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a aThis lecture discussed Monte Carlo simulation and its use in evolutionary models of space debris. Monte Carlo simulation involves repeatedly sampling random inputs from a probability distribution to produce distributions of possible outcomes. For space debris models, it involves generating quantities like positions and solar activity randomly and running deterministic computations. While Monte Carlo simulation provides probabilistic information, typical reporting of results only includes mean and sometimes standard deviation, which can lead to incorrect conclusions about modeling studies. The lecture highlighted challenges and opportunities for better presenting probabilistic outputs.
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40.pdf
This lecture discusses issues with reporting the results of evolutionary models and Monte Carlo simulations of space debris populations. Specifically, using only the mean and standard deviation to report results can be problematic and lead to incorrect conclusions. As an example, the lecturer analyzes a past IADC study on the benefits of active debris removal. The lecture then introduces a probabilistic framework that overcomes some of the limitations of a simple statistical approach. This framework allows expressing the confidence and uncertainty around outcomes in a more meaningful way. While an improvement, some issues around "impossible" answers still remain and will be explored in the next activity-based lecture.
38.pdf
This lecture discusses models for predicting the evolution of space debris. Simple "particles-in-a-box" models are transparent but lack accuracy and flexibility. More complex "evolutionary" models are needed to answer important questions by simulating individual objects and their interactions over time while accounting for uncertainties. Key properties like object types and orbits must be included to predict the effects of mitigation measures and new operations on the debris environment. Monte Carlo simulation is introduced as the approach used by evolutionary models.
37.pdf
This lecture introduced Talent's analytic model of space debris growth which mirrors an earlier systems model but with additional complexity. Talent's model uses a differential equation approach to model the number of orbital objects over time based on deposition from launches, atmospheric decay, and collision rates. The model predicts equilibrium populations where sources and sinks are balanced. Results from Talent's 1992 paper were presented to illustrate how the model can provide insights into the fundamental behavior and long-term evolution of the space debris population.
34.pdf
This lecture introduces mathematical modeling of space debris. It discusses what models are, what they can and cannot do, and qualities of good models. Models can explain system behavior, translate between scales, and enable prediction. They come in various forms and complexities. The lecturer notes that all models are wrong but some are useful, and that forming a model requires balancing accuracy, transparency, and flexibility. The next lecture will further explore what models can and cannot do and what makes a good model.
43.pdf
This lecture provides an overview of the DAMAGE evolutionary model for modeling space debris. DAMAGE was developed over three years starting in 1999 to model the long-term evolution of the debris environment in high Earth orbit. It incorporates various support models, like orbital propagation, collision prediction, break-up models, and failure models. DAMAGE can perform 200-year simulations in around two hours. Similar models are used by other space agencies. The next few lectures will cover the algorithms behind each support model.
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This lecture introduces the NASA standard breakup model, which was developed using data from the SOCIT series of HVI experiments and other sources. The model can be used to calculate the number, mass, area-to-mass ratio, and velocity of fragments resulting from explosions or collisions in space. It provides empirical equations to estimate these values as a function of fragment size and other parameters based on historical data from events like satellite breakups and hypervelocity impact tests. The model is implemented in simulations to analyze and predict the evolution of space debris populations over time.
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This lecture discusses issues with reporting the results of evolutionary models and Monte Carlo simulations of space debris populations. Specifically, using only the mean and standard deviation to report results can be problematic and lead to incorrect conclusions. As an example, the lecturer analyzes a past IADC study on the benefits of active debris removal. The lecture then introduces a probabilistic framework that overcomes some of the limitations of a simple statistical approach. This framework allows expressing the confidence and uncertainty around outcomes in a more meaningful way. While an improvement, some issues around "impossible" answers still remain and will be explored in the next activity-based lecture.
38.pdf
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37.pdf
This lecture introduced Talent's analytic model of space debris growth which mirrors an earlier systems model but with additional complexity. Talent's model uses a differential equation approach to model the number of orbital objects over time based on deposition from launches, atmospheric decay, and collision rates. The model predicts equilibrium populations where sources and sinks are balanced. Results from Talent's 1992 paper were presented to illustrate how the model can provide insights into the fundamental behavior and long-term evolution of the space debris population.
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This lecture introduces mathematical modeling of space debris. It discusses what models are, what they can and cannot do, and qualities of good models. Models can explain system behavior, translate between scales, and enable prediction. They come in various forms and complexities. The lecturer notes that all models are wrong but some are useful, and that forming a model requires balancing accuracy, transparency, and flexibility. The next lecture will further explore what models can and cannot do and what makes a good model.
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This lecture provides an overview of the DAMAGE evolutionary model for modeling space debris. DAMAGE was developed over three years starting in 1999 to model the long-term evolution of the debris environment in high Earth orbit. It incorporates various support models, like orbital propagation, collision prediction, break-up models, and failure models. DAMAGE can perform 200-year simulations in around two hours. Similar models are used by other space agencies. The next few lectures will cover the algorithms behind each support model.
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1) How uncertainties in satellite characteristics and the atmosphere lead to uncertainties in re-entry predictions. Predictions are most accurate within 10 days and least accurate beyond that.
2) Methods for calculating risks to humans, including equivalent casualty cross-section and modeling debris footprint as a 2D Gaussian.
3) Long-term risks are low, estimated at 1 casualty every 45 years based on historical re-entries.
56.pdf
The lecture discusses common misconceptions about the Kessler Syndrome, a concept developed by NASA scientist Donald Kessler warning of the risk of increasing amounts of space debris. Some of the misconceptions addressed are that it would be a quick collision chain reaction, that there would be no way to stop it once started, and that it would mean an end to all space travel. The lecture presents examples of these misconceptions in media reports and research articles and aims to explain in upcoming lectures why these ideas are likely incorrect.
57.pdf
This lecture discusses techniques for calculating probabilities using combinatorics, and applies them to scenarios involving satellite collisions and drawing playing cards. Two scenarios are presented:
1) Calculating probabilities of different outcomes from 10 satellite conjunctions each with a 5% chance of collision.
2) Drawing 10 cards from a deck and calculating probabilities of different numbers of hearts. The chance of a heart on each draw is 1/4. Probabilities are calculated using combinations, multiplication of probabilities, and subtraction of complementary events.
55.pdf
(1) Donald Kessler introduced the idea of a "critical population density" of space debris in 1978 and 1991, where above this density collisions would produce debris faster than it decays.
(2) In 2001, Kessler introduced the concept of a "critical number of objects" and applied a stability model showing regions of low Earth orbit have exceeded the critical level and become unstable.
(3) Kessler's work showed the space debris population could exponentially increase without further launches if the critical threshold is surpassed, known as the "Kessler Syndrome," though this was sometimes misunderstood to mean an immediate effect rather than gradual increase.
54.pdf
This lecture discusses carrying capacity and resilience as alternative representations of space sustainability. It uses a predator-prey model to demonstrate carrying capacity for two interacting populations. Solving problems like space debris is described as a "super wicked problem" due to the lack of central authority, conflicting stakeholders, and difficulty establishing irreversible solutions.
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2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
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39.pdf
- 1. Space Environment Lecture 39 – Space Debris (Vol. 4) Evolutionary models & MC Simulation Professor Hugh Lewis SESA3038 Space Environment
- 2. Overview of lecture 39 • In the last lecture we introduced ‘evolutionary’ models, which enable us to answer important questions about the space debris population and the individuals in it. • We ended with a brief look at the uncertainties that need to be captured within these models and introduced Monte Carlo simulation • In this lecture we take a look at what Monte Carlo simulation is and how it is implemented in our evolutionary models • We end with a hint that some important problems still occur – in particular, with respect to the reporting of results from these models Space Environment – Space Debris (Vol. 4)
- 3. Monte Carlo Simulation Space Environment – Space Debris (Vol. 4) • Monte Carlo methods are a broad class of computational algorithms that reply on repeated random sampling to obtain numerical results (Wikipedia) • Monte Carlo simulation produces distributions of possible outcome values by repeating the random sampling a large number of times • Typical Monte Carlo method: 1. Define the domain of possible inputs 2. Generate inputs randomly from a probability distribution over the domain 3. Perform a deterministic computation on the inputs 4. Aggregate the results
- 4. Monte Carlo Simulation Space Environment – Space Debris (Vol. 4) Example (from Wikipedia): estimate value of 𝜋𝜋 1. Draw a square, then inscribe a quadrant within it 2. Uniformly scatter a given number of points over the square 3. Count the number of points inside the quadrant 4. The ratio of the inside-count and the total sample count is an estimate of the ratio of the two areas: ⁄ 𝜋𝜋 4
- 5. Monte Carlo Simulation Space Environment – Space Debris (Vol. 4) • Monte Carlo method used for space debris evolutionary models: 1. Define the domain of possible inputs 2. Perform a deterministic computation on the inputs 3. Generate quantities (e.g. positions, solar activity) randomly from a probability distribution as needed 4. Aggregate the results
- 6. Evolutionary models Space Environment – Space Debris (Vol. 4) 1 simulation run:
- 7. Evolutionary models Space Environment – Space Debris (Vol. 4) 50 simulation runs:
- 8. Evolutionary models Space Environment – Space Debris (Vol. 4) Average and standard deviation of 50 runs
- 9. Reporting issues Space Environment – Space Debris (Vol. 4) • Evolutionary models make use of a Monte Carlo (MC) simulation approach – MC simulation provides information about the probability distributions in key environment parameters over time, e.g.: • Number of objects • Number of collisions • Spatial density • BUT typical outputs that are reported include only: • Mean (most of the time) • Standard deviation (some of the time) • These typical outputs are not reliable or definitive and their use can lead to incorrect conclusions and misrepresentations of modelling studies • Focus on the challenges and opportunities for presenting model outputs, highlighting the benefits of a probabilistic approach
- 10. Recap of lecture 39 • In this lecture we introduced (only at a very high level) the idea of Monte Carlo simulation and how it is implemented in our evolutionary models • We ended with a hint that some important problems still occur – in particular, with respect to the reporting of results from these models – We will pick this up in more detail in the next lecture Space Environment – Space Debris (Vol. 4)