M.Todinov's name is associated with creating the foundations of risk-based reliability analysis (driven by the cost of failure), the theory of repairable flow networks and networks with disturbed flows and the introduction of general principles for improving reliability and reducing risk which do not rely on reliability data. M.Todinov also pioneered research on reliability dependent on the relative configurations of random variables, creating analytical methodology for evaluating the risk associated with overlapping of random events on a time interval and optimal allocation of fixed budgets to achieve a maximal reduction of technical risk.
A sample of M.Todinov's results includes: the discovery of closed and dominated parasitic flow loops in real networks; the proof that the Weibull distribution is an incorrect model for the distribution of breaking strength of materials and deriving the correct alternative of the Weibull model; a theorem regarding the exact upper bound of properties from random sampling of multiple sources; a general equation for the probability of failure of brittle components with complex shape, the formulation and proof of the necessary and sufficient conditions of the Palmgren-Miner rule and Scheil's additivity rule; deriving the correct alternative of the Johnson-Mehl-Avrami-Kolmogorov equation; formulating the dual network theorems for static flows networks and networks with disturbed flows; discovering the binomial expansion model for evaluating risk associated with overlapping random events on a time interval, developing the method of separation, the method of segmentation, the method of self-reinforcement (self-strengthening) and the method of inversion as new general methods for improving reliability and reducing risk.
M.Todinov’s research has been funded by the automotive industry, nuclear industry, the oil and gas industry and research councils.
Research grants and awards
Recipient of the 2017 prestige IMechE award for risk reduction in Mechanical Engineering (IMechE, UK, 2017)
https://www.imeche.org/careers-education/scholarships-and-awards/prestige-awards/IMechE-Award-for-Risk-Reduction/award-for-risk-reduction-michael-todinov
Recipient of a best lecturer teaching award, as voted by students (Cranfield University, 2005)
- High-speed algorithms for the output flow in stochastic flow networks, (2009-2013), research project funded by The Leverhulme Trust, UK.
- High-speed algorithms for the output flow in stochastic flow networks with tree topology, (2007-2008), consultancy project funded by British Petroleum.
- Reliability Value Analysis for BP Taurt Development (2005-2006), consultancy project funded by Cooper Cameron.
- Reliability allocation in complex systems based on minimizing the total cost (2004-2007), research project funded by by EPSRC.
- Modelling the probability of failure of mechanical components caused by defects (2003-2005), research project sponsored by British Petroleum.
- Developing the BP reliability strategy, generic models and software tools for reliability analysis and setting reliability requirements based on cost of failure and minimum failure-free operating periods (2002-2004), research project funded by British Petroleum.
- Modelling a single-channel AET production system versus a dual-channel AET system (2005), consultancy project sponsored by Total.
- Reliability case for all-electric subsea control system (2004), consultancy project funded by BP and Total.
- Modelling the uncertainty associated with the ductile-to-brittle transition temperature of inhomogeneous welds (2002), research project funded by NII/HSE, UK.
- Developing efficient statistical models and software for determining the uncertainty in the location of the ductile-to-brittle transition region for multi-run welds (2001-2002), research project sponsored by the Nuclear Installations Inspectorate, HSE/NII, UK.
- Developing efficient statistical methods and software for fitting the variation of the impact energy in the ductile/brittle transition region for sparse data sets (1998-2000), research project sponsored by the Nuclear Installations Inspectorate, HSE/NII, UK.
- Statistical modelling of Brittle and Ductile Fracture in Steels, research project funded by EPSRC (1998-2000).
- Probabilistic Approach for Fatigue Design and Optimisation of Cast Aluminium Structures (1997-1998) research project funded by EPSRC.
- Modelling the temporal and residual stresses of Si-Mn automotive suspension springs, (1994-1997), research project funded by EPSRC and DTI.
- Six research projects related to mathematical modelling of heat- and mass-transfer during heat treatment of steels and mathematical modelling of non-isothermal phase transformation kinetics during heat treatment of steels, funded by the Bulgarian Ministry of Science and Education in the period (1988-1994).
- Optimal guillotine cutting out of one-and two-dimensional stock in the batch production, (1986-1987), research project funded by the Union of the Mathematicians, Bulgaria.
Research impact
Research highlights
- Creating the foundations of the theory of repairable flow networks and networks with disturbed flows. High-speed algorithms for analysis, optimisation and control in real time of repairable flow networks.
- Discovering the existence of closed and dominated flow loops in real networks and developing algorithms for their removal.
- Revealing the drawbacks of the successive shortest-path strategy for minimising the transportation cost from multiple interchangeable origins to multiple destinations and developing the correct alternative.
- Creating the foundations of risk-based reliability analysis – driven by the cost of system failure. Formulation of the principle of risk-based design.
- Creating the theoretical foundations of the maximum risk reduction attained within limited risk-reduction resources.
- Creating the theoretical foundations for evaluating the risk associated with overlapping random demands on a time interval.
- Introducing the concept 'stochastic separation' and a new reliability measure based on stochastic separation.
- Introducing the method of 'stochastic pruning' and creating on its basis ultra-fast algorithms for determining the production availability of complex networks.
- Formulation and proof of the upper bound variance theorem regarding the exact upper bound of properties from sampling multiple sources.
- Formulation and proof of the damage factorisation theorem – the necessary and sufficient condition for the validity of the Palmgren-Miner rule.
- An equation for the probability of fracture controlled by random flaws for components with complex shape.
- Theoretical and experimental proof that the Weibull distribution does not describe correctly the probability of failure of materials with flaws and a derivation of the correct alternative.
- A general equation related to reliability dependent on the relative configurations of random variables.
- Revealing the drawbacks of the maximum expected profit criterion in the case of risky prospects containing a limited number of risk-reward bets.
- Formulation and proof of the damage factorisation theorem – the necessary and sufficient condition for the validity of the Palmgren-Miner rule.
- An equation for the probability of fracture controlled by random flaws for components with complex shape.
- Theoretical and experimental proof that the Weibull distribution does not describe correctly the probability of failure of materials with flaws and a derivation of the correct alternative.
- A general equation related to reliability dependent on the relative configurations of random variables.
- Revealing the drawbacks of the maximum expected profit criterion in the case of risky prospects containing a limited number of risk-reward bets.