Optimal Initial Perturbations Research Articles

Sequential Quadratic Programming (SQP) for optimal control in direct numerical simulation of turbulent flow

The current work focuses on the development and application of an efficient algorithm for optimization of three-dimensional turbulent flows, simulated using Direct Numerical Simulation (DNS) or Large-Eddy Simulations, and further characterized by large-dimensional optimization-parameter spaces. The optimization algorithm is based on Sequential Quadratic Programming (SQP) in combination with a damped formulation of the limited-memory BFGS method. The latter is suitable for solving large-scale constrained optimization problems whose Hessian matrices cannot be computed and stored at a reasonable cost. We combine the algorithm with a line-search merit function based on an L1-norm to enforce the convergence from any remote point. It is first shown that the proposed form of the damped L-BFGS algorithm is suitable for solving equality constrained Rosenbrock type functions. Then, we apply the algorithm to an optimal-control test problem that consists of finding the optimal initial perturbations to a turbulent temporal mixing layer such that mixing is improved at the end of a simulation time horizon T. The controls are further subject to a non-linear equality constraint on the total control energy. DNSs are used to resolve all turbulent scales of motion, and a continuous adjoint formulation is employed to calculate the gradient of the cost functionals. We compare the convergence speed of the SQP L-BFGS algorithm to a conventional non-linear conjugate-gradient method (i.e. the current standard in DNS-based optimal control), and find that the SQP algorithm is more than an order of magnitude faster than the conjugate-gradient method.

Optimal nonlinear excitation of decadal variability of the North Atlantic thermohaline circulation

Nonlinear development of salinity perturbations in the Atlantic thermohaline circulation (THC) is investigated with a three-dimensional ocean circulation model, using the conditional nonlinear optimal perturbation method. The results show two types of optimal initial perturbations of sea surface salinity, one associated with freshwater and the other with salinity. Both types of perturbations excite decadal variability of the THC. Under the same amplitude of initial perturbation, the decadal variation induced by the freshwater perturbation is much stronger than that by the salinity perturbation, suggesting that the THC is more sensitive to freshwater than salinity perturbation. As the amplitude of initial perturbation increases, the decadal variations become stronger for both perturbations. For salinity perturbations, recovery time of the THC to return to steady state gradually saturates with increasing amplitude, whereas this recovery time increases remarkably for freshwater perturbations. A nonlinear (advective) feedback between density and velocity anomalies is proposed to explain these characteristics of decadal variability excitation. The results are consistent with previous ones from simple box models, and highlight the importance of nonlinear feedback in decadal THC variability.

Optimal perturbations of gravitationally unstable, transient boundary layers in porous media

AbstractWe study the linear stability of gravitationally unstable, transient, diffusive boundary layers in porous media using non-modal stability theory. We first perform a classical optimization procedure, using an adjoint-based method, to obtain the perturbations at the initial time $t= {t}_{p} $ that have a maximum amplification at a final time $t= {t}_{f} $. We then investigate the sensitivity of the optimal perturbations to the initial time, ${t}_{p} $, and the final time, ${t}_{f} $, as well as different measures of perturbation amplification. Due to the transient nature of the base state, we demonstrate that there is an optimal initial perturbation time, ${ t}_{p}^{o} $. By rescaling the problem, we develop analytical relationships for the optimal initial time and wavenumber in terms of aquifer properties. We also demonstrate that the classical optimization procedure essentially recovers the dominant perturbation structures predicted by a quasi-steady modal analysis. Although the classical optimal perturbations are mathematically valid, we observe that due to physical constraints, they are unlikely to reflect analogous laboratory experiments. Therefore, we propose a modified optimization procedure (MOP) that constrains the optimization to physically admissible initial perturbation fields. We compare the results of the classical and modified optimization procedures with quasi-steady modal analyses and initial value problems commonly used in the literature. Finally, we validate the predictions of the modified optimization scheme by performing direct numerical simulations (DNS) that emulate the onset of convection in physical systems.

Modal and transient dynamics of jet flows

The linear stability dynamics of incompressible and compressible isothermal jets are investigated by means of their optimal initial perturbations and of their temporal eigenmodes. The transient growth analysis of optimal perturbations is robust and allows physical interpretation of the salient instability mechanisms. In contrast, the modal representation appears to be inadequate, as neither the computed eigenvalue spectrum nor the eigenmode shapes allow a characterization of the flow dynamics in these settings. More surprisingly, numerical issues also prevent the reconstruction of the dynamics from a basis of computed eigenmodes. An investigation of simple model problems reveals inherent problems of this modal approach in the context of a stable convection-dominated configuration. In particular, eigenmodes may exhibit an exponential growth in the streamwise direction even in regions where the flow is locally stable.

Adjoint based optimization and control of a separated boundary-layer flow

An adjoint based optimization procedure for the nonlinear Navier–Stokes system is implemented and applied to the dynamics of a separated boundary-layer flow over a bump. For this open flow configuration, boundary conditions which are compatible between the direct and adjoint system are implemented using the influence matrix technique. Beyond a critical Reynolds number, the flow is unstable and subject to instabilities with multiple time-scales. Computing iteratively optimal initial perturbations, the most sensitive regions to forcing are highlighted. Wall blowing–suction actuators are then introduced at these locations and their capability of controlling the unstable linear and nonlinear dynamics is explored, by means of the adjoint based numerical algorithm.

Calculation of global optimal initial and boundary perturbations for the linearised incompressible Navier–Stokes equations

This study considers numerical methods for computation of optimal boundary and initial perturbations to incompressible flows. Similar to previous work, constrained Lagrangian functionals are built and gradient optimisation methods are applied to optimise perturbations that maximise the energy of perturbations in the computational domain at a given time horizon. Unlike most of the previous work in this field we consider both optimal initial and boundary condition problems and demonstrate how each can be transformed into an eigenvalue problem. It is demonstrated analytically and numerically that both optimisation and eigenvalue approaches converge to the same outcome, even though the optimisation approach may converge more slowly owing to the large number of inflection points. In a case study, these tools are used to calculate optimal initial and boundary perturbations to the Batchelor vortex. It is observed that when the flow is asymptotically stable, the optimal inflow perturbation is similar to the most unstable local eigenmode, while when the flow is stable/weakly unstable, the spatial distribution of the optimal inflow perturbation is similar to the local optimal initial perturbation.

Optimal Initial Perturbations for Ensemble Prediction of the Madden–Julian Oscillation during Boreal Winter

AbstractAn initialization strategy, tailored to the prediction of the Madden–Julian oscillation (MJO), is evaluated using the Goddard Earth Observing System Model, version 5 (GEOS-5), coupled general circulation model (CGCM). The approach is based on the empirical singular vectors (ESVs) of a reduced-space statistically determined linear approximation of the full nonlinear CGCM. The initial ESV, extracted using 10 years (1990–99) of boreal winter hindcast data, has zonal wind anomalies over the western Indian Ocean, while the final ESV (at a forecast lead time of 10 days) reflects a propagation of the zonal wind anomalies to the east over the Maritime Continent—an evolution that is characteristic of the MJO.A new set of ensemble hindcasts are produced for the boreal winter season from 1990 to 1999 in which the leading ESV provides the initial perturbations. The results are compared with those from a set of control hindcasts generated using random perturbations. It is shown that the ESV-based predictions have a systematically higher bivariate correlation skill in predicting the MJO compared to those using the random perturbations. Furthermore, the improvement in the skill depends on the phase of the MJO. The ESV is particularly effective in increasing the forecast skill during those phases of the MJO in which the control has low skill (with correlations increasing by as much as 0.2 at 20–25-day lead times), as well as during those times in which the MJO is weak.

Non-normal dynamics of time-evolving co-rotating vortex pairs

AbstractTransient energy growth of disturbances to co-rotating pairs of vortices with axial core flows is investigated in an analysis where vortex core expansion and vortex merging are included by adopting a time-evolving base flow. The dynamics of pairs are compared with those of individual vortices in order to highlight the effect of vortex interaction. Three typical vortex pair cases are studied, with the pairs comprised respectively of individually inviscidly unstable vortices at the streamwise wavenumber that maximizes the individual instabilities, viscously unstable vortices also at the streamwise wavenumber maximizing the individual instabilities and asymptotically stable vortices at streamwise wavenumber zero. For the inviscidly unstable case, the optimal perturbation takes the form of a superposition of two individual helical unstable modes and the optimal energy growth is similar to that predicted for an individual inviscid unstable vortex, while where the individual vortices are viscously unstable, the optimal disturbances within each core have similar spatial distributions to the individually stable case. For both of these cases, time horizons considered are much lower than those required for the merger of the undisturbed vortices. However, for the asymptotically stable case, large linear transient energy growth of optimal perturbations occurs for time horizons corresponding to vortex merging. Linear transient disturbance energy growth exhibited by pairs in this stable case is two to three orders of magnitude larger than that for a corresponding individual vortex. The superposition of the perturbation and the base flow shows that the perturbation has a displacement effect on the vortices in the base flow. Direct numerical simulations of stable pairs seeded by optimal initial perturbations have been carried out and acceleration/delay of vortex merging associated with a dual vortex meandering and vortex breakup related to axially periodic acceleration and delay of vortex merging are observed. For axially invariant cases, the sign of perturbation has an effect, as well as magnitude; the sign dependence relates to whether or not the perturbation adds to or subtracts from the swirl of the base flow. For a two-dimensional perturbation that adds to the swirl of the base flow, seeding with the linear optimal disturbance at a relative energy level $1\ensuremath{\times} 1{0}^{\ensuremath{-} 4} $ induces the pair to move towards each other and approximately halves the time required for merger. Direct numerical simulation shows that the optimal three-dimensional perturbation can induce the vortex system to break up before merging occurs, since the two-dimensional nature of vortex merging is broken by the development of axially periodic perturbations.

Optimal inflow boundary condition perturbations in steady stenotic flow

AbstractWe determine optimal inflow boundary perturbations to steady flow through a straight inflexible tube with a smooth axisymmetric stenosis at a bulk-flow Reynolds number $\mathit{Re}= 400$, for which the flow is asymptotically stable. The perturbations computed produce an optimal gain, i.e. kinetic energy in the domain at a given time horizon normalized by a measure of time-integrated energy on the inflow boundary segment. We demonstrate that similarly to the optimal initial condition problem, the gain can be interpreted as the leading singular value of the forward linearized operator that evolves the boundary conditions to the final state at a fixed time. In this investigation we restrict our attention to problems where the temporal profile of the perturbations examined is a product of a Gaussian bell and a sinusoid, whose frequency is selected to excite axial wavelengths similar to those of the optimal initial perturbations in the same geometry. Comparison of the final state induced by the optimal boundary perturbation with that induced by the optimal initial condition demonstrates a close agreement for the selected problem. Previous works dealing with optimal boundary perturbation considered a prescribed spatial structure and computed an optimal temporal variation of a wall-normal velocity component, whereas in this paper we consider the problem of a prescribed temporal structure and compute the optimal spatial variation of velocity boundary conditions over a one-dimensional inflow boundary segment. The methodology is capable of optimizing boundary perturbations in general non-parallel two- and three-dimensional flows.

Application of the conditional nonlinear optimal perturbation method to the predictability study of the Kuroshio large meander

A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations. The results show that the model was able to capture the essential features of these path variations. We used one simulation of the model as the reference state and investigated the effects of errors in model parameters on the prediction of the transition to the Kuroshio large meander (KLM) state using the conditional nonlinear optimal parameter perturbation (CNOP-P) method. Because of their relatively large uncertainties, three model parameters were considered: the interfacial friction coefficient, the wind-stress amplitude, and the lateral friction coefficient. We determined the CNOP-Ps optimized for each of these three parameters independently, and we optimized all three parameters simultaneously using the Spectral Projected Gradient 2 (SPG2) algorithm. Similarly, the impacts caused by errors in initial conditions were examined using the conditional nonlinear optimal initial perturbation (CNOP-I) method. Both the CNOP-I and CNOP-Ps can result in significant prediction errors of the KLM over a lead time of 240 days. But the prediction error caused by CNOP-I is greater than that caused by CNOP-P. The results of this study indicate not only that initial condition errors have greater effects on the prediction of the KLM than errors in model parameters but also that the latter cannot be ignored. Hence, to enhance the forecast skill of the KLM in this model, the initial conditions should first be improved, the model parameters should use the best possible estimates.

Transient growth of secondary instabilities in parallel wakes: Anti lift-up mechanism and hyperbolic instability

This paper investigates the three-dimensional temporal instabilities and the transient growth of perturbations on a Von Kármán vortex street, issuing from the development of the primary instability of a parallel Bickley velocity profile typical of a wake forming behind a thin flat plate. By solving iteratively the linearized direct Navier Stokes equations and its adjoint equations, we compute the optimal perturbations that exhibit the largest transient growth of energy between the initial instant and different time horizons. At short time horizons, optimal initial perturbations are concentrated on the points of maximal strain of the base flow. The optimal gain of energy and the mechanism of instability are well predicted by local theories that describe the lagrangian evolution of a perturbation wave packet. At time of order unity, hyperbolic region leads the dynamics. Only at large time (t ≥ 20), the growth is led by the most amplified eigenmode. This eigenmode evolves, when the wavenumber increases, from perturbation centred in the core of the vortices, to perturbations localised on the stretching manifold of the hyperbolic points. At finite and large time, the gain in energy is initially associated with a mechanism reminiscent to the anti lift-up mechanism described by Antkowiak and Brancher [J. Fluid Mech. 578, 295 (2007)] in the context of an axisymmetric vortex. Presently, the optimal initial condition (the adjoint modes at large time) corresponding to streamwise streaks localised on the contracting manifold of the hyperbolic point induces streamwise vortices aligned with the stretching manifold of the hyperbolic point (the direct modes). The localisation on distinct manifolds of direct and adjoint eigenmodes is more pronounced when the Reynolds number is increased. An interpretation is proposed based on a balance between diffusion and stretching effects that predicts the thickness of the energy containing region for the adjoint and the direct mode decreasing as 1/Re. The extra gain of energy due to non normal effects grows, since direct and adjoint modes are localised in different regions of space, i.e., the stretching and contracting manifold, a novel effect of the so called convective non normality associated with the transport of the perturbation by the base flow.

Assessing non-normal effects in thermoacoustic systems with mean flow

In this paper, non-normal interactions in a thermoacoustic system are studied, using a low-order expansion of the state variables in terms of eigenmodes. The thermoacoustic eigenmodes are determined as solutions of the Helmholtz equation or the linearized Euler equations, respectively, in the presence of a time-lagged heat source. Subsequently, non-normal effects are evaluated in a post-processing analysis based on the computed eigenmodes. In the case where the eigenmode analysis is based on the linearized Euler equations, effects of a non-zero mean flow velocity can be taken into account. The energy associated with the eigenmodes may then contain contributions of convected entropy and vorticity modes as well as the acoustic field. The notion of transient growth of perturbation energy is thus extended from an expression based on the classical acoustic energy density to a form based on a generalized disturbance energy. The expansion in terms of eigenmodes is computationally efficient, making the approach potentially applicable to complex, 3D configurations including non-trivial boundary conditions and spatio-temporal distributions of heat release fluctuations. In the present paper, the method is applied to a 1D configuration that consists of a duct including a 1D heat source, followed by a choked isentropic nozzle. It is shown that for such a case, it is essential to include the contribution of entropy perturbations in the calculation of the optimal initial perturbation and the maximum transient energy growth. Subsequently, the impact of increasing mean flow Mach number and increasing strength of flame/acoustic interaction on non normal effects is assessed in a parameter study.

Empirical singular vector method for ensemble El Niño–Southern Oscillation prediction with a coupled general circulation model

[1] Optimal initial perturbation is an important issue related to the improvement of the current seasonal climate prediction. In this study, we have applied the empirical singular vector method to ensemble El Niño–Southern Oscillation (ENSO) prediction with the Seoul National University coupled general circulation model. It is found that from the empirical linear operator, the leading singular mode, which represents the fast growing error mode in the tropical Pacific, shows El Niño–like perturbation in the present coupled model. When the singular vector is used as an initial perturbation, the forecast skill of ENSO is significantly improved. Further, it is demonstrated that the predictions with the singular vector have a more reliable ensemble spread, suggesting a potential merit for a probabilistic forecast.

Ensemble Construction and Verification of the Probabilistic ENSO Prediction in the LDEO5 Model

Abstract El Niño–Southern Oscillation (ENSO) retrospective ensemble-based probabilistic predictions were performed for the period of 1856–2003 using the Lamont-Doherty Earth Observatory, version 5 (LDEO5), model. To obtain more reliable and skillful ENSO probabilistic predictions, first, four ensemble construction strategies were investigated: (i) the optimal initial perturbation with singular vector of sea surface temperature anomaly (SSTA), (ii) the realistic high-frequency anomalous winds, (iii) the stochastic optimal pattern of anomalous winds, and (iv) a combination of the first and the third strategy. Second, verifications were conducted to examine the reliability and resolution of the probabilistic forecasts provided by the four methods. Results suggest that reliability of ENSO probabilistic forecast is more sensitive to the choice of ensemble construction strategy than the resolution, and a reliable and skillful ENSO probabilistic prediction system may not necessarily have the best deterministic prediction skills. Among these ensemble construction methods, the fourth strategy produces the most reliable and skillful ENSO probabilistic prediction, benefiting from the joint contributions of the stochastic optimal winds and the singular vector of SSTA. In particular, the stochastic optimal winds play an important role in improving the ENSO probabilistic predictability for the LDEO5 model.

Optimal wave packets in a boundary layer and initial phases of a turbulent spot

The three-dimensional global optimal dynamics of a flat-plate boundary layer is studied by means of an adjoint-based optimization in a spatial domain of long – but finite – streamwise dimension. The localized optimal initial perturbation is characterized by a pair of streamwise-modulated counter-rotating vortices, tilted upstream, yielding at the optimal time elongated streaks of alternating sign in the streamwise direction. This indicates that perturbations with non-zero streamwise wavenumber have a role in the transient dynamics of a boundary layer. A scaling law is provided, describing the variation of the streamwise modulation of the optimal initial perturbation with respect to the streamwise domain length and to the Reynolds number. For spanwise-extended domains, a near-optimal three-dimensional perturbation is extracted during the optimization process; it is localized also in the spanwise direction, resulting in a wave packet of elongated disturbances modulated in the spanwise and streamwise directions. The nonlinear evolution of the optimal and near-optimal perturbations is investigated by means of direct numerical simulations. Both perturbations are found to induce transition at lower levels of the initial energy than local optimal and suboptimal perturbations. Moreover, it is observed that transition occurs in a well-defined region of the convected wave packet, close to its centre, via a mechanism including at the same time oscillations of the streaks of both quasi-sinuous and quasi-varicose nature. Hairpin vortices are observed before transition; they have an active role in the breakdown of the streaks and result in a turbulent spot which spreads out in the boundary layer.

Excitation of SST anomalies in the eastern equatorial Pacific by oceanic optimal perturbations

A generalized stability analysis is used to explore the excitation of sea-surface temperature anoma- lies in the eastern equatorial Pacific by optimal initial perturbations in temperature and salinity within an ocean general circulation model. We find perturbations that can efficiently modify the SST of the Nino3 region with an approximately 9-month delay. The time interval between the end of March and mid-April is particularly favorable for these perturbations to cause subsequent changes in the eastern equatorial Pacific. This sensitivity is related to two critical factors: during the boreal spring Equinox the heat content of the western equatorial Pacific reaches its seasonal maximum, whereas the zonal winds along the equator relax. The optimal initial anomalies in temperature and salinity have a complex spatial structure extending between 20?S and 20?N. This large meridional extent of the anomalies allows for a strong focus- ing effect - signals from different locations reach the eastern equatorial Pacific simultaneously thus generating a strong transient warming in a relatively small region. Ocean adjustment to the optimal perturbations involves a basin-size Rossby wave that propagates westward and induces a large-scale anomalous eastward advection along the equator, which acts on the mean east-west temperature gra- dient and gradually warms SST in the east. At the same time, a continuum of Kelvin waves are being excited, which reduce the thermocline slope along the equator and deepen the thermocline in the east- ern equatorial Pacific. Thus, the Rossby wave and Kelvin waves work constructively to generate the transient warming of the Nino3 SST. An idealized model with two variables is formulated to illustrate these ideas and, in particular, show the importance of zonal advection feedback for the amplitude and duration of the transient warming. Ultimately, this study highlights the importance of non-normal dynamics for generating an efficient transient growth of SST anomalies in the tropical Pacific even in the absence of coupled ocean-atmosphere interactions.

The Role of Ocean Dynamics in the Optimal Growth of Tropical SST Anomalies

AbstractThe role of ocean dynamics in optimally exciting interannual variability of tropical sea surface temperature (SST) anomalies is investigated using an idealized-geometry ocean general circulation model. Initial temperature and salinity perturbations leading to an optimal growth of tropical SST anomalies, typically arising from the nonnormal dynamics, are evaluated. The structure of the optimal perturbations is characterized by relatively strong deep salinity anomalies near the western boundary generating a transient amplification of equatorial SST anomalies in less than four years.The associated growth mechanism is linked to the excitation of coastal and equatorial Kelvin waves near the western boundary following a rapid geostrophic adjustment owing to the optimal initial temperature and salinity perturbations. The results suggest that the nonnormality of the ocean dynamics may efficiently create large tropical SST variability on interannual time scales in the Atlantic without the participation of air–sea processes or the meridional overturning circulation. An optimal deep initial salinity perturbation of 0.1 ppt located near the western boundary can result in a tropical SST anomaly of approximately 0.45°C after nearly four years, assuming the dynamics are linear. Possible mechanisms for exciting such deep perturbations are discussed. While this study is motivated by tropical Atlantic SST variability, its relevance to other basins is not excluded.The optimal initial conditions leading to the tropical SST anomalies’ growth are obtained by solving a generalized eigenvalue problem. The evaluation of the optimals is achieved by using the Massachusetts Institute of Technology general circulation model (MITgcm) tangent linear and adjoint models as well the the Arnoldi Package (ARPACK) software for solving large-scale eigenvalue problems.

An extension of conditional nonlinear optimal perturbation approach and its applications

Abstract. The approach of conditional nonlinear optimal perturbation (CNOP) was previously proposed to find the optimal initial perturbation (CNOP-I) in a given constraint. In this paper, we extend the CNOP approach to search for the optimal combined mode of initial perturbations and model parameter perturbations. This optimal combined mode, also named CNOP, has two special cases: one is CNOP-I that only links with initial perturbations and has the largest nonlinear evolution at a prediction time; while the other is merely related to the parameter perturbations and is called CNOP-P, which causes the largest departure from a given reference state at a prediction time. The CNOP approach allows us to explore not only the first kind of predictability related to initial errors, but also the second kind of predictability associated with model parameter errors, moreover, the predictability problems of the coexistence of initial errors and parameter errors. With the CNOP approach, we study the ENSO predictability by a theoretical ENSO model. The results demonstrate that the prediction errors caused by the CNOP errors are only slightly larger than those yielded by the CNOP-I errors and then the model parameter errors may play a minor role in producing significant uncertainties for ENSO predictions. Thus, it is clear that the CNOP errors and their resultant prediction errors illustrate the combined effect on predictability of initial errors and model parameter errors and can be used to explore the relative importance of initial errors and parameter errors in yielding considerable prediction errors, which helps identify the dominant source of the errors that cause prediction uncertainties. It is finally expected that more realistic models will be adopted to investigate this use of CNOP.

Nonnormal Frontal Dynamics

Abstract The generalized stability of the secondary atmospheric circulation over strong SST fronts is studied using a hydrostatic, Boussinesq, two-dimensional f-plane model. It is shown that even in a parameter regime in which these circulations are stable to small perturbations, significant nonnormal growth of optimal initial perturbations occurs. The maximum growth factor in perturbation total energy is 250 and is dominated by the potential energy, which obtains a growth factor of 219 two to five hours after the beginning of the integration. This domination of potential energy growth is consistent with the observation that the available potential energy (APE) of the secondary circulation is larger by two orders of magnitude than the kinetic energy as well as with the transfer of kinetic to potential perturbation energy at the beginning of the growth of the perturbations. The norm kernel is found to significantly influence the structure of the optimal initial perturbation as well as the energy obtained by the mature perturbations, but the physical mechanism of growth and the structure of the mature perturbations are robust.

An optimal experimental design approach to model discrimination in dynamic biochemical systems

Finding suitable models of dynamic biochemical systems is an important task in systems biology approaches to the biosciences. On the one hand, a correct model helps to understand the underlying mechanisms and on the other hand, one can use the model to predict the behavior of a biological system under various circumstances. Typically, before the correct model of a biochemical system is found, different hypothetical models might be reasonable and consistent with previous knowledge and available data. The main goal now is to find the best suited model out of different hypotheses. The process of falsifying inappropriate candidate models is called model discrimination. We have developed a new computational tool to compute optimal experiments for biochemical kinetic systems with underlying ordinary differential equation (ODE) models for the purpose of model discrimination. We were inspired by the demands of biological experimentalists which perform one run measurement where perturbations to the system are possible. We provide a criterion which calculates the number and location of time points of optimal measurements as well as optimal initial conditions and optimal perturbations to the system. The model discrimination algorithm described here is implemented in C++ in the package ModelDiscriminationToolkit. The source code can be downloaded from http://omnibus.unifreiburg.de/~ds500/_software.html.