Life-Cycle Assessment

Individual Project Assignment 1

Risk-based assessment of systems condition

Civil engineering systems such as buildings, roads, or railways are designed for a long lifetime. Moreover, these products serve as supporting infrastructure for various activities of our society. Various factors such as weather, daily usage, severe events (such as earthquakes, floods or landslides) and their combination contribute to systems deterioration and sometimes to their failure.  Therefore, it is essential to assess systems’ integrity during operation, to determine their current condition and to investigate possible ways these might fail. These activities are necessary to support decisions related to maintenance and repair activities. In this assignment, you will learn:

•   to create models to understand how systems change state,

•   to take different factors into account, which lead to system deterioration or even failure,

•   to determine the probability of failure of a system, and

•   to determine the value of information for predicting states.

This assignment requires to complete the following tasks:

1.   Choose a civil engineering system and inform. us.

2.   Conduct background research to understand how the states ofthe chosen system change

during lifetime, which are the possible ways your system can degrade and/or fail as well as the factors leading to degradation and failure. The research should draw on a number of sources ranging from books that you can find in the TU Berlin library to online resources on the web.  Please transparently make the resources/literature you use for this task traceable.

We also expect you to provide us with a list of the references you used. In your text, please refer to these resources wherever possible.

3.   Establish a statistical model using the Markov Chain method. For this, use the states identified during the background research conducted in task two.

4.   Create a fault tree model based on factors and possible failure modes of your system

identified during task two. Calculate the possible failure modes ofthe chosen system, its subsystems, and components.

5.   Calculate the probabilities of system failure over its lifetime.

6.   Calculate MTTF and MTTR

7.   Calculate the Value of Information

To guide you through the above-stated tasks, we provide a step-by-step tutorial.  The tutorial was created using the R software – an open source “programming language and environment for statistical computing and graphics” (https://cran.r-project.org/). The tutorial is designed to minimize the need of prior knowledge ofthe R software.  Of course, some effort in getting familiar with R as suggested in the lecture will be helpful. You should know how to run commands and execute scripts using R- Studio. You can work on your own installation or in the computer labs of the Civil Engineering Institute.

Assessment:

When grading the report, we are expecting to find the following points:

(1) Domain clarity and transparency of background research,

(2) Markov chain implementation and results discussions from the engineering perspective.

(3) Clarity of Fault tree implementation and discussion of results from an engineering standpoint, and

(4) MTTF and MTTR calculations

(5) Value of Information Clarity with reflection on the engineering applications

On top of the above, clarity of the written report also represents grading criteria. Please note that we expect that the results discussion is done from the perspective of the selected engineering domain. Moreover, avoid discussing the implementation too much and focus more on the discussions from an engineering standpoint. Please discuss clearly what engineering decision can be made with models and how these models can potentially improve these decisions.

1.        Written report (20 Portfolio points)

Please submit a written report of 3000 words that includes the results of the background research, the table summarizing the states and failure models identified, and any further supporting written or graphical information that you deem necessary to support your work. Present the development of the above stated tasks and analyze the results from the perspective of your civil engineered system.  The reference list should be appended at the end of the report but will not count towards the number of pages.

Expected deliverables:

Please submit your report in pdf format. Also submit your Rscript. file. Upload these two files through the ISIS website. Make sure you submit everything before the deadline on ISIS. All files should allow us to easily identify your student number and your name. They also should be professionally formatted.

IMPORTANT NOTES:

PLEASE DO NOT SUBMIT .ZIP FILES. PLEASE DO NOT SUBMIT WORD DOCUMENTS. PLEASE  MAKE  SURE  TO  PROPERLY  SUBMIT  YOUR  WORK  SO  THAT  IT  IS  NOT  A “DRAFT.” WE CANNOT GRADE DRAFTSAND WE WILL NOT GRADE LATE SUBMISSIONS WITHOUT PRIOR PERMISSION BASED ON THE OFFICIAL REGULATIONS.

Individual Project Assignment 1 Tutorial

System deterioration during lifetime

Understanding the potential changes in a system's condition throughout its life cycle is crucial for assessing reliability. System conditions change not only due to ageing but also because of external factors like weather, usage patterns, hazards, and special events. Asset managers face the daily challenge of tracking system degradation to determine the best time for maintenance, rehabilitation, repairs, or replacements. These considerations are essential during a system's design and engineering phases, aiming to enhance its performance and extend its life cycle.

Engineering Domain Selection

In every engineering challenge, it's essential to define the problem domain, which directs our focus to a specific discipline or area. This tutorial addresses the deterioration of concrete bridges over their lifespan. Here, concrete bridges are our system of interest. Concrete is a predominant material in bridge design, known for its durability over a typical 120-year life span and adaptability to various conditions. However, like any engineered system, bridges can deteriorate or even fail due to several factors. Engineers must account for both gradual deterioration and potential sudden failures in their designs, using various models to capture different aspects.

This tutorial is structured as follow:

1.   Prerequisite — supporting tools.

2.   Bridge deterioration modelling

3.   Bridge failure modelling

4.   MTTR and MTTF

5.   Value of Information (VoI)

1. Prerequisite – supporting tools

As a first step, we need to start by installing R and RStudio. This tutorial is using the following versions:

•   R

•   RStudio

You can use the same version, but it is suggested to upgrade to the latest version of both R and RStudio. For the installation instructions, we provide you in ISIS a step-by-step tutorial, R introduction section. You can also see free resources (courses and handbooks) to get yourself step- by-step into R.

You can find there here:

https://isis.tu-berlin.de/course/view.php?id=36026

The tutorials are also based on windows system. There might be some problems with packages for different versions on different systems, such as MacOS. So, bear this in mind if you’re working on a different system than windows. Bear also in mind that any updates to the R or RStudio versions might require you to reinstall/update the packages to new versions. We only support the installation on the computers in our PC pools. You can of course use your own laptop but we do not guarantee support for every single laptop.

Start RStudio and in the console run the following lines, to install the required packages we are going to use in this tutorial:

install .packages(“expm“)

install .packages(“FaultTree”, repo="http://R-Forge.R-project.org")

install .packages(“reshape2“)

install .packages(“ggplot2“)

These packages are needed for different stages in the assignment. You can learn more about the functionality and use cases of them either on RStudio or by the handbook and courses provided on ISIS. Please note that you need to run these commands only once. Then you will be able to use the packages every time you need. Do not include these lines in your R-Script, as it is not necessary to run these commands every time you run the script. – you can delete or turn them into comments with a “#” symbol.

To get started with the next part, please got to the main menu File → New File → R Script. to start a new script. The shortcut for this is Ctrl+Shift+N. In the new appeared window, right on top, write the following code line:

rm (list = ls())

Every time when you run your script, this command will clean your environment. By this, you make sure that you cannot use any of the variables you created previously, and the environment is clean, allowing you to use only the data and variables you initialize with your current script.

Make sure that you save you newly created file. Go to File → Save As and choose a name for your file as well as a location where you want to save and access it later. You will have to do this only once. Later on, as you are working and adding more code lines to your file, you can use File → Save of the shortcut Ctrl+S to save your progress. Make sure that you save your script file on a regular basis to avoid possible data loss.

To use the packages you installed previously, please add the following code lines to your script.

library(expm)

library(FaultTree)

library(reshape2)

library(ggplot2)

At this point, we are ready to start with the next part ofour assignment – concrete bridge deterioration modelling.

Important notes before going through the tutorial:

1.   The purpose of the tutorial is to give you an example. Your system is different and you need to keep that in mind for all steps. The process is the same, but the details, focus and results will of course be different.

2.   Learning the method is much more important than the tool, since tools are always changing over time. You could apply the same method using totally different tools. For simplicity, we give the tutorials using R as an opportunity to learn and practice a fantastic tool. So, please stick with it so that we can support you within your project, but focus more on the method and the purpose of using it for your specific case study.

3.   Always have references for every single detail that is not yours, such as the lifetime of your system and probabilities of deterioration, etc. If the figures, numbers, or details are from your own tests or assumptions, clearly write that so we know where you got the information. Some numbers and details, however, cannot be assumed without references, so be careful.

Referencing is super important from many different angles.

4.   Explain your steps. The tutorial gives in depth explanations for why and how every step is done. In your project, you should instead focus on describing in detail the steps of your research and method to reach the results and conclusion afterwards. We need to see that you understand the method from your writing and explanation.

5.   Structure your paper to give all the required details in the assignment.

2.   Concrete Bridge deterioration modelling

Modelling deterioration over a system’s lifetime helps asset managers and designers to understand how a system behaves under various conditions. During its lifetime, a system might suffer from various  transformations.  These  transformations  are  system  specific,  and  usually  are  already predefined by the domain standards. To capture these transformations, assets managers use specific terminology to define these transitions, called states. At a specific point in lifetime, the system is categorized as being in a specific condition state. Taking concrete bridges domain as an example for this  tutorial,  the  asset  managers  are  using  numerical  values  called  rating,  as  well  as  textual descriptions  of the current condition  of a  specific bridge. Table  1  shows  an  example  of rating categories from USA.

Table 1 – Possible states ofa bridge during lifetime (Kim and Yoon, 2009)

As shown in table 1, each specific rating is accompanied by specific technical actions, such as maintenance or repairs. These states are specific to the USA and are defined as standard by the Federal Highway Administration. This means that, every time the asset managers asses the condition of a specific bridge, they must follow strict guidelines regarding the categorization of it.

Moreover, each organization managing a portfolio of bridges, wants to know in advance what kind of interventions (technical actions) need to be taken and when. To do this, they need to create models to simulate various scenarios. From the perspective of good operation, state 3 is the most critical, as the bridge needs to be closed for rehabilitation (Jiang and Sihna, 1989).

To find out how a bridge transitions from one state to another during lifetime, we need to create a model which can capture this behaviour. The Markov chain is one good method supporting these types of studies. A good introduction to the Markov chain method is given in the reading assignment planned for week 2.

A first step in creating a state-based model is to define the states of the system. In the case of our bridge, the states are the ones defined in table 1. Using R to support this task, we will start by adding a simple vector containing the name of the states:

stateNames <- c("Excellent", "Very good", "Good",

                "Satisfactory", "Fair", "Poor", "Serious")

To continue with the model creation, we need to figure out a set of probabilities that will indicate the likelihood that a bridge in a state “si” will transition to another state of the system “sj”. Making  the connection with our example, this can be rephrased as “the probability that the bridge having the condition rated as “good” will deteriorate so much that the asset managers will rate it next time as “satisfactory” or “fair”. We will cover the situation when we talk about repairs later in this tutorial.

At this point, we start simple by considering only the deterioration of the bridge. Skimming the domain literature, we find a set of probabilities we can use for our concrete bridge example (Jiang and Sihna, 1989).  For the implementation in R, we will add the following probabilities vector. You need to have probabilities from literature based on the system that you choose.

p <- c(0.815, 0.794, 0.787, 0.980, 0.981, 0.737, 1)

Within this vector, we have a set of probabilities which indicates the likelihood that the bridge remains in its current condition. For example, if we assume that a the current condition of a specific bridge is rated as “Excellent”  there are 81.5% changes that next year the bridge will be rated again “Excellent”, while 18.5% chances that the bridge will deteriorate and next year will be rated as “Very good”. Using this vector of probabilities, we can build a transition matrix, which capture  the logic exemplified above. To implement this in R, add the following lines of code.

statesProb <- matrix(c(p[1], 1-p[1], 0, 0, 0, 0, 0,

0, p[2], 1-p[2], 0, 0, 0, 0,

0, 0, p[3], 1-p[3], 0, 0, 0,

0, 0, 0, p[4], 1-p[4], 0, 0,

0, 0, 0, 0, p[5], 1-p[5], 0,

0, 0, 0, 0, 0, p[6], 1-p[6],

0, 0, 0, 0, 0,   0,    p[7]), nrow = 7, byrow = TRUE)

row.names(statesProb) <- stateNames

colnames(statesProb) <- stateNames

statesProb

The transition matrix should look like this.

> statesProb

Excellent Very good Good Satisfactory Fair Poor Serious

Excellent 0.815 0.185 0.000 0.000 0.000 0.000 0.000

Very good 0.000 0.794 0.206 0.000 0.000 0.000 0.000

Good 0.000 0.000 0.787 0.213 0.000 0.000 0.000

Satisfactory 0.000 0.000 0.000 0.980 0.020 0.000 0.000

Fair 0.000 0.000 0.000 0.000 0.981 0.019 0.000

Poor 0.000 0.000 0.000 0.000 0.000 0.737 0.263

Serious 0.000 0.000 0.000 0.000 0.000 0.000 1.000

As shown above, the transition matrix has a column and a line for each state we defined. On the diagonal, we have the probabilities that the bridge will remain rated with the same condition. Taking the second row as an example, on which we have the values for the condition “Very good” there are 0.00 chances that the bridge will be rated as “Excellent”, 79.4% chances that the bridge will be rated  as “very good” and 20.6% chances that the bridge will be rated “Good”.

Using the matrix, we can create a simulation model which allows us to find out what will happen with our bridge after a specific number of years, knowing the current condition of the bridge. This kind of simulation helps the asset managers identify when to plan maintenance, repairs, or replacements. The implementation in R is simple, as indicated in the code bellow.

forecast <- function(years, probMatrix, initialState) {

return(round(initialState %*% (probMatrix %^% years), 3))

}

In the above code, we created a function called forecast, which takes as input the years, the probability matrix we defined previously as well as the initial state (current condition) of our system.

Let’s say that we want to find out what is going to happen with our bridge in 10 years, knowing that the current condition of the bridge is “Very good”.

initialState <- matrix(c(0,1,0,0,0,0,0),nrow=1, byrow=TRUE)

no.years <- 10

forecast(no.years, statesProb, initialState)

The output you will get looks like the one presented below:

> forecast(no.years, statesProb, initialState)

Excellent Very good  Good Satisfactory  Fair Poor Serious

[1,]         0       0.1 0.248      0.603 0.047 0.001  0.001

This result indicates that after 10 years there are:

•    10% chances that the bridge condition will be “Very good”

•   24.8% chances that the bridge condition will be “Good”

•   60.3% chances that the bridge condition will be “Satisfactory”

•   4.7% chances that the bridge condition will be “Fair”

•   0.1% chances that the bridge condition will be “Poor”

•   0.1% chances that the bridge condition will be “Serious”

This shows that in 10 years there is a big chance (60.3%) that the bridge will need major maintenance works. We need to keep in mind that we have not included any types of maintenance interventions (e.g., repairs) in our model. The model shows that there is a good chance that in 10 years the system condition will degrade from a Very good  condition to a  Satisfactory  one without any repairs. Considering that the expected lifetime of a concrete bridge is at least 120 years, the asset managers need to think of performing various maintenance strategies so that the bridge will reach its expected lifetime. Nevertheless, another limitation of the model is that it considers the deterioration of the concrete bridge in normal conditions without considering the possible failure scenarios.

The previous implementation gave us the possibility to see what is going to happen at a specific point in time – after 10 years. To have a better overview of how the bridge will degrade over time, we can expand the simulation model to output all the results for the expected lifetime -120 years.

The implementation in R is straight forward, as shown in the code below.

no.years <- 120

initialState <- matrix(c(1,0,0,0,0,0,0),nrow=1, byrow=TRUE)

years <- as.matrix(seq(1,no.years,1))

results <- t(apply(X = years, 1, FUN = forecast, statesProb, initialState))

results <- rbind(initialState, results)

colnames(results) <- stateNames

head(results)

tail(results)

In this implementation, we also add the initial state to the results suing the rbind() function. The output is stored in the results matrix, where head() and tail() allow us to have a look at the probabilities of the bridge state of the first six years and at the end of the period of 120 years.

> head(results)

Excellent Very good  Good Satisfactory  Fair Poor Serious year

1     1.000    0.000 0.000      0.000 0.000   0     0   0

2     0.815     0.185 0.000      0.000 0.000   0     0   1

3     0.664     0.298 0.038      0.000 0.000   0     0   2

4     0.541     0.359 0.091      0.008 0.000   0     0   3

5     0.441     0.385 0.146      0.027 0.000   0     0   4

6     0.360     0.388 0.194      0.058 0.001   0     0   5

> tail(results)

Excellent Very good Good Satisfactory  Fair Poor Serious year

116         0       0   0      0.134 0.284 0.021  0.560 115

117         0       0   0      0.132 0.282 0.021  0.566 116

118         0       0   0      0.129 0.279 0.021  0.571 117

119         0       0   0      0.126 0.276 0.021  0.577 118

120         0       0   0      0.124 0.274 0.021  0.582 119

121         0       0   0      0.121 0.271 0.020  0.587 120

We see that the simulation starts with the initial values we provided as input for the initial state, and over time the condition of the bridge deteriorates. After 120 years, there is a big chance (58.7%) that the rating of the bridge is “Serious”, and the operator will need to close the bridge to perform. serious rehabilitation works.

To have an overview of the system degradation from its inception until its expected lifetime, we can represent the results graphically. To do this, we will perform various operations to manipulate the results variable so that it is easy to plot. This is an important point to clearly represent the data in your plot.

results <- as.data.frame(results)

results$year <- 0:no.years

molten.results <- melt(results, id=c("year"))

head(molten.results)

colnames(molten.results) <- c("year", "condition", "probability")

In the first step, we convert the results type to dataframe. Next, we add a new column called years and use it as an id to transform the dataframe into a three columns set containing the year, condition and probability variables. Once we’ve done this, we can create a lines plot:

p1 <- ggplot() +

geom_line(aes(y = probability, x = year, colour = condition), linewidth=1,

data = molten.results, stat="identity") +

ggtitle("Bridge System - Probability of states - 120 years") p1

The figure we obtained is presented below. At this point, we can analyse the results of the model from the engineering perspective. Considering that we only included the transition of the system from one condition to another in normal conditions, we can see that the first need for intervention (e.g. minor repair) is after almost 10 years when there is a big probability that the bridge will be in the state “Good”. Moreover, we see that once the system reached the “Good” condition, the probability of moving to “Satisfactory” state increases, reaching the peak after 25 years. One important decision the engineers of the system can make is to prescribe some maintenance intervention after 10 years, so that the probability of staying in “Good” state increases. We can see that without any interventions the probability of being in “Good” decreases while the probability of moving to the “Satisfactory” state rapidly increases. Nonetheless, without any kind of interventions the expected lifetime might decrease from 120 years to around 85-95 when we can see that the probability that the bridge is achieving the “Serious” increases. At this point, the engineers need to come up with a suitable maintenance plan. But of course, We also need to think about cases when the system design and build is not perfect, and some failure events might occur due to various factors.

The model we developed so far only considers the continuous degradation of the bridge under normal conditions of operation. The model can be further updated by taking into consideration possible events which might lead to bridge failure.  To refine the model, in the next part of the tutorial we will create a model which help the asset managers to identify the likelihood of bridge failure in case of special events occurrence using Fault tree models.