My title https://doi.org/10.14311/APP.2022.36.0015 Acta Polytechnica CTU Proceedings 36:15–24, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague STRUCTURAL ASSESSMENT AND EXPECTED UTILITY GAIN Sebastian Thönsa, b a Lund University, Faculty of Engineering, Box 117, 221 00 Lund, Sweden b BAM Federal Institute for Materials Research and Testing, Unter den Eichen 87, 12205 Berlin, Germany correspondence: sebastian.thons@kstr.lth.se Abstract. This paper contains an introduction, probabilistic formulation, and exemplification (1) of system state and utility actions, (2) system state and utility action value analysis and (3) a threshold formulation for a predicted information and action decision analysis. The approaches build upon structural condition assessment and provide a basis for the condition management by maximising the expected utility for information and actions before information acquirement and action implementation. Following the basic distinction of system state and utility actions, strengthening, replacement, repair, load reduction and consequence reduction actions are formulated. With an exemplary study encompass- ing an expected utility calculation and an action value analysis, it is demonstrated how expected utility optimal physical system changes can be identified before implementation. The threshold formulation for a predicted information and action decision analysis relies on the equality of the decision theoretical posterior action optimality condition. By extending the exemplary predicted action decision analyses with different structural health information (SHI), the threshold formulation is exemplified and the optimal condition management strategies are identified. Keywords: Structural condition management, action uncertainty modelling, action and information value. 1. Introduction Condition assessment is usually understood as a structural reliability analysis with additional information. Most commonly it is performed with obtained information, i.e., by posterior structural reliability updating. However, condition assessment constitutes a part of the structural condition management, i.e., ensuring the integrity and functionality of a system over time. The structural condition management may require measurements to learn about the structural condition and actions to adapt the structural condition. These two basic means of structural condition management should be performed efficiently, i.e., in a way that measurements and actions are planned to maximise their technological, economic and risk reduction effects. An efficient structural condition management can be performed and planned by the utilisation, adaptation and the application of the Bayesian decision theory [1] to structures; or more widely to built environment systems. The decision theoretical context of structural condition assessment and management necessitates (1) a system state model, (2) a utility model, (3) that the information acquirement state is considered in the probabilistic modelling and (4) that the relevant actions can be modelled. Whereas points (1) to (3) have been extensively developed over the last decade, see e.g., [2–17], the action modelling remains a challenge. Relevant actions for a condition management would encompass e.g., structural modifications and utility changes. Further, it would be required to analyse the expected action utility prior to the decision to implement an action. This paper focusses on the introduction and formulation of system state and utility actions as well as the action value analysis building upon [18] and [19] in Sections 2 and 3. The action modelling in Section 2 includes the introduction of an action uncertainty modelling and the formulation of strengthening, replacement, repair, load reduction and utility actions in conjunction with a limit state function representative for a highly correlated series system including extreme events and deterioration. Based on the action uncertainty modelling, predicted and implemented action decision analyses are formulated (Section 3). In Section 4, the action modelling is exemplified and expected utility theorem consistent action values for various actions are quantified. Section 5 contains a decision theoretical formulation of predicted information and action decision analyses (PIPA DA) and a derivation for continuous and direct structural health information (SHI). It is shown how this SHI formulation can be discretised and solved. The in Section 4 introduced example is further developed in Section 6 and the value of the condition management is quantified and separated into measurement information and system state and utility actions. Section 7 includes and a summary and concluding remarks. 15 https://doi.org/10.14311/APP.2022.36.0015 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en Sebastian Thöns Acta Polytechnica CTU Proceedings 2. System performance and action modelling This section encompasses the formulation of the system state analysis, i.e., a structural reliability analysis in a decision theoretical context, and the combination of system state reliability and a utility model to quantify the system performance (Section 2.1). In Section 2.2, a probabilistic action modelling in introduced. 2.1. System state analysis and system performance analysis A generic component limit state function gX1 , describing the component state event X1, may be formulated with the resistance R, the damage D and the loading S, which are subjected to the resistance and loading model uncertainties MR, MD and MS , respectively: X1 : gX1 = MR · R (MD · D) − MS · S ≤ 0 (1) The resistance may be decomposed in the section property Z and the material strength Rmat. Both may be subjected to the influence of deterioration, i.e., the design variable is subjected to section deterioration (MD,Z · DZ ) and the material strength is influenced by degrading material properties (MD,Rmat · DRmat ): X1 : gX1 = MR · Z (MD,Z · DZ ) · Rmat (MD,Rmat · DRmat ) − MS · S ≤ 0 (2) In assessing normatively an expected utility-based decision or a decision value, the benefits, costs and consequences of the system states are modelled. Based on these models, the preference of decision makers can be described using the concept of a utility function implying the context of a descriptive decision analysis [20]. In engineering decision analysis, the utility function is rather linear and usually based on monetary values, where the utilities of the system states are expressed in terms of costs or, generally, negative consequences. In the following, the utility function is thus omitted and a normative decision analysis performed. The system states are described by Xl (see above) resulting in a utility u (Xl) . The system performance USP , i.e., the expected system utility, is then calculated as the expected value of a probability mass function (where the system states denote realisations of a discrete random variable), i.e.: USP = EXl [u (Xl)] = ∑ Xl u(Xl) · P (Xl) (3) 2.2. Action modelling The expected system performance (see above) can be influenced by physical changes affecting (1) the utility of the system states and (2) the resistance and/or the load of the system states. This basic distinction leads to the denotation of utility actions and system state actions, respectively. The latter type can be associated with actions performed by an engineer as it includes e.g., design, repair and strengthening actions. Beyond the distinction of action types, an action implementation state and uncertainty modelling is required to analyse and to optimise the expected of the utility before action implementation (see Section 1). It is thus in the further distinguished between a predicted or implemented action. The explicit modelling of the m implementation states Yk,m and the modelling of implementation uncertainties are introduced. A utility action is described with the system state utilities u(Xl, ak, Yk,m), the implementation states Yk,m and the implementation uncertainties P (Yk,m) and the costs of the action c(ak). The index m may be used for distinguishing e.g., with m = 1 . . . 3 full, partial or failed action implementation. A system state action ak is described with the system state probabilities P (Xl(ak, Yk,m)) beside the implementation uncertainties and the costs. In the context of existing structures, examples for system state actions are e.g., repair, replacement, strengthening and loading actions. A repair action can be modelled by reversing deterioration effects due to mechanical reshaping of the component. The repair action including the action implementation uncertainties (ak, Yk,m) is then allocated to the damage, i.e., D(ak, Yk,m) affecting the material resistance or the section properties: X1 : gX1 = MR · Z (MD,Z · DZ ) · Rmat (MD,Rmat · DRmat (ak, Yk,m)) − MS · S ≤ 0 (4) X1 : gX1 = MR · Z (MD,Z · DZ (ak, Yk,m)) · Rmat (MD,Rmat · DRmat ) − MS · S ≤ 0 (5) A replacement action would result in a damage free component with same, similar or new material properties: X1 : gX1 = MR · Z · Rmat(ak, Yk,m) − MS · S ≤ 0 (6) A strengthening action results in an enhanced resistance of a component by e.g., section enlargement, material addition or the replacement with a stronger material, i.e., Z(aS,k, Yk,m, . . .) and Rmat(aS,k, Yk,m, . . .): 16 vol. 36/2022 Structural assessment and expected utility gain UtilitiesActions System state action Chance ChanceChoice System state and utility management ImplementationSystem states kalX Utilities u (Objective) function ( ) lSP X l U E u X= é ùë û ,k mY Utility action ( ) ( ) ( )S k ,m l k k ,mkPA Y l kX a ,Ya U maxE E u X c aé ù= -é ùë ûë û ( ) ( ) U k ,m l k PA Y X l k,m k ka U maxE E U X ,Y ,a c aé ùé ù= -ë ûë û System statesActions ka lX Implementation ,k mY Utility u System performance (SP) analysis Predicted system state action (PSA) decision analysis Predicted utility action (PUA) decision analysis Figure 1. System performance functions and objective functions for predicted action decision analyses. X1 : gX1 = MR · Z(ak, Yk,m, MD,Z · DZ ) · Rmat(MD,Rmat · DRmat ) − MS · S ≤ 0 (7) X1 : gX1 = MR · Z(MD,Z · DZ ) · Rmat(ak, Yk,m, MD,Rmat · DRmat ) − MS · S ≤ 0 (8) Actions on the load side can be a load application for testing purposes or the change of use leading to a modified loading, S(aS,k, Yk,m): gX1(aS,k ,Yk,m) = MR · Z(MD,Z · DZ ) · Rmat(MD,Rmat · DRmat ) − MS · S(ak, Yk,m) ≤ 0 (9) Utility actions may include a benefit enhancement due to an enhanced functionality or a consequence reduction in case of failure. A utility action is subjected to action implementation uncertainties dependent on the system states, i.e., u(Xl, Yk,m, ak). For illustration purposes, the expected utility quantification of an implemented action analysis can be written as: UIA = EYk,m [EXl [U (Xl, Yk,m, ak) − c(ak)]] = ∑ Xl ∑ Yk,m P (Xl) · P (Yk,m) · u(Xl, ak) (10) A utility action can be further detailed to consequence reduction ((c(Xl, ak), Equation (11)), benefit and functionality enhancement (b(Xl, ak) , Equation (12)) and (Equation (13)) cost reduction actions in conjunction with the (normative) utility model characteristics: UIA = ∑ Xl ∑ Yk,m P (Xl) · (b(Xl) − P (Yk,m) · c(Xl, ak) − c(ak)) (11) UIA = ∑ Xl ∑ Yk,m P (Xl) · (P (Yk,m) · b(Xl, ak) − c(Xl) − c(ak)) (12) UIA = ∑ Xl ∑ Yk,m P (Xl) · (b(Xl) − c(Xl) − P (Yk,m) · c(ak)) (13) 3. Predicted action decision analysis and action value analysis The objective function for a predicted action decision analysis (PA DA) can be written for system state and utility actions. For both formulations, the action is selected for maximising the expected value of the utility, i.e., for maximising the system performance. 17 Sebastian Thöns Acta Polytechnica CTU Proceedings UPA = max ak ( ∑ Yk,m ∑ Xl u(Xl, ak, Yk,m) · P (Xl (ak, Yk,m)) − c(ak) ) (14) For the notation of the action types, an index U for a utility action and an index S for a system state action are introduced. The objective function for a predicted utility action (PAU) DA may be written with the action implementation uncertainty P (Yk,m, which is assigned to the utility. The action cost is here considered as deterministic for simplicity. UPA = max ak ( ∑ Yk,m ∑ YXl u(Xl, ak) · P (Yk,m) · P (Xl) − c(ak) ) (15) The objective function for a predicted system state action (PAU) DA is written analogous with the action dependent system state probability P (Xl(ak, Yk,m)) and without the action influence on utility: Variable Mean CoV Characteristic value Distribution Reference Load S with a ref- erence period of 1 year 1.0 0.2 0.98 Quantile Gumbel E.g., JCSS Probabilistic Model Code [21], [22] representative for live and traffic loads Load model uncer- tainty MS 1.0 0.1 Logn. E.g., JCSS Probabilistic Model Code [21], Part 3.9 (2001): Model uncertainty for moments in frames, [22] Resistance R 1.0 0.05 0.05 Quantile Logn. Generic, JCSS Probabilistic Model Code [21], [22] Resistance model uncertainty MR 1.0 0.05 - Logn. JCSS Probabilistic Model Code [21], Part 3.9 (2001): Model Un- certainties, [22] Deterioration D 0.1 0.02 Logn. Generic Deterioration model uncer- tainty MD 1.0 0.1 Norm. Generic Damage resis- tance transfer function tD tD (MD · D) = 1 − MD · D Generic Safety factor γS 1.5 for one dominating action Between 1.35 and 1.5, accord- ing to EN 1990 (2010) Safety factor γR 1.0 for steel Between 1.0 and 1.5 according to material specific Eurocodes Consequence CF ∼ U (20.0, 40.0) [14] Table 1. Probabilistic system performance models. UPA = max ak ( ∑ Yk,m ∑ YXl u(Xl) · P (Xl(ak, Yk,m)) · P (Yk,m) − c(ak) ) (16) The system performance and objective functions for the introduced PA DAs are visualised with decision trees, generalised and summarised in Figure 1. An action value can be quantified in analogy to an information value as the gain of an expected utility by a predicted action, VP A, i.e., as the difference between the maximised expected utility of a predicted action DA (UP A) and the system performance (USP ): VP A = UP A − USP (17) The action value may be normalised (V P A) to the system performance without an action implementation, i.e.: V P A = (UP A − USP ) / USP (18) 18 vol. 36/2022 Structural assessment and expected utility gain Action type and uncertainty Space Description Probabilistic model Cost and consequence model System state actions a a0 Do nothing − − a1 Strengthening of section 1.2 · γ 2.0% a2 Replacement with higher strength 1.2 · E[Rmat] 2.0% a3 Repair MD · D = 0 1.0% a4 Load reduction S/1.2 0.5% a5 Consequence reduction − 0.3% U: Uniform distribution, Tr: Triangular distribution Table 2. Action type and cost models. Action type and uncertainty Space Description Probabilistic model Implementation uncertainty Y Y1 Strengthening performance P (Y1) ∼ T r(0.95, 1.05, 1.10) Y2 Replacement performance − Y3 Repair performance P (Y3) ∼ T r(0.9, 0.95, 1.0) Y4 Load reduction uncertainty P (Y3) ∼ N (1.0, 0.1) Y5 Cons. reduction uncertainty P (Y1) ∼ T r(0.85, 0.95, 1.05) N: Normal distribution, Tr: Triangular distribution Table 3. Action uncertainty models. It should be noted that per definition, the action value analysis includes the cost of the action for consistency with the expected utility theorem. 4. Exemplary study The predicted system state and utility action DA is studied for an existing and deteriorated structure, for which the optimal risk reduction action is to be found. The system performance model includes the limit state function (2) representative for a highly correlated structural series system subjected to direct and indirect system failure consequences (Section 4.1). The system state actions "section strengthening", "component replacement", "component repair" and "load reduction" as well as the utility action "consequence reduction" are probabilistically modelled and exemplified. 4.1. System performance model The system state model is represented with Equation (2). For a semi-probabilistic safety concept, it can be shown that the section property can be decomposed to a central safety factor γ (see e.g., [23]), i.e., the product of the resistance and the loading safety factors (γR and γS , respectively), and the ratio rk of the characteristic resistance and loading values (Rk and Sk, respectively). The influence of the damage on the resistance is modelled with a damage transfer function tD : Z = γ · rk · tD (MD · D) = γR · γS · Sk Rmat, k · tD (MD · D) (19) The limit state function (2) becomes with focussing on cross section rather than material deterioration: X1 : gX1 = MR · γ · rk · tD (MD · D) · Rmat − MS · S ≤ 0 (20) The probabilistic model and the references are summarised in Table 1. 4.2. Action model Following the introduction of the action type and uncertainty model in Section 2.2, a strengthening, a replacement, a repair, and a load reduction and a consequence reduction action are modelled (Table 2). The section strengthening leads to an increase of 20% of the section property, whereas the replacement with a higher strength material leads to an increase of the expected resistance by 20% with a constant variability. Both have a cost of 2.0%. The repair action sets the deterioration to 1.0 and costs 1.0%. The loading reduction action leads to decrease of the loading by 20% with the cost 0.5%. The consequence reduction sets the direct and indirect consequences in case failure to a Uniform distribution between 10.0 and 20.0 with a cost of 0.3%. 19 Sebastian Thöns Acta Polytechnica CTU Proceedings Figure 2. System performance normalised relative action values without the action costs (left side, grey) and with action costs (left side, black) and total expected action cost and risks (right). The action implementation uncertainties are modelled continuous, i.e., with a Triangular distribution accounting for a known range and most probable value (Table 3). The strengthening action provides most probably a higher strengthening (1.05) than envisaged (Table 2) within a range between 0.95 and 1.10. The component replacement is subjected to negligible action implementation uncertainties. The repair performance is subjected to on site execution uncertainties with a mode of 0.95 and a range of 0.9 to 1.0 of repairing the deterioration. The load reduction uncertainty is Normal distributed and on average as expected and uncertain with a standard deviation of 0.1. The consequence reducing usage uncertainty is in the range of 0.85 to 1.05 with a mode of 0.95. 4.3. Predicted action and action value analysis The results of the predicted action DA and the action value analysis are depicted in Figure 2. The load reduction action leads to the lowest expected costs and risks due to the comparably high load reduction including the uncertainties and the low action costs (Figure 2, left). It also provides the highest action value including its costs, followed by the also relatively cheap consequence reduction action (Figure 2, right, black). The load reduction action is identified as the optimal action in consistency with the expected utility theorem. The action values without their costs would be significantly higher for strengthening, replacement and repair (Figure 2, right, grey). 5. Information and integrity management value analysis The value of predicted information VP I and the value of information and actions are quantified as the gain of an expected and optimised utility by SHI or SHI and actions, respectively [1, 18]. The value of predicted information is then the difference between the expected and maximised utilities of a predicted information and action DA (UP IP A) and a predicted action DA (UP A): VP I = UP IP A − UP A (21) The difference between the expected and maximised utilities of a PIPA DA and the system performance (UP A) is referred to as the value of the structural condition management encompassing information and actions VP IP A: VP IP A = UP IP A − USP (22) The decision values may be normalised by the subtrahend in analogy to Equation (18): V P IP A = (UP IP A − USP ) / USP (23) It should also be noted that the information value can be calculated relative to system performance. In this case, the information value is divided by the expected system performance utility: 20 vol. 36/2022 Structural assessment and expected utility gain V P I = (UP IP A − UP A) / USP (24) 5.1. Predicted information and action DA by threshold determination A general form of a PIPA DA can be derived for utility and system state actions (building upon the formulations in Figure 1). For the SHI acquirement strategies with the information outcomes Zi,j and costs c(ii), the PIPA DA objective function in extensive form constitutes: UP IP A = max ii EZi,j [ max ak EYk,m [ EXl(ak ,Yk,m |Zi,j [u(Xl, ak, Yk,m] ] − c(ak) ] − c(ii) (25) In the following it will be shown that the above formulation (25) can be solved for continuous information outcomes by discretising to two complementary outcomes. Continuous information outcomes are basically any measurement of a random variable contained in the system state function. Per definition they are referred to direct SHI . With consideration of the model uncertainty determination process in a multiplicative formulation [21], the model uncertainty can be understood as the measurable model outcome prediction normalised with the precise measurements of a structural reliability property. For a continuous model uncertainty outcome MM,i of information acquirement strategy with index i, Equation (25) is readily rewritten: UP IP A = max ii EMM,i [ max ak EYk,m [ EXl(ak ,Yk,m |mM,j [u(Xl, ak, Yk,m] ] − c(ak) ] − c(ii) (26) The extensive form equation (26), can be rewritten with an obtained, i.e. posterior, information and predicted action decision analysis (OIPA DA) providing UOIP A: UP IP A = max ii EMM,i [UOIP A(mM,i)] − c(ii) (27) UOIP A(MM,i) = max ak EYk,m [ EXl(ak ,Yk,m )|mM,i [u(Xl, ak, Yk,m) ] + c(ak) (28) The expectation operator in regard to the information can be written for continuous random variables: UOIP A = max ii ∫ MM,i UOIP A(mM,i) · fMM,i (mM,i) dmM,i − c(ii) (29) The measurement threshold tM,i,k is now found as the action-wise, i.e., ak dependent, expected posterior utility equality of "do nothing" and the predicted action, i.e.: tM,i,k : EXl|tM,i,k [u(Xl)] = EYk,m [EXl(ak ,Yk,m )|tM,i,k [u(Xl, ak, Yk,m]] + c(ak) (30) The integral in Equation (29) can then be split up into two sub-integrals and the expected utility maximisation can be performed outside the integrals: UP IP A = max ik ,ak   mM =tM,i,k∫ −∞ EXl|mM [u(Xl)] · fMM,i (mM,i) dmM,i + ∞∫ mM =tM,i,k [ EYk,m [ EXl(ak ,Yk,m )|mM [u(Xl, ak, Yk,m] ] + c(ak) ] · fMM,i (mM,i) dmM,i −c(ii)   (31) The integration can be rewritten for the model uncertainty density functions providing: UP IP A = max ik ,ak   mM =tM,i,k∫ −∞ EXl|mM [u(Xl)] · dFMM,i (mM,i) + ∞∫ mM =tM,i,k [ EYk,m [ EXl(ak ,Yk,m )|mM [u(Xl, ak, Yk,m] ] + c(ak) ] · dFMM,i (mM,i) −c(ii)   (32) 21 Sebastian Thöns Acta Polytechnica CTU Proceedings The two complementary outcomes Zi,1 and Zi,2 for action k = 1 are then defined with Equations (33) and the integrals can be solved by calculation of the pre-posterior probability for direct information [12]: Zi,1 : M ∣∣tM,i,1 −∞ P (Zi,1) = FMM,i (tM,i,1) Zi,2 : M ∣∣∞ tM,i,1 P (Zi,2) = 1 − FMM,i (tM,i,1) (33) It should be noted that there is no further assumptions nor probabilistic models about information outcomes required [24]. 6. Exemplary study The application of the threshold determination approach (Equations (30), (32) and (33)) lead for the in Section 4 introduced example to Equation (34): Given a realisation of the measurement, the threshold is to be found for which the optimal action changes to action implementation instead of do nothing. The measurement is subjected to a measurement uncertainty , which is Normal distributed with a mean of 1.0 and a coefficient of variation of 0.03. The information cost equals 0.001, e.g. according to [11]. tM,k : P ( X1 ∣∣tM,k, MU) · E[CF ] = P(X1∣∣tM,k, MU , ak, Yk,m) · E[CF (ak, Yk,m)] + c(ak) (34) With the introduced limit state functions (see Section 4.1), the threshold dependent probabilities of the failure state are calculated for damage information (Equation (35)), loading information (Equation (36)) and resistance information (Equation (37)). P ( X1, tM,D,k, MU ) = P ( MR · Z(tM,D,k · MU · D) · Rmat − MS · S ≤ 0 ) (35) P ( X1, tM,R,k, MU ) = P ( MR(tM,R,k · MU ) · Z(D) · Rmat − MS · S ≤ 0 ) (36) P ( X1, tM,S,k, MU ) = P ( MR · Z(D) · Rmat − MS (tM,S,k · MU ) · S ≤ 0 ) (37) The solution of the first integral in Equation ( 31), i.e. the calculation of the pre-posterior probability, is readily performed for damage information with the to the interval [0.0, tM,D,k] truncated (index T ) probability distribution of MD [12]: P ( X1, tM,D,k, MU ) = P ( MR · Z ( MD [ 0.0, tM,D,k ]T · MU · D) · Rmat − MS · S ≤ 0) (38) The full solution of Equation (31) for damage, loading and resistance information is performed analogous. The PIPA and value DA in threshold formulation (Equations (32) and (21) to (24)) result in the relative predicted action and information values for damage, load and resistance measurements (Figure 3, left side). The damage measurement has no value for damage repair nor for replacement due to the nature of the actions. For the actions "load reduction" and "consequence reduction", damage monitoring leads regardless of and dependent on the damage realisation to higher expected utility and is thus not predictable. The integrity management strategies with the highest values (38.0% to 63.1%) are load and resistance measurements for the replacement, load reduction system state actions and the "consequence reduction" utility action. When considering separately the system performance related information values (Figure 3, right side), it is observed that there are only positive information values for (1) load and resistance measurements in conjunction with the replacement action and (2) for load measurements for the strengthening and repair actions. Only for the replacement action, measurement information contributes significantly to the condition management strategy value (see Figure 3 and Figure 2, right side). The optimal condition management strategies are thus replacement with load measurement (VP IP A = 63.1 % of the system performance), replacement with resistance measurement (VP IP A = 58.1 %of the system performance) and load reduction (VP A = 57.5 % of the system performance). 7. Summary and concluding remarks This study builds upon structural condition assessment and provides a basis for the condition management by maximising the expected utility for information and actions before information acquirement and action implementation. The study is intended for progress towards consistent probabilistic, decision theoretical and built environment system relevant modelling of actions, information, expected utility quantification and value. 22 vol. 36/2022 Structural assessment and expected utility gain Figure 3. Relative predicted action and information values for damage, load and resistance measurements. The study encompasses an introduction, probabilistic formulation, and exemplification (1) of system state and utility actions, (2) system state and utility action value analysis and (3) of a threshold formulation for predicted information and action decision analyses. The introduced probabilistic action modelling facilitates to distinguish between system state and utility actions, i.e., between actions influencing the reliability of the structural components and actions influencing the utility model. The action uncertainty modelling includes the distinction of an implemented or predicted action, the action implementation states and the action implementation uncertainties. With an action value decision analysis as introduced, the optimal action with consideration of the action costs can be identified before action implementation in consistency with the expected utility theorem. This is demonstrated for the system state actions strengthening, replacement, repair, load reduction and the utility action: consequence reduction. The threshold formulation for a predicted information and action decision analysis relies on the equality of the decision theoretical posterior action optimality condition, i.e., that the action is implemented according to the higher expected posterior utility. The threshold formulation is derived on the basis of direct SHI and the measurability of model uncertainties. The identification of the threshold facilitates the quantification of the SHI value for continuous measurement information and provides readily the decision rule, i.e., for which measurement outcomes the action implementation is optimal. The application of the information value threshold formulation and the action value analysis show exemplarily which structural integrity management strategies are optimal and how the action values and information values contribute to each strategy value. Acknowledgements The Kalix Bridge (TRV 2021/58089, EF 173793) and the CondtionValue (TRV / BBT 2021/51600) projects funded by Trafikverket, Sweden, are gratefully acknowledged. References [1] H. Raiffa and R. Schlaifer. Applied statistical decision theory. Wiley classics library, Originally published: Boston : Division of Research, Graduate School of Business Administration, Harvard University, 1961. ed. New York: Wiley (2000), 356 p., 1961. [2] D. Diamantidis, M. Sykora, and H. Sousa. Quantifying the Value of Structural Health Information for Decision Support: TU1402 Guide for Practicing Engineers, ed: COST Action TU1402, 2019. [3] P. F. Giordano, M. P. Limongelli. 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Limongelli, On Uncertainty, Decision Values and Innovation. the International Conference on Uncertainty in Mechanical Engineering (ICUME), Darmstadt, Germany, June 7 to 8, 2021. 24 https://doi.org/10.3390/infrastructures4030056 https://doi.org/10.1016/j.ress.2020.106814 https://doi.org/10.3389/fbuil.2020.00014 https://doi.org/10.1111/mice.12332 https://www.jcss-lc.org/publicationsjcss/ https://doi.org/10.1016/j.strusafe.2020.101957 https://doi.org/10.1080/15732479.2021.1890139 https://doi.org/10.1186/s43065-021-00027-0 https://doi.org/10.1016/j.marstruc.2020.102888 https://doi.org/10.1177/1475921720981833 https://doi.org/10.1016/j.strusafe.2018.09.002 Acta Polytechnica CTU Proceedings 36:15–24, 2022 1 Introduction 2 System performance and action modelling 2.1 System state analysis and system performance analysis 2.2 Action modelling 3 Predicted action decision analysis and action value analysis 4 Exemplary study 4.1 System performance model 4.2 Action model 4.3 Predicted action and action value analysis 5 Information and integrity management value analysis 5.1 Predicted information and action DA by threshold determination 6 Exemplary study 7 Summary and concluding remarks Acknowledgements References