Nonlinear Search Algorithm Research Articles

A simple weighting method for inverting earthquake source parameters using geodetic multisource data under Bayesian algorithm

SUMMARY More accurate inversion of source fault geometry and slip parameters under the constraint of the Bayesian algorithm has become a research hotspot in the field of geodetic inversion in recent years. In nonlinear inversion, the determination of the weight ratio of the joint inversion of multisource data is more complicated. In this context, this paper proposes a simple and easily generalized weighting method for inversion of source fault parameters by joint geodetic multisource data under the Bayesian framework. This method determines the relative weight ratio of multisource data by root mean square error (RMSE) value and can be extended to other nonlinear search algorithms. To verify the validity of the method in this paper, this paper first sets up four sets of simulated seismic experiment schemes. The inversion results show that the joint inversion weighting method proposed in this paper has a significant decrease in the large residual value compared with the equal weight joint inversion and the single data source joint inversion method. The east–west deformation RMSE is 0.1458 mm, the north–south deformation RMSE is 0.2119 mm and the vertical deformation RMSE is 0.2756 mm. The RMSEs of the three directions are lower than those of other schemes, indicating that the proposed method is suitable for the joint inversion of source parameters under Bayesian algorithm. To further verify the applicability of the proposed method in complex earthquakes, the source parameters of the Maduo earthquake were inverted using the method of this paper. The focal depth of the inversion results in this paper is closer to the focal depth released by the GCMT agency. In terms of strike angle and dip angle, the joint inversion in this paper is also more inclined to the GCMT results. The joint inversion results generally conform to the characteristics of left-lateral strike-slip, which shows the adaptability of this method in complex earthquakes.

Multistart Nelder–Mead Neural Network Algorithm for Earthquake Source Parameter Inversion of 2017 Bodrum–Kos Earthquake

AbstractA multistart Nelder–Mead neural network algorithm (multi NM-NNA) is presented, the purpose of which is to solve the problem that the existing nonlinear search algorithms are unstable when i...

Noisy Effect on Nonlinear Quantum Search Algorithm

AbstractIn this paper, we investigate the effects of three single‐qubit quantum noise channels on the quantum nonlinear search algorithm proposed by Abrams and Lloyd. We focus on the gates of the nonlinear part of the algorithm and consider the case where the quantum noise channel only affects the qubit on which the gate is proceeding. Assuming that quantum noise effects occur after using the gates of the nonlinear part of the algorithm, we find that the quantum nonlinear search algorithm appears to be very resilient to the quantum noise when the desired state does not exist in the first register and is subject to the phase damping channel or the depolarising channel.

Section-Based Approach Optimizes Unconventional-Reservoir-Fracture Spacing

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 186107, “Optimization of Spacing and Penetration Ratio for Infinite-Conductivity Fractures in Unconventional Reservoirs: A Section-Based Approach,” by S. Liu, SPE, and P.P. Valko, SPE, Texas A&M University. The paper has been peer reviewed and published in the December 2017 SPE Journal. In this paper, the authors consider the development plan of shale gas or tight oil with multiple multistage fractured laterals in a large square drainage area that they call a “section” (usually 640 acres in the US). A section-based optimization of the fracture array is proposed to provide some general statements regarding spacing of wells and fractures. The approach is dependent on a reliable and efficient productivity-index (PI) calculation for the boundary-dominated state (BDS). The information derived from the section-based optimization method and the efficient and reliable algorithm for PI calculation should help the design of multistage fracturing in shale-gas or ultralow-permeability oil formations. Introduction During the last decade, multiple studies have been conducted on various aspects of fracture design. Most of these use a numerical simulation that requires a large number of inputs, which, at the early stages of development, may be in-accessible or burdened by substantial uncertainty. Many of these works use quite sophisticated nonlinear search algorithms. In this work, however, only that part of the problem that can be addressed in rather general terms is considered. Therefore, simplifying assumptions are made to a point at which numerical results can be delivered. The results will provide some insight and useful bounds on achievable productivity. The methodology is dependent on an accurate numerical solution of a well-defined eigenvalue problem and, as such, can provide reference values for various research fields relying heavily on the diffusivity equation. In the complete paper, a method that combines the finite-element method (FEM) with Richardson extrapolation is introduced to calculate the single-fracture PI both for constant-pressure and constant-rate wellbore conditions. Then, with the reliable PI for a single fracture, a convenient section-based optimization is conducted involving only two integer decision variables: the number of columns and the number of rows of the fracture array. Because the constant-pressure wellbore condition is more realistic, the overall PI of the section in the BDS flow regime is considered as the objective function. Two parameters are suggested as the main decisive factors: the dimensionless total fracture length and the feasible range of fracture half-length. In the present approach, the actual optimization takes a simple form of enumeration of a limited number of discrete cases; therefore, advanced nonlinear search algorithms are not involved. Those algorithms become irreplaceable when petrophysical and economic details are incorporated and the structure of the objective function loses its transparent nature, but such situations are beyond the focus of the present work.

A Riemannian Model to Orthonormalized Partial Least Squares

One of the most common ways used to ensure the smooth operation of projects in multivariate analysis (MVA) is the use of developed metrics in Euclidean spaces, which are approximations, generally coarse, in non-Euclidean spaces. Metrics in non-Euclidean spaces implies the need to make calculations on curved surfaces studied in differential geometry. In thus paper it is proposed a Riemannian model to orthonormalized partial least squares (OPLS). Results using generalized Stiefel manifold as well a nonlinear search algorithm are developed.

Design of a barcode-like waveguide nanostructure for efficient chip–fiber coupling

A barcode-like waveguide nanostructure with discretized multilevel pixel lines is designed and optimized by a nonlinear search algorithm. We obtain the design of a one-dimensional multilevel nanostructure with −1.04 dB efficiency for surface normal coupling to a standard single-mode fiber. Another design is achieved from the automatic optimization process, which enables polarization-independent coupling to a single-mode fiber. The optimum coupling efficiency is simulated to be −2.83 dB for TE and −3.49 for TM polarization centered near the 1550 nm wavelength. Polarization-dependent loss of less than 1 dB over 45.3 nm is achieved.

Concise quantum associative memories with nonlinear search algorithm

The model of quantum associative memories (QAM) we propose here consists in simplifying and generalizing that of Rigui Zhou \etal \cite{zhou2012} who uses the quantum matrix with binary decision diagram and nonlinear search algorithm in his model. It is worth noting that David Rosenbaum put forth the quantum matrix with binary decision diagram \cite{Rosenbaum2010} and Abrams and Llyod did the nonlinear algorithm. \cite{Abrams1998} Our model gives the possibility to retrieve one of the sought states in multi-values retrieving scheme when a measure on the first register is done. It is better than Grover's algorithm and its modified form which need $\mathcal{O}(\sqrt{\frac{2^n} {m}})$ steps when they are used as the retrieval algorithm. $n$ is the number of qubit of the first register and $m$ the number of values $x$ for which $f(x)=1$. As the nonlinearity makes the system highly susceptible to noise, an analysis of the influence of the single qubit noise channels on the Nonlinear Search Algorithm of our model of QAM, shows a fidelity of about $0.7$ whatever the number of qubits present in the first register.

An Integrated Approach Based on Principal Component and Multivariate Process Capability for Simultaneous Optimization of Location and Dispersion for Correlated Multiple Response Problems

ABSTRACT Product quality is generally defined by a family of critical characteristics, or so-called responses. In this article, a new integrated approach is proposed that has the ability to reduce the response space dimensionality and also considers both location and dispersion effects in a correlated multiple response optimization problem. The proposed approach uses a principal component (PC)-based multivariate process capability index (MCpmk;PC) as an objective function for optimization. In addition, the nonlinear search algorithm can efficiently determine the best trade-off solution in the orthogonal PC space. Three different cases are selected to illustrate the effectiveness of the new proposed approach compared to a few selected existing approaches.

Quantum Associative Neural Network with Nonlinear Search Algorithm

Based on analysis on properties of quantum linear superposition, to overcome the complexity of existing quantum associative memory which was proposed by Ventura, a new storage method for multiply patterns is proposed in this paper by constructing the quantum array with the binary decision diagrams. Also, the adoption of the nonlinear search algorithm increases the pattern recalling speed of this model which has multiply patterns to \(O( {\log_{2}}^{2^{n -t}} ) = O( n - t )\) time complexity, where n is the number of quantum bit and t is the quantum information of the t quantum bit. Results of case analysis show that the associative neural network model proposed in this paper based on quantum learning is much better and optimized than other researchers’ counterparts both in terms of avoiding the additional qubits or extraordinary initial operators, storing pattern and improving the recalling speed.

Optical microcirculatory skin model: assessed by Monte Carlo simulations paired with in vivo laser Doppler flowmetry

An optical microvascular skin model, valid at 780 nm, was developed. The model consisted of six layers with individual optical properties and variable thicknesses and blood concentrations at three different blood flow velocities. Monte Carlo simulations were used to evaluate the impact of various model parameters on the traditional laser Doppler flowmetry (LDF) measures. A set of reference Doppler power spectra was generated by simulating 7000 configurations, varying the thickness and blood concentrations. Simulated spectra, at two different source detector separations, were compared with in vivo recorded spectra, using a nonlinear search algorithm for minimizing the deviation between simulated and measured spectra. The model was validated by inspecting the thickness and blood concentrations that generated the best fit. These four parameters followed a priori expectations for the measurement situations, and the simulated spectra agreed well with the measured spectra for both detector separations. Average estimated dermal blood concentration was 0.08% at rest and 0.63% during heat provocation (44 degrees C) on the volar side of the forearm and 1.2% at rest on the finger pulp. The model is crucial for developing a technique for velocity-resolved absolute LDF measurements with known sampling volume and can also be useful for other bio-optical modalities.

A Diffractive Optical Element Designed for Arbitrary Pattern Beam Shaping by Use of Iterative Optimization Algorithm

Techniques of diffractive optical elements (DOEs) based on computer-generated holograms are surveyed. This type of DOE is numerically designed and optimized by using an iterative diffraction algorithm or a nonlinear search algorithm. In this report, a beamshaper designed by employing the former type of algorithm is presented. The beamshaper is capable of transforming an incident Gaussian beam into a specific beamshape, which has a complicated pattern modeled on a printed circuit with a spatial resolution of tens of micron. The actual procedure for designing the beamshaper and the criteria used to determine the design parameters are reported. Furthermore, an evaluation of the designed and fabricated beamshaper and several ideas for improvingit are discussed.

Parameter estimation in modulated, unbranched reaction chains within biochemical systems

Modern biology is increasingly developing techniques for measuring time series of global gene expression and of many simultaneous proteins or metabolites. These data contain valuable information on the dynamics of cells, which has to be extracted with computational means. Given a suitable mathematical model, this extraction is in principle a straightforward regression task, but the complexity and nonlinearity of the differential equations that describe biological systems cause severe difficulties when the systems are of realistic size. We propose a method of stepwise regression that can be applied effectively to linear portions of pathways. The method may be combined with other estimation methods and either directly yields reasonable parameter estimates or at least provides appropriate start values for subsequent nonlinear search algorithms. We illustrate the method with the analysis of in vivo NMR data describing the dynamics of glycolytic metabolites in Lactococcus lactis.

A mixed continuous and discrete nonlinear constrained algorithm for optimizing ship hull structural design

A nonlinear search algorithm for optimizing constrained design of ship structures is presented. The decision variables can be continuous or discrete and the constraints can be homogeneous or inequality nonlinear functions of those variables. The algorithm does not use gradients; therefore, it can work with non-systematized functions such as tables or another class of design routine. It was tested in the structural design of a Patrol Boat and has proved to be a powerful tool decreasing the time expended in preliminary design when it is done by the conventional spiral approach.

Active Nonlinear Tests (ANTs) of Complex Simulation Models

Simulation models are becoming increasingly common in the analysis of critical scientific, policy, and management issues. Such models provide a way to analyze complex systems characterized by both large parameter spaces and nonlinear interactions. Unfortunately, these same characteristics make understanding such models using traditional testing techniques extremely difficult. Here we show how a model's structure and robustness can be validated via a simple, automatic, nonlinear search algorithm designed to actively “break” the model's implications. Using the active nonlinear tests (ANTs) developed here, one can easily probe for key weaknesses in a simulation's structure, and thereby begin to improve and refine its design. We demonstrate ANTs by testing a well-known model of global dynamics (World3), and show how this technique can be used to uncover small, but powerful, nonlinear effects that may highlight vulnerabilities in the original model.

Velocity structure of a gas hydrate reflector at Ocean Drilling Program site 889 from a global seismic waveform inversion

Strong subhorizontal reflectors in the upper few hundred meters of oceanic sediments have been imaged by seismic reflection profiling adjacent to many continental margins. These reflectors are known as “bottom simulating reflectors” (BSRs) as they run roughly parallel to the seabed. BSRs generally have been interpreted as representing the base of a methane gas hydrate stability field. A series of boreholes was drilled in October–November 1992 during leg 146 of the Ocean Drilling Program to examine fluid discharge and its relationship to the BSR, in the Cascadia accretionary wedge. Independently, we performed a global waveform inversion of seismic reflection data collected near site 889. We use a multistep strategy for global waveform inversion of seismic reflection data. The strategy is based on the Bayesian inference theory, in which the a posteriori probability distribution is determined by the a priori probability distribution and the likelihood function relating the data with the model. Three different likelihood functions have been defined relating different parts of the data with different wavelengths of model parameter variation. First, global nonlinear search algorithms are used to estimate the large‐scale features of one‐dimensional velocity variations; then a nonlinear iterative search is used to retrieve the velocity structure in fine detail. At each stage, bounds on the model parameters are estimated. The strategy has been implemented in the slowness and intercept‐time domain. We find that the BSR corresponds to a 15–20 m zone where the velocity drops from about 1.8 km/s to a minimum of 1.4 km/s, suggesting the presence of free methane gas in the low‐velocity zone, and a 15–20 m transition zone where the velocity gradually increases to a velocity of the surrounding sediments. Thus the total thickness of the low‐velocity zone is about 30–40 m. A small or negligible velocity increase just above the BSR, suggests that the hydrate fills less than 10% of the pore space in the sediments. Our result was confirmed by the drilling. The velocity derived using a vertical seismic profile and sonic log from the drill hole agree closely with our result. Waveform inversion can recover detailed and well‐constrained velocity variations from a high‐amplitude target such as a BSR; combined with the detailed interpretation of these velocity variations which the results from site 889 will provide, the inversion approach is a powerful tool for analysis of BSRs elsewhere.

Generalized Weber Problem with Rectangular Regions

The problem of locating one or more new facilities relative to a number of existing rectangular regions is treated for the case where the rectilinear norm is used. The new facilities are to be located such that the total weighted distance is minimized. If there is interfacility interaction among the new facilities, a gradient-free nonlinear search algorithm is utilized. Computational experience suggests that this algorithm is expedient even in the solution of large problems.