Tiêu chuẩn iso tr 15656 2003

Microsoft Word C038528e doc Reference number ISO/TR 15656 2003(E) © ISO 2003 TECHNICAL REPORT ISO/TR 15656 First edition 2003 12 01 Fire resistance — Guidelines for evaluating the predictive capabilit[.]

General

Structural fire behavior under standard fire exposure has typically been assessed through experimental methods outlined in standards like ISO 834 However, alternative calculation methods have emerged to evaluate the fire endurance of structural components Given the importance of fire resistance in safety regulations, it is crucial to objectively assess the accuracy of these calculation methods A review highlighted the rapid advancements in analytical and computational modeling for fire engineering, emphasizing the need for standardized procedures to evaluate model predictions and document software Previous evaluations of fire-specific thermal and structural programs revealed that they are often validated against limited test data, with insufficient general validation of these methodologies.

ASTM has developed ASTM E 1355, Standard guide for evaluating the predictive capability of fire models

ISO/TC 92/SC 4 is currently developing guidelines outlined in ISO/TR 13389, which focuses on the assessment and verification of mathematical fire models These guidelines are designed for various fire models, particularly those predicting fire growth in compartments Numerous papers have evaluated fire models, and some of these will be reviewed in ISO/TR 13389 A notable 1993 review examined seven thermal analysis programs and fourteen structural analysis programs specifically for fire endurance analysis.

An assessment of fire models based on a matrix of criteria and weighting factors has been presented [10]

The evaluation criteria for the system encompass various factors, including field of application (4 points), scientific verification (6 points), precision of method (2 points), physical background (1 point), completeness (2 points), input existence (2 points), user-friendliness (1 point), and approval or experience (2 points), totaling 20 points This system has been implemented in conjunction with existing simplified methods for concrete, structural steel, and timber.

Potential users and their needs

This Technical Report addresses the needs of fire model users, emphasizing the importance of selecting appropriate models that ensure adequate accuracy for specific applications It guides developers of performance-based code provisions and approving officials in verifying that mathematical models operate within their applicable limits and maintain acceptable accuracy levels The methodologies outlined will aid model developers and marketers in documenting the predictive capabilities of their calculation methods Additionally, the report highlights the significance of identifying and documenting precision, limits of applicability, and conducting independent testing Educators can leverage these methods to effectively demonstrate the application and acceptability of the calculation techniques being taught.

This Technical Report serves as a valuable resource for educators training the next generation of model developers, ensuring that future models, which may be more complex and widely available, are utilized effectively within their specific application limits and precision constraints.

Predictive model capabilities, uncertainties of design component (from ISO/TR 12471)

Recent studies have shown improvements in the predictive capabilities of models and software used to simulate fire exposure and the thermal and mechanical behavior of fire-exposed structures Research has focused on compartment fire modeling and the thermal and mechanical behavior of structures Identified sources of error in computer models predicting state variables like temperature or heat flux include unrealistic theoretical and numerical assumptions, errors in numerical solution techniques, and software errors.

Copyright International Organization for Standardization

The Loss Prevention Council outlines key information regarding 10 zone models and 3 field models for compartment fires, including validation degrees, limitations on compartment size, vent numbers, fuel capacity, and user organizations Important insights are gained regarding input/output data, model validation, and potential limitations A survey examines the theoretical foundations of 7 thermal and 14 structural fire-dedicated computer programs, highlighting their strengths and weaknesses The primary differences among these programs stem from the material models used, data input requirements, and the overall user-friendliness and documentation Most fire-dedicated structural programs still need significant improvements, as their lack of user-friendliness and proper documentation hampers effective and universal application.

Comparative calculations of the structural behavior of fire-exposed steel columns were conducted using five different computer programs The results indicate that the ultimate resistance of the columns is quite consistent, with a maximum variation of only 6% between the programs However, notable discrepancies in column displacements were observed, likely due to differing approaches in accounting for residual stresses at elevated temperatures It is crucial to consider that the same mechanical behavior model for steel at transient elevated temperatures, as outlined in ENV 1993-1-2, was utilized in the evaluation of these results.

Eurocode 3 — Design of steel structures — Part 1-2: General rules —– Structural fire design) was used in all computer programs

Sensitivity and uncertainty studies relevant to structural fire design are scarce in the literature, with the most comprehensive research dating back 20 years The methodology from these studies is broadly applicable to various structures and elements To derive effective safety measures, a probabilistic analysis is numerically demonstrated using an insulated, simply supported steel beam with an I-cross section, typical of floor or roof assemblies in office buildings The selected statistics for dead, live, and fire loads reflect those commonly found in such environments.

The design procedure involved identifying and analyzing various sources of uncertainty to effectively utilize laboratory test data The total variance in load-bearing capacity, denoted as var(R), was derived in two key stages: first, assessing the variability in the maximum steel temperature, var(T max), for a specific structure and fire compartment; and second, evaluating the variability in strength theory and material properties at a known T max.

The study reveals the decomposition of total variance in maximum steel temperature (\$T_{max}\$) into component variances based on the insulation parameter \$\kappa_n = \frac{A_i k_i}{V_s d_i}\$ (refer to Figure 1) Here, \$A_i\$ represents the interior surface area of insulation per unit length, \$d_i\$ is the insulation thickness, \$k_i\$ denotes the thermal conductivity of the insulating material averaged over the fire exposure process, and \$V_i\$ is the volume of the steel structure per unit length An increase in \$\kappa_n\$ indicates a reduction in insulation capacity.

Figure 1 — Separation of total variance in maximum steel temperature T max into component variance as a function of insulation parameter κ n

The component variances highlight the stochastic nature of fire load density $ q $ and the uncertainties in insulation properties $ \kappa $, prediction errors in compartment fire theory, and heat transfer to structural members, represented by $ \Delta T_2 $ Additionally, a correction term accounts for discrepancies between laboratory fires and real-life conditions, denoted as $ \Delta T_3 $ Similarly, the total variance in load-bearing capacity $ R $ can be decomposed into component variances based on the insulation parameter $ \kappa_n $ These variances encompass the variability in maximum steel temperature $ T_{\text{max}} $, material strength $ M $, prediction errors in strength theory $ \Delta \Phi_1 $, and differences between laboratory tests and actual fire exposure $ \Delta \Phi_2 $.

Research on the uncertainty of fire-exposed concrete structures is limited A study identifies the total variance in fire resistance and load-bearing capacity, breaking it down into component variances based on the slenderness ratio \$\lambda\$ for eccentrically compressed, reinforced concrete columns These component variances are influenced by several stochastic variables, including the compressive strength of concrete at room temperature (\$f_c\$), the strength of reinforcement at room temperature (\$f_s\$), the cross-section width (\$b\$), the cross-section height (\$h\$), the position of tensile reinforcement (\$x_t\$), the position of compressive reinforcement (\$x_c\$), the yield stress of steel as a function of temperature (\$f_{S,T}\$), and the thermal conductivity of concrete (\$k_c\$).

Figure 2 — Separation of total variance in load bearing capacity R into component variances as a function of insulation parameter κ n

NOTE Concrete B25, percentage of reinforcement à = 0,2 %, b = h = 30 cm, eccentricity e = 0,2 h

Figure 3 — Separation of total variance in resistance or load-bearing capacity R into component variances as a function of slenderness ratio λ for an eccentrically compressed, reinforced concrete column

Recent sensitivity studies on fire engineering design for timber structures have highlighted the impact of charcoal layer penetration in fire-exposed timber, influenced by material inputs in simulation models, particularly thermal conductivity and surface reaction rates Additionally, a first-order reliability analysis (FORM) of fire-exposed wood joist assemblies has been conducted, utilizing non-linear least-square regression on 42 full-scale tests to create a time-to-failure model that predicts the assembly's resistance This analysis defines the exposure parameter based on the duration of a ventilation-controlled compartment fire, considering factors such as fire load, window area, and height, while developing expressions for total system and component variances to determine the safety index β.

Figure 4 — Depth of charring as a function of time for variable thermal conductivity k 2 of charcoal and variable rate of surface reaction β 1

This Technical Report evaluates fire models through seven key components: first, it defines the model and scenario under review; second, it assesses the model's application for specific uses; third, it identifies potential sources of prediction errors; fourth, it examines the theoretical basis and assumptions relevant to the model's application across various problems; fifth, it evaluates the model's mathematical and numerical robustness, along with the accuracy of its computer code; sixth, it analyzes the uncertainty and accuracy of the model's predictions; and seventh, it assesses the model's sensitivity to different parameters.

Comprehensive documentation of calculation models and associated software is essential for evaluating the scientific and technical foundations of these models, as well as the precision of computational methods Proper documentation also mitigates the risk of unintentional misuse of fire models Additionally, scenario documentation offers a thorough overview of the scenarios or phenomena being assessed, which is crucial for the correct application of the model, the formulation of realistic inputs, and the establishment of criteria for evaluating the results.

A model's effectiveness in predicting outcomes must be evaluated based on its quantitative capabilities for a specific application Even deterministic models depend on inputs derived from experimental data, empirical correlations, or engineering estimates Variability in these inputs can result in uncertainties in the model's outputs To address this, sensitivity analysis is employed to measure how uncertainties in the model inputs affect the outputs.

Measurement results are essentially approximations of the specific quantity being measured, and they are only complete when accompanied by a quantitative statement of uncertainty The Guide to the Expression of Uncertainty in Measurement offers valuable guidance for determining this uncertainty in measurements.

It is essential to verify that the computer implementation of the model aligns with the provided documentation Conducting an independent review of the fundamental physics and chemistry within the model guarantees the correct application of the combined sub-models that contribute to the overall framework.

Information on methodologies discussed in this Technical Report can also be found in ISO/TR 13387-3:1999,

Fire safety engineering — Part 3: Assessment and verification of mathatical fire models, and ASTM E 1355

These two documents are the primary documents used to prepare this Technical Report ASTM E 1895,

This standard guide outlines the methodology for systematically evaluating deterministic fire models, catering to model users, developers, and authorities Although it focuses on deterministic fire models, it primarily emphasizes those designed for predicting structural fire behavior, particularly in compartment fires.

6 Definition and documentation of model and scenario

Types of models

Fire models for structures typically include a heat-transfer model that generates the necessary thermal profile for the mechanical model, along with the mechanical model itself Current models for structural fire engineering design have been systematically categorized based on a matrix that contrasts structural models with thermal exposure models This matrix, illustrated in Figure 5, features two distinct types of thermal models.

 H1: the thermal exposure is the standard fire resistance test with the nominal temperature-time curve;

 H 2 : the thermal exposure is that resulting from a real fire

Figure 5 — Matrix of thermal exposure and structural behaviour models

Thermal exposure in a simulated real fire is determined by solving energy and mass balance equations of compartment fires or through established design standards These standards include the parametric fire model from ENV 1991-2-2 and Eurocode 1, which outlines the basis of design and actions on structures exposed to fire, as well as various gas temperature-time curves.

The matrix provides for three types of structural behaviour models These three types of models include:

 S1: the analysis is for single structural elements;

 S2: the analysis is for a substructure;

 S3: the analysis is for the complete load bearing structure of the building

A substructure model describes the mechanical behaviour of a part of the complete load-bearing system of a building with simplified boundary conditions at its outer ends or edges

Models are defined by their failure criteria, which encompass three key aspects: the integrity criterion, which addresses the passage of flames or hot gases; the thermal insulation criterion, focusing on excessive heat transmission and temperature rise; and the load capacity criterion, which pertains to failure due to load or deformation.

The integrity of a structure during a fire is compromised when it fails, which can be assessed through models that incorporate either heat transfer (thermal expansion) or mechanical factors (deflection).

Models can be characterized in terms of their outputs These outputs include the following: a) heat transfer/thermal profile; b) mechanical/deflection; c) mechanical/loss of load capacity; d) integrity: delamination, spalling, dilation

The model can be described in the context of the overall objectives of fire safety design

EXAMPLE Structural response (from ISO 13392) a) Global information

 building, occupants, fire loads, fire scenarios environment

 size of fire/smoke, thermal profile

 building and content condition b) Evaluations

Documentation

Proper model documentation should include the model's name and version, developer(s), and relevant publications for further details It is essential to clearly outline the model's intended uses, limitations, and results, as well as define the type of model Additionally, information regarding the evaluation scenarios is crucial, including descriptions of the phenomena of interest, predicted quantities, and the required accuracy for each Other important details encompass the model's inherent assumptions, governing equations, numerical methods used for solving these equations, and how individual solutions are coupled Furthermore, additional assumptions related to the model's uses, the necessary input data for operation, and property data defined or assumed during model development should also be provided.

ASTM E 1472 serves as a guide for documenting computer software used in fire models, emphasizing the importance of comprehensive technical documentation and a user’s manual It is crucial to outline the model's range of applications and its validity concerning the data range utilized during its development.

Deterministic versus probabilistic

Quantitative analyses encompass both deterministic and probabilistic design procedures Deterministic models predict a single outcome based on established physical, chemical, and thermodynamic relationships, while probabilistic models estimate the likelihood of various potential outcomes, particularly unwanted events These probabilistic models utilize statistical data on fire start frequencies and the reliability of fire protection systems, alongside deterministic evaluations of possible fire scenarios For effective integration of probabilistic models with analytical models of relevant processes, distinct levels must be identified.

 an exact evaluation of the failure probability, using multi-dimensional integration or Monte Carlo simulation;

 an approximation evaluation of the failure probability, based on First Order Reliability Methods (FORM);

 a practical design format calculation, based on partial safety factors and taking into account characteristic values for action effects and response capacities

Sources of errors in predictions

Sources of errors in the predictive capabilities of fire models come in various forms [1] These include errors in

 assumptions used in the model,

 numerical solutions of the model equations,

 software representation of the model, and

 hardware used to run the software

Issues related to the model's application may arise from misunderstandings of the model itself or its numerical solution methods Commonly noted is the lack of sufficient documentation, which can lead to errors Additionally, simple mistakes in entering input data or interpreting output results can occur.

Models are inherently approximations of reality, and using inappropriate algorithms or incorrect physics to represent fire processes can lead to significant errors It is essential to clearly identify constants and default values in computer software models, as incorrect or unverified values can introduce further inaccuracies, especially when the model is applied beyond its intended scope Additionally, uncertainty in the range of plausible numerical values for parameters is common, and oversimplifying fire phenomena may result in the exclusion of critical processes Therefore, an independent review of the theoretical foundations of a model is necessary to ensure its validity.

A review of thermal and structural programs for fire analysis reveals that empirical and arbitrary assumptions are frequently employed to align theoretical predictions with experimental outcomes Thermal computer codes often rely on boundary condition parameters that are adjusted without adequate scientific justification, while structural models suffer from insufficient material property inputs due to incomplete models Additionally, it has been noted that structural analyses in fire scenarios are highly sensitive to the temperature state of the structure, a factor that many studies tend to overlook.

Numerical techniques, such as finite difference and finite element methodologies, are essential for solving mathematical equations in models The application of unsuitable numerical algorithms can lead to errors in predictions Various numerical methods may yield slightly different results and exhibit varying levels of stability Additionally, the accuracy of numerical solutions is influenced by the resolution of the grids of nodes or elements used in the calculations.

Software errors can arise from inaccurate coding that fails to represent the model and its numerical solution procedures effectively These coding errors significantly impact model predictions Additionally, the performance of specific software may be compromised by errors in the hardware operating system or the programming language used for coding Furthermore, insufficient documentation and the lack of access to the symbolic coding of computer programs can hinder the evaluation of software errors.

To operate software effectively, reliable hardware is essential, and advancements in computer technology have made personal computers the standard Common hardware issues can arise from design or manufacturing defects in microprocessors.

Model application and use

Model evaluation begins with thorough documentation of relevant scenarios, providing a detailed description of the phenomena under consideration This documentation is essential for the correct application of the model, as it helps in creating realistic inputs and establishing criteria for assessing the evaluation results.

Model evaluation is crucial for identifying potential errors in predictive fire models, focusing on the accuracy of model inputs, the selection of appropriate models, the correctness of calculations, and the interpretation of results By assessing specific scenarios with varying levels of expected outcomes, these evaluations help address multiple sources of error It is recognized that different levels of evaluation may be incorporated into a single model assessment, utilizing various methodologies to ensure comprehensive analysis.

These methodologies are intended to evaluate the ability of the user to select the appropriate model and input given different levels of problem description and specified input

In blind calculation, the model user receives a basic scenario description and must create suitable model inputs, including geometry, material properties, and fire descriptions This methodology relies on the user's judgment to provide additional details necessary for accurate simulation It not only demonstrates the comparability of models under real-world conditions but also evaluates the user's capability to generate appropriate input data for the models.

The model user receives a comprehensive description of inputs, including geometry, material properties, and fire characteristics, during the specified calculation This test serves as a follow-up to the blind calculation, offering a thorough comparison of the underlying physics in the models within a fully defined scenario.

In open calculation, users receive comprehensive information about the scenario, including geometry, material properties, fire descriptions, and results from experimental tests or benchmark model runs This detailed data aids in evaluating both blind and specified calculations By comparing open and blind calculations, any deficiencies in the available input for the blind calculation become evident.

Different models necessitate varying levels of detail in problem descriptions across three evaluation levels Some models demand precise geometric details, while others may only require basic compartment volume information Additionally, certain models need comprehensive fire descriptions, including heat release rate, pyrolysis rate, and species production rates, while for others, these factors can be derived as outputs Ultimately, a suitable problem description is essential for effective simulation at each evaluation level.

For models for structural fire behaviour, input can include:

 load or design variations: level of load and end conditions;

The article discusses the variations in materials, focusing on their mechanical properties at room temperature, thermal properties, and other parameters influencing the temperature profiles of the modeled structure It also addresses the mechanical properties of all materials at elevated temperatures within the structure.

The article highlights the focus on zone models of compartment fires while referencing ASTM E 1591-00, which serves as a standard guide for gathering necessary data for deterministic fire models Additionally, it points out the importance of enhanced data for fire model inputs, as discussed in ISO/TR 15655, which outlines tests for the thermo-physical and mechanical properties of structural materials at elevated temperatures for fire engineering design.

Model theoretical basis

The model's theoretical foundation must be evaluated by qualified experts who are well-versed in the chemistry and physics of fire phenomena, as well as the material's response to thermal and structural stresses, ensuring they have no ties to the model's development This independent assessment should encompass:

 an assessment of the completeness of the documentation, particularly with regard to the assumptions and approximations;

 an assessment of whether there is sufficient scientific evidence in the open scientific literature to justify the approaches and assumptions being used;

 an assessment of the empirical or reference data used for constants and default values in the code for accuracy and applicability in the context of the model.

Model solution

To ensure that the computer implementation of a model aligns with the stated documentation, it is essential to conduct thorough evaluations of its mathematical and numerical robustness Various methods, including analytical tests, code checking, and numerical tests, can be employed for this purpose While analytical testing is a robust approach for verifying the functionality of models based on numerical solutions, it is important to note that analytical solutions are often limited to simpler scenarios Therefore, simplifying the desired scenario may yield portions of the model for which known mathematical solutions exist.

Verifying code on a structural basis, ideally through a third-party review, can be done manually or with code-checking software to identify irregularities While this code-checking process enhances confidence in the program's data processing capabilities, it does not guarantee the program's overall adequacy or accuracy A straightforward evaluation method involves comparing the printed output with the entered values.

Numerical techniques employed to solve models can introduce errors in predictions These numerical tests involve analyzing the size of the residuals derived from the system of equations' solutions.

ISO/TR 15656:2003(E) emphasizes the use of numerical accuracy indicators and residual reductions to assess numerical convergence, as detailed in section 7.4.2.

Mathematical models often take the form of differential or integral equations, which can be quite complex, making analytical solutions difficult or unattainable To obtain approximate solutions, numerical techniques are employed, where the continuous mathematical model is transformed into a discrete numerical model The implications of discretization errors are addressed in the following sections.

A continuous mathematical model can be discretized in various ways, leading to different discrete models For an accurate approximation of the continuous model's solution, the discrete model must replicate its properties and behavior This ensures that the discrete solution converges to the continuous problem's solution as the discretization parameters, such as time step and space mesh, decrease Achieving this convergence requires meeting the criteria of consistency and stability Consistency ensures that the discrete model closely approximates the continuous model according to a specific norm, which varies based on the problem Stability guarantees that error terms do not escalate as the computation progresses.

The continuous mathematical model typically consists of a set of partial differential equations (PDE) By applying semidiscretization in space, we derive a set of ordinary differential equations (ODE), which can be either linear or non-linear Higher-order differential equations can be converted into systems of first-order equations; however, this discussion will focus solely on first-order equations To create the full discrete model, the ODE is discretized in the time domain, often utilizing methods such as finite difference or finite element methods The resulting set of linear or non-linear algebraic equations is then solved using suitable numerical techniques, including Gauss and Newton methods.

Fire problems often involve complex interactions between various physical processes, including chemical, thermal, and mechanical responses These processes can operate on significantly different time scales, leading to numerical challenges known as stiffness Traditional numerical methods may struggle with stiff problems, as they tend to focus on rapid changes that may not be as critical as the overall solution trend To address these challenges, specialized algorithms have been developed for effectively solving stiff problems.

Discretization can lead to a stiff discrete model, particularly evident in heat conduction equations described by partial differential equations (PDEs) When these equations are semidiscretized in space, they yield a stiff ordinary differential equation (ODE) Notably, the stiffness of the semidiscrete model escalates as the spatial discretization parameter, or mesh, is reduced.

A stiff discrete problem can emerge from a non-stiff original continuous problem In non-linear scenarios, the model's behavior and stiffness may evolve over time as the solution progresses.

In the analysis and performance of temporal algorithms, stability is crucial for demonstrating the convergence of the solution algorithm Algorithms that require a restriction on the time step for stability are termed conditionally stable, while those without such restrictions are known as unconditionally stable Stable integration typically results in decaying solutions, akin to the analytical solutions of continuous ordinary differential equations (ODEs) Conversely, unstable methods can produce unbounded and oscillating numerical solutions depending on the time step size It's essential to recognize that a numerical model may exhibit instability even if the continuous model remains stable Additionally, there are instances where the original continuous model is inherently unstable, making accurate solutions unattainable through any numerical method.

Time integration of ordinary differential equations (ODEs) can be performed using explicit or implicit numerical quadrature algorithms The explicit method, often referred to as time marching, calculates new solution values based solely on previous values, with the forward Euler algorithm being a common example In contrast, implicit methods, such as backward Euler, Crank-Nicolson, and the midpoint family method, require both old and new values for their calculations While explicit methods are conditionally stable, all implicit methods exhibit unconditional stability in linear cases.

Using inadequate algorithms, such as unstable or conditionally stable methods, to integrate stiff systems of ordinary differential equations (ODEs) can lead to unbounded solutions and significant errors The stability of the integration process, which affects the accuracy of the approximate solution, is influenced by the more rapidly varying components of the solution, even after the integration has been performed.

Stiff equations present a common challenge, necessitating the tracking of solution variations on the shortest time scale to ensure integration stability, despite accuracy allowing for larger time steps A viable solution to this issue is the implementation of implicit methods.

In non-linear problems, the stability regions of solutions evolve alongside the solutions themselves, leading to potential changes in stability conditions Notably, the unconditional stability of the implicit trapezoidal (Crank-Nicolson) integration scheme does not extend into the non-linear regime However, methods from the generalized midpoint family can maintain unconditional stability even in non-linear scenarios.

Comparison of model results

To assess the accuracy of the model's predictive results, several comparative analyses can be employed, including a) comparisons with standard empirical evaluation tests and b) comparisons with non-standard empirical evaluation tests.

ISO/TR 15656:2003(E) © ISO 2003 — All rights reserved 15 c) empirical evaluation with documented fire experience, and d) evaluation with proven benchmark models including analytical tests and other programs

Evaluating the predictive capability of structural fire endurance models primarily involves comparing them with empirical data Key results for comparison include thermal profiles of structural components, mechanical behavior under specific temperature profiles, and fire resistance times It is essential to define the evaluation of the model based on its applicable range.

Comparing model predictions with empirical data is essential in model development For effective verification and validation, it is crucial that predictions are generated independently of the experimental data used for comparison, except for necessary input data Adjusting the fit between measurements and predictions should be avoided to maintain the integrity of the evaluation process.

For structural fire behavior calculations, the standard testing method is ISO 834 or equivalent national tests Model predictions can be evaluated against empirical failure criteria and related observations It is essential to consider the uncertainty in both experimental data and model results, particularly regarding model input variability A key uncertainty in ISO 834 tests is the definition of fire exposure, which may differ between experimental tests and model simulations.

When comparing with previously published test data, it is crucial to ensure that the test accurately simulates the model scenario ISO 834 tests, aimed at rating assemblies, often lack comprehensive data on the test specimen and its response to fire exposure While key measurements may be taken, the predictive capabilities can be evaluated by comparing predicted and measured values of significant variables, key fire events, and behavioral traits Conducting tests specifically for model evaluation allows for the collection of additional data.

The ISO 834 test is often viewed as a comprehensive evaluation; however, actual structure tests or non-standard assessments may be necessary to accurately assess specific scenarios These simulations should closely replicate the key characteristics of the scenarios being evaluated, ensuring that the data includes enough detail—such as initial conditions and time scales—to correlate predicted and measured outcomes Recent studies have documented the behavior of multistorey steel-framed buildings in fire conditions, including comparisons with fire models.

The validity of experimental data is crucial when comparing it with computer-predicted temperature regimes, as some studies have shown that experimental temperature measurements can be erroneous due to factors like excessive moisture around thermocouple tips Therefore, a comprehensive evaluation of the experimental data is essential for model assessment This evaluation should systematically address uncertainties by understanding their sources, quantifying them, conducting sensitivity analyses to determine their impact on predictions, and employing data comparison techniques to manage these uncertainties effectively.

See 7.6 for further discussion of this topic

Evaluating a model can also be achieved by comparing it with documented fire experiences It is essential to assess the reliability of statistical data related to fire experiences Additionally, other types of documented fire experiences can be utilized for this evaluation.

Proven benchmark models, including empirical and analytical types, offer a valuable method for evaluating model results It is crucial to ensure that these benchmark models are assessed for relevant scenarios Predictive capabilities can be evaluated by comparing predicted values, key events, and behavioral traits from both models When data is available, it is important to consider the variability in the sensitivity of model predictions Additionally, analytical testing can effectively verify model functionality when applicable situations with known mathematical solutions exist, although such cases are often limited.

A recently published evaluation scheme assesses computer codes for finite element and finite difference models used to calculate temperatures in fire-exposed structures This scheme begins with a simple analytical solution and progresses to more complex scenarios involving non-linear boundary conditions and temperature-dependent material properties, without relying on experimental data It employs repeated analyses with increasing elements or time steps to evaluate model reliability, with codes that yield smoothly converging results deemed more trustworthy The evaluation includes seven reference scenarios: a) comparison with analytical results using constant material properties; b) incorporation of non-linear boundary conditions; c) integration of non-linear boundary conditions with temperature-dependent thermal properties; d) consideration of latent heat from water content in common building materials; e) analysis of a composite of steel and concrete; f) examination of a composite of steel and mineral wool; and g) assessment of radiation heat transfer across one- and two-dimensional voids.

The development and standardization of reference fire tests, benchmark models, and reference scenarios would improve the reliability of model evaluations

Simple evaluations of structural models can be useful [23] Simple questions that can be examined include the following

 Does a symmetric load case yield symmetric deflections and reactions?

 Does summation of reactions equal summation of load?

 Does the sum of moments, horizontal forces, lateral forces (3-D) and vertical forces equal zero at joints?

 Are deflections consistent with the structural system conditions? For example, are fixed connections shown as displaced?

 What is the orientation of loads? For example, are vertical loads transferred as truly vertical loads on sloped members, such as snow on rafters?

Recent studies have offered insights into quantifying the comparison between model predictions and empirical data, which are often described in vague qualitative terms like "good" or "reasonable." Determining the most suitable method for this quantification can be challenging The required level of agreement for any predicted quantity varies based on its typical application, the nature of the comparison, and the specific context being evaluated.

ISO/TR 15656:2003 outlines methods for making comparisons in various contexts, particularly focusing on single-point comparisons like structural failure times These comparisons can be represented as absolute differences (model value minus reference value) or relative differences ((model value - reference value) / reference value) When comparing two time-based curves, the quantitative analysis should consider the curves' characteristics For steady-state or nearly steady-state comparisons, the results can be expressed as average absolute or average relative differences.

For effective comparisons, it is essential to express the differences in either absolute or relative terms, especially when variations are rapid Additionally, utilizing a time-integrated value of the quantity in question can enhance the comparison To ensure objectivity, subjective judgments should be minimized, and results should be presented quantitatively.

Measurement uncertainty of data (from ISO/TR 13387-3)

Much of this subclause is taken from reference [27]

This subclause aids experimenters in quantifying measurement uncertainty and helps model users assess the reliability of experimental data for empirical model verification It is important to note that not all published experimental data will provide uncertainty information.

Measurement results are essentially approximations of the specific quantity being measured, and they are only complete when accompanied by a quantitative statement of uncertainty According to the International Council on Weights and Measures, the uncertainty in measurement results typically comprises several components, which can be categorized based on the methods used to estimate their numerical values.

 Type A, those which are evaluated by statistical methods;

 Type B, those which are evaluated by other means

Uncertainty in measurements is typically categorized into two types: random and systematic Each type contributes to the overall uncertainty, represented by an estimated standard deviation known as standard uncertainty, denoted as $ u_i $, which is the positive square root of the estimated variance $ u_i^2 $ For category A uncertainty components, the standard deviation $ s_i $ is derived from statistical estimation, with the relationship $ u_i = s_i $ Conversely, category B uncertainty components are represented by $ u_j $, an approximation of the standard deviation, calculated as the positive square root of $ u_j^2 $, based on an assumed probability distribution In this case, the standard uncertainty is simply $ u_j $.

7.6.2 Type A evaluation of standard uncertainty

A Type A evaluation of standard uncertainty utilizes valid statistical methods for data analysis, such as calculating the standard deviation of the mean from independent observations This can involve using the least squares method to fit a curve to the data, allowing for the estimation of curve parameters and their standard deviations However, this Technical Report does not provide in-depth statistical techniques for conducting these evaluations.

7.6.3 Type B evaluation of standard uncertainty]

A type B evaluation of uncertainty is usually based on scientific judgement using all the relevant information available, which may include a) previous measurement data;

Understanding the behavior and properties of relevant materials and instruments is essential, along with adhering to manufacturer specifications Additionally, calibration reports and uncertainties associated with reference data from handbooks play a crucial role in ensuring accuracy and reliability.

To ensure reliable evaluations of uncertainty components, it is crucial to utilize high-quality information by varying all measurement-dependent parameters as much as possible Whenever feasible, incorporating empirical models based on long-term quantitative data, along with check standards and control charts, can help confirm that the measurement process is statistically controlled.

The combined standard uncertainty, denoted as $ u_c $, represents the estimated standard deviation of a measured result It is derived by combining individual standard uncertainties $ u_i $ from both Type A and Type B evaluations, utilizing the law of propagation of uncertainty or the root-sum-of-squares method This measure of combined standard uncertainty $ u_c $ is commonly employed in uncertainty analysis.

The combined standard uncertainty $ u_c $ quantifies the uncertainty in measurement results, but a more useful measure is the expanded uncertainty $ U $, which defines the interval around the measurement result $ y $ where the true value of the measurand $ Y $ is likely to be found Expanded uncertainty is calculated by multiplying the combined standard uncertainty $ u_c(y) $ by a coverage factor $ k $, leading to the relationship $ U = k u_c(y) $ This allows for a confident assertion that the true value $ Y $ lies within the interval defined by $ y $ and $ U $.

The coverage factor $ k $ is selected based on the desired confidence level, typically ranging from 2 to 3 When the normal distribution is applicable and the uncertainty $ u_c $ is minimal, a coverage factor of $ k = 2 $ corresponds to a confidence level of about 95%, while $ k = 3 $ indicates a confidence level exceeding 99% Currently, the standard practice internationally is to utilize $ k = 2 $.

To accurately report measurement uncertainty, it is essential to include the uncertainty value $ U $ along with the coverage factor $ k $ used in its calculation, or alternatively, report $ u_c $ When presenting a measurement result and its associated uncertainty, ensure that the report contains this information or references a relevant published document.

The article outlines a comprehensive list of standard uncertainty components, detailing their degrees of freedom when applicable, along with the calculated value of $ u $ Each component is categorized based on the method employed for estimating its numerical values, whether through statistical analysis or alternative approaches.

 A detailed description of how each component of standard uncertainty was evaluated.

Model sensitivity

Deterministic models inherently contain uncertainties, making sensitivity analysis crucial for understanding how variations in model parameters influence outcomes This analysis highlights the impact of uncertainties in input data, the rigor of the modeling process, and the adequacy of numerical methods A thorough sensitivity analysis identifies key variables and establishes acceptable value ranges for each input, enhancing the reliability of model predictions.

ISO/TR 15656:2003 emphasizes the importance of demonstrating how output variables are affected by changes in input data It also serves to alert potential users about the necessary precautions when selecting inputs and operating the model Additionally, the document provides guidance on which parameters should be closely monitored during large-scale fire experiments.

A sensitivity study, as outlined in BS DD 240-1, aims not only to verify the accuracy of results but also to assess the importance of individual parameters in fire safety engineering This study serves as a guide for determining the necessary accuracy of input data It is crucial to identify how critical a specific system is to the overall safety outcomes If a particular system or assumption is deemed critical, it may warrant the inclusion of redundancy in the design or the execution of a probabilistic analysis.

Fire models are generally formulated using a set of ordinary differential equations represented as \$\frac{dz}{d\tau} = f(z, p, \tau)\$ with the initial condition \$z(\tau = 0) = z_0\$ In this context, \$z = (z_1, z_2, \ldots, z_m)\$ denotes the solution vector, which may include variables such as mass, temperature, or volume The vector \$p = (p_1, p_2, \ldots, p_n)\$ consists of input parameters like room area, room height, and heat release rate, while \$\tau\$ represents time.

The solutions to these equations are typically not available in explicit form and require numerical methods for determination To analyze the sensitivity of this set of equations, it is essential to compute the partial derivatives of the output $ z_j $ concerning the input $ p_i $.

(for j = 1, …, m and i = 1, ,n) should be examined

The selection of parameters to be investigated will be aided by the knowledge and familiarity of the investigator with the thermal and mechanical behaviour of materials

 scenario specific data, such as the geometry of the domain, the environmental conditions, and specifics of the fire description;

 property data, such as thermal conductivity, density and heat capacity;

 numerical constants, such as turbulence model constants, entrainment coefficients and orifice constants

It is essential to differentiate between internal and external parameters in a model Internal parameters offer insights into the accuracy of the physics and mathematics used in the model to represent real fire behavior and should be verified In certain models, users can manipulate these internal parameters, such as numerical factors like relaxation, numerical grid, and the number of iterations in CFD-field models Conversely, external parameters are those that users can adjust as inputs, and they can be categorized accordingly.

 Fire scenario: derived from the standard time-temperature curve or methodologies for natural fires and the distribution of fuels

 Thermophysical: the thermophysical properties of the materials can influence the development of the temperature profiles, hence properties such as conductivity, specific heat and density are necessary input

 Mechanical: The structural behaviours depend on the physical and mechanical properties of the materials

Conducting a sensitivity analysis of a complex fire model is challenging due to the extensive input data required and the multiple output variables predicted over time The number of model runs needed increases significantly with the number of input parameters and independent variables, making a full factorial experiment impractical in terms of time and resources.

Partial factorial experiments are often sufficient for understanding the effects of varying input parameters and significant interactions, allowing for the neglect of third- and higher-order interactions For sensitivity analysis in models with numerous parameters, efficient methods enable analysis with a manageable number of simulations In the case of highly non-linear fire models, Latin Hypercube sampling is typically the preferred method.

Latin Hypercube sampling divides the range of input parameters into N equal probability intervals, from which one value is randomly selected for each interval This process generates N possibilities for each input parameter, and one value is randomly chosen from these possibilities for the initial simulation The procedure is repeated N times to create N sets of parameters for a total of N model simulations Software tools are available to facilitate the calculation of parameter values for Latin Hypercube sampling.

Sensitivity analysis methods are crucial for evaluating fire models, with the choice of method depending on available resources and the specific model under consideration Two prevalent approaches in this field are global methods and local methods.

Global methods generate sensitivity measures that are averaged across the full spectrum of input parameters However, these methods necessitate an understanding of the probability density functions of the input parameters, which are typically unknown in the context of fire models.

Local methods generate sensitivity measures for specific input parameters, necessitating repetition across a range of inputs to assess overall model performance Finite difference methods can be utilized without altering the model's equations, but they require careful parameter selection for accurate estimates Direct methods enhance the model's equation set by integrating sensitivity equations derived from it, which are then solved alongside the model's equations to determine sensitivities However, these direct methods need to be integrated into the design of a fire model and are rarely available for pre-existing models Several classes of local methods are noteworthy and are detailed using the nomenclature of Equation (1).

Finite difference methods provide estimates of sensitivity functions by approximating the partial derivatives of an output z i with respect to an input p i as finite differences: j m z p

This method is simple to implement, but the selection of ∆p m is crucial for achieving accurate estimates To derive the first-order sensitivity equations, k + 1 model runs are necessary, which can be executed either as a larger system or in parallel.

Direct methods derive the sensitivity differential equations from the model's system of ordinary differential equations: d dt j m z p

The sensitivities are obtained by solving these equations alongside the model's system of differential equations Calculating the first-order sensitivities necessitates a single model run These sensitivities can be integrated directly into the model, resulting in a unified set of $ n + (nãk) $ differential equations, or they can be decoupled, allowing for iterative solutions of the model and sensitivity equations using the model's output and a suitable interpolation method.

With the Response Surface Method, an appropriate vector of functions is fit to a selected set of model runs

The metamodel is designed to replicate the behavior of the original model while being simpler and more analyzable By selecting suitable functions, the metamodel facilitates easier analysis Sensitivity analysis is conducted by solving the equations of the metamodel, with the Jacobian of the solution representing the sensitivity equations.

Examples of sensitivity analyses for compartment zone models are given in reference [9]

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Tiêu đề	Fire Resistance — Guidelines For Evaluating The Predictive Capability Of Calculation Models For Structural Fire Behaviour
Trường học	International Organization for Standardization
Chuyên ngành	Fire Resistance
Thể loại	Technical report
Năm xuất bản	2003
Thành phố	Geneva

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