# Staff Profiles

## Professor Michael T Todinov

MSc, PhD, DEng

### Professor in Mechanical Engineering

Department of Mechanical Engineering and Mathematical Sciences

Faculty of Technology, Design and Environment

Michael Todinov conducts research and teaching in the area of Reliability, Risk , Probabilistic modelling, Network optimization, Uncertainty quantification, Mechanics of materials and Engineering Mathematics. From the University of Birmingham, Michael todinov holds a PhD related to mathematical modelling of thermal and residual stresses and a higher doctorate Doctor of Engineering (DEng) which is the engineering equivalent of Doctor of Science (DSc). The higher doctorate was awarded for fundamental contributions in the area of new probabilistic concepts and models in Engineering.

Engineering Reliability and Risk Management

Engineering Mathematics and Modelling

Fracture Mechanics

Advanced Stress Analysis

MATLAB programming and modelling with MATLAB

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 new domain-independent methods for improving reliability and reducing risk. 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.
- Developing new domain-independent methods for reiability improvement and risk reduction.
- 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.

- Todinov M.T., Reliability analysis based on the losses from failures,
*Risk Analysis*v.26(2), (2006), pp.311-335. - Todinov M.T., Limiting the probability of failure for components containing flaws,
*Computational Materials Science,*v.32, (2005), pp.156-166. - Todinov M.T., Reliability analysis and setting reliability requirements based on the cost of failure,
*International Journal of Reliability, Quality and Safety Engineering,*v.11(3), (2004), pp.1-27. - Todinov M.T., Uncertainty and risk associated with the Charpy impact energy of multi-run welds,
*Nuclear Engineering and Design,*v.231, (2004), pp.27-38. - Todinov M.T., Setting reliability requirements based on minimum failure-free operating periods,
*Quality and Reliability Engineering International,*v.20, (2004), pp.273-287. - Todinov M.T., A new reliability measure based on specified minimum distances before the locations of random variables in a finite interval,
*Reliability Engineering and System Safety,*v.86, (2004), pp.95-103. - Todinov M.T., Reliability governed by the relative locations of random variables in a finite interval,
*IEEE Transactions on Reliability,*v.53(2), (2004), pp.226-237. - Todinov M.T., On Coolen's comments related to statistics of defects in one-dimensional components,
*Computational Materials Science,*v.29, (2004), pp.253-258. - Todinov M.T., Statistics of inhomogeneous media formed by nucleation and growth,
*Probabilistic Engineering Mechanics,*v.18, (2003), pp.139-149. - Todinov M.T., Modelling consequences from failure and material properties by distribution mixtures,
*Nuclear Engineering and Design,*v.224, (2003), pp.233-244. - Todinov M.T., Distribution mixtures from sampling of inhomogeneous microstructures: variance and probability bounds of the properties,
*Nuclear Engineering and Design,*v.214, (2002), pp.195-204. - Todinov M.T., Statistics of defects in one-dimensional components,
*Computational Materials Science,*v.24 (2002), pp.430-442. - Todinov M.T., Distribution of properties from sampling inhomogeneous materials by line transects,
*Probabilistic Engineering Mechanics,*v.17, (2002), pp.131-141. - Todinov M.T., An efficient method for estimating from sparse data the parameters of the impact energy variation in the ductile-to-brittle transition region,
*International Journal of Fracture*v.111, (2001), pp.131-150. - Todinov M.T., Estimating the probabilities of triggering brittle fracture associated with the defects in the materials,
*Materials Science and Engineering A,*v.302(2), (2001), pp.235-245. - Todinov M.T., Estimating the parameters of the impact energy variation in the ductile-brittle transition region from complete and sparse data sets,
*Computational Materials Science,*v.21, (2001), pp.111-123. - Todinov M.T., Probability distribution of fatigue life controlled by defects,
*Computers and Structures,*v.79, (2001), pp.313-318. - Todinov M.T., Necessary and sufficient condition for additivity in the sense of the Palmgren-Miner rule,
*Computational Materials Science,*v.21, (2001), pp.101-110. - Todinov M.T., On some limitations of the Johnson-Mehl-Avrami-Kolmogorov equation,
*Acta Materialia,*48 (2000) 4217-4224. - Todinov M.T., Probability of fracture initiated by defects,
*Materials Science and Engineering*A A276, (2000), pp.39-47. - Todinov M.T., M.Novovic, P.Bowen and J.F.Knott. Modelling the impact energy in the ductile/brittle transition region of C-Mn multi-run welds,
*Materials Science and Engineering A,*A287, (2000), pp.116-124. - Todinov M.T., Residual stresses at the surface of automotive suspension springs,
*Journal of Materials Science,*v.35, (2000), pp.3313-3320. - Todinov M.T., On some applications of the random transects,
*Modelling and Simulation in Materials Science and Engineering,*v.7, (1999), pp.525-539. - Todinov M.T., Fitting impact fracture toughness data in the transition region,
*Materials Science and Engineering A,*A265, (1999), pp.1-6. - Todinov M.T., Influence of some parameters on the residual stresses from quenching,
*Modelling and Simulation in Materials Science and Engineering,*v.7, (1999), pp.25-41. - Todinov M.T., Maximum principal tensile stress and fatigue crack origin for compression springs,
*International Journal of Mechanical Sciences,*v.41, (1999), pp.357-370. - Todinov M.T., Alternative Approach to the problem of additivity,
*Metallurgical and Materials Transactions B,*29B, (1998), pp.269-273. - Todinov M.T., A probabilistic method for predicting fatigue life controlled by defects,
*Materials Science and Engineering A, A255,*(1998), pp.117-123. - Todinov M.T., Mechanism for the formation of the residual stresses from quenching,
*Modelling and Simulation in Materials Science and Engineering,*v.6, (1998), pp.273-291. - Todinov M.T., A new approach to the kinetics of a phase transformation with constant radial growth rate,
*Acta Materialia,*v.44, (1996), pp.4697-4703. - Todinov M.T., J.F.Knott and M.Strangwood. An assessment of the influence of complex stress states on martensite start temperature,
*Acta Materialia,*v.44, (1996), pp.4909-4915

### Areas of expertise

**Reliability and risk modelling, Uncertainty quantification**

**General methods for improving reliability and reducing risk**

**Mechanics of Materials, Material Science and Avanced Stress analysis**

**Computer Science, Algorithms, Discrete mathematics**

**Applied probability, probabilistic modelling, Monte Carlo simulation techniques**

**Modelling and simulation of heat and thermochemical treatment of materials**

**Stochastic flow networks, repairable flow networks. static flow networks, networks with**

**disturbed flows, reliability networks, stochastic graphs**

**Mathematical optimisation and optimisation algorithms under uncertainty**

**A****dvanced C/C++ programming**

**MATLAB programming**

### Other experience

CRANFIELD UNIVERSITY (2005-2006), CRANFIELD, BEDFORD, MK43 0AL

HEAD OF RISK AND RELIABILITY

(Leading the research, consultancy and teaching in the area of Reliability, Risk and Uncertainty modelling in the School of Applied Sciences, Cranfield University)

CRANFIELD UNIVERSITY (2002-2004), CRANFIELD, BEDFORD, MK43 0AL

BP LECTURER IN RELIABILITY ENGINEERING AND RISK MANAGEMENT

(Research, consultancy, teaching, and supervision in the area of Reliability, Risk and Uncertainty quantification in the School of Applied Sciences)

THE UNIVERSITY OF BIRMINGHAM (1994-2001), BIRMINGHAM, EDGBASTON, B15 2TT, UK

RESEARCH SCIENTIST

(Managed and conducted research in the area of uncertainty modelling related to fracture and fatigue; modelling the uncertainty in the location of the ductile-to-brittle region of nuclear pressure vessel steels; probability of fracture initiated by flaws; improving the reliability of mechanical components through mathematical modelling.

TECHNICAL UNIVERSITY OF SOFIA (1989-1994), BULGARIA

RESEARCH SCIENTIST

(Managed a number of research projects in the area of modelling and simulation in heat and mass transfer and phase transformations, funded by the Bulgarian Ministry of Science and Education)