (GWP) during a building service life of 50 years. 0 1.0 1.5 2.25 Period (s)5 4 3 2 1EALC( 10-4)EALA( 10-5)10 8 6 4 2 0 1.0 1.5 2.25 Period (s)5 4 3 2 1EALS( 10-5) 0 1.0 1.5 2.25 Period (s) 5 4 3 2 1EALC( 10-4) 5 4 3 2 1EALC( 10-4)EALA( 10-5)10 8 6 4 2 EALA( 10-5)10 8 6 4 2 5 4 3 2 1EALS( 10-5) 5 4 3 2 1EALS( 10-5)0 1 2 3 Floor Area (ft2 104)0 1 2 3 Floor Area (ft2 104)0 1 2 3 Floor Area (ft2 104) 0 400 600 800 Average Beam Area(in2)0 400 600 800 Average Beam Area(in2)0 400 600 800 Average Beam Area(in2)Figure 7. Comparison of loss values v ariation with respects to building period, floor area, a nd average beam area 14 Embodied GWP due to earthquake -related repairs was also accounted for through the cost ratio approach. In this approach, it is assumed that the ratio of repair -related GWP to initial embodied GWP is directly related to the ratio of repair cost to the building construction cost. As shown in Figure 8, embodied GWP is linearly related to building gross area (and consequently weight) with an R-squared value of 0.98 . This high R -squared value is mainly due to the small values of seismic loss, resulting in embodied GWP being a function of initial construction GWP (and hence proportional to building footprint). It should be noted that not all topol ogy-related parameters have a high correlation to the embodied GWP [47]. 4.3. ML -assisted early design 4.3.1. Data -driven surrogate models The performance inventory was used to generate data -driven surrogate models through a n ML pipeline depicted in Figure 9.a. This ML pipeline splits the database into training and testing sets, select s candidate features (using statistical or recursive feature elimination (RFE) methods), select s an algorithm, tune s the ML model hyperparameters, and finally, evaluat es them based on measures such as R -squared or root mean square error. Five algorithms were examined, and the model R2=0.04 R2=0.98 Height (ft) Gross Floor Area (ft2)GWP (kgCO2)Figure 8. Comparison of embodied GWP relationship to height and floor area Performance DatabaseSplit Database Feature Selection ML AlgorithmModel TrainingModel EvaluationMLR RF XGBSVM KNNStatistical RFE Grid Search Randomized Search Cross -validation1.0 0.5 0 H Ly FA WL (a) (c) Sobol IndexTotalFirst-order(b) Observed EALPredicted EAL Figure 9. ML-assisten early design module results: (a) ML pipeline to train data -driven surrogate models, (b) SVM prediction of total loss on training set, (c) Sensitivity assessments of SVM to model predictors: height ( H), Y-dimnesion ( Ly), floor area (FA), lateral weight (WL), average beam area ( ̅̅̅), average beam area in the first floor ( ̅̅̅̅̅), average beam reinforcement ratio () 15 accuracy was compared. The results show that su pport vector machines (SVM ) provide the highest accuracy, predict ing total seismic loss with an R-squared value of 0.92 (Figure 9.b) using only crude topological and design parameters. Nevertheless, the loss prediction values were sensitive to how the building cost function is form ulated. The highest accuracy is achieved when the loss is defined in terms of actual dollar s spent (cost function as a multiplier of building footprint) , whereas defining loss as the percentage of replacement cost (cost function of unity) leads to the lowest accuracy [47]. ML models error can be decomposed into two competing factors : bias and variance. Bias quantifies the average difference between actual response values and model prediction, whereas variance measures the variability in ML model prediction for a given data. There is a tradeoff between ML model bias and variance: simpler models might not be adequate for prediction ( i.e., high bias) yet exhibit low v ariance, whereas flexible models might result in excellent prediction (i.e., low bias), yet the models’ accuracy might not be consistent ( i.e., high variance). Figure 10 compares the bias and variance of studied ML algorithms to predict the structural and collapse losses. First, the k-nearest neighbor show s high bias and variance for both loss types, resulting in a large overall error. Multiple linear regression generally shows lower variance for both loss types ; however , it is highly b iased for collapse lo ss prediction. For structural losses, it can be observed that MLR shows the lowest variance, whereas SVM show s the lowest bias. All models except for extreme gradient boosting and SVM show high bias for collapse los s. To predict total loss, t he selected SVM model use s building height (H), dimension perpendicular to the analyzed frame (Ly), floor area (FA), lateral weight (WL), average beam area over the entire building ( ̅̅̅), average beam area over the first floor ( ̅̅̅̅̅), and average bea m longitudinal rebar percentage ( ̅̅̅). As shown in Figure 9.c, a variance -based sensitivity assessment showed that the SVM model’s prediction variance is dominated by the higher -order interaction of all these predictors. Among different predictors, floor area, height , and average beam area were the most influential predictors for total loss. Structural loss 0.18 0.14 0.10 0.06 0.02MLRRF XGBSVMKNNMSECollapse loss MLR RF XGB SVMKNN5 4 3 2 1MSEBias VarianceFigure 10. Comparison of embodied GWP relationship to height and floor area 16 4.3.2. Sequential design space exploration As described in Section 3.2.1, a sequential workflow was created by linking knowledge -based, data-driven, and low -order mechanistic surrogate models. The knowledge -based model is achieved by regressing loss values from literature ( query through INSSEPT , among other data bases ) for the reported building gross area. The developed SVM model was used as the data -driven surrogate model. Lastly, an equivalent SDOF was developed to derive low -order mechanistic models , where spring character istics were calibrated based on the result of the pushove r analysis of similar concrete frames in the literature. The assumption made to develop the equivalent SDOF assumptions could impact loss prediction . Therefore, sensitivity assessments were performed to identify the critical decisions. Figure 11 compares different loss values obtained from equivalent SDOF and detailed assessment for three considered frames (denoted as frames 1,2, and 3) . Overall, the di fference between simplified and detailed dynamic models vary across different loss type. For example, while there is a significant difference between structural losses of SDOF and MDOF models for the second frame, the collapse losses are very close. Second , as can be observed by comparing Figures 1 1.a-c to 10.d -f, the inclusion of cyclic deterioration in the SDOF model did not notably change the loss prediction (collapse losses are more sensitive to this value) . Lastly, the estimated loss values are highly sensitive to the factor relating SDOF displacement to MDOF drift. Currently, empirical values are suggested for this mapping [62]. However, the comparison between Figure 11.d-f and 1 1.g-i Figure 1 1. Comparison of different loss types estimated from equivalent SDOF and detailed analysis. Figures a -c are calculated using a γ=0 and empirical factors to related SDOF displacement to MDOF drift, Figures d -f are caucluated using γ=50 and empirical factors, Figures g -i are calculated using γ=50 and calibrated factors. A B C A B C A B C A B C A B C A B C A B C A B C A B CSDOF MDOF(a) (b) (c) (d) (e) (f) (g) (h) (i) 17 suggests that even when this value is obtained directly from sensitivity assessment, the final loss values can be drastically different from the detailed assessment . In addition, empirical factors could result in a woefully inacc urate loss estimate for a given frame (e.g., frame 2) . Lastly, the difference between losses obtained by different factors varies across frames and loss types, pointing to a more complex relationship. The workflow was applied to estimate the loss for a 4 -story building with five 27 -foot bays in each direc tion. Here , the only available information is building foo tprint, location, and construction cost. Figure 12 shows the resultant loss ranges predict ed by the workflow. The results of the surrogate models a re compared to the 12 design variations assessed based on a detailed PBEE assessment. The knowledge -based surrogate models provide a larger range, mainly because the current performance inventories are governed by concrete frames designed for California that must resist larger seismic forces. The developed SVM used ranges of input variables for lateral weight and beam design information (from code minimum and maximum range), resulting in a loss range that encompas ses the median and variance pr edicted by the detailed assessment. Lastly, the pushover results of a 4 -story building from the literature w ere used to calibrate the SDOF model. Since the literature building was located in California, a scaled pushover curve was also used to represent th e lower bound for the site in Charleston. As shown in Figure 1 2, the sequence approximately converges to the median loss results from a detailed assessment using incomplete data. The average prediction from data -driven models is 10.5% larger than the avera ge loss predicted by detailed design. The average prediction from the low -order dynamic model is about 11.9% smaller than the detailed model. 4.4. ML -assisted detailed design The results from the early design stage characterize the RC frame properties such as lateral weight, footprint, and average beam area. An experienced structural engineer can use this information to generate some preliminary design s. Next, the designer can perform pushover analysis on the generated alternatives and uses the P2M netw ork to evaluate the seismic performance. As discussed in Section 3.2, P2M also provides an efficient means to change frame properties and map the changes to the final seismic performance measures. It should be noted that future work to create mapping funct ions between early design estimates and member sizing could sidestep this step, resulting in an end -to-end simulation framework . Figure 1 2. KBS: knowledge -based, DDS -F: data -driven (full), DDS -R: data -driven (reduced), PBS: physics -based DDR 18 The discussed network was trained on the compiled frame inventory to develop P2M for the current site . The results showed average prediction accuracy of 84% for a test -to-training ratio of unity (half of the database was used for testing) [39]. A sensitivity assessment on different neural network types suggested that LSTM networks can provide the highest accuracy with an average R2 of 87% , only 4.4% lower accuracy than the detailed analysis results. The average differen ce between P2M and the detailed analysis estimate for the slope and intercept of the PSDM model were 2.7% and 5.7%, re spectively [39]. 5. Conclusion 5.1. Summary This study presented a conceptual framework to integrate ML methods into the PBEE framework for a holistic seismic design. The presented framework comprises two modules for earl y and detailed design. The early design module uses supervised ML algorithms to directly estimate seismic loss using geometric configura tion and average design parameters estimable by an experienced designer. Combing these models with simplified mathematical relationship s based on the knowledge base and low -order mechanistic models provided a means to quick ly predict a performance range fo r a given frame without any detaile d design information. After parametrizing the possible range for design parameters, finite element models could be developed for average (or minimum and maximum) values to perform a pushover ana lysis. The resultant pushov er curve (and its variations for parametrized frame properties) can be fed into a deep -learning engine to estimate seismic demand models, and consequently , fragility and loss values, preventing the need for complicated time -history analysis. The same appro ach can be extended to other performance measures reliant on quantit ative analysis (such as environmental impacts), leading to a holistic seismic design. Several major findings of this study are as follows:  ML methods can scale PBEE assessments over a building inventory and provide accurate predictions subjected to different levels of available information on topolo gy and design.  ML models can be trained to estimate earthquake -related repair cost s using only crude topological and design parameters for a given site and structural system . ML model accuracy was sensitive to the building replacement cost values.  Among studie d algorithms, s upport vector machines and gradient boosting methods provide the highest a ccuracy. The prediction of support vector machines was dominated by higher -order interactions of predictors, where building height, floor area, and average beam section area were the most influential features in predicting concrete frame repair cost.  Although simpler regression -based models could be adequate for structural loss predictions, they show high bias for collapse loss estimation.  An e quivalent SDOF system c an provide reasonable accuracy to predict seismic loss of symmetric concrete frames . The accuracy of SDOF systems var ies across different loss types, and is sensitive to the factors relating its displacement to the building inter -story drift. 19  The “shape” of pushover curves successfully encodes salient dynamic properties of the frame systems, w hich can be decoded into probabilistic seismic demand models through a deep learning architecture . This model can propagate component -level uncertainties into fragility functions, allowing for a fast estimate of seismic loss for different design decisions. 5.2. Limitations Despite the current framework advantages to extend PBEE to different design stages, several limitations need further research to improve frameworks automation and easy scaling as follows:  The methodology required an automated seismic design module to provide code - conforming member sizing. In the current case study, a pseudo -directional sampling -based approach was used to generate member sizes, which does not meet the requirements of a caref ul seismic design and prevent an end -to-end framework.  The framework is applied to a site with moderate seismicity. To ensure generalizability, testbeds for sites with high seismicity should be investigated. Nevertheless, the current literature indicates that ML models can estimate drift with high accuracy for sites with high seismicity, suggesting th at applying the framework to those sites is possible .  Although pushover analys es are relatively less computationally expensive, they require developing a finite element model. Future work is needed to create a mapping function between the properties of an equivalent SDOF and detailed FEM to sidestep this issue.  The framework was ap plied to an inventory of only concrete frames. However, a more extensive and diverse inventory comprising different structural systems, is needed to evaluate the framework generalizability, particularly for system selection at early design. 20