Uncertainty Quantification Approach Research Articles

Efficient Bilevel Surrogate Approach for Optimization Under Uncertainty of Shock Control Bumps

The assessment of uncertainties is essential in aerodynamic shape optimization problems to come up with configurations that are more robust against operational and geometrical uncertainties. However, exploring the stochastic design space significantly increases the computational cost. The aim of this paper is to develop a framework for efficient optimization under uncertainty by means of a bilevel surrogate approach and to apply it to the robust design of a retrofitted shock control bump over an airfoil. The framework combines a surrogate-based optimizer with an efficient surrogate-based approach for uncertainty quantification. The optimizer efficiently finds the global optimum of a given quantile of the quantity of interest through the combination of adaptive sampling and a moving trust region. At each iteration of the optimization, the surrogate-based uncertainty quantification uses an active infill criterion to accurately quantify the quantile requiring a reduced number of samples. Two different quantiles of the drag are chosen for the design of the shock control bump: the 95% to increase the robustness at off-design conditions, and the 50% for a configuration that is preferred for day–to-day operations. In both cases, the optimum bumps are more robust, compared to the one obtained through classical deterministic optimization.

Hierarchical approach for uncertainty quantification and reliability assessment of guided wave-based structural health monitoring

In this article, a hierarchical approach is proposed for the design and assessment of a guided wave-based structural health monitoring system for the detection and localisation of barely visible impact damage in composite airframe structures. The hierarchical approach provides a systemic and practical way to establish guided wave-based structural health monitoring systems for different structures in the presence of uncertainties and to quantify system performance. The proposed approach is carried out in four steps: (1) determine optimal sensor placement for the target structure and its plausible impact scenarios, (2) set detection threshold for global damage index based on the noise level present in the required environmental and operations conditions, (3) detect damage in critical locations and quantify detection performance by calculating the probability of detection, probability of false alarm and detection accuracy and (4) locate the detected damage while also quantifying the accuracy of location estimation and the probability of correctly indicating if the damage is in an area critical to the integrity of the structure. The proposed approach is demonstrated in aircraft carbon fibre-reinforced polymer structures from coupon level (simple flat panels) to sub-component level (large flat panel with multiple carbon fibre-reinforced polymer stringers and aluminium frames) for the detection and localisation of barely visible impact damage.

Efficient uncertainty quantification for permeability of three-dimensional porous media through image analysis and pore-scale simulations.

In this paper, we propose an efficient coupled approach for uncertainty quantification of permeability for randomly reconstructed three-dimensional (3D) pore images, where the porosity and two-point correlations of a realistic sandstone sample are honored. The Joshi-Quiblier-Adler approach and Karhunen-Loève expansion are utilized for quick reconstruction of 3D pore images with reduced random dimensionality. The eigenvalue problem for the covariance matrix of 3D intermediate Gaussian random fields is solved equivalently by a kernel method. Then, the lattice Boltzmann method is adopted to simulate fluid flow in reconstructed pore space and evaluate permeability. Lastly, the sparse polynomial chaos expansion (sparse PCE) integrated with a feature selection method is employed to predict permeability distributions incurred by the randomness in microscopic pore structures. The feature selection process, which is intended to discard redundant basis functions, is carried out by the least absolute shrinkage and selection operator-modified least angle regression along with cross validation. The competence of our proposed approach is validated by the results from Monte Carlo simulation. It reveals that a small number of samples is sufficient for sparse PCE with feature selection to produce convincing results. Then, we utilize our method to quantify the uncertainty of permeability under different porosities and correlation parameters. It is found that the predicted permeability distributions for reconstructed 3D pore images are close to experimental measurements of Berea sandstones in the literature. In addition, the results show that porosity and correlation length are the critical influence factors for the uncertainty of permeability.

Analysis of Turbulence Model Uncertainty for Shock-Wave/Boundary-Layer Interaction Simulations

The purpose of this paper is to present results of an uncertainty and sensitivity analysis study of commonly used turbulence models in Reynolds-averaged Navier–Stokes codes due to the epistemic uncertainty in closure coefficients for shock-wave/turbulent boundary-layer interaction simulations. The study focuses on the analysis of an axisymmetric shock-wave/boundary-layer interaction (ASWBLI) turbulence model validation case including an axisymmetric cylindrical body with a trailing-edge flare of 20 deg at an upstream Mach number of 7.11. The Spalart–Allmaras, the Wilcox 2006 , and the Menter shear-stress transport turbulence models are considered in the stochastic analyses of the ASWBLI, which used the FUN3D flow solver. The uncertainty quantification approach involves stochastic expansions based on nonintrusive polynomial chaos to efficiently propagate the uncertainty. Sensitivity analysis is performed with Sobol indices to rank the relative contribution of each closure coefficient to the total uncertainty for several output flow quantities. The results of the current study identify a set of closure coefficients that contribute most to the uncertainty in various output quantities of interest, which are also consistent with the similar shock-induced separation studies.

A hybrid approach combining DNS and RANS simulations to quantify uncertainties in turbulence modelling

Uncertainty quantification (UQ) has recently become an important part of the design process of countless engineering applications. However, up to now in computational fluid dynamics (CFD) the errors introduced by the turbulent viscosity models in Reynolds-Averaged Navier Stokes (RANS) models have often been neglected in UQ studies. Although Direct Numerical Simulations (DNS) are physically correct, obtaining a large enough set of DNS data for UQ studies is currently computationally intractable. UQ based only on RANS simulations or on DNS thus leads to physical and statistical inaccuracies in the output probability distribution functions (PDF). Therefore, three hybrid methods combining both RANS simulations and DNS to perform non-intrusive UQ are suggested in this work. Low-fidelity RANS simulations and high-fidelity DNS are combined to give an approximation of an output PDF using the advantages of both data sets: the physical accuracy via the DNS and the statistical accuracy via the RANS simulations. The hybrid methods are applied to the flow over 2D periodically arranged hills. It is shown that the Gaussian CoKriging (GCK) method is the best hybrid method and that a non-intrusive hybrid UQ approach combining both DNS and RANS simulations is possible, with both physically more accurate and statistically better PDF.

Data-driven uncertainty quantification for systematic coarse-grained models

ABSTRACT In this work, we present methodologies for the quantification of confidence in bottom-up coarse-grained models for molecular and macromolecular systems. Coarse-graining methods have been extensively used in the past decades in order to extend the length and time scales accessible by simulation methodologies. The quantification, though, of induced errors due to the limited availability of fine-grained data is not yet established. Here, we employ rigorous statistical methods to deduce guarantees for the optimal coarse models obtained via approximations of the multi-body potential of mean force, with the relative entropy, the relative entropy rate minimization, and the force-matching methods. Specifically, we present and apply statistical approaches, such as bootstrap and jackknife, to infer confidence sets for a limited number of samples, i.e., molecular configurations. Moreover, we estimate asymptotic confidence intervals assuming adequate sampling of the phase space. We demonstrate the need for non-asymptotic methods and quantify confidence sets through two applications. The first is a two-scale fast/slow diffusion process projected on the slow process. With this benchmark example, we establish the methodology for both independent and time-series data. Second, we apply these uncertainty quantification approaches on a polymeric bulk system. We consider an atomistic polyethylene melt as the prototype system for developing coarse-graining tools for macromolecular systems. For this system, we estimate the coarse-grained force field and present confidence levels with respect to the number of available microscopic data.

Efficient Quantification of the Impact of Demand and Weather Uncertainty in Power System Models

This paper introduces a new approach to quantify the impact of forward propagated demand and weather uncertainty on power system planning and operation models. Recent studies indicate that such sampling uncertainty, originating from demand and weather time series inputs, should not be ignored. However, established uncertainty quantification approaches fail in this context due to the data and computing resources required for standard Monte Carlo analysis with disjoint samples. The method introduced here uses an m out of n bootstrap with shorter time series than the original, enhancing computational efficiency and avoiding the need for any additional data. It both quantifies output uncertainty and determines the sample length required for desired confidence levels. Simulations and validation exercises are performed on two capacity expansion planning models and one unit commitment and economic dispatch model. A diagnostic for the validity of estimated uncertainty bounds is discussed. The models, data and code are made available.

Uncertainty Quantification Approach on Numerical Simulation for Supersonic Jets Performance

One of the main issues addressed in any engineering design problem is to predict the performance of the component or system as accurately and realistically as possible, taking into account the variability of operating conditions or the uncertainty on input data (boundary conditions or geometry tolerance). In this paper, the propagation of uncertainty on boundary conditions through a numerical model of supersonic nozzle is investigated. The evaluation of the statistics of the problem response functions is performed following ‘Surrogate-Based Uncertainty Quantification’. The approach involves: (a) the generation of a response surface starting from a DoE in order to approximate the convergent–divergent ‘physical’ model (expensive to simulate), (b) the application of the UQ technique based on the LHS to the meta-model. Probability Density Functions are introduced for the inlet boundary conditions in order to quantify their effects on the output nozzle performance. The physical problem considered is very relevant for the experimental tests on the UQ approach because of its high non-linearity. A small perturbation to the input data can drive the solution to a completely different output condition. The CFD simulations and the Uncertainty Quantification were performed by coupling the open source Dakota platform with the ANSYS Fluent® CFD commercial software: the process is automated through scripting. The procedure adopted in this work demonstrate the applicability of advanced simulation techniques (such as UQ analysis) to industrial technical problems. Moreover, the analysis highlights the practical use of the uncertainty quantification techniques in predicting the performance of a nozzle design affected by off-design conditions with fluid-dynamic complexity due to strong nonlinearity.

Blending measurements and numerical models: a novel methodological approach for land subsidence prediction with uncertainty quantification

Abstract. The use of numerical models for land subsidence prediction above producing hydrocarbon reservoirs has become a common and well-established practice since the early '90s. Usually, uncertainties in the deep rock behavior, which can affect the forecast capability of the models, have been taken into account by running multiple simulations with different constitutive laws and mechanical properties. Then, the most uncertain parameters were calibrated to reproduce available subsidence measurements. The objective of this work is to propose a novel methodological approach for land subsidence prediction and uncertainty quantification by integrating the available monitoring information in numerical models using ad hoc Data Assimilation techniques. The proposed approach allows to: (i) train the model with the available data and improve its accuracy as new information comes in, (ii) quantify the prediction uncertainty by providing confidence intervals and probability measures instead of deterministic outcomes, and (iii) identify the most appropriate rock constitutive model and geomechanical parameters. The methodology is tested in synthetic models of production from hydrocarbon reservoirs. The numerical experiments show that the proposed approach is a promising way to improve the effectiveness and reliability of land subsidence models.

Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics

Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. We propose an efficient uncertainty quantification framework utilizing a multilevel multifidelity Monte Carlo (MLMF) estimator to improve the accuracy of hemodynamic quantities of interest while maintaining reasonable computational cost. This is achieved by leveraging three cardiovascular model fidelities, each with varying spatial resolution to rigorously quantify the variability in hemodynamic outputs. We employ two low-fidelity models (zero- and one-dimensional) to construct several different estimators. Our goal is to investigate and compare the efficiency of estimators built from combinations of these two low-fidelity model alternatives and our high-fidelity three-dimensional models. We demonstrate this framework on healthy and diseased models of aortic and coronary anatomy, including uncertainties in material property and boundary condition parameters. Our goal is to demonstrate that for this application it is possible to accelerate the convergence of the estimators by utilizing a MLMF paradigm. Therefore, we compare our approach to single fidelity Monte Carlo estimators and to a multilevel Monte Carlo approach based only on three-dimensional simulations, but leveraging multiple spatial resolutions. We demonstrate significant, on the order of 10 to 100 times, reduction in total computational cost with the MLMF estimators. We also examine the differing properties of the MLMF estimators in healthy versus diseased models, as well as global versus local quantities of interest. As expected, global quantities such as outlet pressure and flow show larger reductions than local quantities, such as those relating to wall shear stress, as the latter rely more heavily on the highest fidelity model evaluations. Similarly, healthy models show larger reductions than diseased models. In all cases, our workflow coupling Dakota’s MLMF estimators with the SimVascular cardiovascular modeling framework makes uncertainty quantification feasible for constrained computational budgets.

Evaluation of ensemble methods for quantifying uncertainties in steady-state CFD applications with small ensemble sizes

Bayesian uncertainty quantification (UQ) is of interest to industry and academia as it provides a framework for quantifying and reducing the uncertainty in computational models by incorporating available data. For systems with very high computational costs, for instance, the computational fluid dynamics (CFD) problem, the conventional, exact Bayesian approach such as Markov chain Monte Carlo is intractable. To this end, the ensemble-based Bayesian methods have been used for CFD applications. However, their applicability for UQ has not been fully analyzed and understood thus far. Here, we evaluate the performance of three widely used iterative ensemble-based data assimilation methods, namely ensemble Kalman filter, ensemble randomized maximum likelihood method, and ensemble Kalman filter with multiple data assimilation for UQ problems. We present the derivations of the three ensemble methods from an optimization viewpoint. Further, a scalar case is used to demonstrate the performance of the three different approaches with emphasis on the effects of small ensemble sizes. Finally, we assess the three ensemble methods for quantifying uncertainties in steady-state CFD problems involving turbulent mean flows. Specifically, the Reynolds averaged Navier–Stokes (RANS) equation is considered the forward model, and the uncertainties in the propagated velocity are quantified and reduced by incorporating observation data. The results show that the ensemble methods cannot accurately capture the true posterior distribution, but they can provide a good estimation of the uncertainties even when very limited ensemble sizes are used. Based on the overall performance and efficiency from the comparison, the ensemble randomized maximum likelihood method is identified as the best choice of approximate Bayesian UQ approach among the three ensemble methods evaluated here.

Advanced Studies and Statistical Treatment for Sodium-Cooled Fast Reactor Pin Failures During Unprotected Transient Overpower Accident

Usually, simulation tools are validated based on experimental data considering a best estimate simulation case; however, there is no quantification of this validation, which remains based on rough expert judgment. This technical note presents advanced validation treatment of the simulation tool OCARINa devoted to unprotected transient overpower (UTOP) accidents on two CABRI tests considering this time a Best Estimate Plus Uncertainty (BEPU) approach. The output results of interest are both scalar physical data such as the time and location of the pin failure and associated molten mass and vector data such as temperature axial distribution or temperature evolution versus time. This approach is a first step in quantifying the degree of agreement between the calculation results and the experimental results. It is of great interest for the verification, validation, and uncertainty quantification approach, which leads to the qualification of scientific calculation tools. Within the framework of the Generation IV Sodium-cooled Fast Reactor (SFR) research and development project in which the CEA is involved, OCARINa is a physical tool, relevant for performing preconceptual design studies and devoted to simulation of UTOP accidents on heterogeneous cores. Such accidents could not be simulated with mechanistic calculation tools such as SAS4A or SIMMER with their current capabilities; the thermomechanical models are not finalized in the SIMMER tool, and the SAS4A tool is validated only for homogeneous cores. The final objective aims at deriving the variability of the main results of interest to quantify the safety margins. The final use of the OCARINa tool being to perform sensitivity studies on the various possible sodium fast nuclear preconceptual core designs, the validation of this tool is first discussed at the pin scale (where separate-effects test measurements are available) based on statistical treatment. This enables one to determine the lacks and uncertainties of this tool. The modeling is then extended from local pin behavior to global core behavior adding a point-kinetics neutronic model. Final simulations of UTOP accidents caused by a uniform space reactivity ramp on an SFR core are realized taking into account the specificities of the pins of the various assemblies. The orders of magnitude of mechanical energy released are derived.

Uncertainty Quantification in Mooring Cable Dynamics Using Polynomial Chaos Expansions

Mooring systems exhibit high failure rates. This is especially problematic for offshore renewable energy systems, like wave and floating wind, where the mooring system can be an active component and the redundancy in the design must be kept low. Here we investigate how uncertainty in input parameters propagates through the mooring system and affects the design and dynamic response of mooring and floaters. The method used is a nonintrusive surrogate based uncertainty quantification (UQ) approach based on generalized Polynomial Chaos (gPC). We investigate the importance of the added mass, tangential drag, and normal drag coefficient of a catenary mooring cable on the peak tension in the cable. It is found that the normal drag coefficient has the greatest influence. However, the uncertainty in the coefficients plays a minor role for snap loads. Using the same methodology we analyze how deviations in anchor placement impact the dynamics of a floating axi-symmetric point-absorber. It is shown that heave and pitch are largely unaffected but surge and cable tension can be significantly altered. Our results are important towards streamlining the analysis and design of floating structures. Improving the analysis to take into account uncertainties is especially relevant for offshore renewable energy systems where the mooring system is a considerable portion of the investment.

Arbitrary polynomial chaos expansion method for uncertainty quantification and global sensitivity analysis in structural dynamics

Uncertainty quantification (UQ) and global sensitivity analysis (GSA) of dynamic characteristics of complex systems subjected to uncertainty are jointly investigated in this paper. An efficient approach based on arbitrary polynomial chaos expansion (aPCE) is presented for analytical, unified implementation of UQ and GSA in structural dynamics. For UQ of dynamic characteristics, statistical moments and probability distributions of dynamic characteristics are analytically derived. Specifically, the aPCE is used to analytically calculate the statistical moments, and then the maximum entropy principle (MEP) is adopted to derive the closed-form expressions of the probability distributions using the obtained statistical moments. As an extension of UQ, GSA, which aims to assess the quantitative contributions of different structural parameters to the resultant variations of dynamic characteristics, is also analytically achieved by simply post-processing the aPCE coefficients. The present aPCE UQ and GSA method is highly computationally efficient for large-scale, complex structures, and it is also generally applicable independent of parameter distributions. The proposed aPCE-based approach for UQ and GSA is validated through a numerical truss bridge by the brute-force Monte Carlo simulation (MCS), and then is applied to a long-span steel arch bridge.

Model‐based hypothesis testing of uncertain software systems

SummaryNowadays, there exists an increasing demand for reliable software systems able to fulfill their requirements in different operational environments and to cope with uncertainty that can be introduced both at design‐time and at runtime because of the lack of control over third‐party system components and complex interactions among software, hardware infrastructures and physical phenomena. This article addresses the problem of the discrepancy between measured data at runtime and the design‐time formal specification by using aninverse uncertainty quantificationapproach. Namely, we introduce a methodology calledMETRICand its supporting toolchain to quantify and mitigate software system uncertainty during testing by combining (on‐the‐fly)model‐based testingandBayesian inference. Our approach connects probabilistic input/output conformance theory with statistical hypothesis testing in order to assess if the behaviour of the system under test corresponds to its probabilistic formal specification provided in terms of aMarkov decision process. An uncertainty‐aware model‐based test case generation strategy is used as a means to collect evidence from software components affected by sources of uncertainty. Test results serve as input to a Bayesian inference process that updates beliefs on model parameters encoding uncertain quality attributes of the system under test. This article describes our approach from both theoretical and practical perspectives. An extensive empirical evaluation activity has been conducted in order to assess the cost‐effectiveness of our approach. We show that, under same effort constraints, our uncertainty‐aware testing strategy increases the accuracy of the uncertainty quantification process up to 50 times with respect to traditional model‐based testing methods.

Resolution-based spectral clustering for brain parcellation using functional MRI

BackgroundBrain parcellation is important for exploiting neuroimaging data. Variability in physiology between individuals has led to the need for data-driven approaches to parcellation, with recent research focusing on simultaneously estimating and partitioning the network structure of the brain. New methodWe view data preprocessing, parcellation, and parcel validation from the perspective of predictive modeling. The goal is to identify parcels in a way that best generalizes to unseen data. We utilize an uncertainty quantification approach from image science to define parcels as groups of unresolvable variables in the predictive model. Model parameters are chosen via cross-validation. Parcellation results are compared based on both their repeatability as well as their ability to describe held-out data. ResultsThe approach provides insight and strategies for open questions such as the choice of evaluation metrics, selection of model order, and the optimal tuning of preprocessing steps for functional imaging data. Comparison with existing methodsWe compare new and established approaches using functional imaging data, where we find the proposed approach produces parcellations which are both more accurate and more repeatable than the current baseline clustering method. The metrics also demonstrate potential problems with overfitting for the baseline method, and with bias for other methods. ConclusionsClustering of resolution provides a principled and robust approach to brain parcellation which improves on the current baseline.

DeepPIPE: A distribution-free uncertainty quantification approach for time series forecasting

Time series forecasting is a challenging task as the underlying data generating process is dynamic, nonlinear, and uncertain. Deep learning such as LSTM and auto-encoder can learn representations automatically and has attracted considerable attention in time series forecasting. However, current approaches mainly focus on point estimation, which leads to the inability to quantify uncertainty. Meantime, existing deep uncertainty quantification methods suffer from various limitations in practice. To this end, this paper presents a novel end-to-end framework called deep prediction interval and point estimation (DeepPIPE) that simultaneously performs multi-step point estimation and uncertainty quantification for time series forecasting. The merits of this approach are threefold: first, it requires no prior assumption on the distribution of data noise; second, it utilizes a novel hybrid loss function that improves the accuracy and stability of forecasting; third, it is only optimized by back-propagation algorithm, which is time friendly and easy to be implemented. Experimental results demonstrate that the proposed approach achieves state-of-the-art performance on three real-world datasets.

Multifidelity Uncertainty Quantification of a Commercial Supersonic Transport

The objective of this work was to develop a multifidelity uncertainty quantification approach for efficient analysis of a commercial supersonic transport concept. An approach based on point-collocation, nonintrusive polynomial chaos was formulated in which a low-fidelity model could be corrected using multiple higher-fidelity models. The formulation and methodology also allows for the addition of uncertainty sources not present in the lower-fidelity models. To demonstrate the applicability and potential computational savings of the multifidelity polynomial chaos approach, two model problems were explored. The first was a supersonic airfoil with three levels of modeling fidelity, each capturing a gradual increase in modeling of the underlying flow physics. As much as 50% computational cost reduction was observed using the multifidelity approach, while predicting nearly the same amount of uncertainty in drag. The second problem was a commercial supersonic transport. This model had three levels of fidelity that included two different modeling approaches and the addition of physics between the fidelity levels. Results of this analysis yielded nearly a 70% computational savings to predict a comparable amount of uncertainty in ground noise. Both problems illustrate the applicability and significant computational savings of the multifidelity method for efficient and accurate uncertainty quantification.

Tissue-Type Classification With Uncertainty Quantification of Microwave and Ultrasound Breast Imaging: A Deep Learning Approach

A deep learning approach is proposed for performing tissue-type classification of tomographic microwave and ultrasound property images of the breast. The approach is based on a convolutional neural network (CNN) utilizing the U-net architecture that also quantifies the uncertainty in the classification of each pixel. Quantitative tomographic reconstructions of dielectric properties (complex-valued permittivity), ultrasonic properties (compressibility and attenuation), as well as their combination, with the corresponding actual tissue-type classification constitute the training set. The CNN learns to map the quantitative property reconstructions to a single tissue-type image. The level of confidence in predicting a tissue-type at each pixel is determined. This uncertainty quantification is diagnostically critical for biomedical applications, especially when attempting to distinguish between cancerous and healthy tissues. The Gauss-Newton Inversion algorithm is used for the quantitative reconstruction of both dielectric and ultrasonic properties. Electromagnetic and ultrasound scattered-field data is obtained from MRI-derived numerical breast phantoms. Several numerical breast phantoms types, from fatty to dense, are considered. The proposed classification and uncertainty quantification approach is shown to outperform a previously studied tissue-type classification method based on a Bayesian approach.

Comparison of intrusive and nonintrusive polynomial chaos expansion-based approaches for high dimensional parametric uncertainty quantification and propagation

We present an uncertainty quantification (UQ) algorithm using the intrusive generalized polynomial chaos (gPC) expansion in combination with dimension reduction techniques and compare the UQ accuracy and computational efficiency of the intrusive gPC-based UQ algorithm to other sampling-based nonintrusive methods. The successful application of intrusive gPC-based UQ is associated with the stochastic Galerkin (SG) projection, which yields a family of models described by several coupled equations of gPC coefficients. Using these coefficients, the evolution of uncertainty in a dynamic system can be quickly determined when there is probabilistic uncertainty in the system. While elegant, when dealing with models that involve complex functions (e.g., nonpolynomial terms) and larger numbers of uncertainties, SG projection becomes computationally intractable and cannot be applied directly to solve gPC coefficients in real-time. To address this issue, the generalized dimension reduction method (gDRM) is used to convert a high-dimensional integral involved in the SG projection into several lower-dimensional integrals that can be easily solved. To show the accuracy of UQ, the algorithm in this work is compared to sampling-based approaches such as the nonintrusive stochastic collocation (SC) and Monte Carlo (MC) simulations using three cases: a nonlinear algebraic benchmark, a penicillin manufacturing process, and autocrine signalling networks of living cells.